Hyper Dimensional Philosophizing

[Oppressed]

I started replying to the thread “Hyper Dimensional Design” because the idea of dimensions beyond what we can normally see is interesting to me. But, I think the thread may be ignored because the original poster was associating it with things like numerology.

For those crazy people who simply enjoy thinking about more dimensions and/or those interested in the science of exploring what might be and the philosophy of what might be, I want to start a thread with the more pure topic of dimensions beyond what we can see and what those dimensions might mean for our existence.

To begin I want to mention some things as I understand them. First, what are the fundamental dimensions that we know of? I believe they are:
1) Length (meter)
2) Mass (kilogram)
3) Time (second)
4) Electrical Current (ampere)
5) Temperature (kelvin)
6) Amount (mole)
7) Luminous Intensity (candela)

There are also a couple angles, but they are considered supplementary dimensions:
8) Plane Angle (radian)
9) Solid Angle (steradian)

Then there are a great number of dimensions derived from these. For example:
10) Area
12) Volume
13) Material Density
14) Force
15) Velocity
16) Momentum
17) Acceleration
18) Power
19) Energy
20) Heat
and so on.

Keep in mind that these dimensions are terms we have created to try and describe how our world works. So far, these terms have served us well in this capacity.

[GodMark2]

You seem to be confusing "Units" and "Measures" with "Dimensions".

Units are an ammount of something, like a liter. It's always the same amount, one liter is the same size as any other. Meters, feet, grams, radians and seconds all work the same way.

Measures are a count of the units in something. And you can have multiples of them. Put two separate liters together, and you have... Two Liters! Those liters have a measure of 2, when measured in liters. It would have a measure of 2000 when measured in cubic centimeters.

Dimensions are completely different. The basic concept of a dimension can be thought of as the number of ways you can move, without changing your position in the other dimensions. Say you were confined to a piece of paper. You could move left and right without changing your position up and down any. And you could do the reverse. This shows that, on a piece of paper, Left-Right and Up-Down are two different dimensions. now, on a piece of paper, that's as many different ways to move as there are. You can't move any other direction without leaving the paper, so Paper had two dimensions. On the Earthm you can move North-South, East-West, and Up-Down, each without affecting your position in any of the other directions, and you can't move in any direction other then those, so Earth = 3 dimentional.

You seem to be confusing the ability to take units and combine them (distance / time = velocity, distance / time * mass = momentum) with the ability to move in different directions.

Now, the String Hypothesis posits that there may be many other dimensions, but that most of them are so small that we can't tell if we're moving along them. At this point, this is a mere mathematical curiosity, with no experimental evidence (i.e. it can't be considered real).

[Jimbo07]

You might like to start with this thread...

Dimensions (http://forums.randi.org/showthread.php?t=57806)

[Oppressed]

Actually, what I have stated above is correct. Many people do not understand this and that is why I started out with it, to raise the awareness of what dimension can mean.

What most people think of as dimension is in terms of space as defined by three spatial dimensions length, width and height. Space can be defined with three dimensional variables for most applications but not all. There are three common different ways the basic or simple model of space can be derived:
1) Cartesian coordinates using three dimensions of length.
2) Cylindrical coordinates using two dimensions of length and one dimension of plane angle.
3) Spherical coordinates using one dimension of length and two dimensions of plane angle.

In the consideration for talking about hyper spatial dimensions another thing to keep in mind is that we can’t separate the dimension of time from the discussion. Time is a dimension very unlike that of length.

There are two important points I am trying to make here. One is that what an additional dimension might be like may not be anything like the fundamental dimension of length. Two is that the simple models we have do help us define space are good, but there are points where the models fail. It is because of this failure of the simple model that we seek out a better model that will not fail.

A last thing I want to comment on is to stress that fictional ideas for hyperspace or astral space. This is meant to be a discussion for the fun of it.

[Beausoleil]

You seem to be confusing "Units" and "Measures" with "Dimensions".



No, Oppressed is right (mostly). This is the basis of "dimensional analysis".

It's not usually associated with the term "hyperdimensional", however, so in that sense the thread is likely to become confused.

[Oppressed]

Beausoleil,

I can easily make mistakes about how our currently accepted science we have for modeling our existence. I can also sometimes have a difference of opinion over some concepts accepted as fact by the majority.

But, if you can point out a mistake and show me how I made the mistake, I will correct it. If I have a difference of opinion I will change my opinion to shift with what I believe to be most likely true, thus if you present a good enough argument, you can change my mind. Of course, sometimes I might argue the point of view for something I think less likely to be true, because doing so is a good exercise. I do not believe it is wise to hold a single opinion without seriously considering other opinions.

But, I believe the point I am trying to make in the beginning here about dimension is an important one for this discussion.

People tend to think about hyper spatial dimensions as only consisting of something like the 3 spatial dimensions we use to describe space without time. So when they think of adding more dimensions in order to achieve a possible description of hyper space, the come up with extra dimensions that are like the fundamental dimension of length, but somehow different.

The fundamental dimension of time is nothing like the dimension of fundamental dimension length, yet when discussing this subject we should be beginning with 3 dimensions of length and 1 dimension of time.

Does a dimension required to describe hyper space, or some dimensional space beyond what we understand, need to be like the dimension of length? I believe that there is a good change it would not. If such a dimension we so similar to length then there we be a good chance we would already detect it, so something about it has to be different enough as to make it hard for us to detect and understand.

Realizing that dimensions can be very unlike the fundamental dimension length, it is a good exercise to examine what dimensions we know of can be like. How different can the dimensions we already know about be from each other?

It could take only a single fundamental dimension we do not yet understand in order to create a model for hype space. Then, the other dimensions of hyper space might be derived from that newly discovered fundamental dimension and the other existing fundamental dimensions we already know.

