[Merged] Deeper than primes [Archive] - Page 6

The Man

24th December 2008, 02:14 AM

No, my claim is that length is defined independently of any location and it is the non-local building-block of any given coordinate system, where the value of some coordinate is the result of the interaction between Extension(length, that is non-local by nature, and its simplest representation is a line-segment) and Conservation(accurate position, that is local by nature and its simplest representation is a point).

Well, my claim was that it is easy to define length within a coordinate system and you kept saying “no”. Now you assert length as a “building-block of any given coordinate system” which would make the definition of length a prerequisite of a coordinate system and not only easy to define but required to be defined in order to establish a coordinate system, by your own assertion.

As far as you’re new assertion goes “that length is defined independently of any location”, that is patently false. In some coordinate systems we can define length as the difference between coordinates along a linier axis that passes through both of those coordinates (very simple). Making the specific location of one coordinate to the other that difference along that axis. So it is not independent of any location it is just independent of the location of one of those two points, the displacement from that location to the other point is entirely dependent on that length. Do not confuse absolute location (within a coordinte system) with relative location, they are both still locations.

In other words, you don't understand what Coordinate system is (you use it without understanding it).

No, you do not seem to understand coordinate systems; this all started with your question to me about parallel and non-local in my research. In answering your question I used an X, Y, Z coordinate system, but I limited the lines to a single coordinate plane for simplicity and gave them an offset in an axis orthogonal to their lengths, thus coordinates. Your subsequent responses have all been about length along a single axis and not addressing the non-local parallel lines of my coordinate answer. I could have made it more complex involving all of the axis of that coordinate system, but I doubt you would have actually addressed my answer. In some coordinate systems, when not considering an axis that passes through both points, length can still be defined as the square root of the sum of the squares of the differences between the coordinates of those points. A little more complicated but still easy (for any grade school student). Similarly, in relativity, a space time separation (a length) takes the form S2 = (T*c)2-X2-Y2-Z2 ( T being time and c the speed of light). In a polar coordinate system we can even define the length of an arc segment of some circle’s circumference as the angle subtended (in radians) times the radius of that circle, again very easy. You have yet to respond to my previous question about how your non-coordinate (or pointless) system deals with curves. Coordinate systems make such definitions easy. Now if you really what to consider the nature of parallel lines and even “ultraparallels” (a new word for your salad), and not just length, non-Euclidean geometry would be where to start.

The undefined asspect of my theory is in your mind, because you are an ignorent of your mind (you are not a significant factor of your research, and this ignorence is the core of the paradigm of your school of thought).

What, do you mean that paradigm which requires those professing new and paradigm shifting ideas to explain them coherently and consistently themselves?

The undefined aspect of your theory remain undefined because, well, you have not defined them (at least to us) and those few definitions you do give are contradictory, like “< AND >” defines a line segment as non-local to some point with that segment being a non-local “atom” yet your defining relation for that non-locality is a compound and thus so is the line segments non-locality.

Happy now? (sorry, you are not there, I actually talking to noone).

I usually am happy and I am still here, although you do seem to prefer talking to yourself.

doronshadmi

24th December 2008, 04:51 AM

You have yet to respond to my previous question about how your non-coordinate (or pointless) system deals with curves. Coordinate systems make such definitions easy.,

... not only easy to define but required to be defined in order to establish a coordinate system,
Exactly as an atom is a composed element by you, You are unable to get the hierarchy of dependency of X on its building-blocks.

Length is a building-block of a coordinate system (X) and not vice versa.

Building-blocks are not defined by their results, but they expressed by their results.

Coordinate system is a composed thing (the result of building-blocks' interaction) where its building-blocks are not.

Only point or only line-segment is not a coordinate system, but an interaction between point and line-segment is a coordinate system.

By understand the fundamental building-blocks of X, we can define new interactions and get new outcomes, as clearly shown in http://forums.randi.org/showpost.php?p=4291308&postcount=1242 .

The Man

28th December 2008, 01:14 PM

Exactly as an atom is a composed element by you, You are unable to get the hierarchy of dependency of X on its building-blocks.

Simply choosing to call something “an atom” does not make it “an atom”, especially when you then go and divide it into “< AND >”attributes for your non-local (more then one relation to a given point) definition. Just as calling something “building-blocks” does not give anything any “dependency” based on your simple choice of ascriptions. Those “<” and “>” ascriptions are the “building-blocks” (relations to a given point) of your definition of non-local for a line segment with respect to some point and hence in referring to it as a non-local “atom” “You are unable to get the hierarchy of dependency of” that line segment’s non-locality “on its building-blocks” that you ascribed yourself.

Length is a building-block of a coordinate system (X) and not vice versa.

No, defined locations (or points) on a plane or in space is the “building block of a coordinate system”. Please provide a definition of length that does not require or entail the differentiation of locations (or points)? That “building-block of a coordinate system” is “the building-block of” length, although the term “building-block” is a misnomer as neither is actually constructed from or of points but simply defined by points as in the case of a length or defines and differentiates between points on a plane or in space as in the case of a coordinate system.

Building-blocks are not defined by their results, but they expressed by their results.

Building blocks are defined, well, by their definitions which in turn determine their “results”. A length being defined by points does not make it a “building-block” of a coordinate system which defines and differentiates between points on a plane or in space, but a length can be the result of some coordinate systems definition and differentiation between the points defining that length.

Coordinate system is a composed thing (the result of building-blocks' interaction) where its building-blocks are not.

Coordinate systems are theoretical abstractions which are composed of theoretical abstractions, one being the theoretical abstraction of a plane or space and the other being the theoretical abstraction of relative locations or the differentiation of location between two points with in that plane or space, which can serve as a definition of length within that coordinate system.

Only point or only line-segment is not a coordinate system, but an interaction between point and line-segment is a coordinate system.

Neither “Only point”, “only line-segment” nor even the “interaction between point and line-segment” requires or defines a coordinate system. However the “interaction” between two points or more definitively the relative position of one point to the other can be the definition of length and even a line segment within some coordinate systems.

By understand the fundamental building-blocks of X, we can define new interactions and get new outcomes, as clearly shown in http://forums.randi.org/showpost.php?p=4291308&postcount=1242 .

I would be more then happy to see you define any of your “interactions”. Any one can “define new interactions and get new outcomes” the problem is do those “interactions” or “outcomes” represent anything “fundamental” about “X” and that is only determined by those definitions of “X” and of those “interactions”. Often the “new outcomes” are only related to the lack of definition of the “new interactions” or of “X”, once definitively established those “new outcomes” become just the same old outcomes going under some assumed names.

The Man

28th December 2008, 03:16 PM

Little 10 Toes

28th December 2008, 08:24 PM

Why? because you cannot get the "atom" part?I think The Man summed most of it up.

So what? I am talking about extension and not about any result of it.
Please define then "Extension".

What basic ideas, the old one? Well, the basic ones that you can't grasp. You mentioned "Exactly as an atom is a composed element by you, You are unable to get the hierarchy of dependency of X on its building-blocks." I don't compose atoms. I am composed of elements, atoms, molecules, protiens, thoughts, feelings, emotions. I compose music (if I could write music and know the musical scale). But I digress.

Do you agree that when I take a drinking straw and insert it through a cup lid, that the whole straw is in the lid? This is a three dimentional analogy of a two dimentional line intersecting a perpindicular plane. It's also something that I have asked you previously but you may have missed it.

doronshadmi

29th December 2008, 04:07 AM

Doron, for the further amusement and amazement of readers, we can define a coordinate system that does not involve ‘length’. Can you describe that coordinate system and if so how can you assert “Length is a building-block of a coordinate system (X) and not vice versa.”?
The Man please define a coordinate system that does not need length or anything that is equivalent to Length, in order to be defined.

Be aware that I generalize Length to relation between elements.

So please show a coordinate system that no relation is used by it.

doronshadmi

29th December 2008, 05:54 AM

doronshadmi

29th December 2008, 06:10 AM

In addition to http://forums.randi.org/showpost.php?p=4302018&postcount=1260

For example: R set is the result of a Relation\Element Interaction, where Relation is expressed as the property that is not limited to any particular element (it is the non-local property of R set) end Element is expressed as the property that is limited to each member (it is the local property of R set, where any any R Element cannot be in AND out of R because R set has only local elements).

R set is a 1D coordinate system because non-locality is one of its building-blocks.

Please show a coordinate system that non-locality (Length, in the case of metric space) is not its building-block (for example: 0D coordinate system).

doronshadmi

29th December 2008, 06:38 AM

A length being defined by points...

No, a length is not defined by points, because it is a property of a non-local atom.

For example:

What is the exact location of ___ ?

You may use some local atoms (points) along ___ , but no infinitely many local atoms can determine the exact location of a non-local atom because . ___ are independent exactly as {}(empty-set) and {x}(non-empty set) are independent.

Cardinality is the result of __ . interaction and this result is naturally stronger than total isolation ( there can be more than one local element) and weaker than total connectivity (no magnitude that is the result of many local elements is total connectivity).

The Man

29th December 2008, 04:02 PM

The Man please define a coordinate system that does not need length or anything that is equivalent to Length, in order to be defined.

Be aware that I generalize Length to relation between elements.

So please show a coordinate system that no relation is used by it.

Well another unique ‘generalization’, in this case, go figure. Have you given up on not being definitive for the general properties of ‘generalization’ and in that generalization what are the elements related by your ‘generalization’ of ‘length’, could they be coordinates or points? Making those elements or points the definition of that ‘length’? Also as a line segment is essentially your ‘generalized’ ‘length’ (the relation between two points, specifically the location of one relative to the other) it would then be a “relation between elements” as I asserted your statements required before. As such the line segment is always non-local regardless of the observation used by your own assertion.

At the risk of beating to death a horse that you seem bound and determined to ignore. How does your ‘generalization’ of ‘length’ deal with points on an arc segment of a circumference? We can define the length of that arc segment, the length of the cord between the points or the angle that subtends that arc segment, all perhaps different values and in one case different units. How does your new ‘generalized’ ‘length’ paradigm shift compare with the specific detail I just described that is readily available in the current paradigm?

So a length of 5 units is a relation, a length of 2 units is a relation, a length of 3 units is a relation, subtraction (-) is a relation and equals (=) is a relation. So where is your relation element interaction in 5 units – 2 units = 3 units ?

Fortunately not everyone is restricted by your lack of definition. So can you describe a coordinate system that does not involve length as defined by

http://dictionary.reference.com/browse/length

the first reference

1. the longest extent of anything as measured from end to end: the length of a river.

As provided by the Random House Unabridged Dictionary, © Random House, Inc. 2006

or not?

You can do what ever you what with your own definitions and generalizations, except it seems effectively explain them.

Do you agree that when I take a drinking straw and insert it through a cup lid, that the whole straw is in the lid? This is a three dimentional analogy of a two dimentional line intersecting a perpindicular plane. It's also something that I have asked you previously but you may have missed it.

[ ] represents a lid

__ represents a straw.

__ [ ] is "the straw is out of the lid" (it is local w.r.t the lid)

[ __ ] is "the straw in the lid" (it is local w.r.t the lid)

[_]_ is "the straw in AND out of the lid" (it is non-local w.r.t the lid)

Well that would depend on how you define “in the lid” (for example would that also include in the cup which would technically be below the lid), the thickness of the lid, the length of the straw and how far it has been inserted. You must try to be definitive; generalizations will generally get you nowhere.

No, a length is not defined by points, because it is a property of a non-local atom.

Well by your latest “generalization” of ‘length’ as “relation between elements” then the relation of “uncle” is an applicable “generalization” of your ‘length’

For example:

What is the exact location of ___ ?

Exactly on space “ “ after the word “of” and one space before the “?” in your in your question.

What is the exact ‘length’ of your “___” example in ‘uncles’

You may use some local atoms (points) along ___ , but no infinitely many local atoms can determine the exact location of a non-local atom because . ___ are independent exactly as {}(empty-set) and {x}(non-empty set) are independent.

Not an “infinitely many local atoms” only two points to define a line segment. As far as “exact” location goes one point is located exactly the length of the segment away from the other point.

Cardinality is the result of __ . interaction and this result is naturally stronger than total isolation ( there can be more than one local element) and weaker than total connectivity (no magnitude that is the result of many local elements is total connectivity).

More word salad and you did not even try to use the “ualtraparallel” I gave you for Christmas.

jsfisher

29th December 2008, 05:26 PM

Do you agree that when I take a drinking straw and insert it through a cup lid, that the whole straw is in the lid? This is a three dimentional analogy of a two dimentional line intersecting a perpindicular plane.

I assume you meant the more common one-dimensional line. That aside, though, that's a very odd usage of "in" you are toting around. By your logic, since a line can be "in" a perpendicular plane by virtue of its point of intersection, then the plane must be "in" the line by the same reasoning.

By extension, a line is "in" any point along the line.

doronshadmi

30th December 2008, 03:28 AM

The Man,

Please read http://forums.randi.org/showpost.php?p=4289171&postcount=1231 .

Also as a line segment is essentially your ‘generalized’ ‘length’ (the relation between two points, specifically the location of one relative to the other) it would then be a “relation between elements” as I asserted your statements required before. As such the line segment is always non-local regardless of the observation used by your own assertion.

No,

Length is a properly of a non-local Element

Relation is non-local by nature and it is not an Element (where "by nature" means: invariant under observation).

The generalization is based on the common property of Non-locality that is fundamental for Relation and an Element like a line-segment (straight or not, it does not matter).

How does your ‘generalization’ of ‘length’ deal with points on an arc segment of a circumference?
Given any pair of points along some arc segment, there is always an arc segment between the pair of points that these points do not cover.

In this case we are already deal with a coordinate system that is based on non-locality\locality interaction, where (if only elements are considered) a line-segment is the non-local building block and a point is the local building-block of that coordinate system.

You still do not distinguish between the results (the second level, represented as coordinate system) and the building-blocks (the first level, represented as a line-segment or a point, where each one of them is not a coordinate system but it is the building-block of a coordinate system).

So a length of 5 units is a relation,

We are talking about the common property of non-locality that is fundamental to Relation and an Element like a line segment.

Relation is non-local by nature exactly as a point is local by nature (where "by nature" means: invariant under observation).

If a line-segment (which its non-locality is variant under observation) is equivalent to Relation, then in this case observation is ignored and only its non-local property is considered.

If only its non-local property is considered, then units have no significant, for example:

The length of _ is called 1.

The sum of the length of _ _ _ _ _ is called 5.

_____ is an atom called 5, which is not the same as _ _ _ _ _ that is the sum of units
called 1 (and named as 5)

_____ is non-local w.r.t to _ _ _ _ _ because given any set of 5 _ , it is not the 5 _____ atom.

ONN 5, for example, is the result of _____ (non-locality) and _ _ _ _ _ (locality) interaction (ONN 5 is not limited to any particular value and each local element can be a conservation of any wished thing, where its non-local extension enables the relation between the elements, no matter if the conserved values are in superposition, or not).

In other words, the organic natural numbers are the result of an interaction between mutually independent qualities, where the interaction of these qualities enables the existence of cardinality (cardinality is the expression of this interaction exactly as coordinate system is the expression of non-locality\locality interaction that is and interaction between qualities) .

These qualities can be expressed as NXOR connective (the logical expression of Non-locality)\ XOR (the logical expression of Locality), as shown in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

doronshadmi

30th December 2008, 04:11 AM

I assume you meant the more common one-dimensional line. That aside, though, that's a very odd usage of "in" you are toting around. By your logic, since a line can be "in" a perpendicular plane by virtue of its point of intersection, then the plane must be "in" the line by the same reasoning.

By extension, a line is "in" any point along the line.

jsfisher, I did not write the the quote that you replied to it.

It was http://forums.randi.org/showpost.php?p=4301396&postcount=1259 Little 10 Toes.

doronshadmi

30th December 2008, 05:41 AM

For example:

What is the exact location of ___ ?
Exactly on space “ “ after the word “of” and one space before the “?” in your in your question.

Space is non-local w.r.t ___ where ___ is local w.r.t space if it is on the space.

In that case ___ non-locality is not considered.

If ___ non-locality is considered then no collection of local elements like points can determine its exact location because no collection of points along a line is a non-local atom.

Little 10 Toes

30th December 2008, 07:30 AM

Do you agree that when I take a drinking straw and insert it through a cup lid, that the whole straw is in the lid? This is a three dimentional analogy of a two dimentional line intersecting a perpindicular plane. It's also something that I have asked you previously but you may have missed it.
First of all, I said it, not you. If you are going to quote me, make sure that you include the "" at the begining of your post.

Second of all, you didn't answer my question

[ ] represents a lid

__ represents a straw.

__ [ ] is "the straw is out of the lid" (it is local w.r.t the lid)

[ __ ] is "the straw in the lid" (it is local w.r.t the lid)

[_]_ is "the straw in AND out of the lid" (it is non-local w.r.t the lid)

It is a very simple question. I'll repeat it further along in this post.

Also, nice way you selected 6 words from The Man's post:
[quote=The Man;4300575]"A length being defined by points... "

Let's not answer the post, let alone quote a paragraph or use the complete sentence, let's use 6 words.:rolleyes:

Here's the paragraph with the "quote" that you used underlined.

Building blocks are defined, well, by their definitions which in turn determine their “results”. A length being defined by points does not make it a “building-block” of a coordinate system which defines and differentiates between points on a plane or in space, but a length can be the result of some coordinate systems definition and differentiation between the points defining that length.

Back to the regularly scheduled post...
Well that would depend on how you define “in the lid” (for example would that also include in the cup which would technically be below the lid), the thickness of the lid, the length of the straw and how far it has been inserted. You must try to be definitive; generalizations will generally get you nowhere.

Now you're assuming The Man.:D I'll be clearer in my question at the end of this post. Thanks for being on top of it.

I assume you meant the more common one-dimensional line. That aside, though, that's a very odd usage of "in" you are toting around. By your logic, since a line can be "in" a perpendicular plane by virtue of its point of intersection, then the plane must be "in" the line by the same reasoning.

By extension, a line is "in" any point along the line. Well, doronshamdi thinks that a line can be in and out of a plane.

So here's the v2.0 analogy. Do you agree that when I insert a drinking straw halfway through a soda cup lid, the whole straw is contained inside the lid? The length of the straw can be any size, we will assume that the thickness of the lid is 0.0 units. This is a three dimentional analogy of the interaction of two 2D objects.

Aepervius

30th December 2008, 09:23 AM

The Man please define a coordinate system that does not need length or anything that is equivalent to Length, in order to be defined.

I can define a system where only angle/azimuth are present. Length in such system would be hardly definable. (or maybe I am wrong). Also I betcha you can define some nasty transform to go from one system of coordiante into another and transform the space youa re using into something non euclidien.

doronshadmi

30th December 2008, 11:23 AM

I can define a system where only angle/azimuth are present. Length in such system would be hardly definable. (or maybe I am wrong). Also I betcha you can define some nasty transform to go from one system of coordiante into another and transform the space youa re using into something non euclidien.
Can you define this angle\azimuth by using only a point?

Be aware that a point has exactly 0 length.

So Length exists as a fundamental property of any coordinate system but at least two basic states (0 length and non-0 length) are needed in order to define a useful coordinate system.

I call a 0 length element a local element and a non-0 length element a non-local element.

Relation (which is not an element) is equivalent to a non-local element by its non-local property, but it is invariant under observation unlike a non-local element that is variant under observation.

The Man

30th December 2008, 12:21 PM

The Man,

Please read http://forums.randi.org/showpost.php?p=4289171&postcount=1231 .

Again I read it soon after you posted it, are you sure you want to insist of some remarks.

No,

Length is a properly of a non-local Element

Relation is non-local by nature and it is not an Element (where "by nature" means: invariant under observation).

The generalization is based on the common property of Non-locality that is fundamental for Relation and an Element like a line-segment (straight or not, it does not matter).

So your ‘Length’ is a property of a non-local ‘Element’ yet your ‘Relation’ is “not an Element” thus there is no ‘generalization’ of your ‘length’ to your ‘Relation’ since one is a ‘property’ of what the other is specifically not (an ‘Element’). Even your convoluted, vague and unique definitions or generalizations belie the validity of your assertions.

You still have not said what ‘Elements’ your generalized ‘Relation’ of ‘Length’ is relating for a line segment.

You have now inferred that ‘Length’ is not a property of a local ‘Element’. Since a line segment is defined as having extents in only one dimension their can be no such thing as a local line segment or a line segment without length. Confirming my assertion that in your notions and by your own ascriptions a line segment must always be non-local as well as a ‘Relation’ between two points. Again you say “No” then follow that with statements agreeing with my assertions is that deliberate or do you simply not understand or care what you say after you respond with “No”? Of course if ‘Length’ is both a local and non-local property of a line segment then you can have local line segments but then your generalization of ‘Length’ to ‘Relation’ becomes even more problematic since its non-locality would be just one particular observation type of a property of an ‘Element’ while ‘Relation’ is specifically not an ‘Element’.

Given any pair of points along some arc segment, there is always an arc segment between the pair of points that these points do not cover.

I have no idea what you mean by “that these points do not cover”, but there are an infinite number of circular arc segments between any two points. The straight line segment can also be considered just another circular arc segment but just one on a circle of infinite radius.

In this case we are already deal with a coordinate system that is based on non-locality\locality interaction,

No you have not; you have not defined “non-locality” or “locality” in any consistent manor or “non-locality\locality interaction” let alone “a coordinate system that is based on non-locality\locality interaction”. Simple claiming that coordinate systems are bases on “non-locality\locality interaction” is not the same as defining those terms, defining that interaction and then defining a coordinate system bases on that interaction. You simply what to take the current body of exiting consistent and mutually beneficial work, stick on your own undefined terms, interactions contradictions and inconsistencies on them for your own benefit to claim you have come up with something new. Again this is a paradigm many of us have seen repeated over and over again on this forum, if it gives you any solace you’re certainly not alone.

where (if only elements are considered) a line-segment is the non-local building block and a point is the local building-block of that coordinate system.

As I stated before, a line segment is just one specific case of an infinite number of possible arc segments between any two points, you have only dealt with or considered (and extremely poorly) that one specific case. Again we can define a coordinate system that does not require length for its definition (or as a “building block”), encompasses that infinite number of not only arc segments but also an infinite number of line segments between any two points and can easily be used to show some specific value of length for some line segment as just one specific case of that coordinate system. Once again can you describe that coordinate system?

You still do not distinguish between the results (the second level, represented as coordinate system) and the building-blocks (the first level, represented as a line-segment or a point, where each one of them is not a coordinate system but it is the building-block of a coordinate system).

Again absolutely false, unique and defined locations (or points) on a plane or in space are a coordinate system, A value of length can be the result of some defined coordinate system. Just because you choose to distinguish things in an inconsistent and contradictive manor does not mean that others do not distinguish those same things just because they are not being inconsistent and contradictive like you.

We are talking about the common property of non-locality that is fundamental to Relation and an Element like a line segment.

No you are talking about that and doing in your usual inconsistent and contradictive manor.

Relation is non-local by nature exactly as a point is local by nature (where "by nature" means: invariant under observation).

If a line-segment (which its non-locality is variant under observation) is equivalent to Relation, then in this case observation is ignored and only its non-local property is considered.

Technically it would not mean “observation is ignored” in order for observation to be ignored the line segments non-locality would have to be invariant under changes of observation. What you mean is that only one set of observations (where the line segment is considered non-local) is being considered. Oops that would mean an exclusive perspective; you mean that ‘Relation’ and ‘Elements’ can be ‘equivalent’ under one set of observations? That makes your entire ‘Relation’/ ‘Element’ interaction observationally dependent or only fully applicable under the other set of ‘local’ observations, how one eyed and ‘local’ of you.

If only its non-local property is considered, then units have no significant, for example:

The length of _ is called 1.

The sum of the length of _ _ _ _ _ is called 5.

_____ is an atom called 5, which is not the same as _ _ _ _ _ that is the sum of units
called 1 (and named as 5)

_____ is non-local w.r.t to _ _ _ _ _ because given any set of 5 _ , it is not the 5 _____ atom.

Now you’re just being silly again it does not have to be a “set of 5 _” scale works just as well “_____” is 5 times “_” and you can still have both as ‘atoms’. Units are related to scale and although we can define a coordinate system without using any line lengths we can also define them using some length of some specific line segment. If we define a coordinate system with your “_____” as the unit length then the length of “_____” is 1 and the length of “_” is 1/5. Alternatively as in your example if we define “_” as the unit length then the length of “_” is 1 and the length of “_____” is 5. This does not mean that we must consider “_____” as the sum of 5 “_” in the latter coordinate system it just means that we can just as we can consider it a 5 times scale of “_”. Likewise we do not have to consider “_” as one of five parts of “_____” or a 1/5th scale of “_____” in the former coordinate system but we can. We could in fact define a different coordinate system not based on either of those two lengths and just relate them within that coordinate system. The only deference between these coordinate systems is scale or specifically the scale of the unit length that could be used to define them.

So I guess you’re not going to answer my question.

So a length of 5 units is a relation, a length of 2 units is a relation, a length of 3 units is a relation, subtraction (-) is a relation and equals (=) is a relation. So where is your relation element interaction in 5 units – 2 units = 3 units ?

ONN 5, for example, is the result of _____ (non-locality) and _ _ _ _ _ (locality) interaction (ONN 5 is not limited to any particular value and each local element can be a conservation of any wished thing, where its non-local extension enables the relation between the elements, no matter if the conserved values are in superposition, or not).

In other words, the organic natural numbers are the result of an interaction between mutually independent qualities, where the interaction of these qualities enables the existence of cardinality (cardinality is the expression of this interaction exactly as coordinate system is the expression of non-locality\locality interaction that is and interaction between qualities) .

These qualities can be expressed as NXOR connective (the logical expression of Non-locality)\ XOR (the logical expression of Locality), as shown in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

No time for word salad today so I’ll just cut right to the chase.

ONN 5, for example, is the result of _____ (non-locality) and _ _ _ _ _ (locality) interaction

In standard mathematics (locality and non-locality not with standing) we call that self identity, which you claimed to use but clearly do not. That self identity is the basis of term rewriting (which I have mentioned to you before) where we can replace “_____” with “_ _ _ _ _” and visa a versa, again it does not mean we have to replace them, just that we can. Under term rewriting the general goal is simplification, “_____” (or 5) is a simpler form then “_ _ _ _ _” (or 1+1+1+1+1) so “_ _ _ _ _” would normally be replaced with “_____”. The reverse is, as I said, also possible it is just that their or no specific conditions for making things more complex “___ _ _” (or 3+1+1) would be just as good as “_ ___ _” (1+3+1) both are similarly complex but there is only one simplest form “_____” (or 5). When the term “atom” was first coined it referred to something thought to be indivisible that “atom”, the physical “atom” most of us are familiar with, is still called an “atom” but it was found to be comprised of sub elements. Since that time, atom has also become a term used to describe something in its simplest form, so 5 would be an atom in that regard where 1+3+1 or 3+1+1 would not. The fact that we can replace the simpler form 5 with a more complex form 3+1+1 does not make 5 any less of an atom (or the simplest form) or mean that 5 must be comprised of sub elements like 3+1+1 it just means that by self identity that both 5 and 3+1+1 are valid considerations or means of representing a value of 5. The elements are there if you would just use them and use them correctly, the problem is you would find that most of what you are claiming as new has already been established in a more consistent and coherent fashion. Consistency is not hard, but you just have to keep your eye (or eyes if your prefer) on it, it can easily get away from you in the exhilaration of thinking you have developed something new, as seems to be your case.

The Man

30th December 2008, 12:38 PM

Space is non-local w.r.t ___ where ___ is local w.r.t space if it is on the space.

In that case ___ non-locality is not considered.

If ___ non-locality is considered then no collection of local elements like points can determine its exact location because no collection of points along a line is a non-local atom.

Those spaces were adjacent to your "___", how much more "local" can they get?

Can you answer my ‘Length’ generalized to ‘Relation’ question?

What is the exact ‘length’ of your “___” example in ‘uncles’

The Man

30th December 2008, 12:40 PM

Now you're assuming The Man.:D I'll be clearer in my question at the end of this post. Thanks for being on top of it.

Oops, sorry I would not want to make an ASS of U and ME. For the life of me I could not figure where Doron had asked that question and did not feel like digging though all his nonsense. Of course once the quote was correctly attributed I remembered your question easily. I am sure given sufficient definition, we will most likely agree. Unfortunately Doron does not seem capable of defining anything sufficiently even for him to agree with himself.

Oh and thanks for giving the context of Dorons six word quote, for some one who thinks of things as ‘atoms’ he certainly has a problem with responding to things in their entirety.

The Man

30th December 2008, 12:41 PM

I can define a system where only angle/azimuth are present. Length in such system would be hardly definable. (or maybe I am wrong). Also I betcha you can define some nasty transform to go from one system of coordiante into another and transform the space youa re using into something non euclidien.

Excellent Aepervius, exactly the coordinate system I was referring to and you are not wrong, in fact because of the lack of length it defines the coordinates on the surface of any sphere of any diameter, encompassing arc segments of any length and, as the cords, line segments of any length. Any particular length value just becomes one specific instance of some specific sphere radius. In other words in order to get a length for an arc segment, or a line segment (cord) out you have to put a length in, radius of the sphere. In the limit where the radius approaches infinity the cord length approaches the arc segment length. At an infinite radius they are the same or a line segment is just an arc segment of infinite radius.

The Man

30th December 2008, 01:35 PM

Can you define this angle\azimuth by using only a point?

Be aware that a point has exactly 0 length.

So Length exists as a fundamental property of any coordinate system but at least two basic states (0 length and non-0 length) are needed in order to define a useful coordinate system.

I call a 0 length element a local element and a non-0 length element a non-local element.

Relation (which is not an element) is equivalent to a non-local element by its non-local property, but it is invariant under observation unlike a non-local element that is variant under observation.

Finally now we have a simple and definitive explanation of your ‘local element’ and your ‘non-local’ element, and it only took 1271 post. Actual this explains a lot more like your assertions that “no collection of points along a line is a non-local atom” basically saying that no matter how many times you add 0 length for points, even an infinite number of times, you can not get a line of some finite length. This is a common misconception that most grade school student are able to get past in the first geometry class. A line segment is not a collection of points; it is the difference in location between two points. Yes within any finite or infinite length there are an infinite number of points, but since each of those points has 0 length that finite or infinite length is not a collection of those points. In other words those points reside on that line but the line is not a construct of those points. To give you an example I often reside in my car and currently several CD’s and maps reside in my car but my car is not a construct of me, CD’s or maps. Similarly a series of numbers called a vehicle identification number uniquely defines my car yet again my car is not a constructed of numbers. The same goes for a line segment, two point uniquely define that line segment yet like my car a line segment is not constructed from what uniquely defines it, points. 1271 posts and hopefully now we can finial get to the heart of the matter.

Apathia

30th December 2008, 05:53 PM

Delete.
I've gotta stay out of this.
Good Luck, The Man!

The Man

31st December 2008, 06:36 AM

Delete.
I've gotta stay out of this.
Good Luck, The Man!

Thanks, Apathia, but I wish you would reconsider. You certainly seem to have a better grasp of the philosophical aspects of Dorons assertions then I ever could.

doronshadmi

31st December 2008, 06:58 AM

two point uniquely define that line segment yet like my car a line segment is not constructed from what uniquely defines it, points. 1271 posts and hopefully now we can finial get to the heart of the matter.

The Man,

I limited Non-locality\Locality Interaction to the particular case of Metric Space in order to help you to get my notions.

But these notions are not limited to Metric Space (as explained along the 1271 posts).

Since you get Non-locality\Locality Interaction in terms of Metric Space, let us continue our dialog under this limited case.

two point uniquely define that line segment yet like my car a line segment is not constructed from what uniquely defines it, points.
Definition must define the essence of the defined thing.

No collection of 0 length elements can define the essence of a non-0 length element because of a very simple and fundamental reason:

Each 0 length element has an exact location w.r.t to other elements, where each non-0 length does not have an exact location w.r.t other elements in the case of Metric Spase.

For example: Each time that we use the word "between" it means that there is an element that its location cannot be determined by the elements that are located on its edges.

Furthermore, given a location based on 0 length element, there is a non-0 length element that its location extends the location of the 0 length element.

In other words, no collection of 0 length elements can cover a non-0 length element because a non-0 length element is essentially different than a 0 length element.

The essential difference is:

0 length element is local by nature (where "local by nature" means: invariant under observation).

Non-0 length element is non-local by nature (where "local by nature" means: invariant under observation, where the invariant state of a non-0 element holds in the case of Metric Space).

doronshadmi

1st January 2009, 03:18 AM

A line segment is not a collection of points; it is the difference in location between two points.

"Difference in location" cannot be defined only by local elements like points, because no point is an extension of some location.

Only a line-segment (straight or not) is an extension of some location, and this extension is exactly the non-local properly of a line-segment (straight or not) that no point has.

In other words, any given coordinate system is the result of non-local atom \ local atom interaction.

doronshadmi

1st January 2009, 07:25 AM

you mean that ‘Relation’ and ‘Elements’ can be ‘equivalent’ under one set of observations?

No, I mean that non-locality is the same whether it is expressed by relation or by element.

As for observations:

Relation is non-locally invariant under observation.

Point (which is an element) is locally invariant under observation.

Line (which is an element) is locally or non-locally variant under observation, but it is considered as non-locally invariant under Metric Space research.

Look what you are doing, you ask questions and come to conclusions without giving yourself the chance to get an answer that is based on different perspective of the researched subject.

Your rushing dialog's style is the "best" recipe of how not to understand alternative notions of some researched subject, as you show all along our dialog.

jsfisher

1st January 2009, 07:57 AM

"Difference in location" cannot be defined only by local elements like points, because no point is an extension of some location.

Only a line-segment (straight or not) is an extension of some location, and this extension is exactly the non-local properly of a line-segment (straight or not) that no point has.

Can you prove this? You'd need to show there is some place along a line where no point exists or two places between which no point exists. I'm betting you can't demonstrate either.

Also, you'd be unable to distinguish between open, closed, and half-open intervals were your view adopted.

doronshadmi

1st January 2009, 08:07 AM

Again absolutely false, unique and defined locations (or points) on a plane or in space are a coordinate system, A value of length can be the result of some defined coordinate system.

Any unique value is the result of the interaction of non-local and local building-blocks.

By using operations on the unique results you simply expose the building-blocks that enable it in the first place.

For example:

The unique value 3 can be length 3 (that has no special location, for example:5-2=800-797=3-0= … = 3)

or

position 3 (that has special location, for example: number 3 along the real-line).

One may say:" number 3 can get its meaning according to infinitely many (maybe useful) alternatives, where some particular cases of these alternatives are interpreted as local or non-local".

My answer: Locality or Non-locality are not limited to some particular meaning of number 3, but they are the building-blocks that enables the existence of number 3 (no matter how it is used) in the first place.

Again Locality is the building-block that enables Conservation and non-locality is the building-block that enables Extension.

Position 3 is a particular expression of Conservation's value, where length 3 is a particular expression of Extension's value.

If Metric Space is considered, then Conservation is expressed as 0 Length element and Extension is expressed as non-0 Length element, where Metric Space is a particular case of Extension\Conservation Interaction (Where Extension is Non-local by nature, and Conservation is Local by nature (where "by nature" means: Invariant under observation)) that enabls the existence of the real-line, in the first place.

doronshadmi

1st January 2009, 09:06 AM

Can you prove this? You'd need to show there is some place along a line where no point exists or two places between which no point exists. I'm betting you can't demonstrate either.

Since . and ___ are atoms (non-composed) then ____ has no . as its sub-element.

In that case given the atom ___ and the atom . , if the domain is any one of the atoms, then ___ belongs AND does not belong to . domain , where . belongs to ___ domain (where no atom a sub-element of the other domain, because both domains are atoms (non-composed)).

Let us start our non-finite game of Non-locality\Locality Interaction:

Given any arbitrary pair of distinct values, there is a non-local value that simultaneously = AND extends (≠) each one of the distinct values, for example:

._______. , where each . is some distinct value and _____ is the simultaneous extension that exists between these values.

You may say: .___.____. , but we are talking about a pair, no matter what scale is used.

In other words, by playing the pair game between distinct values .___. is invariant as long as one value is distinct of the other value.

If we are at infinite magnitude, then no pair of distinct exists because we are beyond any interaction of . and ___ atoms (we have . XOR ___ to deal with, which is a non-researchable state).

Also, you'd be unable to distinguish between open, closed, and half-open intervals were your view adopted.
On the contrary, by understanding __ \ . interaction one enables to understand that any non-finite sequence of distinct values is incomplete (it does not have the complete magnitude of the atomic state) as long as he deals with collections of distinct values.

[0,1] is the incomplete sequence of distinct values that has smallest and biggest distinct values.

[0,1) is the incomplete sequence of distinct values that has smallest and no biggest distinct value.

(0,1] is the incomplete sequence of distinct values that has no smallest but has the biggest distinct value.

(0,1) is the incomplete sequence of distinct values that has no smallest and has no biggest distinct values.

doronshadmi

1st January 2009, 09:49 AM

Now you’re just being silly again it does not have to be a “set of 5 _” scale works just as well “_____” is 5 times “_” and you can still have both as ‘atoms’.

Now you’re just being silly again, no set of more than one _ exists unless _ is gathered with another _ by some rule, which is non-local w.r.t to any particular thing that obeys the rule.

I other words a set of more than a one member is at least - - interaction (Non-Locality \ Locality Interaction).

Edit:

Units are related to scale and although we can define a coordinate system without using any line lengths we can also define them using some length of some specific line segment. If we define a coordinate system with your “_____” as the unit length then the length of “_____” is 1
No,

Scale cannot be defined unless non-locality interacts with locality.

In order to distinguish between the elements we are using the non-local property that enables us to compare and give unique name to each local element.

No scale unit is define able unless - - - - - interaction is used where ______ is the non-local aspect of this interaction and - - - - - is the local aspect of this interaction.

jsfisher

1st January 2009, 11:03 AM

Since . and ___ are atoms (non-composed) then ____ has no . as its sub-element.

You know, you'd communicate a lot more effectively if you used words rather than typewriter art. Be that as it may, if we were to accept lines as your "non-composed" entities, then it would be meaningless to consider the intersection of two lines.

This is not a very useful set of concepts your are trying to construct.

...
Given any arbitrary pair of distinct values, there is a non-local value that simultaneously = AND extends (≠) each one of the distinct values

Your usage of equal and not-equal continue to defy their common meanings.

...
[0,1] is the incomplete sequence of distinct values that has smallest and biggest distinct values.

It is a line segment on the number line extending between the point designated as 0 and the point designated 1, inclusive of both points.

[0,1) is the incomplete sequence of distinct values that has smallest and no biggest distinct value.

Again, no.

As I implied before, your insistence that lines and line segments are indivisible entities rules out a whole lot of useful Mathematics. Then again, your novel view of sets and their elements completely voids all of Set Theory, so it is only fair the various branches of geometry are destroyed as well.

doronshadmi

1st January 2009, 02:40 PM

if we were to accept lines as your "non-composed" entities, then it would be meaningless to consider the intersection of two lines.
Not at all.

By consider Metric Space, the intersection between non-0 length elements (which are non-composed and non-local) is the location of a 0 length element, known as point.

The name of this location is the result of Non-locality\Locality Interaction.

Non-locality\Locality Interaction is very useful because it enables us to understand better the fundamental connections that enables us to do mathematical research, in the first place.

It is a line segment on the number line extending between the point designated as 0 and the point designated 1, inclusive of both points.
I agree with you.

It is the non-local atom (line-segment) that enables the connection between local atoms (points), but no sequence of non-local\local connections is complete as the non-local ur-element, which is the non-finite line itself.

As I implied before, your insistence that lines and line segments are indivisible entities rules out a whole lot of useful Mathematics. Then again, your novel view of sets and their elements completely voids all of Set Theory, so it is only fair the various branches of geometry are destroyed as well.
No, Non-locality\Locality Interaction simplifies and repairs many fundamental paradoxes, without needing special axioms or ugly thing like proper classes, as clearly seen in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf.

The Man

1st January 2009, 10:19 PM

The Man,

I limited Non-locality\Locality Interaction to the particular case of Metric Space in order to help you to get my notions.

But these notions are not limited to Metric Space (as explained along the 1271 posts).

Since you get Non-locality\Locality Interaction in terms of Metric Space, let us continue our dialog under this limited case.

Ok,
but for those interested
http://en.wikipedia.org/wiki/Metric_space

In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined.
The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line connecting them.

Definition must define the essence of the defined thing.
No definition can just be defining the limits which may or may not constitute its “essence” (whatever you mean by that).

No collection of 0 length elements can define the essence of a non-0 length element because of a very simple and fundamental reason:

Each 0 length element has an exact location w.r.t to other elements, where each non-0 length does not have an exact location w.r.t other elements in the case of Metric Spase.
Again a line segment is not a collection of points and a Metric is specifically “where a notion of distance (called a metric) between elements of the set is defined.” So defining the “exact location w.r.t other elements” is exactly what a metric entails.

For example: Each time that we use the word "between" it means that there is an element that its location cannot be determined by the elements that are located on its edges.
Absolutely false that “location” can only “determined by the elements that are located on its edges”.

Furthermore, given a location based on 0 length element, there is a non-0 length element that its location extends the location of the 0 length element.
In other words, no collection of 0 length elements can cover a non-0 length element because a non-0 length element is essentially different than a 0 length element.
A point is a 0 length element, a location can be a point, a line, a plane, a volume whatever one choose to consider the location for some given application. Which is of course defined “by the elements that are located on its edges” (for anything other then a point)

The essential difference is:

0 length element is local by nature (where "local by nature" means: invariant under observation).

Non-0 length element is non-local by nature (where "local by nature" means: invariant under observation, where the invariant state of a non-0 element holds in the case of Metric Space).
These are simply your ascriptions and you have never been able to demonstrate any of them as the “nature” of anything but yourself.
However you are making your misunderstanding clearer. A metric space is a set with a metric or distance function. It is a way of representing locations not as points but a “set” or basically a sphere (in 3D space) around a given point with a radius greater then zero (basically breaking the space down into “unit” spheres. In fact metric space is defining locations as non 0 dimension elements (the “sets”) so your “non-local by nature” and “invariant state” that “holds in the case of Metric Space” is actually the definition of “local” in metric space.

The Man

1st January 2009, 10:44 PM

Any unique value is the result of the interaction of non-local and local building-blocks.

By using operations on the unique results you simply expose the building-blocks that enable it in the first place.

For example:

The unique value 3 can be length 3 (that has no special location, for example:5-2=800-797=3-0= … = 3)

or

position 3 (that has special location, for example: number 3 along the real-line).

That is because a length is not a location but it can be the relation of one location to another in some coordinate system

One may say:" number 3 can get its meaning according to infinitely many (maybe useful) alternatives, where some particular cases of these alternatives are interpreted as local or non-local".

You can say that all you want but it still does not make it meaningful.

My answer: Locality or Non-locality are not limited to some particular meaning of number 3, but they are the building-blocks that enables the existence of number 3 (no matter how it is used) in the first place.

Again Locality is the building-block that enables Conservation and non-locality is the building-block that enables Extension.

Your answer is only to a question or problem that you have invented in your head.

Position 3 is a particular expression of Conservation's value, where length 3 is a particular expression of Extension's value.

Position 3 is a particular expression of a relative location on some axis that is length 3 away from the origin and from position 6

If Metric Space is considered, then Conservation is expressed as 0 Length element and Extension is expressed as non-0 Length element, where Metric Space is a particular case of Extension\Conservation Interaction (Where Extension is Non-local by nature, and Conservation is Local by nature (where "by nature" means: Invariant under observation)) that enabls the existence of the real-line, in the first place.
You expressed notions about Metric Space are absolutely false.

doronshadmi

2nd January 2009, 08:45 AM

No definition can just be defining the limits which may or may not constitute its “essence” (whatever you mean by that).
This is the basic mistake of the current paradigm. Definition has to define the essence of the defined thing where limit is some part of this essence. But the essence is not less than Whole\Parts Interaction where the Whole is the non-local aspect of this essence and some given part (and limit is nothing but a part of the essence) is local w.r.t the Whole but can be non-local w.r.t other parts (for example: a non-0 dimension element w.r.t 0 dimension element). Also there are parts that are local only w.r.t other parts (for example: any 0 dimension element).

However you are making your misunderstanding clearer. A metric space is a set with a metric or distance function. It is a way of representing locations not as points but a “set” or basically a sphere (in 3D space) around a given point with a radius greater then zero (basically breaking the space down into “unit” spheres. In fact metric space is defining locations as non 0 dimension elements (the “sets”) so your “non-local by nature” and “invariant state” that “holds in the case of Metric Space” is actually the definition of “local” in metric space.

The Empty set is not less than Whole\Parts interaction where the existence of the set is based on its Whole property where any investigated part does not belong to the Whole.

Without the existence of the whole we cannot determine that it has no parts.

Some analogy:

The Empty set is like a tree that has no branches. We cannot define the tree with no branches (the empty set) if the trunk is not considered. So the minimal existence of a tree (a set) is a tree with no branches (the trunk, which is equivalent to the empty set by this analogy).

|{}| = 0 (the number of branches of a tree with no branches) is possible only if the notions of trunk (Non-Locality) exists independently of the notion of branch (Locality).

In that case a set is not less than the result of the type of the interaction between non-locality (the trunk) and locality (the branches).

Non-locality is the Extension of any given collection and Locality is the Conservation of any given collection.

Since the concept of Set is not less than the result of Extension\Conservation Interaction, than no set is complete because Extension is one of its essential properties.

By understanding the above, a better and simpler understanding of the concept of Set is achieved, Russell's Paradox does not need any special treatment in order to be avoided (simply because Non-locality and Locality are mutually independent) and proper classes are avoided (for the same reason).

Again a line segment is not a collection of points and a Metric is specifically “where a notion of distance (called a metric) between elements of the set is defined.” So defining the “exact location w.r.t other elements” is exactly what a metric entails.
Metric Space is some particular result if Non-locality(Extension)\Locality(Conservation) Interaction.

Absolutely false that “location” can only “determined by the elements that are located on its edges”.
No problem. Please define the exact location of a line-segment (all along its length, without any gap) by using points.

A point is a 0 length element, a location can be a point, a line, a plane, a volume whatever one choose to consider the location for some given application. Which is of course defined “by the elements that are located on its edges” (for anything other then a point)
Wrong, No edge(s) of X is all of X (where a point is excluded)

doronshadmi

2nd January 2009, 01:26 PM

oppsss...

doronshadmi

2nd January 2009, 02:29 PM

You expressed notions about Metric Space are absolutely false.
Your understanding of the fundamental building-blocks that enable Metric space in the first place, does not hold water.

That is because a length is not a location but it can be the relation of one location to another in some coordinate system
In other words, a non-0 length element has no location (it is non-local) as a 0 length element has (it is local).

Position 3 is a particular expression of a relative location on some axis that is length 3 away from the origin and from position 6
In other words, length 3 axis (which is non local) enables the Extension from 0 length element (which is local) called position 3 to 0 length element (which is local) called position 3 and vice versa.

Look how many unnecessary and complicated maneuvers you do in order to avoid the simple notion of Non-locality\Locality Interaction as the building-blocks of any coordinate system.

It is clear that you don't grasp the analogy in post #1242 and the rest of http://forums.randi.org/showpost.php?p=4291308&postcount=1242 .

Your answer is only to a question or problem that you have invented in your head.
My inventions and my head are inseparable part of one and only one realm, whether it is abstract or not.

Also your head is inseparable part of this one and only one realm, which is the result of Singularity if it is expressed as Relation\Element Interaction.

Without REI there is no researchable realm ( http://www.geocities.com/complementarytheory/UR.pdf ).

You don't get it because you were trained to get things by ignore Singularity as the basis of all there is (whether it is abstract or not):

http://www.geocities.com/complementarytheory/OM.jpg

doronshadmi

3rd January 2009, 08:53 AM

It is a way of representing locations not as points but a “set” or basically a sphere (in 3D space) around a given point with a radius greater then zero (basically breaking the space down into “unit” spheres. In fact metric space is defining locations as non 0 dimension elements (the “sets”) so your “non-local by nature” and “invariant state” that “holds in the case of Metric Space” is actually the definition of “local” in metric space.

This is simply ridicules. No non-0 length element has an exact location as a 0 length element has.

If 0 length element is equivalent to black color, then no non-black color is black color (no non-local element is local element).