It could be that it would take additional dimensions of length and/or time. Perhaps it could be described as 10 dimensions of length and 1 dimension of time. But, especially considering this is an exercise for fun and need not be stuck in what has support in science, suppose you described a space time with 3 dimensions of length and 3 dimensions of time? Suppose you describe space as having a new fundamental dimension, which for the fun of it, we will call astral, and then we use 9 dimensions, 3 of length, 3 of astral and 3 of time?

Some of these models for fun could give rise to explaining some fantasy and science fiction events, such as parallel worlds, time travel, hyper spatial travel and such. They would almost certainly not stand up to scientific testing for being valid, but, the process of thinking about such things might lead us to think of a model that will be better than any we currently have.

[PixyMisa]

Length, mass, time and electrical charge (not current) are fundamental.

Temperature, luminous intensity and current are derived. Temperature is a measure of energy; luminous intensity of power; and current of the flow of charge. SI makes these base units, but that's just for convenience, and not a reflection of how things actually work.

Quantity is of course dimensionless; it's just a number. A mole is not a dimension but a constant.

[Jimbo07]

No, Oppressed is right (mostly). This is the basis of "dimensional analysis".

I guess it depends on how we're using the word "dimension."

Dimension at Wikipedia (http://en.wikipedia.org/wiki/Dimension)

There is a definite confusion here as to how the word is being used. Is it being used to describe units (as in the description of physical parameters)? Is it being used to describe what we might think of as the 4-dimensional spacetime?


It's not usually associated with the term "hyperdimensional", however, so in that sense the thread is likely to become confused.

Uses of the prefix "hyper":

Dimension at Wolfram MathWorld (http://mathworld.wolfram.com/Dimension.html)

ETA: PixyMisa, it depends who you ask and what the purpose is:

Dimensional Analysis at Guelph (http://www.physics.uoguelph.ca/tutorials/dimanaly/)

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...

[PixyMisa]

ETA: PixyMisa, it depends who you ask and what the purpose is
Absolutely.

Dimensional Analysis at Guelph (http://www.physics.uoguelph.ca/tutorials/dimanaly/)

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...
Yep. Oppressed is mixing his contexts, though; dimensional analysis can't be mapped directly to space-time dimensions that way.

Luminous intensity can be described within standard 4-dimensional space-time, for example, but charge and mass are different.

[Jimbo07]

Oppressed is mixing his contexts, though; dimensional analysis can't be mapped directly to space-time dimensions that way.


Agreed.

...

So... Oppressed... is this thread supposed to be about fiction or science?


A last thing I want to comment on is to stress that fictional ideas for hyperspace or astral space. This is meant to be a discussion for the fun of it.

I'm a BIG fan of science fiction, both hard-sci-fi and pure fantasy. Are you trying to find the places where some kind of technical definition of dimension (and then, we'd have to define which) can be co-opted for a piece of fiction?

i.e. do we wanna create some Star Trek-esque technobabble?

[Oppressed]

PixyMisa,

I’ve tried to explain this but have appeared to have failed. Well, I am not always the best at explaining what I mean, but I will try again.

4 dimensional space-time described in Cartesian coordinates consists of three dimensions of length and one dimension of time. If you are going to talk about some kind of space that has more than these 4 dimensions, then you need to add dimensions. The question is, what kind of dimensions? Do you add more dimensions of length? Would that really work? Do you add more dimensions in time?

Or do you have to add some other type of dimension? But what can a dimension be?

To limit your concept of what a dimension can be hobbles your ability to consider something beyond our current knowledge.

If the extra dimensions were that simple to describe and/or detect, it would not be a question. If such dimensions exist then they are almost certainly something different enough from length that it explains why we can not so easily detect and explain it.

Because we are so familiar with the dimension of length and of using three dimensions of length to define a space, it is an easy natural tendency to try to envision some greater dimensional space in terms of 4, 5 or 6 dimensions of length. However, if something like hyperspace exists, it is likely to require some kind of dimension unlike length.

Perhaps a single extra dimension would suffice and that dimension would function like some type of energy state where it is difficult but not impossible to change such energy states. Nothing in real life supports this, but if you wanted to explain how spaceships in science fiction jump through hyperspace, this might do it. This added dimension would not resemble either length or time.

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.

Just to make sure how I am using “Hyper Dimensional Philosophizing” is clear, I mean te following. With regard to the simple accepted model of space-time that we have, consisting of 3 spatial dimensions and 1 temporal dimension, Hyper Dimensional is referring to these 4 accepted dimensions plus one or more other dimensions.

[PixyMisa]

PixyMisa,

I’ve tried to explain this but have appeared to have failed. Well, I am not always the best at explaining what I mean, but I will try again.
No, it's okay. We understand what you mean, and you may well be right - it's just that some of the details in your original post are wrong.

So mass and charge might well be explained by additional dimensions, but all of the others can be explained in terms of what we already have.

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.
That's incorrect. :) You are, as has been noted, confusing dimensional analysis with space-time.

Let's examine something simple, like motion in a straight line.

We can define position on that line using a single dimension of space - call it s.
We can define speed on that line using one dimension of space and one dimension of time s and t. Speed is the change in s over a period of t, so it's sxt-1. That doesn't mean we have -1 time dimensions, though.
Acceleration is the rate of change of speed over time: sxt-2. That doesn't mean we now have two time dimensions (or -2, for that matter). We're just looking at how speed varies over time. We can look at the rate of change in acceleration too, and so on. The dimensions of the value we get change, but it's still the same old one dimension of space and one of time.

Also, angles aren't a different dimension; they're a different co-ordinate system. You can specify a location in 3-dimensional space using two angles and a distance, and indeed that's what astronomers do.