The sphere around a given location, is non-local (around) w.r.t the given point (where only this point has the exact location, or in other words, only the point is local).

There is no intermediate state between being local and being non-local, exactly as there is no intermediate state between being the empty set and a non-empty set.

The Man

3rd January 2009, 11:27 AM

This is the basic mistake of the current paradigm. Definition has to define the essence of the defined thing where limit is some part of this essence. But the essence is not less than Whole\Parts Interaction where the Whole is the non-local aspect of this essence and some given part (and limit is nothing but a part of the essence) is local w.r.t the Whole but can be non-local w.r.t other parts (for example: a non-0 dimension element w.r.t 0 dimension element). Also there are parts that are local only w.r.t other parts (for example: any 0 dimension element).

The Empty set is not less than Whole\Parts interaction where the existence of the set is based on its Whole property where any investigated part does not belong to the Whole.

Without the existence of the whole we cannot determine that it has no parts.

Some analogy:

The Empty set is like a tree that has no branches. We cannot define the tree with no branches (the empty set) if the trunk is not considered. So the minimal existence of a tree (a set) is a tree with no branches (the trunk, which is equivalent to the empty set by this analogy).

|{}| = 0 (the number of branches of a tree with no branches) is possible only if the notions of trunk (Non-Locality) exists independently of the notion of branch (Locality).

In that case a set is not less than the result of the type of the interaction between non-locality (the trunk) and locality (the branches).

Non-locality is the Extension of any given collection and Locality is the Conservation of any given collection.

Since the concept of Set is not less than the result of Extension\Conservation Interaction, than no set is complete because Extension is one of its essential properties.

By understanding the above, a better and simpler understanding of the concept of Set is achieved, Russell's Paradox does not need any special treatment in order to be avoided (simply because Non-locality and Locality are mutually independent) and proper classes are avoided (for the same reason).

Metric Space is some particular result if Non-locality(Extension)\Locality(Conservation) Interaction.

It is not a mistake, the current paradigm works and produces or results in the production of the whole host of technologies we use today. What can your paradigm do other then give you an excuse to claim your paradigm is the fundamental building blocks of everything, without being able to demonstrate how the current paradigm has been so successful. Simply claiming you have the basis of everything does not entitle you to claim or impugn the successfulness of the current body of work. You have to first be able to express the current body of work within the current paradigm (which you have not done and it seems can not do), show some deficiency of the current body of work with in the current paradigm (which you have not done and it seems can not do), then show how your new program resolves that problem (which you have not done and it seems can not do). So far all you have shown are the problems with interrupting the current body of work by your new paradigm. Without your new paradigm those ‘problems’ do not exists.

As far as Russell’s Paradox goes, it was a way of showing the naive nature of Frege’s axioms of extensionality and unlimited set abstraction. However your assertions are not even just about going back to such a naïve interpritation, you want to go back even further by being even less definitive and just casting away the contradiction by calling a member of any set both in and not in the set. We went over this on the other thread before, simply ignoring a paradox or replacing it with another paradox (the member of a set is in and not in the set) is not resolving a paradox. The fact remains that Russell's paradox is avoided by the classifications definition developed for that purpose. So claiming you can avoid Russell's paradox is irrelevant that you have to introduce some other paradox to do it shows you were just kidding yourself about being able to avoid Russell's paradox.

No problem. Please define the exact location of a line-segment (all along its length, without any gap) by using points.

Did that a long time ago in the X,Y,Z coordinate system examples.

Wrong, No edge(s) of X is all of X (where a point is excluded)

No, but that is all that is needed to define location X from not location X, it is called a border (and we went over inclusive and exclusive borders in the other thread as well).

The Man

3rd January 2009, 12:31 PM

Your understanding of the fundamental building-blocks that enable Metric space in the first place, does not hold water.

Containers hold water, while metric space helps us to define the shapes of those containers.

In other words, a non-0 length element has no location (it is non-local) as a 0 length element has (it is local).

No exactly the words I used, length is a relative location, your “other words” result in your own meaning.

In other words, length 3 axis (which is non local) enables the Extension from 0 length element (which is local) called position 3 to 0 length element (which is local) called position 3 and vice versa.

Look how many unnecessary and complicated maneuvers you do in order to avoid the simple notion of Non-locality\Locality Interaction as the building-blocks of any coordinate system.

No, again exactly the words I used and have used multiple times, length is a relative location relating the location of one point to the location of another point along a linier axis that passes through both points. No one needs any “maneuvers” to avoid your “Non-locality\Locality Interaction as the building-blocks of any coordinate system” because you have not defined a coordinate system that is uniquely based on that “interaction” which you have never defined anyway, oh except to claim it “as the building-blocks of any coordinate system” which you think defines it and defines it “as the building-blocks of any coordinate system”. If only it were that easy, then whatever anyone claimed was so would be so, which of course would not make thing easy.

It is clear that you don't grasp the analogy in post #1242 and the rest of http://forums.randi.org/showpost.php?p=4291308&postcount=1242 .

It is clear that you do not understand the current paradigm that you claim to be shifting from.

My inventions and my head are inseparable part of one and only one realm, whether it is abstract or not.

Absolutely no one I have read on this or any of your other threads has disagreed with that fact, which is why you find yourself unable to separate from your notions and consider the current paradigm in its own regard.

Also your head is inseparable part of this one and only one realm, which is the result of Singularity if it is expressed as Relation\Element Interaction.

Without REI there is no researchable realm ( http://www.geocities.com/complementarytheory/UR.pdf ).

You don't get it because you were trained to get things by ignore Singularity as the basis of all there is (whether it is abstract or not):

http://www.geocities.com/complementarytheory/OM.jpg

Horse hockey, here you go again insisting that everything is inseparable from your notions in order to claim some vapid assertion of validity for your notions. While the rest of the world has progressed and is progressing separate from your notions, so with your notion of inseparability invalidated so to are your notions.

The Man

3rd January 2009, 01:57 PM

This is simply ridicules. No non-0 length element has an exact location as a 0 length element has.

If 0 length element is equivalent to black color, then no non-black color is black color (no non-local element is local element).

The sphere around a given location, is non-local (around) w.r.t the given point (where only this point has the exact location, or in other words, only the point is local).

There is no intermediate state between being local and being non-local, exactly as there is no intermediate state between being the empty set and a non-empty set.

Well that is what metric space is about, generalized locations or locations with some “wiggle room”. The best analogy would be like a Finite Element Analysis for coordinate systems.

http://en.wikipedia.org/wiki/Neighborhood_(mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where you can wiggle the point a bit without leaving the set.
This concept is closely related to the concepts of open set and interior.

http://en.wikipedia.org/wiki/Manifold

In mathematics, more specifically topology, a manifold is a mathematical object that looks locally like Euclidean space. Euclidean space is either a point, a line, a plane etc... So to look locally like Euclidean space intuitively means that you can zoom into a tiny region, T, inside this object that looks like a tiny region in Euclidean space. More formally, a manifold is a mathematical space in which every point has a neighborhood homeomorphic to Euclidean space. Note that the global structure of the manifold may be much more complicated. For example, any point on the (two-dimensional) sphere has a small region surrounding it that looks like a (curved) tiny region in the plane, despite the fact that the sphere looks nothing like the plane. In discussing manifolds, the idea of dimension is important. For example, lines are one-dimensional, and planes are two-dimensional.
In a one-dimensional manifold (or one-manifold), every point has a neighborhood that looks like a segment of a line. Examples of one-manifolds include a line (trivial), a circle (any arc in the circle looks like a (curved) line), and two separate circles. In a two-manifold, every point has a neighborhood that looks like a disk. Examples include a plane (trivial), the surface of a sphere (similar to a circle, any curved disk on the circle looks like a disk), and the surface of a torus. The trivial example of an n-manifold is the n-dimensional Euclidean space.

Did you not know about the aspects of topological space and specifically metric space before you added it to your word salad?

doronshadmi

4th January 2009, 05:54 AM

length is a relative location relating the location of one point to the location of another point along a linier axis that passes through both points.

No,

Length > 0 element is the result of non-locality that is found between 0 length elements.

Non-locality is the extensive property of any given coordinate system and Locality is the conservative property of any coordinate system.

In other words Extension and Conservation are mutually independent properties of any given result that is based on the interaction between them, where Metric Space is one of these results.

You force Locality on Non-locality by using twisted names like "relative location" just in order to avoid Non-locality.

By doing that you become ignorant of the building-blocks that stand at the basis of any researchable framework, that actually enables to define the rigorous foundations of the mathematical science as a researchable environment.

You did not demonstrate even once that you grasp REI and your X,Y,Z argument is a good example of your ignorance of REI.

I am talking about the understanding of the building-blocks that enables X result, which give us the ability to be extended beyond X result, and you are talking about X result by doing your best in order to avoid any notion that is based also on Extension.

By your conservative approach we can understand why a line-segment is determined by two points, because form this notion, the line-segment's extension property is avoided and all we get is the conservation notion that is represented by local elements like 0 length elements.

We do not need more than that in order to understand why a researchable framework that is based on both Non-locality(Extension)\Locality(Conservation) Interaction is more interesting and fruitful than any approach that sticks only to Locality and Conservation as its fundamental paradigm.

The rest of what you wrote in any one of your last posts is based on this non-interesting paradigm.

While the rest of the world has progressed and is progressing separate from your notions

It has progressed because Extension and Non-locality are used whether they are researched or not.

Your brain works even if you don't have any rigorous knowledge of how it works, but it does not mean that because your brain already works you will do nothing on order to increase your knowledge of how it works.

I put Non-locality(Extension) as a fundamental principle of any comprehensive knowledge in addition to Locality(Conservation), where you are doing your bast in order to avoid Non-locality(Extension) as a fundamental property of any given body of knowledge.

That is why you can't grasp my flying-machine analogy at http://forums.randi.org/showpost.php?p=4291308&postcount=1242 in particular, and the rest of http://forums.randi.org/showpost.php?p=4291308&postcount=1242 in general.

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where you can wiggle the point a bit without leaving the set.
http://en.wikipedia.org/wiki/Neighborhood_(mathematics)

"wiggle the point a bit without leaving the set" is simply a ridicules way to avoid the simple and straightforward knowledge of Non-locality(Extension) as a fundamental property of the researched framework.

In this case the researched framework is called a set, where the inherent non-locality that enables distinct localities to be gathered with each other, is ignored (the property of Extension is ignored) and only the property of Conversation is researched, by ignoring the fact that a set is the result of at least Non-locality(Extension)\ Locality(Conservation) Interaction.

In general, all you do is to quote thinks from the internet that show the current understanding of these concepts, and you do exactly nothing in order to get them from non-standards points view.

show some deficiency of the current body of work with in the current paradigm (which you have not done and it seems can not do), then show how your new program resolves that problem (which you have not done and it seems can not do).

It is clearly done in http://forums.randi.org/showpost.php?p=4265780&postcount=1027

But since you are
http://forums.randi.org/showpost.php?p=4266596&postcount=1043 there is no use to continue this dialog simply because you do not wish to make even a single step from your current location (after all Extension is fundamentally avoided by you).

For the last time, look how simple and beautiful is my suggestion of the researchable.

The researchable is the result of at least Conservation AND Extension.

The symbol of Conservation is . where The symbol of Extension is __

Without .__ interaction no researchable framework exists.

By .__ interaction word salads like http://en.wikipedia.org/wiki/Manifold are avoided, and the fundamental building-blocks of Research-ability are considered (are researched).

There is no homeomorphism from . to __ unless one claims that __ is a searched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …

The homeomorphism of . __ is Singularity, which appears as the interaction of . __ building-blocks, http://www.geocities.com/complementarytheory/OM.jpg

and we are a significant factor of this interaction, as shown by ONNs in http://www.geocities.com/complementarytheory/MonadCK.pdf .

doronshadmi

4th January 2009, 08:16 AM

Here is a correction of the last part of my previous post:

There is no homeomorphism from . to __ unless one claims that __ is a stretched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …

The homeomorphism of . __ is Singularity, which appears as the interaction of . __ building-blocks, http://www.geocities.com/complementarytheory/OM.jpg

and we are a significant factor of this interaction, as shown by ONNs in http://www.geocities.com/complementarytheory/MonadCK.pdf .

jsfisher

4th January 2009, 08:30 AM

For the last time, look how simple and beautiful is my suggestion of the researchable.

If it is so simple and beautiful, why does it deny so much? Set union is meaningless in your novel approach. Line intersection is meaningless in your novel approach. You have yet to demonstrate a single advantage to your approach, and you claim it to be the only correct one.

Rather than continuing to yell, "I'm right! I'm right!", while accusing the rest of us of being too stupid to comprehend you insight, how about showing us some result?

doronshadmi

4th January 2009, 08:49 AM

If it is so simple and beautiful, why does it deny so much? Set union is meaningless in your novel approach. Line intersection is meaningless in your novel approach. You have yet to demonstrate a single advantage to your approach, and you claim it to be the only correct one.

Rather than continuing to yell, "I'm right! I'm right!", while accusing the rest of us of being too stupid to comprehend you insight, how about showing us some result?

http://forums.randi.org/showpost.php?p=4311740&postcount=1287

The results are all over this thread. Start from post #1.

The Man

4th January 2009, 09:13 AM

No,

Length > 0 element is the result of non-locality that is found between 0 length elements.

Non-locality is the extensive property of any given coordinate system and Locality is the conservative property of any coordinate system.

In other words Extension and Conservation are mutually independent properties of any given result that is based on the interaction between them, where Metric Space is one of these results.

You force Locality on Non-locality by using twisted names like "relative location" just in order to avoid Non-locality.

All locations are relative. Absolute location just refers to a location relative to where one happens to pick as the origin for their coordinate system. While, generally, relative location refers to locations relative to some point other then the origin of that coordinate system (but of course I have told you that before). If you can establish some absolute reference frame so that all locations are not relative locations, then you might have something. Many others have tried but all have failed.

By doing that you become ignorant of the building-blocks that stand at the basis of any researchable framework, that actually enables to define the rigorous foundations of the mathematical science as a researchable environment.

As always the ignorance remains yours.

You did not demonstrate even once that you grasp REI and your X,Y,Z argument is a good example of your ignorance of REI. .

Well you have not been able to “demonstrate even once that you grasp REI” and it is your notion, you just bandy it about like some magical “charm of making” that should suddenly make everything be mystically based on it as the “building-blocks”. It is not some incantation, you have to be able to prove it and not just say it.

I am talking about the understanding of the building-blocks that enables X result, which give us the ability to be extended beyond X result, and you are talking about X result by doing your best in order to avoid any notion that is based also on Extension. .

While I am talking about effective applications of abstract theories, whenever you find yourself with one, please let us know.

By your conservative approach we can understand why a line-segment is determined by two points, because form this notion, the line-segment's extension property is avoided and all we get is the conservation notion that is represented by local elements like 0 length elements.

Well since the line segment must extend from one point to the other in order to be defined by those points, this is probably the most ridiculous statement you have every made, but I am not through your post yet.

We do not need more than that in order to understand why a researchable framework that is based on both Non-locality(Extension)\Locality(Conservation) Interaction is more interesting and fruitful than any approach that sticks only to Locality and Conservation as its fundamental paradigm.

Sure we do, you need to specifically define those terms, that ‘interaction’ and show specifically how it is more “fruitful” then the current paradigm, which is, if you have not noticed yet and your previous statement indicates that, not limited by the restrictions you whish to place on it by your notions.

The rest of what you wrote in any one of your last posts is based on this non-interesting paradigm.

Well this almost beat out the other statement as the most ridiculous thing you have ever said. So you find the current paradigm and all that has been developed as a result of it uninteresting. No wonder, as you only seem interested in yourself and your notions.

It has progressed because Extension and Non-locality are used whether they are researched or not.

Your brain works even if you don't have any rigorous knowledge of how it works, but it does not mean that because your brain already works you will do nothing on order to increase your knowledge of how it works.

So no one knows what they are doing except you, yet these other people are able to effectively explain the “rigorous knowledge” they are applying while you can not.

I put Non-locality(Extension) as a fundamental principle of any comprehensive knowledge in addition to Locality(Conservation), where you are doing your bast in order to avoid Non-locality(Extension) as a fundamental property of any given body of knowledge.

That is why you can't grasp my flying-machine analogy at http://forums.randi.org/showpost.php?p=4291308&postcount=1242 in particular, and the rest of http://forums.randi.org/showpost.php?p=4291308&postcount=1242 in general.

http://en.wikipedia.org/wiki/Neighborhood_(mathematics)

"wiggle the point a bit without leaving the set" is simply a ridicules way to avoid the simple and straightforward knowledge of Non-locality(Extension) as a fundamental property of the researched framework.

In this case the researched framework is called a set, where the inherent non-locality that enables distinct localities to be gathered with each other, is ignored (the property of Extension is ignored) and only the property of Conversation is researched, by ignoring the fact that a set is the result of at least Non-locality(Extension)\ Locality(Conservation) Interaction.

In general, all you do is to quote thinks from the internet that show the current understanding of these concepts, and you do exactly nothing in order to get them from non-standards points view.

Again it is your point of view, it is your responsibility to show us what can be gotten from it and specifically how the standard point of view arises from it, simply claiming it as the “building blocks” only demonstrates that as your point of view and we already know it is your point of view.

It is clearly done in http://forums.randi.org/showpost.php?p=4265780&postcount=1027

But since you are
http://forums.randi.org/showpost.php?p=4266596&postcount=1043 there is no use to continue this dialog simply because you do not wish to make even a single step from your current location (after all Extension is fundamentally avoided by you).

For the last time, look how simple and beautiful is my suggestion of the researchable.

I wish it was the last time, but I find that unlikely. Again simplicity and beauty are not determining factors in the application of abstract concepts. In fact if history teaches us anything is that the most useful concepts are complex and ugly (to most).

The researchable is the result of at least Conservation AND Extension.

The symbol of Conservation is . where The symbol of Extension is __

Without .__ interaction no researchable framework exists.

By .__ interaction word salads like http://en.wikipedia.org/wiki/Manifold are avoided, and the fundamental building-blocks of Research-ability are considered (are researched).

As manifolds are an essential part of general relativity calculations, it is a full meal and not just a salad. Of course you could very easily demonstrate the effectiveness of your notions by calculating the curvature of space-time by gravity while avoiding manifolds. Oh, but that’s right you do not use your notions to actually do anything, but just claim them as the basis of what already works without them.

There is no homeomorphism from . to __ unless one claims that __ is a searched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …

The homeomorphism of . __ is Singularity, which appears as the interaction of . __ building-blocks, http://www.geocities.com/complementarytheory/OM.jpg

and we are a significant factor of this interaction, as shown by ONNs in http://www.geocities.com/complementarytheory/MonadCK.pdf .

Again your notions do not limit anyone but yourself.

jsfisher

4th January 2009, 09:59 AM

http://forums.randi.org/showpost.php?p=4311740&postcount=1287

As is your custom, the link you provided is non-responsive to the issue raised. You notions, concepts, beliefs are destructive to fundamental Mathematics. You provide no evidence to contradict my claim.

Here are a few reminders:

You have told us that the 2 in {2,3,5,7,11,13,...} (the set of prime numbers) is different from the 2 in {2,4,6,8,...} (the set of even whole numbers). The two sets have no element in common and therefore their intersection is empty.

You have told us that the union of the members of {{1,2,3},{2,5}} is {{1,2,3},{2,5}}.

Both your claims contradict basic Set Theory. To accept your point of view requires we abandon Set Theory in rubble.

The results are all over this thread. Start from post #1.

Were that true, you should have no trouble pointing out just a single real, significant, positive result. Just one. Instead you continue to fold back onto your own assumptions.

doronshadmi

4th January 2009, 10:18 AM

Again your notions do not limit anyone but yourself.

Really?

Please prove that there is homeomorphism ( http://en.wikipedia.org/wiki/Homeomorphism ) between a point and a line.

If you do that, we can use it to prove that 0 = 1 or {} = {x}.

So please use your notions in order to avoid "my limitations".

If you are unable to prove that 0 = 1 or {} = {x} , you simply have no choice but to accept my argument that there is no homeomorphism between a point and a line, or in other words, they are mutually independent and cannot be defined by each other exactly as two axioms are not defined by each other.

I am waiting ...

Little 10 Toes

4th January 2009, 10:41 AM

A line is a "collection" of points. Please use your "notions" to avoid that limitation. Oh your avoidance of my question is noted. Since you cannot answer simple yes/no questions, I'll try to continue to be a observer not laughing too hard at work so I can keep my job.

doronshadmi

4th January 2009, 10:51 AM

You have told us that the 2 in {2,3,5,7,11,13,...} (the set of prime numbers) is different from the 2 in {2,4,6,8,...} (the set of even whole numbers). The two sets have no element in common and therefore their intersection is empty.

You have told us that the union of the members of {{1,2,3},{2,5}} is {{1,2,3},{2,5}}.

Not al all.

My argument simply says that {} exists wether it is a member of some set (for example: {{}, ...}) or not a member of any set ( for example: {}).

This fact holds for any given set, empty or not.

In that case the result of the union of the members of {{1,2,3}}u{{2,5}} is {{1,2,3},{2,5}} where {1,2,3}u{2,5} is {1,2,3,5} where set {1,2,3} or set {2,5} exist even if they are not members of any other set.

By understanding this fact {{1,2,3},{2,5}}u{{1,2,3},{2,5}} is {{1,2,3},{2,5}}
where {1,2,3}u{2,5} is not the union of the members of {{1,2,3},{2,5}}.

{1,2,3,5} is the result of union of the members of {1,2,3} and {2,5}, where no one of those two sets must be a member of another set, in order to exist.

jsfisher

4th January 2009, 11:44 AM

{1,2,3,5} is the result of union of the members of {1,2,3} and {2,5}, where no one of those two sets must be a member of another set, in order to exist.

Two absurdities for in the space on one sentence.

(1) {1,2,3,5} is the union of the members of {1,2,3} and {2,5}.
(2) A set can only exist if it is not a member of another set.

jsfisher

4th January 2009, 11:53 AM

...{{1,2,3}}u{{2,5}}...

Doron,
Are you under the impression that {{1,2,3}} is a member of {{1,2,3},{2,5}}?

doronshadmi

4th January 2009, 11:55 AM

Two absurdities for in the space on one sentence.

(1) {1,2,3,5} is the union of the members of {1,2,3} and {2,5}.
(2) A set can only exist if it is not a member of another set.

No,

(1) {1,2,3}u{2,5} = {1,2,3,5}
(2) Any set exists even if it is not a member of any other set.

The Man

4th January 2009, 11:59 AM

Really?

Please prove that there is homeomorphism ( http://en.wikipedia.org/wiki/Homeomorphism ) between a point and a line.

If you do that, we can use it to prove that 0 = 1 or {} = {x}.

So please use your notions in order to avoid my limitations.

If you are unable to prove that 0 = 1 or {} = {x} , you simply have no choice but to accept my argument that there is no homeomorphism between a point and a line, or in other words, they are mutually independent and cannot be defined by each other exactly as two axioms are not defined by each other.

I am waiting ...

First off no one has claimed that there was homeomorphism from a line to a point other then you.

There is no homeomorphism from . to __ unless one claims that __ is a searched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …

The homeomorphism of . __ is Singularity, which appears as the interaction of . __ building-blocks,

I imagine you meant that to be a line as a starched point. So then prove your own assertion, that the stretching of a point into a line would be an example of homeomorphism between a line and a point, that the result “is Singularity” and “which appears as the interaction of . __ building-blocks”. Do not ask people to prove assertions that you make.

Secondly your argument was not that “there is no homeomorphism between a point and a line” it was “There is no homeomorphism from. to __ unless one claims that __ is a searched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …” to make the argument you claim to have made the statement would have had to have been more like..

“There is no homeomorphism from . to __ even if one claims that __ is a searched . , which is equivalent to the claim that 0 = 1 or {}={x} etc …”

and you would have needed to leave out that other statement where you assert “The homeomorphism of . __ is Singularity, which appears as the interaction of . __ building-blocks,” basically claiming homeomorphism from a line to a point in your assertions.

Additionally the well established fact that deforming a line segment into a point is not permissible under the formal definitions of homeomorphism in no way requires anyone to accept your notions. Nor is your insistence that proving your stated inequalities as equal in any way required in order to define a line segment with two points and thereby have that line segment as the relative location from one of those points to the other.

Finally just as you notions only limit you, so to do your insistences of what is required to demonstrate the validity of the current paradigm.

I think a good deal of your problem comes from what appears to be your insistence that only a point is a location. Generalized locations such as the neighborhoods required for manifolds, topological space and metric space are locations as well, even though they are not a point. As an idealized example if I take a piece of paper (essentially a rectangular plane) and write on it, then everything written on that paper is located on (or is local to) that paper. Later if I want to locate something that I had written I need first to locate that piece of paper. This can be assisted by giving that piece of paper a more general location like a page number in some book, that book a location on some shelf, that shelf some location on a wall, that wall some location in a room, that room some location in a library and the library some location on our globe. Points are an abstract notion of location; practical applications of location are more general. Located Some where on a sphere is a volume, that volume is the library, located within that volume is another volume which is the room, located on one side of that volume of the room is a plane that is the wall, located along that plane of the wall is an orthogonal plane that is the shelf, located on that plane of the shelf is another volume which is the book, located within the volume of the book is another plane that is the page, located upon that plane of the page is what I had written.

doronshadmi

4th January 2009, 11:59 AM

Doron,
Are you under the impression that {{1,2,3}} is a member of {{1,2,3},{2,5}}?

No I am under the impression that the union between the members of set {{1,2,3}} and set {{2,5}} is {{1,2,3},{2,5}} ( and so is the case of {{1,2,3},{2,5}}u{{1,2,3},{2,5}} that is {{1,2,3},{2,5}} ).

jsfisher

4th January 2009, 12:23 PM

No I am under the impression that the union between the members of set {{1,2,3}} and set {{2,5}} is {{1,2,3},{2,5}} ( and so is the case of {{1,2,3},{2,5}}u{{1,2,3},{2,5}} that is {{1,2,3},{2,5}} ).

The original question had to do with the union of the members of {{1,2,3},{2,5}}. I don't know why you introduced all these other sets.

No matter. Your latest claim, that the union of the members of {{1,2,3}} and of the members of {{2,5}} is {{1,2,3},{2,5}} contradicts Set Theory as well as anything else you have posted.

For your reference:

The members of {{1,2,3}} and {{2,5}} are {1,2,3} and {2,5}, respectively.
The union of those members is {1,2,3,5}, not {{1,2,3},{2,5}}
Therefore, the union of the members of {{1,2,3}} and {{2,5}} is {1,2,3,5}.

doronshadmi

4th January 2009, 12:25 PM

First off no one has claimed that there was homeomorphism from a line to a point other then you.

You are not writing to the point.

Again my argument is this:

There is no homeomorphism between a point and a line or in other words, they are mutually independent exactly like two axioms.

By using these axiomatic states that are not derived from each other, one defines a researchable framework, which is the result of the interaction of these fundamental states.

Singularity at its self state is not researchable because nothing is intractable and/or comparable.

A researchable framework is the result of Singularity's expression, which is expressed as the interaction of Non-locality(Extension) with Locality(Conservation).

Your Page and Library analogies show that you are using only the local point of view in order to research some framework.

For example:

The piece of paper is non-local w.r.t to what was written on it, where what was ritten on it is local w.r.t this paper.

The shelf is non-local w.r.t the book that stands on it, where the book is local w.r.t this shelf etc …

In each one of these examples Non-locality AND Locality are considered (are interact with each other)

jsfisher

4th January 2009, 12:26 PM

Any set exists even if it is not a member of any other set.

Then why did you write this:

{1,2,3,5} is the result of union of the members of {1,2,3} and {2,5}, where no one of those two sets must be a member of another set, in order to exist.

(Bolding added.)

doronshadmi

4th January 2009, 02:35 PM

Then why did you write this:

... where no one of those two sets must be a member of another set, in order to exist.

(Bolding added.)

What is the problem?

No set must be a member of another set, in order to exist.

It means that {} existence does not depend on {{},...} existence.

jsfisher

4th January 2009, 03:31 PM

What is the problem?

No set must be a member of another set, in order to exist.

It means that {} existence does not depend on {{},...} existence.

Ummm, no, that isn't precisely what it means. However, you seem to actually mean the right thing even if you didn't express it properly. That being the case, why express it at all? Set Theory has no such requirement, so why do you feel compelled to reiterate there is no such requirement?

You seem hung up on the trivial and the obvious again, like your frequent reminders that sets are unordered.

doronshadmi

5th January 2009, 02:33 AM

Ummm, no, that isn't precisely what it means. However, you seem to actually mean the right thing even if you didn't express it properly. That being the case, why express it at all? Set Theory has no such requirement, so why do you feel compelled to reiterate there is no such requirement?

You seem hung up on the trivial and the obvious again, like your frequent reminders that sets are unordered.

In that case the result {1,2,3,5} is not the union of the members of {{1,2,3},{2,5}}, but it is the union of {1,2,3} and {2,5} where no one of these sets is necessarily a member of some set.

Be aware that the result of some union is based only on the first-level of the unified sets.

In that case {1,2,3,5} union's result has no connection to a set like {{1,2,3},{2,5}}, because {1,2,3,5} is the unified result of the members of the members of {{1,2,3},{2,5}}, which is not set's first-level membership but it is set's second-level membership of the set {{1,2,3},{2,5}}.

sympathic

5th January 2009, 04:09 AM

from: en.wikipedia.org/wiki/Number

... there is no one encompassing definition of number and the concept of number is open for further development.

jsfisher

5th January 2009, 04:40 AM

In that case the result {1,2,3,5} is not the union of the members of {{1,2,3},{2,5}}, but it is the union of {1,2,3} and {2,5} where no one of these sets is necessarily a member of some set.

So, you are (again) saying neither {1,2,3} nor {2,5} are members of {{1,2,3},{2,5}}.

This belief of yours runs contrary to Set Theory.

Be aware that the result of some union is based only on the first-level of the unified sets.

In that case {1,2,3,5} union's result has no connection to a set like {{1,2,3},{2,5}}, because {1,2,3,5} is the unified result of the members of the members of {{1,2,3},{2,5}}, which is not set's first-level membership but it is set's second-level membership of the set {{1,2,3},{2,5}}.

So, according to you, the members of the members of {{1,2,3},{2,5}} are {1,2,3} and {2,5}. Again, your belief runs contrary to Set Theory.

The Man

5th January 2009, 06:21 AM

You are not writing to the point.

You quote one line out of about 30 written and claim I “not writing to the point”.

I guess you missed this, which was directly to your point (and mine).

Additionally the well established fact that deforming a line segment into a point is not permissible under the formal definitions of homeomorphism in no way requires anyone to accept your notions. Nor is your insistence that proving your stated inequalities as equal in any way required in order to define a line segment with two points and thereby have that line segment as the relative location from one of those points to the other.

Again my argument is this:

There is no homeomorphism between a point and a line or in other words, they are mutually independent exactly like two axioms.

By using these axiomatic states that are not derived from each other, one defines a researchable framework, which is the result of the interaction of these fundamental states.

Singularity at its self state is not researchable because nothing is intractable and/or comparable.

A researchable framework is the result of Singularity's expression, which is expressed as the interaction of Non-locality(Extension) with Locality(Conservation).

We do not need homeomorphism to differentiate between a point and a line segment, as has already been asserted a point has no dimensions while a line segment has one. Just because we can differentiate them does not make them “independent” because a line is defined by two (not one but two) points and that line segment represents the relative position of one of those points to the other.

My point hasn’t changed only the words in your salad have. Homeomorphism is specifically about sameness from a topological view point. When two things are not homeomorphic it just means that they do not have same topologies. The only reason anyone would use such a claim to demonstrate independence between a point and a line segment is simply because they do not understand what the terms mean, just as you used Metric Space before without understanding its implications. For some one who claims to have found the fundamental building blocks of all researchable things you certainly do very little research. If you really wanted to understand research then you should stop playing with your building blocks and actually do some research.

Your Page and Library analogies show that you are using only the local point of view in order to research some framework.

For example:

The piece of paper is non-local w.r.t to what was written on it, where what was ritten on it is local w.r.t this paper.

The shelf is non-local w.r.t the book that stands on it, where the book is local w.r.t this shelf etc …

In each one of these examples Non-locality AND Locality are considered (are interact with each other)

Again your assertions lack validity even under your own definition. One of the problems being that your definition of non-local being an element with more then one relation to some other element really does not explicitly involve location or locations. Under your definition the writing on the page would be non-local with respect to that page as it would be an on the page but not the entire area of the page or have more then one relationship with respect to that page. Another page can have the same area as the written page but would not necessarily be on the written page. This second page could have its entire surface covered with ink, but that would not be writing, as writing entails marked and unmarked areas. So those two condition or relationships with respect to the page are needed for it to be writing on a page, that it is on the page and does not include all areas of the page. Also your limitations of local and none local with respect to are counter to your claimed goal of establishing a minimally acceptable format where the majority of the definition comes from the researcher. The current paradigm does just that, it give use the minimum requirements for establishing location but requires the researcher to define what is local and what is none local on their own. That current paradigm fits your stated goal of an MAF better then your own paradigm.

doronshadmi

5th January 2009, 06:47 AM

So, you are (again) saying neither {1,2,3} nor {2,5} are members of {{1,2,3},{2,5}}.

This belief of yours runs contrary to Set Theory.

So, according to you, the members of the members of {{1,2,3},{2,5}} are {1,2,3} and {2,5}. Again, your belief runs contrary to Set Theory.

If a set is in the domain of another set, then and only than it is considered as its member, where the union is between the first-level of membership of some given sets.

jsfisher

5th January 2009, 07:17 AM

If a set is in the domain of another set, then and only than it is considered as its member, where the union is between the first-level of membership of some given sets.

By "in the domain of" you mean "is a member of". The first part of your statement then reduces to "If a set is a member of another set, then and only then is it considered the other set's member." How insightful! (The where-clause appears to be irrelevant to any point you were trying to make.)

The question that was put to you was: What is the union of the members of sets {{1,2,3}} and {{2,5}}.

Your answer was {{1,2,3},{2,5}}, which is just plain wrong.

It would have been correct had the question been "What is the union of the members of sets {{1,2,3}} and {{2,5}}," but it wasn't.

doronshadmi

5th January 2009, 07:27 AM

That current paradigm fits your stated goal of an MAF better then your own paradigm.

The current paradigm does not distinguish between the mutually independent building-blocks and ignores the interactions between them as a significant factor of the results.

Furthermore, by the so called objective existence of the researched the current paradigm cannot explain how these objects interact with each other in the first place, in order to get the non-trivial realm that we are an inseparable factor of it.

Your mechanic paradigm is getting off stage in these days whether you like it or not, and a non-naïve paradigm that rigorously defines the interactions between Conservation AND Extension replaces it in each passing day.

My voice is nothing but the very first glance of a new paradigm of a mathematical science that is based on the awareness of the mathematician as a significant factor of his mathematical research, and how the results are the outcomes of the non-trivial interactions of Conservation AND Extension.

You have failed to get the depth of the topological notion of the mutual independency of Conservation with Extension because you ignore Extension as a fundamental property of your paradigm (you do your "best" in order to Conserve anything in order to avoid any Extension of it, like any "good" dogmatic person).

You are simply ignorant of Singularity at its self state, which is the natural and simplest state of all there is (subjective, objective, abstract or not it does not matter), whether it is expressed as Conservation Extension or Interaction.

doronshadmi

5th January 2009, 07:38 AM

By "in the domain of" you mean "is a member of". The first part of your statement then reduces to "If a set is a member of another set, then and only then is it considered the other set's member." How insightful! (The where-clause appears to be irrelevant to any point you were trying to make.)

The question that was put to you was: What is the union of the members of sets {{1,2,3}} and {{2,5}}.

Your answer was {{1,2,3},{2,5}}, which is just plain wrong.

It would have been correct had the question been "What is the union of the members of sets {{1,2,3}} and {{2,5}}," but it wasn't.

If {1,2,3}u{2,5}={1,2,3,5}, then {{1,2,3}}u{{2,5}}={{1,2,3},{2,5}} where in both cases the result is based on membreship's first-level.

jsfisher

5th January 2009, 07:46 AM

If {1,2,3}u{2,5}={1,2,3,5}, then {{1,2,3}}u{{2,5}}={{1,2,3},{2,5}} where in both cases the result is based on membreship's first-level.

No, the results are based on the meaning of "union".

Be that as it may, the question that was put to you was: What is the union of the members of sets {{1,2,3}} and {{2,5}}.

Your answer was {{1,2,3},{2,5}}.
Your answer was just plain wrong.

Do you wish to amend your answer?

sympathic

5th January 2009, 08:26 AM

x \in \bigcup\mathbf{M} \iff \exists A{\in}\mathbf{M}, x \in A.

doronshadmi

5th January 2009, 09:02 AM

Your answer was {{1,2,3},{2,5}}.
Your answer was just plain wrong.

No the answer is right.

The wrong answer is {1,2,3,5}, which leads us to the wrong conclusion that {1,2,3}={{1,2,3}} and {2,5}={{2,5}}

In other words, the current paradigm of standard Set theory is inconsistant because by this paradigm {AuB} = AuB or in other words, the non-local property of Set is not well defined and therefore used without understanding.

Do you wish to amend your answer?
Do you wish to amend your understanding?

doronshadmi

5th January 2009, 10:23 AM

The Man,

For me Mathematics is what Mathematicians do.

It means that any result is based on the interaction of the observer with the observed, whether the observed is abstract or not.

Furthermore, the observer aspect of any research is its non-local aspect where the observed aspect is its local aspect.

This is exactly the reason of how generalization is possible, in the first place.

Non-locality is not deeper or more abstract than Locality, but they are the minimal building-blocks that enables interaction with each other exactly as two axioms are mutually independent w.r.t each other.

Interaction, Non-locality and Locality are the expressions of Singularity, which is the non-researchable source of any researchable framework, abstract or not.

jsfisher

5th January 2009, 10:25 AM

No the answer is right.

The wrong answer is {1,2,3,5}, which leads us to the wrong conclusion that {1,2,3}={{1,2,3}} and {2,5}={{2,5}}

Ok, thank you for the confirmation. Doron Mathematics is incompatible with Set Theory.

In other words, the current paradigm of standard Set theory is inconsistant because by this paradigm {AuB} = AuB or in other words, the non-local property of Set is not well defined and therefore used without understanding.

Set Theory has no such paradigm.

Do you wish to amend your understanding?

No, I am quite comfortable being able to distinguish between the two phrases:

the union of sets A and B, and
the union of the members of sets A and B.

By the way, you have a technical problem. Since your novel beliefs make the traditional set theories inaccessible, all of your beliefs, concepts, novel views that have Set Theory as an implicit underpinning have to be discarded for lack of basis. That would include cardinality, arithmetic, geometry, counting, and much of logic.

You should focus your attention for now on developing DoronShadmi Set Theory so you have something with which to work.

doronshadmi

5th January 2009, 10:48 AM

Ok, thank you for the confirmation. Doron Mathematics is incompatible with Set Theory.

Set Theory has no such paradigm.

No, I am quite comfortable being able to distinguish between the two phrases:

the union of sets A and B, and
the union of the members of sets A and B.

By the way, you have a technical problem. Since your novel beliefs make the traditional set theories inaccessible, all of your beliefs, concepts, novel views that have Set Theory as an implicit underpinning have to be discarded for lack of basis. That would include cardinality, arithmetic, geometry, counting, and much of logic.

You should focus your attention for now on developing DoronShadmi Set Theory so you have something with which to work.

It works! (for eample: http://www.geocities.com/complementarytheory/NXOR-XOR.pdf ).

Paradigm-shifts are not for lazy parsons.

There is no homeomorphism between a point and a line or in other words, they are mutually independent exactly like two axioms ( http://forums.randi.org/showpost.php?p=4320166&postcount=1312 ).

By generalize a point as the minimal expression of Locality(Conservation) and a line as the minimal expression of Non-locality(Extension) and by interacting between them (where we are a significant factor of the result), the paradigm-shift is inventible because it is an essential property of any non-trivial and researchable framework.

jsfisher

5th January 2009, 11:07 AM

Paradigm-shifts are not for lazy parsons.

Nor are they for industrious rabbis. Either way, you are condemned to exploring your fabricated paradigm shift without the aid of Set Theory.

There is no homeomorphism between a point and a line or in other words, they are mutually independent exactly like two axioms ( http://forums.randi.org/showpost.php?p=4320166&postcount=1312 ).

Why are you jumping from Set Theory - which you reject - to Topology?

The Man

5th January 2009, 01:33 PM

The current paradigm does not distinguish between the mutually independent building-blocks and ignores the interactions between them as a significant factor of the results. .

The building blocks of something are not mutually independent for that something, you are ignoring the interactions you assert as a “significant factor of the results” showing the mutual dependence of and on those “building-blocks” for that result.

Furthermore, by the so called objective existence of the researched the current paradigm cannot explain how these objects interact with each other in the first place, in order to get the non-trivial realm that we are an inseparable factor of it.

You have not demonstrated any objectivity, the ability to research anything nor can you even explain “how these objects interact with each other in the first place, in order to get the non-trivial realm that we are an inseparable factor of it” or what that is supposes to mean. It seems you just want to spew some quasi eastern mystical claims and expect everyone to think of you as some kind of sage.

Your mechanic paradigm is getting off stage in these days whether you like it or not, and a non-naïve paradigm that rigorously defines the interactions between Conservation AND Extension replaces it in each passing day.

Well I’m still waiting for the day when you stop being naïve and start to rigorously define the “interactions between Conservation AND Extension”, but I’m not holding my breath.

My voice is nothing but the very first glance of a new paradigm of a mathematical science that is based on the awareness of the mathematician as a significant factor of his mathematical research, and how the results are the outcomes of the non-trivial interactions of Conservation AND Extension.

Sure and meanwhile we have all been just choking our chickens thinking we know what were doing sending probes flying around the solar system and building even smaller and smaller computers and machines based on our lack of “awareness”

You have failed to get the depth of the topological notion of the mutual independency of Conservation with Extension because you ignore Extension as a fundamental property of your paradigm (you do your "best" in order to Conserve anything in order to avoid any Extension of it, like any "good" dogmatic person).

As far as I know you never even mentioned Extension on this thread until I used the term extents in reference to the extents of a line in only one dimension. Had you actually applied your basics of a researchable framework to actually do any research you would have found that extents or extensions into one or more dimensions is a fundamental property of the current paradigm but it is not mutually independent of points (that you ascribe to “Conservation”) which can define that extent or extension.

You are simply ignorant of Singularity at its self state, which is the natural and simplest state of all there is (subjective, objective, abstract or not it does not matter), whether it is expressed as Conservation Extension or Interaction.

While you remain simply ignorant of the paradigm you claim you what to replace and the importance of actually doing research as opposed to constantly claiming you have found the basis for all research.

The Man,

For me Mathematics is what Mathematicians do.

For me too, let’s see how the two rank in that regard

Current Mathematical Paradigm = Everything currently done with and by math.

Doron’s Paradigm = Nothing (except to try and lay claim to the accomplishments of the Current Mathematical Paradigm)

It means that any result is based on the interaction of the observer with the observed, whether the observed is abstract or not.

Furthermore, the observer aspect of any research is its non-local aspect where the observed aspect is its local aspect.

This is exactly the reason of how generalization is possible, in the first place.

So instead of trying to reconcile generalized locations when applied to your definition of non-local as more then one relation, you now (as usual) simply assimilate generalization as just something else only made possible by your notions. That is more of an ameba paradigm that just ingests everything into some amorphous blob rather then a mathematical paradigm that explains itself effectively then explains other things effectively.

Non-locality is not deeper or more abstract than Locality, but they are the minimal building-blocks that enables interaction with each other exactly as two axioms are mutually independent w.r.t each other.

Interaction, Non-locality and Locality are the expressions of Singularity, which is the non-researchable source of any researchable framework, abstract or not.

Non locality and locality are mutually dependent once you define one the other is defined as what does not meet that first definition, that is what the “NON” does it makes things mutually dependent as opposites.

"the non-researchable source of any researchable framework" and just how could you come to that conclusion unless you were able to at least do some research on that "non-researchable source". Once again you claim the amazing ability to research the non-researchable while seemingly completely unable or unwilling to research anything else.

doronshadmi

6th January 2009, 01:18 AM

Well I’m still waiting for the day when you stop being naïve and start to rigorously define the “interactions between Conservation AND Extension”, but I’m not holding my breath.

Finally I get what a naïve I am (after all, hope is a beautiful illness).

I thought that I am talking to something that is aware of itself as a significant factor of some research, but I was wrong.

All along this thread I was talking to some "quasi eastern mystical" mambo jambo that is not any significant factor of any research.

It is really about time not to try to communicate with some "quasi eastern mystical" mambo jambo.

Some example: "quasi eastern mystical" mambo jambo cannot get the fact that it is an interaction between opposites.

doronshadmi

6th January 2009, 01:25 AM

Why are you jumping from Set Theory - which you reject - to Topology?
Fundamental notions are not limited to any particular mathematical branch.

Fundamental notions are non-local w.r.t to any given branch exactly as a trunk is non-local w.r.t any given branch.

jsfisher

6th January 2009, 04:36 AM

Fundamental notions are not limited to any particular mathematical branch.

Fundamental notions are non-local w.r.t to any given branch exactly as a trunk is non-local w.r.t any given branch.

Perhaps, but, unfortunately, Topology depends on Set Theory. Your views / notions / beliefs leave Set Theory in ruins. Without a proper substitute, Topology doesn't work for you either.

doronshadmi

6th January 2009, 07:48 AM

Perhaps, but, unfortunately, Topology depends on Set Theory. Your views / notions / beliefs leave Set Theory in ruins. Without a proper substitute, Topology doesn't work for you either.

Ho yes it works.

It does not work for any one that gets things only in terms of Conservation (Locality).

And no, Set theory is not some invariant object, and therefore can be chaneged by pradigm-shifts (fundamental extensions).

jsfisher

6th January 2009, 08:39 AM

Set theory is not some invariant object, and therefore can be chaneged by pradigm-shifts (fundamental extensions).

No one has said otherwise. You are posting a straw man.

What you are not posting is anything about your new-and-improved set theory. For some very basic set theoretic operations, like member and union, you want results which are, well, novel. The standard set theories the rest of us know and love don't work in your post "pradigm-shift" world. It is therefore incumbent on you to provide for its replacement and show how to derive the other Mathematics branches from it.

The Man

6th January 2009, 08:54 AM

Finally I get what a naïve I am (after all, hope is a beautiful illness).

I thought that I am talking to something that is aware of itself as a significant factor of some research, but I was wrong.

All along this thread I was talking to some "quasi eastern mystical" mambo jambo that is not any significant factor of any research.

It is really about time not to try to communicate with some "quasi eastern mystical" mambo jambo.

Some example: "quasi eastern mystical" mambo jambo cannot get the fact that it is an interaction between opposites.

I'm Glad to have helped you with your "mambo jambo".

ETA:
I can only hope that someday you will become aware of actual research being the most significant part of any research.

doronshadmi

6th January 2009, 09:11 AM

I'm Glad to have helped you with your "mambo jambo".

ETA:
I can only hope that someday you will become aware of actual research being the most significant part of any research.

"quasi eastern mystical" mambo jambo cannot get anything, it is not glad it is not sad it has no hopes, it is nothing but a mechanical tool that has no impact on anything, internal or external.

doronshadmi

6th January 2009, 09:38 AM

The standard set theories the rest of us know and love don't work in your post "pradigm-shift" world.

It works also under the paradigm-shift, but simpler and more interesting, because the observer is a significant factor of the observed result, which is the gate to the next stage of technology - the technology of consciousness – where Ethics and Formal Logic complement each other under a one comprehensive framework.

The Man

6th January 2009, 10:34 AM

"quasi eastern mystical" mambo jambo cannot get anything, it is not glad it is not sad it has no hopes, it is nothing but a mechanical tool that has no impact on anything, internal or external.

A mechanical tool like a hammer is specifically designed to "impact" things both internal and externally. However, it is your “mambo jambo” and you can make of it what you will, the problem comes when you simply expect others to make of it what you will.

doronshadmi

6th January 2009, 12:11 PM

A mechanical tool like a hammer is specifically designed to "impact" things both internal and externally. However, it is your “mambo jambo” and you can make of it what you will, the problem comes when you simply expect others to make of it what you will.

There is no design without a designer, the problem comes when the designer is not aware of itself. In that case it easily uses its outcomes in order to destroy itself, as a normal mechanical action.