[Ziggurat]

4 dimensional space-time described in Cartesian coordinates consists of three dimensions of length and one dimension of time. If you are going to talk about some kind of space that has more than these 4 dimensions, then you need to add dimensions. The question is, what kind of dimensions? Do you add more dimensions of length? Would that really work? Do you add more dimensions in time?

What distinguishes time from space, as a dimension? Well, in one sense, it's only the sign in the metric for spacetime: d2 = (ct)2 - x2 - y2 - z2. So if you add another dimension, then whether it's time-like or space-like would depend purely one what sign you gave it in the metric. So the metric gives two kinds of intervals: positive and negative, or space-like and time-like (which is which turns out to be arbitrary, but they have to be opposite). It's a lot easier to generalize physical laws when adding more space-like dimensions to our theories than time-like ones, but there's nothing that absolutely precludes doing the latter.

Or do you have to add some other type of dimension? But what can a dimension be?

Well, you could add something else, but you'd need to come up with a new metric which then had three different kinds of separation (space-like, time-like, and something else). But you've got to add it into the metric in such a way that the existing metric is at least some sort of limiting case, which does constrain you. And we know that because the metric I gave above (the Minkowski metric) is at least a good approximation to reality. Just like the Euclidean metric is a good approximation of the Minkowski metric in certain limits.

If the extra dimensions were that simple to describe and/or detect, it would not be a question. If such dimensions exist then they are almost certainly something different enough from length that it explains why we can not so easily detect and explain it.

Extra dimensions can very easily be space-like without being easily detectable. Have you ever heard of compactification (http://en.wikipedia.org/wiki/Compactification_%28physics%29)?

By the way, luminous intensity can not be described only within the standard 4 dimensions of “Space-Time”. I believe that to describe luminous intensity you need 1 dimension of mass, 1 dimension of solid angle, 2 dimensions of length and 3 dimensions of time. If this is incorrect, I am sure someone will correct me.

You are not correct. Your mistake is in assuming that multiple dimensions of time in a unit indicates that it's not describable in terms of 4D spacetime. This is an incorrect assumption. One of the easiest examples to consider to show the problem with this idea is acceleration. What is acceleration? It's the change in velocity per unit time. Velocity is in turn the change in displacement per unit time. So velocity has dimensions of length/time, and acceleration has units of length/time/time. Is acceleration somehow extra-dimensional? No, it isn't. The appearance of two dimensions of time in the definition is the result of acceleration being the second derivative of position with respect to time. Taking further derivatives would increase the number of dimensions of time, but do not require any more time dimensions to exist. d2x/dt2 doesn't require there to be more than one t variable.

Let's follow this a little further. What is force? It's acceleration times mass, so force has dimensions of (mass*length)/(time*time). What is work (aka change in energy)? Work is force multiplied over the distance that force is exerted, and so it has dimensions of (mass*length*length)/(time*time). What is power? Power is work per unit time, so power has dimensions of (mass*length*length)/(time*time*time). Two things to notice: 1) we haven't required any extra dimensions in any of this, and 2) we're one dimension away from luminosity, namely we're missing a solid angle. But what is luminosity? It's simply the power radiated per unit solid angle, which is how we get the dimensions you mentioned. Luminosity is NOT fundamental. It, just like velocity, acceleration, force, work, and power, is a derived quantity.

[Davo]

It may be shown mathematically there could be other dimensions, but practically is there any physical evidence for there being any other dimensions outside x,y,z and time ? Could anyone clarify/dispute this ?

[Ziggurat]

It may be shown mathematically there could be other dimensions, but practically is there any physical evidence for there being any other dimensions outside x,y,z and time ? Could anyone clarify/dispute this ?

Basically in all those theories, the extra dimensions are compactified (http://en.wikipedia.org/wiki/Compactification_%28physics%29). Basically this means wrapping that dimension into a loop. It's like the surface of an infinite straw: it's two-dimensional, but if the length scales you're interested in are much larger than the circumference of the straw, then it looks one-dimensional. Finding physical evidence for compactified dimensions may be extremely difficult, even if those ideas are correct.

[Oppressed]

I pull many of the references I make from published resources in science. For example, the list of dimensions I give in the beginning are from such a resource. I did not just pick them out of the air and give them my own definition. It could be the resource is wrong, incomplete or how one might wants to view it different.

When dueling in syntax is more important than the underlying point, well, we can have fun with that to I guess.

What we call space-time we describe using terms we created from our observations of space-time. The fact that in our attempt to describe this we typically use 3 dimensions of length and one dimension of time does not mean all dimensions are limited to length and time.

By definition of “dimension” is “to measure out”. It is related to something you can measure. When we measure something we measure it in relation to something else, to place it in some kind of a useful structure to help us understand it. In the process we have developed commonly acceptable ways of measuring something in relation to other things, such as area. Area is a dimension derived from the dimension of length and requires 2 dimensions of length to define it in Cartesian coordinates.

In our measuring of space time we typically use 4 dimensions, but the number and types of dimensions greatly exceed that of the 4 used in the typical definition of space-time. Just as this simple definition of space time requires 4 dimensions to describe it, luminous intensity measured in candela requires multiple dimensional references to describe it. Granted the number of references I made are high, because what is required in some cases is a single dimension squared or cubed.

It well may be that to define some types of hyper dimensional space what will be required is not new dimensions but the inclusion of some dimensions we are already familiar with, such as mass. How well do we really, truly understand mass? What if mass is really directly tied with all real measurements of space, so that in reality space-time consists of 5 dimensions (3 length, 1 time and 1 mass)? What if the phenomena of mass is really from the warping of the 4 commonly considered dimensions of space-time? What is, somehow you could take an area of mass and straighten out this warping and the result was the disappearance of the mass, probably also resulting in a massive release of energy that had been held in the warped space.