In order to avoid a designed tool like a hummer to destroy the designer, the designer has to be aware of itself as an inseparable part of the impact of its designs.

For the past 3000 years of western school of thought the designer was thought to ignore itself as a significant factor of its designs. As a result it became an ignorant of its own development, where real development is not less than Logical and Ethical as complements of a one developed realm.

This ignorance is going to manifest itself some day as the designer's self destruction, where the "hummers" that will be used are going to be more and more sufficient in the near future (for example: an anti-matter bomb instead of the current "hummer" known as Hydrogen bomb).

Parameter L of Drake equation ( http://en.wikipedia.org/wiki/Drake_equation ) is first of all related to us, but as long as persons like The Man are the main stream of Modern Science, there is no one to talk with because persons like The Man simply living in the past, where a hummer was just a hummer, and they do not wish to take any responsibility of their blind actions until it is too late.

Instead of develop their self awareness, they look at awareness as "quasi eastern mystical" mambo jambo simply because the methods of how to do that were not learned by the western school of thought, where by this school the designer is explicitly ignored as a an inseparable part of the educational method of how to get the requested results.

We are clearly in a time where this idiotic Educational method is going to fully fulfill itself, we are going to use our designed hummers against the designer, the horrible joke is that the designer trained itself for the past 3000 years for this "glories moment" of the designer's self destruction of its ignorance.

The difference between people like The Man and me is that The Man's school of thought is going for (blind) real (it is going to destroy the designer without even know it, because this school of thought is based on the designer's ignorance in order to fulfill its goals), where I am going for the school of thought that is aware of the designer is an inseparable part of its results, which gives us better chances to avoid self made destruction.

You are unaware of how dangerous are the scientists of today that still use the western philosophy that ignores the researcher as a significant factor of its results, whether they are abstract or not, it does not matter.

The Man

6th January 2009, 01:09 PM

doronshadmi

6th January 2009, 01:31 PM

zooterkin

6th January 2009, 01:56 PM

With respect to my previous post, please look how The Man uses a hummer in http://www.randi.org/forumlive/showpost.php?p=4117846&postcount=40 in order to represent his philosophical view of existence.

Well, that's a debating tactic I'd not come across before. I suspect I could be persuaded, at least by some people, who were using that approach on me...

jsfisher

6th January 2009, 02:49 PM

Well, that's a debating tactic I'd not come across before. I suspect I could be persuaded, at least by some people, who were using that approach on me...

I think it was Bill Clinton that first used the hummer in a formal debate.

The Man

6th January 2009, 03:09 PM

I can steadfastly attest to the fact that I have never used or have had used on me a hummer as a debating tactic.

Speaking of debating tactics Doron, you no longer seem interested in addressing your assertions or counter arguments to your assertions and now simply attempt to impugn my character. Understandable as one will be equally as ineffective as the other in supporting your notions.

The Man

6th January 2009, 07:41 PM

Come to think of it, a hummer might not be a bad philosophical view of existence. Thanks, Doron you’re finally starting to make sense, that blowing/sucking complementation/interaction and all.

Little 10 Toes

6th January 2009, 09:14 PM

With respect to my previous post, please look how The Man uses a hummer in http://www.randi.org/forumlive/showpost.php?p=4117846&postcount=40 in order to represent his philosophical view of existence.

Furthermore, he tells us that "** This research project is not recommended and would be considered illegal under existing law." not because we can harm ourselves but because it is against some existing law, which is not related to the existence of any awareness, by its ignorance of itself.

Wow. From truth tables, to set theory, to geometry, to topology, these are all things that you jump to, but yet can't explain with your ideas. Funny that you once again, misquote people.

The topic of The Man's post was "Consciousness.....a basic rule of physics " where you derailed the thread and caused it to be closed (http://www.randi.org/forumlive/showpost.php?p=4195326&postcount=374). Remember that?

The thread was (in a nutshell) about the original poster stating that "FOR EXISTENCE, YOU MUST HAVE CONSCIOUSNESS".

In addition, he was responding to a post. Here's the whole post:
original quote from RandFanYeah, that's the point. Setting aside idealism for the moment, existence is only a state of mind. Yep, even if we assume materialism over idealism it still doesn't change the fact that the world out there only exists in our minds. Something isn't any different than nothing unless there is something to appreciate it.

Philosophical claptrap, the fact is that our minds only exist in our minds as for the existence of everything else; well you can pay that no mind if you want but that is not advisable. If you think a hammer does not exist (except in your mind) then try to think the hammer away as you bash yourself in the head with it (or have someone else do it if they don’t mind) until you prove the hammer does not exist, your mind does not exist or you finally choose to mind the existence of the hammer (and perhaps the other person) outside of your mind and bashing you in the head. I doubt you will execute the first blow before you recognize the existence of the hammer over the existence of your mind. Should you execute one or more blows and even choose the claw side of the hammer to strike with, then I might doubt the applicability of the existence of your mind but not the applicability of the existence of the hammer.**

** This research project is not recommended and would be considered illegal under existing law.

How does “something to appreciate it” constitute nothing? So, “Something isn't any different than nothing” when nothing is not nothing because you choose to require “something to appreciate it” for it to be nothing?

Why do you care about The Man's belief of consciousness? Why do you care about him making the point that things still exist whether or not you believe they do? Why did you bring it up? Do you know the difference between a hummer and hammer? Why can't you answer simple questions? Why do you keep changing mathematical subjects? Why can't you teach anyone your "ideas"? Why should anyone care about your "ideas"? What good are they?

Four hummers I can think of:
One who hums, the military type vehicle, something X-rated, Monica Lewinski

The Man

6th January 2009, 11:25 PM

Wow. From truth tables, to set theory, to geometry, to topology, these are all things that you jump to, but yet can't explain with your ideas. Funny that you once again, misquote people.

Thanks again, L 10 T, for giving the context in another example of quote mining. Unfortunately, I feel some responsibility for some of the jumps you mentioned. As I tried to explain things Doron keyed off of some term or phrase (that he could not demonstrate an understanding of), leading me to explain things more and another attempt to obfuscate by misused terminology. The central aspects of Doron’s assertions (as given by him) are eastern philosophies. Unfortunately such philosophies are steeped in mysticism and once you start trying to define and establish them they lose that mystic or mysterious quality which makes them so appealing to some. You just have to believe, L 10 T, then it will all make sense, but still be of little practical or mathematical use.

doronshadmi

7th January 2009, 02:43 AM

doronshadmi

7th January 2009, 02:46 AM

Wow. From truth tables, to set theory, to geometry, to topology, these are all things that you jump to, but yet can't explain with your ideas. Funny that you once again, misquote people.

The topic of The Man's post was "Consciousness.....a basic rule of physics " where you derailed the thread and caused it to be closed (http://www.randi.org/forumlive/showpost.php?p=4195326&postcount=374). Remember that?

The thread was (in a nutshell) about the original poster stating that "FOR EXISTENCE, YOU MUST HAVE CONSCIOUSNESS".

In addition, he was responding to a post. Here's the whole post:

Why do you care about The Man's belief of consciousness? Why do you care about him making the point that things still exist whether or not you believe they do? Why did you bring it up? Do you know the difference between a hummer and hammer? Why can't you answer simple questions? Why do you keep changing mathematical subjects? Why can't you teach anyone your "ideas"? Why should anyone care about your "ideas"? What good are they?

Four hummers I can think of:
One who hums, the military type vehicle, something X-rated, Monica Lewinski

http://forums.randi.org/showpost.php?p=4325896&postcount=1341

doronshadmi

7th January 2009, 03:19 AM

Well, having designed things used around the world from gun and missile cases to automated computer controlled data acquisitions systems and even some of the electrical transmission and distribution connectors that might be bringing power to your computer, I can tell you that the designers focus should be on the design. A designer as focused on himself as you appear to be is likely to create a bad design, if any, as you have done.
Both the designer and the designed are considered by my suggested school of thought.

Actually this is exactly the meaning of Development by my school of thought, which is: deeper interactions between the designed and the designer, which is, in my opinion, the best guarantee of the survival of the designer in the long run, which enables him to improve his designs and himself during improved interactions, where the Ethical leg and the Formal Logical leg serves a one body of knowledge.

The Man, by your school of thought there is no connection between Ethics and Formal Logic. As a result the designer increases his chances to use his designs against itself, because by the western school of thought he is trained day by day to ignore himself in order to get some requested result. One of the possible results is self destruction just because the designer's presence is ignored until it is too late.

Your personal-only understanding of my argument clearly demonstrates how your school of thought did not develop the interactions between the designed and the designer for the past 3000 years.

In other words, you are unable to understand http://forums.randi.org/showpost.php?p=4325896&postcount=1341 argument, and this is exactly the reason why your school of thought is so dangerous. It simply enables its scholars to easily use more and more sufficient "hammers" on their heads until the exact value Parameter L of Drake equation ( http://en.wikipedia.org/wiki/Drake_equation ) is finally achieved, which is after all the requested result of any school of thought that its goal is "rigorous" determination and definition of anything, isn't it?

This is exactly the reason why scholars that are trained by the western school of thought cannot understand fundamental notions like Non-locality, Extension, Incompleteness, Parallel, Openness, Paradigm-Shift, etc. … as essential properties of any meaningful and valuable researchable framework.

My suggestion is to establish a school of thought that is based on non-naive interaction between Western AND Eastern school of thoughts.

doronshadmi

7th January 2009, 08:34 AM

By the Western-only school of thought, scholars are rigorously ignorant of themselves as significant factors of the results, whether these results are abstract or not.

By the Eastern-only school of thought, scholars are rigorously ignorant of results that may come from themselves, because the results are generally ignored and only their selves are considered.

I think that it is about time to build the bridges beyond the ignorance of each X-only viewpoint.

The Man

7th January 2009, 08:37 PM

No, I am interested about the school of thought that shapes your character.

Experience shapes my character, not a “school of thought”.

Both the designer and the designed are considered by my suggested school of thought.

Actually this is exactly the meaning of Development by my school of thought, which is: deeper interactions between the designed and the designer, which is, in my opinion, the best guarantee of the survival of the designer in the long run, which enables him to improve his designs and himself during improved interactions, where the Ethical leg and the Formal Logical leg serves a one body of knowledge.

The Man, by your school of thought there is no connection between Ethics and Formal Logic. As a result the designer increases his chances to use his designs against itself, because by the western school of thought he is trained day by day to ignore himself in order to get some requested result. One of the possible results is self destruction just because the designer's presence is ignored until it is too late.

For my “school of thought” you need to pay the tuition of experience and thereby learn the “connection between Ethics and Formal Logic” for yourself, as it can only be a personal connection and it is not an easy school.

“Experience is the worst teacher; it gives the test before the lesson”

(I do not remember how that quote is from.)

Just how would your “school of though” limit the possibility of a design being used against the designer?

Your personal-only understanding of my argument clearly demonstrates how your school of thought did not develop the interactions between the designed and the designer for the past 3000 years.

I do not see how understanding can be anything but personal just as the connection between ethics and formal logic must be. Is it that you simply propose imposing your personal understanding, ethics, informal logic and “school of thought” on others?

The interaction between designer and the design is well established and trivial. The designer designs what is designed.

In other words, you are unable to understand http://forums.randi.org/showpost.php?p=4325896&postcount=1341 argument, and this is exactly the reason why your school of thought is so dangerous. It simply enables its scholars to easily use more and more sufficient "hammers" on their heads until the exact value Parameter L of Drake equation ( http://en.wikipedia.org/wiki/Drake_equation ) is finally achieved, which is after all the requested result of any school of thought that its goal is "rigorous" determination and definition of anything, isn't it?

How a design is used depends on the user not the designer, the design itself or the intended use it was designed for. Survival cases we manufactured could be used to hurt or kill someone just as a hammer could, but that is not the designed application of either. If your “school of thought” is an attempt to restrict possible uses or users, I do not see how that goal can be obtained.

This is exactly the reason why scholars that are trained by the western school of thought cannot understand fundamental notions like Non-locality, Extension, Incompleteness, Parallel, Openness, Paradigm-Shift, etc. … as essential properties of any meaningful and valuable researchable framework.

Oh, they understand them alright, that their understanding is different, easily explainable and practically applicable while your understanding is not, well that is not theirs or anyone’s fault but your own.

My suggestion is to establish a school of thought that is based on non-naive interaction between Western AND Eastern school of thoughts.

Then my suggestion would be that is where you should start, by first establishing the parameters of those schools of though, identifying the differences and similarities, but that would require actual research and not just your personal speculations.

doronshadmi

8th January 2009, 03:40 AM

Oh, they understand them alright, ...

No they don't, and you are some particular example that can be used without a loss of generality (http://en.wikipedia.org/wiki/Without_loss_of_generality).

Experience shapes my character, not a “school of thought”.

“Experience is the worst teacher; it gives the test before the lesson”

If your “school of thought” is an attempt to restrict possible uses or users, I do not see how that goal can be obtained.

This is the basic approach of anyone who wishes to be right instead of wise.

He has no problems to pay by his own life in order to be right ( http://forums.randi.org/showpost.php?p=4326132&postcount=1343 and http://forums.randi.org/showpost.php?p=4327246&postcount=1347 ).

This is the Logic of the majority of the scholars that holds the current and future's technology of our own civilization on this planet, in their hands.

They continue to develop destructive tools (that is an easy task exactly because of the disconnection between Ethics and Formal Logic) and then they blame the ignorant users that use their technological "developments".

The Man, we are living in a time where some test can be easily the last test that determinates the exact value of our L parameter of Drake's equation ( http://en.wikipedia.org/wiki/Drake_equation ) .

Please look over the internet and find by yourself how the current scientific community is aware of parameter L as a factor that is related to our own civilization on this planet.

Also I wish to know what are your operative suggestions (based only on your personal experience, since you claim that you ignore any school of thought's knowledge as a significant factor of your actual actions that are drived from your character) in order to do our best in order to prevent our exact value of L?

doronshadmi

9th January 2009, 06:17 AM

I do not see how understanding can be anything but personal just as the connection between ethics and formal logic must be.
This is a direct result of the reasoning of the trivial X\Not-X excluded-middle Logic, that is used as the main stream of the scientific development of our civilization for the past 3000 years.

Furthermore, because of this trivial approach there is no connection between Western and Eastern school of thoughts and both schools are ignorant of the methods that can define the bridging between them.

In my opinion, we are going to pay by our own life and the life of the future generations (to determine the exact value of L by our own hands) if we not immediately start to develop a comprehensive program that defines the bridging between our Ethical and Formal Logical aspects under a one framework that enables opposites to simultaneously prevent AND complement each other without contradicting (eliminating) each other.

In my opinion, our self awareness as a significant factor of this non-trivial challenge must not be neglected anymore, or in other words, any trivial approach about the attempt to define the non-trivial bridging between Ethics and Formal Logic "helps" to determine the exact value of parameter L of Drake's equation ( http://en.wikipedia.org/wiki/Drake_equation ) of our own civilization.

AGAIN:

Please look over the Internet and find by yourself how the current scientific community is aware of parameter L as a factor that is related to our own civilization on this planet.

Little 10 Toes

9th January 2009, 07:30 AM

...and how does this explain that you can't get basic set theory and basic geometry and can't answer simple questions?

doronshadmi

9th January 2009, 09:39 AM

...and how does this explain that you can't get basic set theory and basic geometry and can't answer simple questions?

http://hypography.com/forums/physics-and-mathematics/8292-the-organic-unity-of-mathematics.html

The Man

9th January 2009, 10:07 AM

This is a direct result of the reasoning of the trivial X\Not-X excluded-middle Logic, that is used as the main stream of the scientific development of our civilization for the past 3000 years.

One of the key factors in chemistry is minimum energy and maximum entropy, opposing factors, and the balance between them that can result. This is not an “excluded-middle” but an interaction of opposites that “the main stream of the scientific development of our civilization for the past 3000 years” is replete with.

Furthermore, because of this trivial approach there is no connection between Western and Eastern school of thoughts and both schools are ignorant of the methods that can define the bridging between them.

Some western philosophies have been influenced by eastern philosophies and visa versa. That any particular school of philosophy has its own unique attributes and considerations does not demonstrate that it was established in ignorance of other schools of philosophy, western or eastern.

In my opinion, we are going to pay by our own life and the life of the future generations (to determine the exact value of L by our own hands) if we not immediately start to develop a comprehensive program that defines the bridging between our Ethical and Formal Logical aspects under a one framework that enables opposites to simultaneously prevent AND complement each other without contradicting (eliminating) each other.

Opposites that “prevent” “each other” would be “contradicting” and “(eliminating) each other” or else they would not “prevent” “each other”.

As I said before the “bridging between our Ethical and Formal Logical aspects” is a personal understanding. Trying to define and then impose ones establishment of such “under a one framework” onto others could be considered by some to be, well, unethical.

In my opinion, our self awareness as a significant factor of this non-trivial challenge must not be neglected anymore, or in other words, any trivial approach about the attempt to define the non-trivial bridging between Ethics and Formal Logic "helps" to determine the exact value of parameter L of Drake's equation ( http://en.wikipedia.org/wiki/Drake_equation ) of our own civilization.

Please show the equation you would use to determine the “exact value” of L and how it is affected by the parameters of your defining “the non-trivial bridging between Ethics and Formal Logic”. Otherwise it remains simply your opinion and apparently not a well informed opinion at that. Common “Ethics and Formal Logic” combined with the desire to maintain them could lead a civilization to isolationism, an aspect demonstrated by history, resulting in such a civilization deliberately limiting or eliminating the release of signs of its existence into space.

AGAIN:

Please look over the Internet and find by yourself how the current scientific community is aware of parameter L as a factor that is related to our own civilization on this planet.

As L represents the length of time the civilizations concerned by the Drake equation (specifically those capable of releasing detectable signs of their existence into space) do in fact release detectable signs of their existence into space, it is specifically about the release of those detectable signs and not the existence of civilizations itself.

ddt

9th January 2009, 11:37 AM

...and how does this explain that you can't get basic set theory and basic geometry and can't answer simple questions?
Don't you get it? It's because of the colors in doron's post! That makes everything different! :p

http://hypography.com/forums/physics-and-mathematics/8292-the-organic-unity-of-mathematics.html

Ah, so instead of linking to previous posts of yourself here, you link to your posts on other fora.

Do you really want us to demolish the load of rubbish in that post?

doronshadmi

9th January 2009, 12:39 PM

As I said before the “bridging between our Ethical and Formal Logical aspects” is a personal understanding. Trying to define and then impose ones establishment of such “under a one framework” onto others could be considered by some to be, well, unethical.

Yes, a tree is a good example of some nature's unethical thing because it has a trunk that is non-local (non-personal) w.r.t any given branch (which is local\parsonal w.r.t the trunk), isn't is The Man?

http://forums.randi.org/showpost.php?p=4330725&postcount=1355

doronshadmi

9th January 2009, 01:06 PM

Do you really want us to demolish the load of rubbish in that post?

You are wellcome.

Definition 1:
Let X and Y be topological spaces; then f : X → Y is a homeomorphism between X and Y if it is a continuous bijection with a continuous inverse.

If there is a homeomorphism between X and Y we say that they are homeomorphic.

Let X be 0-dimesional topological space and let Y be 1-dimesional topological space.

Please prove that X and Y are homeomorphic.

1. If there is a proof that X and Y are non-homeomorphic then X and Y cannot be transfomed to each other (they are mutually independend).

2. If there is a proof that X and Y are homeomorphic then X and Y can be transfomed to each other (they are not mutually independend).

If (2) then also {} and {x} are homeomorphic and so are True\False statments.

If (1) then then also {} and {x} are non-homeomorphic and so are True\False statments.

doronshadmi

9th January 2009, 03:25 PM

Theorem 1: There is no continuous bijection with a continuous inverse between X and Y.

Edit:

Proof: It is obvious if X is necessarily a singleton set and Y is not.

If X is not necessarily a singleton set, then there are many distinct objects in 0-dimensional space, where each object is a 0-dimesion element.

In that case each 0-dimesion object is itself is based of sub-objects … ad infinitum (because we allow more than a singleton set in 0-dimensional space) and no mapping can be found, because there is an endless regression of sub-objects. □

nathan

9th January 2009, 03:44 PM

Yes, a tree is a good example of some nature's unethical thing
Oh wow man, cut down those evil trees -- with hatchet, axe and saw!

ddt

9th January 2009, 04:04 PM

You are wellcome.

Definition 1:
Let X and Y be topological spaces; then f : X → Y is a homeomorphism between X and Y if it is a continuous bijection with a continuous inverse.
[...]

What has that to do with your nonsense post on hypography? That doesn't relate to topology at all.

jsfisher

9th January 2009, 04:12 PM

Theorem 1: There is no continuous bijection with a continuous inverse between X and Y.

Proof: It is obvious because X is necessarily a singleton set, where Y is not. □

Real proofs seldom are based on the "it is obvious" premise.

Be that as it may, since bijections are a type of mapping, and since mappings are founded in Set Theory, and since Doron has rejected Set Theory, unless and until he formulates a substitute, his theorem is without meaning.

Then again, since X and Y are unbounded, the theorem is clearly wrong. A proof by counter-example becomes trivial at whatever point Doron kindly restores meaning to some Mathematical concepts he so callously rejected.

jsfisher

9th January 2009, 04:14 PM

That doesn't relate to topology at all.

Neither does Doron.

jsfisher

9th January 2009, 04:27 PM

Time for a trivia question: What's the topological dimension of the Cantor Set?

doronshadmi

9th January 2009, 04:53 PM

Then again, since X and Y are unbounded, the theorem is clearly wrong. A proof by counter-example becomes trivial at whatever point Doron kindly restores meaning to some Mathematical concepts he so callously rejected.

X and Y are bounend exactly by their own n-dimesional space.

http://forums.randi.org/showpost.php?p=4334865&postcount=1363 was edited.

jsfisher

9th January 2009, 05:00 PM

X and Y are bounend exactly by their own n-dimesional space.

http://forums.randi.org/showpost.php?p=4334865&postcount=1363 was edited.

No, X and Y remain unbounded. Your edit didn't repair that. If you had something in mind for what X and Y are allowed to be, you need to express that. You didn't. X and Y are unbounded.

doronshadmi

9th January 2009, 05:09 PM

No, X and Y remain unbounded. Your edit didn't repair that. If you had something in mind for what X and Y are allowed to be, you need to express that. You didn't. X and Y are unbounded.

http://forums.randi.org/showpost.php?p=4334865&postcount=1363 was edited again.

If you disagree, then please explain why X and Y are unbounded, and why because of it my proof does not hold?

jsfisher

9th January 2009, 05:19 PM

http://forums.randi.org/showpost.php?p=4334865&postcount=1363 was edited again.

If you disagree, then please explain why X and Y are unbounded, and why because of it my proof does not hold?

In that post, X and Y are free variables. They have no bounds placed on them. They are unbounded.

doronshadmi

9th January 2009, 05:41 PM

In that post, X and Y are free variables. They have no bounds placed on them. They are unbounded.

I think that you have missed http://forums.randi.org/showpost.php?p=4334469&postcount=1362 .

X is 0-dimensional topological space.

Y is 1-dimensional topological space.

Theorem 1: There is no continuous bijection with a continuous inverse between X and Y.

Proof: It is obvious if X is necessarily a singleton set and Y is not.

If X is not necessarily a singleton set, then there are many distinct objects in 0-dimensional space, where each object is a 0-dimesion object.

In that case each 0-dimesion object is itself is based of sub-objects … ad infinitum (because we allow more than a singleton set in 0-dimensional space) and no mapping can be found, because there is an endless regression of sub-objects. □

Conclusion: By using the notion of Set, X and Y are non-homeomorphic.

jsfisher

9th January 2009, 05:49 PM

I think that you have missed http://forums.randi.org/showpost.php?p=4334469&postcount=1362.

No, I did not. However, in that post you used X and Y in two different contexts. Moreover, if you expect others to interpret X and/or Y in one post by one of the two usages made of them in another post, then it is incumbent upon you to make that clear.

X is 0-dimensional topological space.

Y is 1-dimensional topological space.

So, one of those could be the Cantor Set, then, right? Which one would that be? Did you know there's a mapping from every point along [0,1] to a point in the Cantor Set?

doronshadmi

9th January 2009, 05:53 PM

No, I did not. However, in that post you used X and Y in two different contexts. Moreover, if you expect others to interpret X and/or Y in one post by one of the two usages made of them in another post, then it is incumbent upon you to make that clear.