As far as space-time only being able to be described in 3 dimensions of length and 1 dimension of time, I very strongly disagree. We may prefer this method, but it is very possible to describe space-time in terms of 1 length, 1 time and 2 angles. It might not be as easy, but it is a matter of point of view.

This is a similar issue with what base number system we think in. It is possible to develop a valid view of space-time to used only spherical coordinate measurements in base 3. We might find it much harder to understand and use such a point of view, but that does not make it any less valid. So it is a valid and provable point of view to define our simple view of space-time in the four dimensions of length, angle, angle and time. It may not feel comfortable for you to view it like this, but it is valid.

Sometimes, to look at things through a different point of view results in finding an easy way to solve a very complex problem which might otherwise prove impossible to solve.

PS: I did not say Luminosity is fundamental, I said it is derived and that it can not be decribed only in the 4 dimensions of space-time, but it requires additional dimensions.

[Ziggurat]

I pull many of the references I make from published resources in science. For example, the list of dimensions I give in the beginning are from such a resource. I did not just pick them out of the air and give them my own definition. It could be the resource is wrong, incomplete or how one might wants to view it different.

There are mistakes in your initial list. Moles, for example, are a unit, but they are dimensionless. So are radians and steradians. Luminous intensity is not, and has never been, a fundamental dimension - as explained above, it is derived from more fundamental unit. Current can be a fundamental dimension, but this is a choice: you can also use charge as the fundamental dimension instead of current.

It well may be that to define some types of hyper dimensional space what will be required is not new dimensions but the inclusion of some dimensions we are already familiar with, such as mass.

Concievably. But without any idea about how to include mass in such a manner, it's just idle speculation. Nothing wrong with that, but it won't get you very far either.

As far as space-time only being able to be described in 3 dimensions of length and 1 dimension of time, I very strongly disagree. We may prefer this method, but it is very possible to describe space-time in terms of 1 length, 1 time and 2 angles. It might not be as easy, but it is a matter of point of view.

All that actually points to is the fact that the word "dimension" has multiple uses which are not perfectly related to each other. Using polar coordinates rather than Cartesian coordinates doesn't change the dimensionality of the space you're describing.

This is a similar issue with what base number system we think in. It is possible to develop a valid view of space-time to used only spherical coordinate measurements in base 3.

The two issues are completely independent. The coordinate system has no connection to the base numbering system you use. But once again: the coordinate system does not change the dimensionality of a space. And physicists are quite used to using alternative coordinate systems to describe the same spaces - including using coordinate systems which aren't spatial at all (ie, momentum-energy space for quantum mechanics).

PS: I did not say Luminosity is fundamental, I said it is derived and that it can not be decribed only in the 4 dimensions of space-time, but it requires additional dimensions.

In your opening post, you asked what "the fundamental dimensions that we know of" were. You then answered your question with a list that included Luminous Intensity. As for not being able to be described only in the 4 dimensions of space-time, well, that's pretty meaningless, and relies (once again) on essentially mixing different usages of the word "dimension". Again, consider the dimensions for acceleration: length/time2. Does that mean there are two dimensions of time? No. It means that the time dimension appears twice in the definition. But it's the same time dimension for both occurances.

[Dutch]

Hyper Dimensional Design has nothing to do with numerology, its based on geometry

[PixyMisa]

Also, angles aren't a different dimension; they're a different co-ordinate system. You can specify a location in 3-dimensional space using two angles and a distance, and indeed that's what astronomers do.
Just reading Oppressed's posts again, and he notes himself that different co-ordinate systems exist and are equivalent, but still posits angles as additional dimensions. Someone here is very confused. :confused:

[Beausoleil]

I guess it depends on how we're using the word "dimension."

Dimension at Wikipedia (http://en.wikipedia.org/wiki/Dimension)

There is a definite confusion here as to how the word is being used. Is it being used to describe units (as in the description of physical parameters)? Is it being used to describe what we might think of as the 4-dimensional spacetime?



Uses of the prefix "hyper":

Dimension at Wolfram MathWorld (http://mathworld.wolfram.com/Dimension.html)

ETA: PixyMisa, it depends who you ask and what the purpose is:

Dimensional Analysis at Guelph (http://www.physics.uoguelph.ca/tutorials/dimanaly/)

In this context, electric current and temperature ARE considered dimensions. What we are going to talk about REALLY Depends on how you're using the word...


I may apply for Randi's prize, having predicted that this thread would become confused....

;)

[PixyMisa]

It was confused in the first post. As others have noted, Oppressed is confusing dimensional analysis with space-time metrics, confusing co-ordinate systems with dimensions, and confusing derived and fundamental units. That's a whole lot of confusion for one post.

[Cuddles]

Just to add to the confusion, as people have already pointed out, there can be debate over whether charge or current should be used as the fundamental unit. However, what no-one has pointed out yet is that there is no such thing as a fundamental unit, or more correctly, the choice of fundamental units is almost entirely arbitrary.

For example, we use length and time as fundamental units, with the standard units being metres and seconds. This means that acceleration can be described as {length}{second}-2. However, it is just as valid to use velocity and time. Acceleration would then be described as {velocity}2{length}-1.

Not all possible choices would be valid, since it must be possible to reduce any units down to the fundamental ones, however, there are many that are valid. The fundamental set that we actually use is based on what was most relevant while the scientific method was being developed. Current is generally stated as one of the fundamental units because it was possible to measure current but charge was much harder. Now that we understand more and have better technology charge seems like a more obvious choice as a fundamental unit, but traditions tend to stick. The same is also true of time. Our current definition of time is actually a conversion from our measure of frequency, but for most people time stays as the fundamental unit because it seems more relevant from their point of view.