So, one of those could be the Cantor Set, then, right? Which one would that be? Did you know there's a mapping from every point along [0,1] to a point in the Cantor Set?

Please reply to http://forums.randi.org/showpost.php?p=4335248&postcount=1373 .

jsfisher

9th January 2009, 06:00 PM

Please reply to http://forums.randi.org/showpost.php?p=4335248&postcount=1373 .

I did. How about you respond to my posts, especially since they all predate your most recent re-re-editing.

doronshadmi

9th January 2009, 06:13 PM

I did. How about you respond to my posts, especially since they all predate your most recent re-re-editing.

The notion of many disjoint objects is false, because they cannot be considered as many if there is nothing that gathers them together.

In other words, disjoint points are like {a} {b} {c} … where the cardinality of it is no more than 1.

Again:

If 0-dimansional topological space is not necessarily a singleton set, then there are many distinct objects in 0-dimensional space, where each object is a 0-dimesion object.

In that case each 0-dimesion object is itself is based of sub-objects … ad infinitum (because we allow more than a singleton set in 0-dimensional space) and no mapping can be found, because there is an endless regression of sub-objects (we get a beast that is inherntly unbounded).

jsfisher

9th January 2009, 06:25 PM

Little 10 Toes

9th January 2009, 06:37 PM

http://hypography.com/forums/physics-and-mathematics/8292-the-organic-unity-of-mathematics.html

...and how does this explain that you can't get basic set theory and basic geometry and can't answer simple questions?

You are wellcome.

Definition 1:
Let X and Y be topological spaces; then f : X → Y is a homeomorphism between X and Y if it is a continuous bijection with a continuous inverse.

If there is a homeomorphism between X and Y we say that they are homeomorphic.

Let X be 0-dimesional topological space and let Y be 1-dimesional topological space.

Nice how you change definitions. What is it, are X and Y topological spaces or are they spaces that you define?

Please give an example of a 0-dimesional space.

Please prove that X and Y are homeomorphic.

1. If there is a proof that X and Y are non-homeomorphic then X and Y cannot be transfomed to each other (they are mutually independend).

2. If there is a proof that X and Y are homeomorphic then X and Y can be transfomed to each other (they are not mutually independend).

If (2) then also {} and {x} are homeomorphic and so are True\False statments.

If (1) then then also {} and {x} are non-homeomorphic and so are True\False statments.

Why are you going from topological spaces to truth tables?

Little 10 Toes

9th January 2009, 06:38 PM

Theorem 1: There is no continuous bijection with a continuous inverse between X and Y.

Edit:

Proof: It is obvious if X is necessarily a singleton set and Y is not. Where is the proof/math?

doronshadmi

9th January 2009, 06:43 PM

In what way is this at all responsive to any of my posts?
You cannot define many objects in 0-dimesional topological space because no more than a one and only one object is considered if each object is disjoint from the other object.

In order to define more than a one object you have to use also a 1-dimensional topological space.

And this is exactly what Cantor's set is, it is the result of the interaction between 1-dimensional topological space AND 0-dimational topological space, where these spaces are mutually independent of the intermediate result between them:

1-dimensional topological space
http://cordelia.mclean.org/~lowen/cantor.gif
0-dimensional topological space

jsfisher

9th January 2009, 06:54 PM

In what way is this at all responsive to any of my posts?
You cannot define many objects in 0-dimesional topological space because no more than a one and only one object is considered if each object is disjoint from the other object.

In order to define more than a one object you have to use also a 1-dimensional topological space.

And this is exactly what Cantor's set is, it is the result of the interaction between 1-dimensional topological space AND 0-dimational topological space, where these spaces are mutually independent of the intermediate result between them...

So, what is the topological dimension of the Cantor Set?

doronshadmi

9th January 2009, 07:00 PM

So, what is the topological dimension of the Cantor Set?
Something between 0 and 1 (it is a fractal).

jsfisher

9th January 2009, 07:03 PM

Something between 0 and 1 (it is a fractal).

Ok, then, You reject standard topology, too.

doronshadmi

9th January 2009, 07:10 PM

Ok, then, You reject standard topology, too.

Cantor's set is less than a line (the atom of non-locality) and more than a point (the atom of locality).

In other words, the whole idea of cardinality and magnitudes do not hold water and we can clearly see How Cantor's set is a particular case of Organic Natural Numbers, that are the results of Non-locality\Locality interaction.

These time please read http://www.upsite.co.il/uploaded/files/251_f91f4a504486c5eb16dc5353c95fab40.pdf .

jsfisher

9th January 2009, 07:22 PM

Cantor's set is less than a line (the atom of non-locality) and more than a point (the atom of locality).

In other words, the whole idea of cardinality and magnitudes does not hold water and we can clearly see How Cantor's set is a particular case of Organic Natural Numbers, that are the results of Non-locality\Locality interaction.

None of this addresses the question of the topological dimension of the Cantor Set. The answer you stated before is wrong, at least according to non-Doron topology.

doronshadmi

9th January 2009, 07:26 PM

None of this addresses the question of the topological dimension of the Cantor Set. The answer you stated before is wrong, at least according to non-Doron topology.
No, in http://forums.randi.org/showpost.php?p=4335387&postcount=1381 I repair standard set theory and topology fundamental mistakes.

jsfisher

9th January 2009, 07:34 PM

No, in http://forums.randi.org/showpost.php?p=4335387&postcount=1381 I repair standard set theory and topology fundamental mistakes.

I must have missed that. What fundamental mistakes in Set Theory are you correcting? Last time we considered standard versus doron Set Theory, there were basic differences in the meaning of membership and the operations, union and intersection.

And, with respect to topology, there's no correction in that post, just the wrong conclusion to a simple question about topological dimension.

doronshadmi

9th January 2009, 07:43 PM

I must have missed that. What fundamental mistakes in Set Theory are you correcting? Last time we considered standard versus doron Set Theory, there were basic differences in the meaning of membership and the operations, union and intersection.

And, with respect to topology, there's no correction in that post, just the wrong conclusion to a simple question about topological dimension.

Ok, there is no use to continue this dialog with you http://forums.randi.org/showpost.php?p=4335387&postcount=1381 goes beyond your head exactly as http://www.upsite.co.il/uploaded/files/251_f91f4a504486c5eb16dc5353c95fab40.pdf is.

jsfisher

9th January 2009, 07:58 PM

Ok, there is no use to continue this dialog with you http://forums.randi.org/showpost.php?p=4335387&postcount=1381 goes beyond your head exactly as http://www.upsite.co.il/uploaded/files/251_f91f4a504486c5eb16dc5353c95fab40.pdf is.

Time to run away, again? You get the wrong answer regarding the topological dimension of the Cantor Set - apparently because you don't even understand the definition of topological dimension - so you accuse me of ignorance rather than correcting your own errors.

Face it, Doron, you are incapable of understanding some very, very basic mathematical concepts. Instead, you imagine a world of partial definitions, contradictions, and gibberish, and scold everyone else for staying rooted in reality.

When you finally get the correct answer to either the topological dimension of the Cantor Set or the union of the members of {{1,2,3}.{2,5}}, let me know. Until then, you are just making stuff up to cover your own ignorance.

doronshadmi

9th January 2009, 08:13 PM

Time to run away, again?

No need to run, after all you are unable to follow me because you are not moving from your spot under your street-light.

Any non-empty set is ther rusult of Non-locality\Locality interaction exactly as can be seen By Cantor's set case.

The empty set is the atomic state that defined as non-local atom ___ or local atom .

In a non-empty set, the outer "{" "}" is the set's non-local aspect, and any member is local w.r.t the set's non-local property, as clearly shown in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

{ }
http://cordelia.mclean.org/~lowen/cantor.gif
... {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} {} ...

jsfisher

9th January 2009, 08:24 PM

Time to run away, again?

No need to run, after all you are unable to follow me because you are not moving from your spot under your street-light.

...<snip>...

None of this, especially the snipped part, has anything to do with topological dimension of the Cantor Set. Is your attention span really so sort you cannot maintain a cohesive dialog at all?

By the way, I don't mean to spoil the surprise for you, but the correct answer to the question, "What is the topological dimension of the Cantor Set?", is 0. Yep, zero. Pretty simple, eh?

doronshadmi

10th January 2009, 03:13 AM

None of this, especially the snipped part, has anything to do with topological dimension of the Cantor Set. Is your attention span really so sort you cannot maintain a cohesive dialog at all?

By the way, I don't mean to spoil the surprise for you, but the correct answer to the question, "What is the topological dimension of the Cantor Set?", is 0. Yep, zero. Pretty simple, eh?
Yes, I know exactly that by your false paradirgm Cantor's Set (that has a 0-dimesional manifold) is bijective to the real-line that is a topological manifold of dimension 1.

This paradigm is false because there is no bijection between each disjoint set of {x}, which is an object of 0-dimesional topological space, and {x,not-x} that cannot be an object of 0-dimesional topological space.

If you don't get it, then try to define a bijection between a signle point (that is no more than {x}) and a line-segment (that is not less than {x,not-x}).

If there is a homeomorfism between 0-dimesional topological space and 0-dimesional topological space, then |{x}|=|{x,not-x}|.

Since this is false, there is no homeomorfism between 0-dimesional topological space and 0-dimesional topological space.

I really which to see how you define Neighbourhood ( http://en.wikipedia.org/wiki/Neighborhood_(mathematics) ) by "wiggle the point a bit without leaving (each disjoint) set" in Cantor's set, by using the current paradigm.

Be aware of the fact that a set cannot be disjoint AND also not disjoint (by Neighbourhood).

doronshadmi

10th January 2009, 07:39 AM

Some correction of the previous post:

If there is a homeomorfism between 0-dimesional topological space and 1-dimesional topological space, then |{x}|=|{x,not-x}|.

Since this is false, there is no homeomorfism between 0-dimesional topological space and 1-dimesional topological space.

http://www.geocities.com/complementarytheory/Cantors.jpg

by using Non-locality\Locality interaction, Cantor's set is the result of the interaction between a line-segment (as a non-local atom) and a point (as a local atom).

jsfisher

10th January 2009, 07:45 AM

Yes, I know exactly that by your false paradirgm Cantor's Set (that has a 0-dimesional manifold) is bijective to the real-line that is a topological manifold of dimension 1.

Geez, where did I say anything like that? (Hint: I didn't.) So, what's going on? Are you making up both sides of the conversation, now?

I asked you a simple question: What is the topological dimension of the Cantor Set. You gave an incorrect answer. This demonstrated quite clearly that you really don't know what the term topological dimension means. Yet, you persist in trying to rally your whole local/non-local confusion around it.

The Man

10th January 2009, 09:50 AM

Yes, a tree is a good example of some nature's unethical thing because it has a trunk that is non-local (non-personal) w.r.t any given branch (which is local\parsonal w.r.t the trunk), isn't is The Man?

Both the trunk and the branch are local to the tree, if you chose to find that relationship “unethical” that is your choice, but that does not make trying to force ones ethical choices onto everyone else any less unethical.

How is nature ethical or unethical, or are you just projecting your ethical determinations onto nature as well?

http://forums.randi.org/showpost.php?p=4330725&postcount=1355

Do you really want comments on a post where you asserted being correct as some counter indication of being “wise”? Certainly, as you are rarely correct, such a consideration might lead you to the incorrect conclusion that you can be “wise” without actually being correct, as it has apparently done.

ETA:
Also I see your were using your usual tactic of quote mining, which simply reflects poorly on your character and your ability to address arguments within the context that they were given.

doronshadmi

10th January 2009, 10:16 AM

Both the trunk and the branch are local to the tree,
You just shifted names. So now the tree is Non-locality and trunk and brach are local w.r.t the tree, which is non-local w.r.t the trunk and brach.

In other words, you use Non-locality\Locality interactions, so what is your point?

jsfisher

10th January 2009, 10:32 AM

Doron,
I am sincerely interested in your answer to the following question. I'm trying to understand your answer to a question previously raised, and your answer, here, may help with that. Here's the question:

What is the sum of the squares of the numbers 3 and 4?

(a) 1
(b) 7
(c) 12
(d) 25
(e) None of the above

The Man

10th January 2009, 10:34 AM

Yes, I know exactly that by your false paradirgm Cantor's Set (that has a 0-dimesional manifold) is bijective to the real-line that is a topological manifold of dimension 1.

This paradigm is false because there is no bijection between each disjoint set of {x}, which is an object of 0-dimesional topological space, and {x,not-x} that cannot be an object of 0-dimesional topological space.

If you don't get it, then try to define a bijection between a signle point (that is no more than {x}) and a line-segment (that is not less than {x,not-x}).

If there is a homeomorfism between 0-dimesional topological space and 0-dimesional topological space, then |{x}|=|{x,not-x}|.

Since this is false, there is no homeomorfism between 0-dimesional topological space and 0-dimesional topological space.

I really which to see how you define Neighbourhood ( http://en.wikipedia.org/wiki/Neighborhood_(mathematics) ) by "wiggle the point a bit without leaving (each disjoint) set" in Cantor's set, by using the current paradigm.

Be aware of the fact that a set cannot be disjoint AND also not disjoint (by Neighbourhood).

It is not homomorphism of a point to a line, it is the homeomorphism of the non-Euclidean neighborhood of a point, which for a point is a line (in a one manifold), into
Euclidian space. There is no such thing as a zero dimensional manifold or topology, simply because there would be no neighborhoods.

If you really want to see how cantor’s set relates to topology and neighborhoods, then you should just look it up. Again actual research is the most significant factor in any research.

http://en.wikipedia.org/wiki/Cantor_set

Topological and analytical properties
As the above summation argument shows, the Cantor set is uncountable but has Lebesgue measure 0. Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space. Since it is also totally bounded, the Heine-Borel theorem says that it must be compact.
For any point in the Cantor set and any arbitrarily small neighborhood of the point, there is some other number with a ternary numeral of only 0s and 2s, as well as numbers whose ternary numerals contain 1s. Hence, every point in the Cantor set is an accumulation point, but none is an interior point. A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the interval.
Every point of the Cantor set is a cluster point of the Cantor set. Every point of the Cantor set is also a cluster point of the complement of the Cantor set.

Sorry all, but this will undoubtedly lead to some other misuse of terminology by Doron.

The Man

10th January 2009, 10:41 AM

You just shifted names. So now the tree is Non-locality and trunk and brach are local w.r.t the tree, which is non-local w.r.t the trunk and brach.

In other words, you use Non-locality\Locality interactions, so what is your point?

That, as usual, you have no idea what you are talking about and that your Local/Non-Local ascriptions are meaningless, as you just demonstrated.

doronshadmi

10th January 2009, 11:10 AM

Geez, where did I say anything like that? (Hint: I didn't.) So, what's going on? Are you making up both sides of the conversation, now?

I asked you a simple question: What is the topological dimension of the Cantor Set. You gave an incorrect answer. This demonstrated quite clearly that you really don't know what the term topological dimension means. Yet, you persist in trying to rally your whole local/non-local confusion around it.

By the standard paradigm the Cantor set is an unusual closed set in the sense that it consists entirely of boundary points (and is nowhere dense, so it has Lebesgue measure 0" ( http://mathworld.wolfram.com/ClosedSet.html )

Since no set of more than a one singleton can be found without the interaction between Lebesgue measure 0 and Lebesgue measure 1, the dimasion of Cantor's set is 0.630929... [base 10, in this case] fractal dimension ( http://mathworld.wolfram.com/CantorSet.html ), which is no more than a single and particular case of non-local numbers.

About non-local numbers, please look at http://www.geocities.com/complementarytheory/TOUM.pdf page 9, that clearly shows how the standard use of Lebesgue measure in cases like Cantor's set, is trivial.

Jsfisher, you are using Lebesgue measure 1 as a hidden assumption in order to define more than a one object in Cantor's set.

jsfisher

10th January 2009, 11:33 AM

By the standard paradigm

Since no set of more than a one singleton can be found without the interaction between Lebesgue measure 0 and Lebesgue measure 1, the
dimasion of Cantor's set is fractal ( http://mathworld.wolfram.com/CantorSet.html ).

Your text isn't supported by the URL you gave. This underscores my point. You adopt things without understanding them.

The current "story arc" for this thread stems from a passing reference to topology by The Man. That apparently sparked your mad Google skills into action by which you have discovered such exciting terms as homeomorphism, topological dimension, neighborhood, and, your latest, manifold.

You don't understand any of them.

For the case at hand, the term at issue is topological dimension. You introduced the term into this thread. You don't understand it. If you did, you'd know the difference between Hausdorff dimension and topological dimension. You might even know how Lebesgue fits in.

The Hausdorff dimension of the Cantor Set is (approximately) 0.631, but the question never was about the Hausdorff dimension, now was it?

doronshadmi

10th January 2009, 11:48 AM

Your text isn't supported by the URL you gave. This underscores my point. You adopt things without understanding them.

The current "story arc" for this thread stems from a passing reference to topology by The Man. That apparently sparked your mad Google skills into action by which you have discovered such exciting terms as homeomorphism, topological dimension, neighborhood, and, your latest, manifold.

You don't understand any of them.

For the case at hand, the term at issue is topological dimension. You introduced the term into this thread. You don't understand it. If you did, you'd know the difference between Hausdorff dimension and topological dimension. You might even know how Lebesgue fits in.

The Hausdorff dimension of the Cantor Set is (approximately) 0.631, but the question never was about the Hausdorff dimension, now was it?

The question was if there is homeomorphism between 0-dimesional topological space and 1-dimensional topological space.

You gave Cantor's set as an example of such homeomorphism.

I show that you are using 1-dimensional topological space as a hidden assumption (in addition to 0-dimestional topological space) in order to be able to define more than a one member of Cantor's disjoint state.

You and The Man are unable to get it.

doronshadmi

10th January 2009, 11:59 AM

That, as usual, you have no idea what you are talking about and that your Local/Non-Local ascriptions are meaningless, as you just demonstrated.

As usual, you have no idea what you are talking about even if you use Local/Non-Local interactions without any understanding, like any normal mechanical tool (which is, after all your goal, isn't it hammer player? ( http://forums.randi.org/showpost.php?p=4330725&postcount=1355 ) and no please don't tell us again that there is no connection between Ethics and Formal Logic, because your inability to get Non-locality\Locality interaction is based exactly on your inability to define the bridge between your Ethical aspects and your formal logical aspects).

jsfisher

10th January 2009, 12:11 PM

The question was if there is homeomorphism between 0-dimesional topological space and 1-dimensional topological space.

You gave Cantor's set as an example of such homeomorphism.

No, I did not. In fact, nobody posting in this thread has proposed any such homeomorphism might exist.

I posed to you a question about topological dimension. You failed to answer the question correctly. You continue to fail to even understand the question.

doronshadmi

10th January 2009, 12:15 PM

No, I did not. In fact, nobody posting in this thread has proposed any such homeomorphism might exist.

I posed to you a question about topological dimension. You failed to answer the question correctly. You continue to fail to even understand the question.

Please tell us what is the topological dimension of the real-line?

jsfisher

10th January 2009, 12:40 PM

Please tell us what is the topological dimension of the real line?

1. (And, just in case it is next on your list, for a single point, 0.)

Care to try again my question: What is the topological dimension of the Cantor Set?

doronshadmi

10th January 2009, 12:56 PM

1. (And, just in case it is next on your list, for a single point, 0.)

Care to try again my question: What is the topological dimension of the Cantor Set?

Cantor's set, by standard paradigm, has 0-dimensional topological space.

The real-line has 1-dimensional topological space.

Are Cantor's-set and R set homeomorphic?

jsfisher

10th January 2009, 01:06 PM

Cantor's set, by standard paradigm, has 0-dimensional topological space.

Finally! Given enough prods and hints and access to Google, you find the correct answer.

The real-line has 1-dimensional topological space.

Are Cantor's-set and R set homeomorphic?

No. Why do you ask?

jsfisher

10th January 2009, 01:15 PM

Cantor's set, by standard paradigm, has 0-dimensional topological space.

The real-line has 1-dimensional topological space.

Are Cantor's-set and R set homeomorphic?

By the way, before we go too far down this particular path, you should know you are being a bit abusive of the term topological space. For example, R1 by itself is just a set, the set of real numbers. It is not a topology. There are many ways to define a topology on R1, and there is even a standard topology for it, but we shouldn't assume, now should we?

doronshadmi

10th January 2009, 01:19 PM

jsfisher

10th January 2009, 01:29 PM

By the way, before we go too far down this particular path, you should know you are being a bit abusive of the term topological space. For example, R1 by itself is just a set, the set of real numbers. It is not a topology. There are many ways to define a topology on R1, and there is even a standard topology for it, but we shouldn't assume, now should we?

Thank you.

Is there homeomorfisim between a single point and a single line?

How curious. You just acknowledged my post about lines and points not being topologies in and off themselves, but you press on assuming they are.

Doron, you are always assuming. You are deviled by your own hidden assumptions. You assume things mean what they do not. You assume others wrote things they didn't. You assume you understand things you don't.

Back to your question, though: In order for me to respond, you'd need to be explicit as to what topologies you had in mind.

doronshadmi

10th January 2009, 01:35 PM

How curious. You just acknowledged my post about lines and points not being topologies in and off themselves, but you press on assuming they are.

Doron, you are always assuming. You are deviled by your own hidden assumptions. You assume things mean what they do not. You assume others wrote things they didn't. You assume you understand things you don't.

Back to your question, though: In order for me to respond, you'd need to be explicit as to what topologies you had in mind.

The dimensional topological space of some set is deteminated by the "smallest" object of such a set (at least according to Cantor's set). Am I right?

what topologies you had in mind
Please show a line segment that does not have at least 1-dimansional topological space.

Please show a point that has more than 0-dimansional topological space.

If a point cannot have more than 0-dimensional toplogical space and a line segemnt has at least a 1-dimensional topological space, then please tell us if there is homeomorfisim between a single point and a single line.

jsfisher

10th January 2009, 01:55 PM

Please show a line segment that does not have at least 1-dimansional topological space.

Let L = the line segment. Topology T = {{}, L}.

doronshadmi

10th January 2009, 02:02 PM

Please show a line segment that does not have at least 1-dimansional topological space.
Let L = the line segment. Topology T = {{}, L}.

P = point. T1 = {{},P}

Is T1 = T?

Is there P that is not in T1 (for example: (T2 = {some non-empty set,P})?

Do you assume that P or L are sets?

jsfisher

10th January 2009, 02:14 PM

[This was inadvertently sent as a private message to DoronShadmi. I meant to post it here. My apologies, Doron, for the misdirected message.]

Let L = the line segment. Topology T = {{}, L}.

P = point. T1 = {{},P}

Is T1 = T?

No, but how is such a question relevant? You asked for a topology on a line segment that yielded something other than a 1-dimensional topological space. I provided on.

This is the first time "equality" has been raised with respect to topologies. Are you confused about the meaning of homeomorphism?

Is there P that is not in T1?

As you have defined T1, clearly not.

doronshadmi

10th January 2009, 02:28 PM

No, but how is such a question relevant? You asked for a topology on a line segment that yielded something other than a 1-dimensional topological space. I provided on.

Is there a topology on a line-segement in such away that a point and a line are indistigushable?

As you have defined T1, clearly not.

Is there P(=point) that is not in T1 (for example: (T2 = {some non-empty set,P})?

Do you assume that P or L are sets?

doronshadmi

10th January 2009, 02:43 PM

Jsfisher,

If a continuous function is one-to-one and onto and if the inverse of the function is also continuous, then the function is called a homeomorphism and the domain of the function is said to be homeomorphic to the range. Another way of saying this is that the function has a natural extension to the topology. If two spaces are homeomorphic, they have identical topological properties, and are considered to be topologically the same. (my bold) The cube and the sphere are homeomorphic, as are (my bold) the coffee cup and the doughnut. (my bold) But the circle is not homeomorphic to the doughnut. http://en.wikipedia.org/wiki/Topology

According to what is written above, are line and point are homeomorphic?

jsfisher

10th January 2009, 02:44 PM

Is there a topology on a line-segement in such away that a point and a line are indistigushable?

What do you mean by indistinguishable?

For that matter, what point are you trying to make? You seem to have dived down this topology path to prove some great universal truth about points and lines, and all you have accomplished so far is prove you don't understand topology.

doronshadmi

10th January 2009, 02:49 PM

What do you mean by indistinguishable?