The point of this rambling is that, as others have said several times but in differnet ways, units and dimensional analysis have absolutely nothing to do with spacial dimensions. Actual spacial dimensions exist however we choose to describe them. Units are semi-arbitrary measures made up to suit our convenience. There is no correlation between the two.

Edit: Just in case any really odd people are actually interested, the usual notation is square brackets rather than curly ones, but the forum software treats them as code so I couldn't use them.

[Dilb]

For example, we use length and time as fundamental units, with the standard units being metres and seconds. This means that acceleration can be described as {length}{second}-2. However, it is just as valid to use velocity and time. Acceleration would then be described as {velocity}2{length}-1.

Acceleration would be {velocity}{time}-1. Presumably you meant velocity and length, which gives {velocity}2{length}-1. Interestingly, this makes time a derived unit {velocity}-1{length}, or length per velocity.

[Oppressed]

Ziggurat,

As I said, I am perfectly capable of making mistakes, just as your are and so is everyone else.

I pulled the list of dimensions in the beginning of this post from another source listing dimensions defined in physics. I cut and pasted the list. When I first looked at the list, I briefly questioned it for completeness but was pulling it out of a reference to try and make a quick point. I found more than one reference that gave the same list.

Looking back at the list more closely, now I understand better why Luminous Intensity keeps popping up. It was in the list I found reference to as a fundamental dimension.

A fundamental dimension is one not made up of any other dimensions. When Luminous Intensity was specifically spoken about I also looked at it as a derived dimension, not a fundamental one, as the initial reference list I cut and pasted indicated. This however is really not a significant issue to become stuck upon.

If you become too stuck in the inability to view things in any other manner than the commonly accepted manner, then you blind yourself to other ways view things which might be equally valid or provide new incite.

The point of mentioning the base number system is to illustrate this. It is very normal for us to think in base 10. But, but allowing ourselves to view things in base 2, 4, 8, 16 and so on, we have made significant progress with regard to computing that otherwise would have been extremely difficult to achieve.

I can describe physical space perfectly well in spherical dimensions. The 3 dimensions of space can be the 3 dimensions used in the spherical coordinate system. Like using base 10 for our normal numerical system, using the Cartesian coordinate system is very familiar to us and thus there is great resistance to consider viewing space some other way. However, just as the base 2 system is a perfectly valid base for a numeric system, the 3 dimensions of the spherical coordinate system are perfectly valid as qualifying for the 3 dimensions of space.

If anything, since one of the major theories is that known space is like an expanding spherical bubble, perhaps the spherical coordinate system is the more appropriate coordinate system to use. Thinking of space in that manner may help to give new incite to things we are trying to describe but are as of yet having difficulty in describing.

[Oppressed]

Cuddles,

I like your comment about the point of arbitrary choices. That is one of the things I’ve been trying to get at.

[Ziggurat]

I can describe physical space perfectly well in spherical dimensions. The 3 dimensions of space can be the 3 dimensions used in the spherical coordinate system.

You are confusing coordinate systems with dimensions, and it's complicated by the fact that you aren't even distinguishing between the different meanings of the word "dimension" either. A change in coordinate systems does nothing to change the dimensionality of a space in any way.

Like using base 10 for our normal numerical system, using the Cartesian coordinate system is very familiar to us and thus there is great resistance to consider viewing space some other way.

Resistance from whom? Not physicists. They routinely change coordinate systems in order to make calculations easier. Often the same space will be described with multiple coordinate systems depending on which aspect one wants to examine - a famous example is the standard black hole, with both Schwartzchild and Kruskal coordinates being commonly used. And both coordinate systems resemble standard spherical coordinates much more than cartesian coordinates, BTW. So you're hardly suggesting anything new here.

If anything, since one of the major theories is that known space is like an expanding spherical bubble, perhaps the spherical coordinate system is the more appropriate coordinate system to use.

I suspect you may be misunderstanding this analogy, but it doesn't matter too much for the present discussion. In any case, people who study cosmology often do use spherical coordinates, so it's not like they're missing anything because of any dogmatic adherence to a particular coordinate system.

[PixyMisa]

Oppressed, let's go back to luminous intensity for a moment.

I noted that this is measure of power (sort of - it's a bit of an oddball), which is measured in watts. A watt has the dimensions of {mass}x{length2}x{time-3}. (We have -3 time dimensions there!)

What's important here, though, is not the number of time dimensions, which we can pretty much manufacture as we choose by looking at ever higher-order derivatives, or the number of length dimensions, but that we also have mass. Mass isn't space, it isn't time, it's something different, and under String Theory and similar models could be represented or otherwise generated by additional dimensions beyond the ones we're familar with.

Charge is another such property. It's not space, or time, or mass, but something different again. Electrons and protons have a mass, they exist and move in 4-dimensional space-time, but they also have a charge.

Mass is related to gravity, and charge to electromagnetism, two of the four fundamental forces. The other two forces are the weak force and the nuclear force, and their effects are known as (you'll love this) flavour and colour. (Note that I'm not a particle physicist, so any time I venture beyond the simple stuff there's a chance that I'm getting it wrong. Since we do have real live physicists on the forum, if I screw up in a major way one of them will probably come along and rescue me. :))

So that's two more things that we might want to model with (or as) additional dimensions, bringing our total up to eight: Three dimensions of length, and one each of time, mass, charge, flavour and colour. Indeed, String Theory and M Theory propose a universe with 10 or 11 dimensions.

So what you are saying - that there are dimensions beyond the usual four that account for the properties of matter - is something that is taken very seriously by physicists. The problem isn't with the basic idea, just with your list of dimensions, because most of those things aren't dimensions at all.

[Oppressed]

PixyMisa,

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists. If we can prove a dimension exists, then I would no longer consider it a hyper dimension.

“Hyper dimensional” means above and beyond “Dimensional”. What is above and beyond “dimensional”? Some dimension beyond what we currently can prove exists.

The root meaning of dimensional means to measure out. The point of a dimension is to aide us in comprehending the measuring out of something. How we go about defining a dimension has many arbitrary elements to it. There are different ways you can measure out something so that the dimensions of how you are measuring that something out are very different and yet what you are measuring out is the same and the results of the measurement are the same, but in different dimensions.

I should have looked more closely at the list, I of physics dimensions I grabbed off the net. When a took a moment to more closely consider the list, I disagree with what is described as fundamental dimensions. To be a fundamental dimension, I would expect that the dimension would be one that was not a measurement of 2 or more other dimensions.

But the general idea was to expand some people’s realization that in discussing this subject a dimension might be something other than what they might have been limiting their view to. When you are going to consider new dimensions that are beyond our current ability to prove they exist, you should be prepared for the idea that the new dimension may be unlike any we know of. To prepare for what that might be, it is good to first think about all the dimensions we have defined and how we have defined them.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?

In your point of view, what are the 3 dimensions of space?

As for the list, the only one I see truly questioning as a dimension is amount. I included it because I have seen it included in lists of dimensions. But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units. http://physics.nist.gov/cuu/Units/units.html. This just goes to further illustrate what a dimension might be arbitrarily defined as by us. We use dimensions to measure things to help us better understand what we are observing. Note that in the list of SI units at the link shows “Luminous Intensity” as a base unit. In similar lists I have seen it listed as a fundamental dimension. But as has been discussed, “Luminous Intensity” is derived from other dimensions.

How some things can be defined is very frequently very arbitrary.

[PixyMisa]

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists. If we can prove a dimension exists, then I would no longer consider it a hyper dimension.
In that case, you're talking nonsense.

There are different ways you can measure out something so that the dimensions of how you are measuring that something out are very different and yet what you are measuring out is the same and the results of the measurement are the same, but in different dimensions.
No. That is completely false. You can define different units, you can apply different co-ordinate systems, but the dimensions never change.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?
They're fundamental.

In your point of view, what are the 3 dimensions of space?
Length, length, and length.

As for the list, the only one I see truly questioning as a dimension is amount.
Amount (that is, moles) is obviously not a dimension. Neither are most of the others. It's very simple: These things are not dimensions!

I included it because I have seen it included in lists of dimensions.
No you didn't. You saw it in a list of units.

But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units.
As I said, units.

This just goes to further illustrate what a dimension might be arbitrarily defined as by us.
No it doesn't.

We use dimensions to measure things to help us better understand what we are observing. Note that in the list of SI units at the link shows “Luminous Intensity” as a base unit. In similar lists I have seen it listed as a fundamental dimension.
No you haven't.

But as has been discussed, “Luminous Intensity” is derived from other dimensions.
Yes. As are the great majority of units in SI.

How some things can be defined is very frequently very arbitrary.
This is particularly true when you persistently confuse the terms used in the definitions.

SI is a system of units, not of dimensions. Each of the units can be described as a set of dimensions. But they are not dimensions themselves.

[Ziggurat]

The point of the thread “Hyper Dimensional Philosophizing” is not to limit ourselves to only the dimension of length, but to consider something dimension beyond length and beyond what we can prove exists.

When you start talking about what you can't prove exists, you run into the problem of talking about stuff you just made up completely. There's limited usefulness in that.

As for the list, the only one I see truly questioning as a dimension is amount. I included it because I have seen it included in lists of dimensions. But, a dimension is about being able to measure out something. We have give definitions to measuring out the amount of a substance, given it the unit of mole and set this definition as common to many people in the widely accepted International System of Units.

A mole is a unit. But it is NOT a dimension. In fact, it is dimensionless. It is a pure number, and pure numbers never have dimensions. When you start talking about moles of something in particular (say, O2), then you've got a dimension, but just moles? That's dimensionless.

This just goes to further illustrate what a dimension might be arbitrarily defined as by us.

Units are completely arbitary. But units are not the same thing as dimensions, and I'm not sure if you've gotten the distinction yet. Inches and centimeters are both units, both are completely arbitrary, they aren't equal to each other, but they have the exact same dimension: length. There is some choice in terms of what dimensions we consider fundamental. For example, between length, time, and velocity, any two can be considered fundamental. But it's not completely arbitrary: you cannot define all three as fundamental, because the relationship between them is not something we are free to choose.

[Oppressed]

I quote:
“In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.”

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

The root definition of dimension is “To Measure Out” meaning in the basest manner that there is some thing that we can measure. Luminous intensity is a dimension, not a spatial dimension, but still a dimension.

I quote:
“Physical-dimension LUMINOUS-INTENSITY-DIMENSION” and
“The fundamental dimension of luminous-intensity, as defined by the SI standard.”
http://www.ksl.stanford.edu/knowledge-sharing/ontologies/html/standard-dimensions/LUMINOUS-INTENSITY-DIMENSION.html

Apparently some people at Stanford University are wrong about defining Luminous Intensity as a dimension. You should contact them and explain to them their mistake.

Granted that Stephen F. Austin State University is not as well known as Stanford, but if you look through the following link, they too define Luminous Intensity as a dimension. They also define amount of substance with the SI units of mole as a dimension. Maybe you better correct them too.
http://observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/12

I quote:
"According to the SI, the mole is not dimensionless, but has its very own dimension, namely "amount of substance", comparable to other dimensions such as mass and luminous intensity.[2]"

http://en.wikipedia.org/wiki/Mole_%28unit%29

Looks like you should straighten out the International System of Units as well.

Looks like there are a whole lot of people that need correction from you over this issue.