For that matter, what point are you trying to make? You seem to have dived down this topology path to prove some great universal truth about points and lines, and all you have accomplished so far is prove you don't understand topology.

Hold your horses, so far we are talking about what is agreed to be called Topology (and it does not say anything about its quality), that's all.

Indistinguishable, in this case, means that if there is the same topology on a point and on a line, then thay are the same objcet.

Please answer to http://forums.randi.org/showpost.php?p=4337034&postcount=1418 .

jsfisher

10th January 2009, 03:06 PM

Please answer to http://forums.randi.org/showpost.php?p=4337034&postcount=1418 .

How about you answer http://forums.randi.org/showpost.php?p=4336620&postcount=1398 first.

doronshadmi

10th January 2009, 03:41 PM

How about you answer http://forums.randi.org/showpost.php?p=4336620&postcount=1398 first.
Let us first finish this subject that both of us in the middle of it.

jsfisher

10th January 2009, 03:50 PM

Let us first finish this subject that both of us in the middle of it.

My question precedes yours. It takes precedence.

doronshadmi

10th January 2009, 03:56 PM

my question precedes yours. It takes precedence.

(e)

3.7320508075688772...[base 10]

jsfisher

10th January 2009, 04:12 PM

(e)

3.7320508075688772...[base 10]

You might want to read the question a bit more carefully:

What is the sum of the squares of the numbers 3 and 4?

doronshadmi

10th January 2009, 04:23 PM

You might want to read the question a bit more carefully:

What is the sum of the squares of the numbers 3 and 4?

3^2+4^2=5^2

And if you want higher powers ask for Wiles Andrew.

jsfisher

10th January 2009, 04:32 PM

3^2+4^2=5^2

And if you want higher powers ask for Wiles Andrew.

Here's the thing I don't understand, Doron. I can ask you, "What is the sum of the squares of the numbers 3 and 4?" and you understand immediately that it is a two step process. Step 1: Squares of the numbers 3 and 4. Step 2: Sum of the results.

However, when I ask you a structurally identical question, "What is the union of the members of the sets {{1,2,3}} and {{2,5}}", you completely skip that first step. Why is that?

It should be: Step 1: Members of the sets {{1,2,3}} and {{2,5}} (answer: {1,2,3} and {2,5}). Step 2: Union of the results (answer {1,2,3,5} = {1,2,3} U {2,5}).

doronshadmi

10th January 2009, 04:39 PM

Here's the thing I don't understand, Doron. I can ask you, "What is the sum of the squares of the numbers 3 and 4?" and you understand immediately that it is a two step process. Step 1: Squares of the numbers 3 and 4. Step 2: Sum of the results.

However, when I ask you a structurally identical question, "What is the union of the members of the sets {{1,2,3}} and {{2,5}}", you completely skip that first step. Why is that?

It should be: Step 1: Members of the sets {{1,2,3}} and {{2,5}} (answer: {1,2,3} and {2,5}). Step 2: Union of the results (answer {1,2,3,5} = {1,2,3} U {2,5}).

Because set {1,2,3} is not necessarily a member of set {{1,2,3}} exactly as 2 is not necessarily power 2 of any other number.

{1,2,3}u{2,5}={1,2,3,5} independently of {1,2,3} or {2,5} as being members of other sets.

This is not the case with the sets {{1,2,3}} and {{2,5}}, where the union between their members is {{1,2,3},{2,5}}, which is consistent with the result of the union between the members of set {1,2,3} and set {2,5}.

I do not accept the non-consistent approach where {AuB}=AuB (the outer "{" and "}" are not just decorations, if we are dealing with formal language).

jsfisher

10th January 2009, 05:03 PM

Because set {1,2,3} is not necessarily a member of set {{1,2,3}}

Yeah, there is that novel view you have. That doesn't explain how you get a definite answer to the question, though, when your novel view gives you an indefinite intermediate result.

Still, the conclusion remains that conventional set theories are not compatible with your novel views. With that comes compatibilities with just about all other branches of Mathematics.

jsfisher

10th January 2009, 05:14 PM

As is your practice, you re-re-edit your posts as you muddle through your thoughts:

{1,2,3}u{2,5}={1,2,3,5} independently of {1,2,3} or {2,5} as being members of other sets.

No one as argued anything different.

This is not the case with the sets {{1,2,3}} and {{2,5}}, where the union between their members is {{1,2,3},{2,5}}

No, that would be the union of the sets {{1,2,3}} and {{2,3}}, not the union of the members of those sets.

You can comprehend "sum of the squares of" but not "union of the members of". Very interesting.

I do not accept the non-consistent approach where {AuB}=AuB (the outer "{" and "}" are not just decorations, if we are dealing with formal language).

No one except you have introduced this "non-consistent approach". No one except you have alleged {A U B} = A U B. Why you would assume (there you go assuming things again) anything in my union-of-members query should be expressed as {A U B} is a mystery.

doronshadmi

10th January 2009, 05:36 PM

Yeah, there is that novel view you have. That doesn't explain how you get a definite answer to the question, though, when your novel view gives you an indefinite intermediate result.

Still, the conclusion remains that conventional set theories are not compatible with your novel views. With that comes compatibilities with just about all other branches of Mathematics.

Jsfisher,

I simply do not ignore the outer "{" and "}" that are the notations of the non-local property of any given set (without it no object (where each object is local w.r.t set's non-local property) is gathered with any other object into some set, whether the objects are members (and then we get a non-empty set) or not members (and we get the empty set) of the considered set).

My argument is that standard Math cannot avoid the non-local property of the concept of set, and as a result it is used as a hidden assumption.

My argument about a point and a line is equivalent to the above. Also in this case non-locality (represented as line-segment) is used as a hidden assumption that enables disjoint objects to be gathered into a one set, where what enables it is the non-locality that is represented by a line segment that its third middle was no removed (in the case of Cantor's set).

A line segment that its third middle was not removed is an equivalent representation of any given "{" and "}" that is the non-local property of a set, which enables objects to be gathered with each other into some complex that is the result of non-locality\locality interactions.

EDIT:

If 0-dimensional topological space means that the dimension of the complex is based on the property of the "smallest" object (a point, in this case), then there is no problem. It is a problem if the importance of the 1-dimensional topological space of the line segment, as the non-locally property of the complex (Cantor's set, in this case), is not understood (and it is not understood by standard Math as clearly can be seen all along our dialog).

jsfisher

10th January 2009, 05:49 PM

I simply do not ignore the outer "{" and "}"

No one asked you to, but rather than ignore them or not ignore them, you in fact insert extra braces.

My argument is that standard Math cannot avoid the non-local property of the concept of set, and as a result it is used as a hidden assumption.

Getting wrong answers to simple questions doesn't help. It is also true the you may a great many hidden assumptions in your thinking. Why is that acceptable?

My argument about a point and a line is equivalent to the above.

You would need to prove their equivalence. You haven't.

doronshadmi

10th January 2009, 06:30 PM

No one asked you to, but rather than ignore them or not ignore them, you in fact insert extra braces.

Getting wrong answers to simple questions doesn't help. It is also true the you may a great many hidden assumptions in your thinking. Why is that acceptable?

You would need to prove their equivalence. You haven't.

(I edited http://forums.randi.org/showpost.php?p=4337399&postcount=1431, sorry).

I am sure that I have hidden assumptions, at least in 3 subjects:

1) I assume that I am understood (which is quit false assumption at this stage).

2) I assume that I interpret what I read from standard Math the same way as the current mathematicians get it (which is mostly a false assumption, because in many cases I see my non-traditional ideas reflected through the researched subjects, and I miss the standard view of it).

3) I assume that if some of my novel ideas are understood and found interesting by some people, then they will try to find out what they can do about it. Also this assumption is quit false.

Most of the people that see my on-the-fly style of work during the dialog with them, dislike this style because it gives them the filling (which is based of course also on my misinterpretation of fundamental agreed mathematical subjects) that I have no arguments or even that I do not understand my own stuff.

I am quit aware of the above, and I am sure that there are more assumptions that are hidden to me, but I am sure that even though there is an interesting stuff that I discover\invent, which grows day by day on top of the general mass that I create by my non-standard leaning style.

Jsfisher,

Please answer to http://forums.randi.org/showpost.php?p=4337034&postcount=1418 .

Little 10 Toes

10th January 2009, 07:24 PM

The word is quite, not quit.

jsfisher

10th January 2009, 08:12 PM

According to what is written above, are line and point are homeomorphic?

Homeomorphisms apply to topological spaces. Lines and points are not, by themselves, topological spaces. You need to include a topology for that. Depending on the topologies used, some resulting topological spaces will be homeomorphic, and others will not be.

doronshadmi

11th January 2009, 02:58 AM

The word is quite, not quit.

Thank you.

doronshadmi

11th January 2009, 03:01 AM

Homeomorphisms apply to topological spaces. Lines and points are not, by themselves, topological spaces. You need to include a topology for that. Depending on the topologies used, some resulting topological spaces will be homeomorphic, and others will not be.
Is there homeomorphism between 0-dimensional topological space and 1-dimensional topological space?

Here is some work about 1-dimensional and 2-dimensional cases http://www.cs.ualberta.ca/~piotr/Mizar/mirror/http/fm/1997-6/pdf6-4/jordan2b.pdf

Can it be extended to 1-dimensional and 2-dimensional cases, or open balls cannot be used in the case of 0-dimensional topological space ?

zooterkin

11th January 2009, 03:06 AM

The word is quite, not quit.

I vote for "quit"...

The Man

11th January 2009, 06:20 AM

As usual, you have no idea what you are talking about even if you use Local/Non-Local interactions without any understanding, like any normal mechanical tool (which is, after all your goal, isn't it hammer player? ( http://forums.randi.org/showpost.php?p=4330725&postcount=1355 ) and no please don't tell us again that there is no connection between Ethics and Formal Logic, because your inability to get Non-locality\Locality interaction is based exactly on your inability to define the bridge between your Ethical aspects and your formal logical aspects).

Again, you fail to demonstrate any understanding of your own notions or what you read. The former you demonstrate by not being able to clearly define the interactions you claim yourself and everyone else are using. The latter you demonstrate by asking someone not to say again what they never said to begin with. Who said “there is no connection between Ethics and Formal Logic”? Finding yourself with your professed ability “to get Non-locality\Locality interaction” please “define the bridge between your Ethical aspects and your formal logical” as I already have done.

The Man

11th January 2009, 06:33 AM

(I edited http://forums.randi.org/showpost.php?p=4337399&postcount=1431, sorry).

I am sure that I have hidden assumptions, at least in 3 subjects:

1) I assume that I am understood (which is quit false assumption at this stage).

2) I assume that I interpret what I read from standard Math the same way as the current mathematicians get it (which is mostly a false assumption, because in many cases I see my non-traditional ideas reflected through the researched subjects, and I miss the standard view of it).

3) I assume that if some of my novel ideas are understood and found interesting by some people, then they will try to find out what they can do about it. Also this assumption is quit false.

Most of the people that see my on-the-fly style of work during the dialog with them, dislike this style because it gives them the filling (which is based of course also on my misinterpretation of fundamental agreed mathematical subjects) that I have no arguments or even that I do not understand my own stuff.

I am quit aware of the above, and I am sure that there are more assumptions that are hidden to me, but I am sure that even though there is an interesting stuff that I discover\invent, which grows day by day on top of the general mass that I create by my non-standard leaning style.

Jsfisher,

Please answer to http://forums.randi.org/showpost.php?p=4337034&postcount=1418 .

Hidden assumptions that you know to be false (as you remark that you do know them to be false) is just you lying to yourself. We know these assumptions of yours to be false so you are only hiding them from yourself. Stop lying to yourself by hoping what you clearly acknowledge as false has some “hidden assumption” of truth.

doronshadmi

11th January 2009, 06:53 AM

please “define the bridge between your Ethical aspects and your formal logical” as I already have done.
Ye, use your designed hammer on your head in order to prove that you are right.

doronshadmi

11th January 2009, 06:57 AM

Hidden assumptions that you know to be false (as you remark that you do know them to be false) is just you lying to yourself. We know these assumptions of yours to be false so you are only hiding them from yourself. Stop lying to yourself by hoping what you clearly acknowledge as false has some “hidden assumption” of truth.

In other words, you did not understand a single word of what I wrote, simply because you are not aware of yourself as the one who understand what it reads, like any normal mechanical tool (which is, after all your goal of how to be right, isn't it?)

Here is some challange for you http://forums.randi.org/showpost.php?p=4338244&postcount=1437 .

doronshadmi

11th January 2009, 08:00 AM

This may be usful:

http://knowledgerush.com/kr/encyclopedia/Kolmogorov_space/

Topological distinguishability

If X is a topological space and x and y are points in X, then x and y are topologically indistinguishable if and only if they have exactly the same neighbourhoods. Otherwise, they are topologically distinguishable. For example, in an indiscrete space, any two points are topologically indistinguishable.

Alternatively, if x belongs to the closure of {y} and y belongs to the closure of {x}, then x and y are topologically indistinguishable; otherwise, they're topologically distinguishable. Topologically distinguishable points are automatically distinct. On the other hand, if the singleton sets {x} and {y} are separated, then the points x and y must be topologically distinguishable.

http://knowledgerush.com/kr/encyclopedia/Indiscrete_space/

Indiscrete space

In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such a space is sometimes called an indiscrete space. Intuitively, this has the consequence that all points of the space are "lumped together" and cannot be distinguished by topological means.

http://knowledgerush.com/kr/encyclopedia/Point/

Point

In classical geometry, a point is an entity that has no extent. In the modern set theoretic approach to topology, this is formalised as: a point in a space X is simply an element of the set X.

In other words, a point is an element of X (it cannot be extended beyond X, which a proprty that is called local by me).

If x is an element of X, then x is local w.r.t to X.

If x is a proper subset of X, then X is non-local w.r.t x.

If x is an element AND not an element of X then x is non-local w.r.t X (for example: any x that is "perpendicular" to X).

jsfisher

11th January 2009, 08:15 AM

This may be usful:

In other words, a point is an element of X (it cannot be extended beyond X, which a proprty that is called local by me).

No, you are just fishing for things to fit your view. You imagined the world to be a certain way and are now trying to find the evidence to match. You are suffering from confirmation bias.

nathan

11th January 2009, 12:00 PM

when is an element of a set not a subset of that set?

The Man

11th January 2009, 01:23 PM

Jsfisher,

According to what is written above, are line and point are homeomorphic?

A little research on homeomorphism might be in order.

http://en.wikipedia.org/wiki/Homeomorphism

Informal discussion
The intuitive criterion of stretching, bending, cutting and gluing back together takes a certain amount of practice to apply correctly — it may not be obvious from the description above that deforming a line segment to a point is impermissible, for instance. It is thus important to realize that it is the formal definition given above that counts.
This characterization of a homeomorphism often leads to confusion with the concept of homotopy, which is actually defined as a continuous deformation, but from one function to another, rather than one space to another. In the case of a homeomorphism, envisioning a continuous deformation is a mental tool for keeping track of which points on space X correspond to which points on Y — one just follows them as X deforms. In the case of homotopy, the continuous deformation from one map to the other is of the essence, and it is also less restrictive, since none of the maps involved need to be one-to-one or onto. Homotopy does lead to a relation on spaces: homotopy equivalence.

There is a name for the kind of deformation involved in visualizing a homeomorphism. It is (except when cutting and regluing are required) an isotopy between the identity map on X and the homeomorphism from X to Y.

(bolding added)

The Man

11th January 2009, 01:28 PM

Ye, use your designed hammer on your head in order to prove that you are right.

So that is how you define "the bridge between your Ethical aspects and your formal logical"?

The Man

11th January 2009, 01:38 PM

In other words, you did not understand a single word of what I wrote, simply because you are not aware of yourself as the one who understand what it reads, like any normal mechanical tool (which is, after all your goal of how to be right, isn't it?)

Oh, I understand it alright; you just don’t seem to be very aware of what you do write, a strange habit you have for one who promotes self-awareness. Perhaps you feel your self-awareness will somehow compensate for your lack of awareness about what you write?

Here is some challange for you http://forums.randi.org/showpost.php?p=4338244&postcount=1437 .

Please see the previous post and link to homeomorphism.

The Man

11th January 2009, 01:49 PM

This may be usful:

In other words, a point is an element of X (it cannot be extended beyond X, which a proprty that is called local by me).

If x is an element of X, then x is local w.r.t to X.

If x is a proper subset of X, then X is non-local w.r.t x.

If x is an element AND not an element of X then x is non-local w.r.t X (for example: any x that is "perpendicular" to X).

However there can be points outside of the parameters of set X. If in that consideration set X is your local classification, then those points outside of X are non-local by that classification. As x is a proper subset of X, all the members of x are in X, so by that definition of proper subset x must also be local where your local consideration is X. If x is an element and not an element of X then x is not a proper subset of X. How do you define a proper subset or an element that is "perpendicular" to a set it is a member of?

jsfisher

11th January 2009, 01:55 PM

when is an element of a set not a subset of that set?

Most of the time. In the set {A,B,C}, A is an element (member) and {A} is a subset.

(I'm guessing the caffeine hadn't kicked in yet when you asked that question.)

Little 10 Toes

11th January 2009, 02:14 PM

Ye, use your designed hammer on your head in order to prove that you are right.

Wow. Take a post from a thread that was closed down when you hijacked it and post it here. If I saw you posting on a gun-care board, would that make it correct to assume you are an armed whacko? [Please note, I don't care what other boards you post on, nor do I care. I don't care if you own firearms or what your view on them are.]

In other words, you did not understand a single word of what I wrote, simply because you are not aware of yourself as the one who understand what it reads, like any normal mechanical tool (which is, after all your goal of how to be right, isn't it?)

Here is some challange for you http://forums.randi.org/showpost.php?p=4338244&postcount=1437 .

Why are you getting upset when you assume that we do understand you?

(I edited http://forums.randi.org/showpost.php?p=4337399&postcount=1431, sorry).

I am sure that I have hidden assumptions, at least in 3 subjects:

1) I assume that I am understood (which is quit[sic] false assumption at this stage).

...snip...

Why do you use the term "non-local"? I assume when you're using "local" you mean an element (of a line or of a set) that the element can't be changed. I don't understand the topographical dicussions, but I'm doing ok when you were talking about sets and lines.

Also you said "In other words, a point is an element of X (it cannot be extended beyond X, which a proprty that is called local by me)." A point can't be extended. The definition you provided, "In classical geometry, a point is an entity that has no extent".

Wikitionary has as the primary definition of extent as: "Range (http://en.wiktionary.org/wiki/range) of values (http://en.wiktionary.org/wiki/value) or locations (http://en.wiktionary.org/wiki/location)." Since a point can't extend, it has none of those.

doronshadmi

11th January 2009, 02:24 PM

No, you are just fishing for things to fit your view. You imagined the world to be a certain way and are now trying to find the evidence to match. You are suffering from confirmation bias.
No, you are unable to get the notion of Non-locality because of your Local-only notion.

doronshadmi

11th January 2009, 02:44 PM

However there can be points outside of the parameters of set X. If in that consideration set X is your local classification, then those points outside of X are non-local by that classification.

A point can be in one and only one relation w.r.t to X; therefore it is local

A line can be with more than a one relation w.r.t X.; therefore it can also be non-local.

As x is a proper subset of X, all the members of x are in X, so by that definition of proper subset x must also be local where your local consideration is X. If x is an element and not an element of X then x is not a proper subset of X. How do you define a proper subset or an element that is "perpendicular" to a set it is a member of?

These definitions are 3 different cases:

Case 1: If x is an element of X, then x is local w.r.t to X.

Case 2: If x is a proper subset of X, then X is non-local w.r.t x.

Case 3: If x is an element AND not an element of X then x is non-local w.r.t X (for example: any x that is "perpendicular" to X).

You concluded that we are talking about the same x in all of these 3 cases, which is a wrong conclusion.

jsfisher

11th January 2009, 02:51 PM

No, you are unable to get the notion of Non-locality because of your Local-only notion.

Back to the ol' stand-by, again?

Doron, you are the one that assumed you could use topology to reinforce your point. You are the one that demonstrated, repeatedly, your knowledge of topology was severely deficient. You are also the one that flounders with many of the simplest of mathematical concepts (like {A,B} being a member of {X, {A,B}, Y}), yet you accuse others of intellectual short-comings.

Rubbish.

doronshadmi

11th January 2009, 03:03 PM

A little research on homeomorphism might be in order.

http://en.wikipedia.org/wiki/Homeomorphism

(bolding added)

Only the formal part of http://en.wikipedia.org/wiki/Homeomorphism is considered.

Again:

A point can be in one and only one relation w.r.t to X; therefore it is local

A line can be with more than a one relation w.r.t X; therefore it can also be non-local.

By the standard notion, a point in a space X is simply an element of the set X.

In other words, the standard formal system is based only on local relation w.r.t X.

In that case, the formal part of http://en.wikipedia.org/wiki/Homeomorphism is unable to prove that 0-dimesion and 1-dimension are homeomorphic.

If you disagree, than please show, by using the formal part, how it is done.

The stage is yours.

jsfisher

11th January 2009, 03:11 PM

In that case, the formal part of http://en.wikipedia.org/wiki/Homeomorphism is unable to prove that 0-dimesion and 1-dimension are homeomorphic.

If you disagree, than please show, by using the formal part, how it is done.

The stage is yours.

Why do you continue to erect this straw man?

doronshadmi

11th January 2009, 03:33 PM

Why do you continue to erect this straw man?

Why straw man?

The Man used this infomal part of wiki ( http://en.wikipedia.org/wiki/Homeomorphism ):

... it may not be obvious from the description above that (bold added)deforming a line segment to a point is impermissible, for instance. It is thus important to realize that it is the formal definition given above that counts.

So, by using the formal part of http://en.wikipedia.org/wiki/Homeomorphism , please show it.

If, because of my English problem, this infomal part actually says that there is no formal way to deform a line segment to a point (and vice versa), then please clearly say it.

jsfisher

11th January 2009, 04:18 PM

If, because of my English problem, this infomal part actually says that there is no formal way to deform a line segment to a point (and vice versa), then please clearly say it.

The passage is saying points and lines* are not topologically equivalent.

*Well, actually the topological spaces derived from points and lines under the standard topology for such things.

doronshadmi

11th January 2009, 04:35 PM

The passage is saying points and lines* are not topologically equivalent.

*Well, actually the topological spaces derived from points and lines under the standard topology for such things.

Does it mean that (by Topology theory) there is no continuous deformation between a line and a point (as can be seen between Mug and Torus in the example below)?:

http://en.wikipedia.org/wiki/File:Mug_and_Torus_morph.gif

jsfisher

11th January 2009, 06:13 PM

Does it mean that (by Topology theory) there is no continuous deformation between a line and a point

(It is not Topology theory. It's just Topology, just like it is just Geometry.)

You sure you want the answer to your question? You have been telling us right that your line segments were atomic things, not divisible into component points. Not so in Topology (or geometry or...). Lines and line segments are sets of points. Impose a suitable topology on them and you get a 1-dimensional topological space consisting of an infinite number of elements. Under that view (the conventional view), there is no continuous deformation from line topological space to point topological space.

However, under the Doron view of line segments, the so-called indiscrete topology is the only one available. Points and lines are then topologically identical.

nathan

12th January 2009, 03:08 AM

Most of the time. In the set {A,B,C}, A is an element (member) and {A} is a subset.

(I'm guessing the caffeine hadn't kicked in yet when you asked that question.)

d'oh! I blame jetlag.

doronshadmi

12th January 2009, 03:57 AM

(It is not Topology theory. It's just Topology, just like it is just Geometry.)

You sure you want the answer to your question? You have been telling us right that your line segments were atomic things, not divisible into component points. Not so in Topology (or geometry or...). Lines and line segments are sets of points. Impose a suitable topology on them and you get a 1-dimensional topological space consisting of an infinite number of elements. Under that view (the conventional view), there is no continuous deformation from line topological space to point topological space.

However, under the Doron view of line segments, the so-called indiscrete topology is the only one available. Points and lines are then topologically identical.
No,

By my view, topology is the result of the interaction between Non-local\Local atomic states.

In means that one and only one state (Singularity) manifests itself as the interaction between at least two independent atoms (where independent atoms are naturally not derived from each other, but they derived from their common property known as singularity, which is indivisible by nature, at its self state).