[PixyMisa]

I quote:
“In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.”
Yes, it's a base unit in SI. That's an entirely arbitrary decision, and as been shown already, it isn't a dimension.

The root definition of dimension is “To Measure Out” meaning in the basest manner that there is some thing that we can measure. Luminous intensity is a dimension, not a spatial dimension, but still a dimension.One more time: You are confusing dimensions with units.

“Physical-dimension LUMINOUS-INTENSITY-DIMENSION” and
“The fundamental dimension of luminous-intensity, as defined by the SI standard.”
http://www.ksl.stanford.edu/knowledge-sharing/ontologies/html/standard-dimensions/LUMINOUS-INTENSITY-DIMENSION.html

Apparently some people at Stanford University are wrong about defining Luminous Intensity as a dimension. You should contact them and explain to them their mistake.That's the documentation for using a computer program; it is not in any way a definition of how physicists use the term.

Granted that Stephen F. Austin State University is not as well known as Stanford, but if you look through the following link, they too define Luminous Intensity as a dimension. They also define amount of substance with the SI units of mole as a dimension. Maybe you better correct them too.
http://observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/12That link is broken, so I can't confirm what you say.

I quote:
"According to the SI, the mole is not dimensionless, but has its very own dimension, namely "amount of substance", comparable to other dimensions such as mass and luminous intensity.[2]"

http://en.wikipedia.org/wiki/Mole_%28unit%29

Looks like you should straighten out the International System of Units as well.

Looks like there are a whole lot of people that need correction from you over this issue.Mostly you - you don't understand the difference between dimensional analysis and spacetime metrics. That in itself is not a problem, the problem is that this remains true after it has been explained to you repeatedly.

Yes, there is very good reason to believe there are more than four dimensions to spacetime. There are real, fundamental properties of matter that can be explained that way.

No, it has nothing to do with SI's selection of base and derived units, which are essentially arbitrary.

You can't just grab onto any use of the word "dimension" as support for your pet idea. It's been shown just how luminous intensity, power, velocity, acceleration and so on are simply combinations of dimensions already well understood. Why do you have a problem with that?

[Oppressed]

observe.phy.sfasu.edu/courses/egr112/lectures112/ZZ-Spring2003/04-Chapter%2014%20Unit%20Conversions.ppt

Page 12

You are confusing the dimensions used in the common view of what we call space time as not a subset of the larger set of defined dimensions. Time is one of the 4 dimensions used in this common view.

What is the dimension of time? It is not length! It is not width! It is not depth!

Time is a dimension.

You can not measure volume with time!

You can not measure area with time!

So in you limited view of what dimensions are, why is time a dimension?

The question is; why are you incapable of understanding the broader definition of what a dimension is?

If we limited our perspective so, particularly if in the process we hobble our creative imagination to only allow thinking about what we think has already been proved and thus make ourselves incapable of considering anything beyond what we already know, we would still be in the dark ages.

Scientific breakthroughs require creative thought going beyond what we already know into the area of the unproven. Then you take the unproven ideas and see if you can prove them. If an unproven idea then leads to a new proven idea, you have made scientific progress.

You are wearing blinders so tight you can even get past the basic realization dimensions are a measurement of something. You want to separate the analysis of “All Dimensions” from the analysis of “Space-Time Dimensions” but the analysis of “Space-Time Dimensions” is a subset of the analysis of “All Dimensions”.

If we are going to consider the possibility of additional dimensions we do not yet know of and therefore we can not prove they exist because you can not prove something you do not know, then you have to be prepared to consider something NEW.

The result might be “Space-Time-Quantumshift”.

We already use expanded dimensional models of space-time to create what appear to be more accurate models. Such models which began as new unproven ideas have since had supportive observations and testing done which give them greater credibility as being true.

[PixyMisa]

You are confusing the dimensions used in the common view of what we call space time as not a subset of the larger set of defined dimensions.
Baloney. I have explained that many physicists believe that this is exactly the case, and shown you some of the properties that might well be explained by those extra dimensions.

Time is one of the 4 dimensions used in this common view.What is the dimension of time? It is not length! It is not width! It is not depth!

Time is a dimension.Yes, it is. Where have I said anything else?

You can not measure volume with time!

You can not measure area with time!

So in you limited view of what dimensions are, why is time a dimension?Because there is no more fundamental property or set of properties that can be used to describe time. This is not true for any of the units on your list with the single exception of mass.

The question is; why are you incapable of understanding the broader definition of what a dimension is?I understand it pretty well. You are simply choosing nonsensical examples.

If we limited our perspective so, particularly if in the process we hobble our creative imagination to only allow thinking about what we think has already been proved and thus make ourselves incapable of considering anything beyond what we already know, we would still be in the dark ages.Maybe so, but if we listened to everyone who spouted random nonsense, we'd still be in the paleolithic.

Scientific breakthroughs require creative thought going beyond what we already know into the area of the unproven. Then you take the unproven ideas and see if you can prove them. If an unproven idea then leads to a new proven idea, you have made scientific progress.What scientific breakthroughs require most is a deep understanding of the existing theory. Also - this is a little beside the point, but still worth saying - scientific theories are never proved, only disproved.

You are wearing blinders so tight you can even get past the basic realization dimensions are a measurement of something.No, you're thinking of units.

You want to separate the analysis of “All Dimensions” from the analysis of “Space-Time Dimensions” but the analysis of “Space-Time Dimensions” is a subset of the analysis of “All Dimensions”.That doesn't mean anything.

If we are going to consider the possibility of additional dimensions we do not yet know of and therefore we can not prove they exist because you can not prove something you do not know, then you have to be prepared to consider something NEW.Maybe, but talking nonsense gets you nowhere.