By the standard view Non-locality is used as a hidden assumption that enables Local objects to be gathered, in the first place.

The Man

12th January 2009, 05:51 AM

A point can be in one and only one relation w.r.t to X; therefore it is local

A line can be with more than a one relation w.r.t X.; therefore it can also be non-local.

A point can be a member of X and either on or not on the boundary of X, if X is a closed set. A point can be not a member of X and either on or not on the boundary of X, if X is an open set.

Just two simple examples that show by your definition of more then one relation to X that any point in X is always non-local to X.

These definitions are 3 different cases:

Case 1: If x is an element of X, then x is local w.r.t to X.

Case 2: If x is a proper subset of X, then X is non-local w.r.t x.

Case 3: If x is an element AND not an element of X then x is non-local w.r.t X (for example: any x that is "perpendicular" to X).

You concluded that we are talking about the same x in all of these 3 cases, which is a wrong conclusion.

Wrong conclusion? Not at all. I did not “conclude” “we are talking about the same x in all of these 3 cases”, your statements simply do not exclude the permissibility of such an assertion. A wrong conclusion would be that an element of a set can not itself be a set, thus a subset and if not the only element of that set, thus a proper subset. That a valid assertion is not the one you want does not make it wrong. That what you write permits the validity of such assertions simply means you were not specific enough, as usual.

So can you answer the question” How do you define a proper subset or an element that is "perpendicular" to a set it is a member of?”

A point can be in one and only one relation w.r.t to X; therefore it is local

A line can be with more than a one relation w.r.t X.; therefore it can also be non-local.

A point can be a member of X and either on or not on the boundary of X, if X is a closed set. A point can be not a member of X and either on or not on the boundary of X, if X is an open set. A point can also be a member of X and either the only member or not the only member of X.

So a point clearly can be in more then “one and only one relation w.r.t to X” where X is some set and therefore can, by your own definition, be non-local with respect to that set.

When it comes to wrong conclusions your notions are full of it (among other things).

doronshadmi

12th January 2009, 06:36 AM

The Man

12th January 2009, 07:37 AM

Does it mean that (by Topology theory) there is no continuous deformation between a line and a point (as can be seen between Mug and Torus in the example below)?:

By topology and the formal definition of homeomorphism that is what it means. However there are other ways of getting from a point (or more specifically some finite collection of points) to a line, such as the dragging example used in the following inductive description of dimension.

http://en.wikipedia.org/wiki/Dimension

There is also an inductive description of dimension: consider a discrete set of points (such as a finite collection of points) to be 0-dimensional. By dragging a 0-dimensional object in some direction, one obtains a 1-dimensional object. By dragging a 1-dimensional object in a new direction, one obtains a 2-dimensional object. In general one obtains an n+1-dimensional object by dragging an n dimensional object in a new direction. Returning to the circle example: a circle can be thought of as being drawn as the end-point on the minute hand of a clock, thus it is 1-dimensional. To construct the plane one needs two steps: drag a point to construct the real numbers, then drag the real numbers to produce the plane.

SEE ALSO

Lebesgue covering dimension
For any normal topological space X, the Lebesgue covering dimension of X is defined to be n if n is the smallest integer for which the following holds: any open cover has an open refinement (a second open cover where each element is a subset of an element in the first cover) such that no point is included in more than n + 1 elements. In this case we write dim X = n. For X a manifold, this coincides with the dimension mentioned above. If no such integer n exists, then the dimension of X is said to be infinite, and we write dim X = ∞. Note also that we say X has dimension −1, i.e. dim X = −1 if and only if X is empty. This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term "functionally open".

http://en.wikipedia.org/wiki/Lebesgue_covering_dimension

AND

[edit] Inductive dimension
The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that (n + 1)-dimensional balls have n dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets.

http://en.wikipedia.org/wiki/Inductive_dimension

As the dimesion of a topological space generaly refers to one of those two.

Formal definition
We want the dimension of a point to be 0, and a point has empty boundary…

So for a point the topological dimension (in a normal space (http://en.wikipedia.org/wiki/Normal_space)) would in fact be -1.

No,

By my view, topology is the result of the interaction between Non-local\Local atomic states.

As you can not effrectivly define local, non-local or that “interaction” your veiw results in nothing but your meaningless claims that “topology is the result”.

In means that one and only one state (Singularity) manifests itself as the interaction between at least two independent atoms (where independent atoms are naturally not derived from each other, but they derived from their common property known as singularity, which is indivisible by nature, at its self state).

Having them “derived from their common property known as singularity” would make them mutualy dependent on that “common property” and thus not independent in that regarad. As you claim that they are “independent” and “derived from their common property known as singularity” that makes that “property known as singularity” divisable into asspects that result in one “independent atom” or the other.

By the standard view Non-locality is used as a hidden assumption that enables Local objects to be gathered, in the first place.

What, you mean like your hidden assumtions that you knew and asserted to be false? Non-locality is not “hidden” “By the standard view”, it is simply left for the user to specify what is local and non-local in their given considerartion. Making the standard veiw far more flexable and not self contradictory like your indefinative view, where all you seem albe to effectivly define are your self contradictions.

doronshadmi

12th January 2009, 07:44 AM

A point can be a member of X and either on or not on the boundary of X, if X is a closed set. A point can be not a member of X and either on or not on the boundary of X, if X is an open set.

Just two simple examples that show by your definition of more then one relation to X that any point in X is always non-local to X.

[a,border] = {x Є S | a =< x =< border}

[a,border) = {x Є S | a =< x < border}

EDIT: The border cannot be a member and not a member of S and so is x w.r.t S if x Є S, or in other words, x is local w.r.t S.

Conclusion: you do not understand non-locality, but use it as a hidden assumption in order to get wrong conclusions about local objects like points.

Wrong conclusion? Not at all. I did not “conclude” “we are talking about the same x in all of these 3 cases”, your statements simply do not exclude the permissibility of such an assertion. A wrong conclusion would be that an element of a set can not itself be a set, thus a subset and if not the only element of that set, thus a proper subset. That a valid assertion is not the one you want does not make it wrong. That what you write permits the validity of such assertions simply means you were not specific enough, as usual.

An object of a set can be also be an ur-element (which is not a set).

As usual you get x only in trems of a local object.

So can you answer the question” How do you define a proper subset or an element that is "perpendicular" to a set it is a member of?”

Think on set S as a plane that its members are line-segments that are on the plane (they are local w.r.t S), but there are olso line-segments that are perpendicular to this plane and therefore they are on (members) AND not-on (not members) w.r.t this plane (they are non-local w.r.t this plane).

No point has this proprty because a point is on XOR not on the plane.

A point can be a member of X and either on or not on the boundary of X, if X is a closed set. A point can be not a member of X and either on or not on the boundary of X, if X is an open set. A point can also be a member of X and either the only member or not the only member of X.

So a point clearly can be in more then “one and only one relation w.r.t to X” where X is some set and therefore can, by your own definition, be non-local with respect to that set.

When it comes to wrong conclusions your notions are full of it (among other things).

Worng!

Again:

[a,border] = {x Є S | a =< x =< border}

[a,border) = {x Є S | a =< x < border}

EDIT: The border cannot be a member and not a member of S and so is x w.r.t S if x Є S, or in other words, x is local w.r.t S and a point cannot be but local w.r.t S.

The Man

12th January 2009, 07:51 AM

One asks:

1) How the one is manifested as not-one and still considered as one?

2) How not-one is manifested as one and still considered as not-one?

My answer:

This is exactly what an organ is, mutual (one=connected) independency (not-one=isolated).

After all this is exactly the reasoning of "one asks" where nothing is researchable if "one"(Non-local w.r.t to its question) and "asks" (Local w.r.t the questioner) are not mutually independent, exactly like two axioms, which enables reseachability in the first place.

If you are reffering to “one” as a whole and “not-one” as the sum of some parts then the relation is trivial, the whole is the sum of its parts.

As it is the "one" doing the "asking" they "are not mutually independent", so your assertion then is that "nothing is researchable". Another one of your “hidden assumtions” that you already know to be false?

doronshadmi

12th January 2009, 08:08 AM

If you are reffering to “one” as a whole and “not-one” as the sum of some parts then the relation is trivial, the whole is the sum of its parts.

Wrong!

____ is not the sum of _ _ _ _ , and this exactly where you fail to get that ____ is non-local w.r.t each _ where _ is local w.r.t ____ , where in general Non-locality and Locality are mutual independent states, which stand as the building-blocks that enable to define a sum.

A sum is not the whole, a sum is the result of the interaction between the whole (Non-locality, Non-particular) and the part (Locality, Paricular).

Your misunderstanding of Sum is equivalent to your misunderstanding of Coordinate system.

In both cases you look at the result without understand what enables it.

The Man

12th January 2009, 08:35 AM

[a,border] = {x Є S | a =< x =< border}

[a,border) = {x Є S | a =< x < border}

In both cases the border is a member of S if x Є S, or in other words, x is local w.r.t S.

Conclusion: you do not understand non-locality, but use it as a hidden assumption in order to get wrong conclusions about local objects like points.

You neglected the open set, that I specifical referanced, where the border is not a member of the set.

(a, b) = {x Є S | a < x < b}

Also in your closed set example “a” is not a member of “border” so elements of “S” have two rlations with S being a menber of S and being or not being on the border of S.

Alos your Clopen (http://en.wikipedia.org/wiki/Clopen_set) example is wrong, if it includes the border then it is closed. It should be…

[a,b) = {x Є S | a =< x < b}

Thus the border “a” of the interval “a” to “b” is included in the set (closed) while the border “b” of that interval is not (open).

Conclusion: your are simply ignorant and expect others to be as well.

An object of a set can be also be an ur-element (which is not a set).

As usual you get x only in trems of a local object.

I specifically said that an element of a set can be a set it self, not that it must be a set. Your false hidden assumtions are coming out of hiding again.

Think on set S as a plane that its members are line-segments that are on the plane (they are local w.r.t S), but there are olso line-segments that are perpendicular to this plane and therefore they are on (members) AND not-on (not members) w.r.t this plane (they are non-local w.r.t this plane).[/qoute]

No point has this proprty because a point is on XOR not on the plane.

No, only the intesetions (single points) of those perpendicular lines, where they cross the plane, are member of the set S. You ignorance is showing again.

The Man

12th January 2009, 08:46 AM

Wrong!

____ is not the sum of _ _ _ _ , and this exactly where you fail to get that ____ is non-local w.r.t each _ where _ is local w.r.t ____ , where in general Non-locality and Locality are mutual independent states, which stand as the building-blocks that enable to define a sum. .

No you simply think they enable you to define “sum”, but since you can not define your local, non-local or “interaction” you can not use them to define “sum” either. We define “sum” as the result of addition.

A sum is not the whole, a sum is the result of the interaction between the whole (Non-locality, Non-particular) and the part (Locality, Paricular).[/qoute]

The interaction between the whole and the part would not be a “sum”, a “sum” is the addtion of parts resulting in a whole.

[QUOTE=doronshadmi;4340926]

Your misunderstanding of Sum is equivalent to your misunderstanding of Coordinate system.

Your lack of understanding is the basis of your notions

In both cases you look at the result without understand what enables it.

In all of your notions you claim it as that whaich “enables” something yet connot demostrate or define what your notion entail, that it can “enable” anything or even demostrate an understanding of what you claim to “enable”.

doronshadmi

12th January 2009, 08:53 AM

We define “sum” as the result of addition

Addition is a relation between objects where Relation is Non-local w.r.t objects and objects are local w.r.t Relation.

In other words, sum is the result of Non-locality\Locality interaction.

You have failed again to get ____ \ _ _ _ _ interaction, and a sum as some result of this interaction.

EDIT: As for http://forums.randi.org/showpost.php?p=4340876&postcount=1466 , I edited it (markad by "EDIT:", as I have learned from you).

doronshadmi

12th January 2009, 10:53 AM

No, only the intesetions (single points) of those perpendicular lines, where they cross the plane, are member of the set S. You ignorance is showing again.

A line-segment is not a set of sub-objects but it is a ur-element, and a ur-element like a line-segment can be a member AND not a member of a given plane (it is "prependicular" to this plane), where this plane is set S.

Actually without ur-elements like a line-segement, there cannot be an extension from 0-demensional topological space to 1-demensional topological space ... etc.

The Man

12th January 2009, 11:16 AM

Addition is a relation between objects where Relation is Non-local w.r.t objects and objects are local w.r.t Relation.

In other words, sum is the result of Non-locality\Locality interaction.

You have failed again to get ____ \ _ _ _ _ interaction, and a sum as some result of this interaction.

EDIT: As for http://forums.randi.org/showpost.php?p=4340876&postcount=1466 , I edited it (markad by "EDIT:", as I have learned from you).

A line-segment is not a set of sub-objects but it is a ur-element, and a ur-element like a line-segment can be a member AND not a member of a given plane (it is "prependicular" to this plane), where this plane is set S.

These are simply your assertions that you can not demonstrate as valid, or is the invalidty of your assertions just another of your “hidden assumptions”?

EDIT: As for http://forums.randi.org/showpost.php?p=4340876&postcount=1466 , I edited it (markad by "EDIT:", as I have learned from you).

I appreciate that and it does indicate that you can learn, which is basically the only reason I am still actively engaging you on this thread. I would prefer however that you try to extend that ability to learn to include the current paradigm you claim to be replacing as well as the limitations and contradictions of the paradigm you propose to replace it with.

Getting back to one of your fundamental notions that a point has one and only one relationship with respect to a set and is therefore always local to that set, we can take this simple example resulting in the “clopen” set S.

(4,5] = {x Є S | 4 < x <= 5}

If x has the value of 5 then it has the following relationships with respect to the set S.

5 is a member of S.
5 is not the only member of S.
5 is a boundary of S.
5 is the only boundary of S that is a member of S.
5 is not a subset of S.

That’s five relationships of that element or point (5) with respect to the set S, without really even trying.

doronshadmi

12th January 2009, 01:02 PM

You neglected the open set, that I specifical referanced, where the border is not a member of the set.

(a, b) = {x Є S | a < x < b}

Also in your closed set example “a” is not a member of “border” so elements of “S” have two rlations with S being a menber of S and being or not being on the border of S.

Alos your Clopen example is wrong, if it includes the border then it is closed. It should be…

[a,b) = {x Є S | a =< x < b}

Thus the border “a” of the interval “a” to “b” is included in the set (closed) while the border “b” of that interval is not (open).

Conclusion: your are simply ignorant and expect others to be as well.

Let us do it this way:

[a,b] = {x Є S | a =< x =< b}

[a,b) = {x Є S | a =< x < b}

b Є S XOR b notЄ S , therefore b is local w.r.t S

5 is a member of S.
5 is not the only member of S.
5 is a boundary of S.
5 is the only boundary of S that is a member of S.
5 is not a subset of S.

5 is a member of S, where the rest are based on this fact.

I am talking about relations of the same level that lead to contradiction if we deal with a local object like a point w.r.t some set.

x is local w.r.t some set if x is a member XOR not a member of some set.

x is non-local w.r.t some set if x is a member AND not a member of some set.

These are simply your assertions that you can not demonstrate as valid,...
No, it is inevitable at the moment that you agree that a line-segment is a ur-element that is perpendicular to the plane.

Little 10 Toes

12th January 2009, 09:03 PM

A line-segment is not a set of sub-objects but it is a ur-element, and a ur-element like a line-segment can be a member AND not a member of a given plane (it is "prependicular" to this plane), where this plane is set S.

Well, well, well. We’re back to line segments and planes. I guess you don’t remember me asking you about drinking straws and cup lids. No matter, I have an easier experiment brought to us from The Science Sorcerer.*

Take a thumbnail size piece of adhesive tape, commonly known as Scotch tape. Take a small needle and poke the needle through the center of the tape. Make sure you are putting the needle perpendicular to the tape. If the piece of tape is horizontal, the needle should be straight up and down. Be careful not to injure yourself while poking the needle through the tape. Now, with the piece of tape held horizontally and the needle is still up and down, bring the tape up to eye level. If held tautly, the piece of tape should look like it disappears. We will call this, “View 1”. Now rotate the tape so that the needle points directly at you. You should be able to fully see the top of the tape. If done correctly, you should only see the point of the needle. This will be called, “View 2”. It might help you if you close one eye while looking at the tape and the needle.

When in View 1, you’ll notice that the tape only touches the needle in one area and in View 2 you see the needle in one spot on the tape.

Let’s call the tape plane T, the needle line segment N, and where the needle pierced the tape perpendicularly as point H. The only place that plane T and line segment N meet is at point H. The remaining “non-H” portion of N is not in T. Real world three dimensional example of a two dimensional interaction.

When two lines intersect each other, the two lines aren’t in the same places except at the point where they intersect. Why should that be any different then when a line, segment or not, intersects a plane?

By the way, a line_segment has very many points in it.

*So I made up a name. Sue me. Props to Mr. Wizard, Bill Nye, and Beakman!

doronshadmi

13th January 2009, 04:46 AM

By the way, a line_segment has very many points in it.

In that case a line-segment is a set of sub-objects (called points).

In my system a line-segment is a ur-element (and ur-elements are not set, or in other words, they are not based on sub-objects as their members).

At the moment that you agree with that, you have no problem to understand that N belongs AND does not belong to T.

N looks like a point from T's viewpoint, but since N is a ur-element then N is on T (like a point) AND not on T (like a line that is not made of sub-objects like points).

After all, this is the whole idea of Extension from n-dimension to n+1-dimension, where this +1 must be non-local (belong AND does not belong) w.r.t the previous dimension, otherwise +1 is another object of the plane and not an extension of 2D to 3D , in this case.

You may think about a point that is not on the plane, but in that case this point is totally isolated from the plane and cannot be used as some extension of the plane into a higher dimension (it does not appear as an object of the plane that used as its extension into 3D).

In order to do that, the object that makes the extension must be a member of the plane (appears as a point on the plane) AND not on the plane (appears as a perpendicular atomic line-segment w.r.t the plane).

1) By the standard definition: A line segment is a connected, non-empty set ( http://en.wikipedia.org/wiki/Line_segment ).

2) By my novel definition: A line-segment is a non-local ur-element (about ur-element: http://en.wikipedia.org/wiki/Ur-element ).

doronshadmi

13th January 2009, 02:09 PM

jsfisher

13th January 2009, 04:49 PM

As for Cantor's set, it is 0-dimension OR 1-dimension according to how it is obsereved:

http://www.geocities.com/complementarytheory/01DIM.jpg

The three red dots (...) means that there are non-finite _ _ states that do not reach 0-dimension (. .) or 1-dimension (___)

Do not reach? What does that mean? The Cantor Set is not a progression of things. The progression presented in the upper half of you picture is simply a visual aid to help understand the Cantor Set.

The Cantor Set is the limit of the progression. It is an uncountably infinite set of points that is everywhere sparse. (And the "everywhere sparse" characteristic guarantees any topological space built from it is 0-dimensional.)

The Man

13th January 2009, 08:27 PM

Let us do it this way:

[a,b] = {x Є S | a =< x =< b}

[a,b) = {x Є S | a =< x < b}

b Є S XOR b notЄ S , therefore b is local w.r.t S

Well now you just misusing notations instead of terminology, but that is nothing new for you.

If you mean your normal assertion that in one case the boundary “b” is in the set and in the other case it is not. That just goes to show that the current paradigm is more flexible and definable while meeting your requirements of an “MAF” then your paradigm is.

5 is a member of S, where the rest are based on this fact.

3 is a member of that set as well but does not share the same relationships with that set as 5 does. Thus membership is not the only relation an element can have with a set, unless you want to make your definition of nonlocal to be dependent on just being or not being a member, which would be a particularly monoptic view.

I am talking about relations of the same level that lead to contradiction if we deal with a local object like a point w.r.t some set.

x is local w.r.t some set if x is a member XOR not a member of some set.

x is non-local w.r.t some set if x is a member AND not a member of some set.

No, it is inevitable at the moment that you agree that a line-segment is a ur-element that is perpendicular to the plane.

Well I will give a specific example of intersecting lines (simpler then planes) but do not have the time now as I am leaving where I am.

Indeed, would that not require the very test we are discussing? Then proving damages might be a problem as well, considering a professed lack of malice and a general agreement on the services to be provided.

The Man

13th January 2009, 10:37 PM

Sorry, but last paragraph of my previous post was something that I was writing at the same time for another thread on this forum and accidently included in my post on this thread. I sincerely apologize to all.

The Man

13th January 2009, 10:53 PM

3 is a member of that set as well but does not share the same relationships with that set as 5 does. Thus membership is not the only relation an element can have with a set, unless you want to make your definition of nonlocal to be dependent on just being or not being a member, which would be a particularly monoptic view.

Sorry again, 4.5 should have been the example I used in this case. That is what I get for trying to rush a post.

The Man

14th January 2009, 12:07 AM

doronshadmi

14th January 2009, 07:00 AM

Do not reach? What does that mean? The Cantor Set is not a progression of things. The progression presented in the upper half of you picture is simply a visual aid to help understand the Cantor Set.

The Cantor Set is the limit of the progression. It is an uncountably infinite set of points that is everywhere sparse. (And the "everywhere sparse" characteristic guarantees any topological space built from it is 0-dimensional.)

Let us play your game.

By the upper case Cantor's set has 0-demension.

By the lower case Cantor's set has 1-demension.

So what dimension Cantor's set has?

doronshadmi

14th January 2009, 07:17 AM

With those set definitions we can clearly define the intersection of these two sets (or perpendicular lines)

You can define the intersection because you used the non-local property of the set in order to connecet between two local proprties. Without this non-local property you cannot distingush between any two given members of the set.

In other words, between any given x and not-x, where x AND not-x are Є X, there is a non-local object that enables the distinction between x AND not-x in the firsts place, and it is non-local w.r.t x and not-x, but it is local w.r.t X.

If the object is "perpendicular" to X, it is the same as if we say that it is non-local w.r.t X.

doronshadmi

14th January 2009, 08:01 AM

Ok, let’s consider two perpendicular lines on an X,Y plane. We can define those intervals along a given ordinate, as an open set X and as an open set Y. Both as follows…

Along the X axis where y = 9
(6,11) = {x Є X| 4 < x < 5}

Along the Y axis where x = 9
(3,16) = {y Є Y| 3 < y < 16}

With those set definitions we can clearly define the intersection of these two sets (or perpendicular lines) as a common proper subset of X ∩ Y = {9} containing as it’s only the member the X and Y values of 9. By Doron’s definitions, as the only member is a single point it can only be local with respect to both sets. However as a proper subset of both sets, by Doron’s definitions, those sets are non-local with respect to that subset and thus those perpendicular intersecting lines are non-local to each other. The current paradigm, lacking the limitations of Doron’s purported supplanting ‘paradigm’, defines this intersection quite specifically, while within Doron’s ‘paradigm’ it remains ambiguous at best. Fortunately, this is not a problem within the current paradigm by having that one of the definitions of ‘local’ can be ‘in the neighborhood of’, within which a neighborhood of the X, Y point (or member) 9 includes points (or members) contains in the set Y but not contained in the set X and similarly contains points (or members) in set the X that are not contained in the set Y. This gives the current paradigm one of the definable aspects of connectivity or connectedness (http://en.wikipedia.org/wiki/Connectedness), where the X and Y value of 9 is the connected component in this example. Which certainly, Doron will claim is only possible due to his local/ non-local interactions. Unfortunately, he can not accurately or specifically define any of those terms or interactions he depends upon, while the current paradigm gives us specific and applicable definitions.

1) If X and Y sets are subsets of the same plane, they cross each other and not perpendicular to each other.

2) If X and Y are perpendicular to each other, it means that the non-local objects that connect members < 9 and members > 9 in sets X or Y, have a common local object called 9 w.r.t them, both in X and Y sets.

The common local object 9 in X,Y sets is the result of the intersection of the non-local properties of sets X and Y w.r.t each other.

The non-local property of X is {x Є X | x < 9 AND x > 9} where x is a ur-element.

The non-local property of Y is {y Є X | y < 9 AND y > 9} where y is a ur-element.

In other words, ur-elements are used as hidden assumptions also in ZF because without them no two members are distinguished from each other.

Please read:

http://forums.randi.org/showpost.php?p=4342535&postcount=1475

http://forums.randi.org/showpost.php?p=4343031&postcount=1476

in order to understand my theory.