Area is not fundamental, it's just {length2}
Volume is not fundamental, it's just {length3}
Velocity is not fundamental, it's just {length}{time-1}
Acceleration is not fundamental, it's just {length}{time-2}

And so on. This is all perfectly well understood, and nothing more is needed. In fact, if you try to shove new dimensions in to explain these things, the maths stops working.

The result might be “Space-Time-Quantumshift”.Again, that doesn't mean anything.

Again, mass, charge, "flavour" and "colour" are real properties that are not described by four-dimensional spacetime, and may indeed constitute additional dimensions. The same cannot be said for your list of units.

We already use expanded dimensional models of space-time to create what appear to be more accurate models. Such models which began as new unproven ideas have since had supportive observations and testing done which give them greater credibility as being true.That's half true. There are such models, as I've said a number of times, and they are taken seriously. But none of the models of space-time with more than 4 dimensions have been experimentally confirmed.

[GodMark2]

The root meaning of dimensional means to measure out.
Incorrect. You should have said "The layman's definition of 'dimension', when used a a verb is 'To measure out'"

Unfortunately, layman's definitions aren't precise enough to get anything meaningful done. So, most words have slightly different definitions in science. Most often, the layman's version is similar to the Scientific version, but the differences are quite important.

The scientific definition of the dimension of a space is "The minimum number of coordinates required to locate a point in that space", which an be shown mathematically to be identical to "The Maximum number of coordinates for a given space, such that changing any one coordinate has no effect on the any remaining coordinate." or, to use your layman's terminology "The number of basic ways the space itself may be measured"

So far, we have found three length dimensions, one time dimension (which can also be described as a length dimension, and indeed must be so described when talking about relativistic events) and one dimension each for mas, charge, flavor, and color.

We can create many different measures of these dimensions, but a measure is distinctly NOT a dimension. We can combine various basic measures to create composite measures, but those composite measures are not dimensions.

When we speak of space, which we have arbitrarily defined in three Cartesian coordinates, are those dimensions really fundamental or are they really a result of our attempt to measure an emergent property of other physical laws that we do not yet fully understand?

In your point of view, what are the 3 dimensions of space?

You have several choices. The common one is Length, length, and length. But you could also use Angle, Length and Length, or even Angle, Angle, and Length. In each case, you need three coordinates, you can't get by with fewer, so space has a maximum dimension "3". In each case, you can change one of the coordinates without affecting the pother two, so space has a minimum dimension "3". Minimum = Maximum -> only one possible answer = "3".

How some things can be defined is very frequently very arbitrary.

Yes, that's why we have the scientific definitions, so when we use a term, we know exactly what each the other is talking about. When you try to use layman's definitions in a scientific discussion, you will often come to completely wrong conclusions.

[Oppressed]

GodMark2:

It is the scientific definition of “Dimension” of which the scientific definition of the “Dimensions of Space” is a subset.

You do mention something which agrees with something I have said, but I am sure others will disagree with you for that. Space can be defined in terms of the dimensions length, angle, angle. But, to be fair, the dimensions of angle are in my opinion derived. I have also heard them referred to as supplemental dimensions but I do not know what difference was intended by that. Angle is generally considered dimensionless but not quite, because is a length divided by a length, which is not truly dimensionless but requires the ratio of two lengths.

I can and have described 3 dimensional space using the dimensions of one length and two angles. But this does not remove the fact that the dimensions of the two angles are derived from two dimensions of length.

But there is another confusion being made here and that is the difference between a dimension and a physical reality. Dimensions are an arbitrary creation of ours. We make up a definition for dimension.

Space simply is. Space exists in its physical reality regardless of how we try to define and measure it with dimensions.

What is not arbitrary about dimensions is how accurately it models the physical reality we are trying to define and measure.

So someone can arbitrarily come up with a definition of physical space, like defining it in three dimensions of length and that model may work pretty darn well. That is, until some people come along, thinking outside the box, using their imagination combined with experimentation, and they find that the 3 dimensions used to define space don’t actually quite work 100%. Those 3 accepted dimensions do not precisely define and measure space.

To help us understand physical existence we have developed the convention of organizing physical quantities in a system of dimensions. The International System of Units has chosen 7 base quantities each of which is regarded as having its own dimension.

From these 7 dimensions which are sometimes referred to as fundamental dimensions, the International System of Units.

The symbol for the fundamental dimension of length is “L”
The symbol for the fundamental dimension of mass is “M”
The symbol for the fundamental dimension of time, duration is “T”
The symbol for the fundamental dimension of electric current is “l”
The symbol for the fundamental dimension of thermodynamic temperature is “Capital Theta”
The symbol for the fundamental dimension of amount of substance is “N”
The symbol for the fundamental dimension of luminous intensity is “J”

I did not make these definitions, a body of highly educated people did.

Why exactly they chose these quantities and dimensions as base I do not know, but they did. Seems to me Luminous Intensity is a derived dimension, but I have not spent that much time trying to figure it out. I for one do not plan on arguing with the community of scientists, engineers and such who selected these seven dimensions as the base upon which the built the SI system of units and measurement.

The whole point of this thread is to discuss for fun the possibility of dimensions which have either not been solidly proven of not proven at all. It is an exercise of imagination and reasoning.

Some dimensions which we are trying to prove really exist relate to the leading edge of physics and the fact that space can NOT be perfectly described in 4 dimensions. We know that our 4 dimensional model of space is flawed and imperfect.

But then there is also the fun of considering dimensions which can not be proven and for that matter are likely to never be proven. These are the dimensions needed for science-fiction. When a spaceship leaps from normal space into hyperspace and then back to normal space while having traveled a normal space distance at a speed many times greater than the speed of light, how might that dimensional space be described? What extra dimensions would be needed?

Both of these topics are fun to me.

But to become bogged down by people who have such blinders on that they can not even realize that we have a plethora of known dimensions besides that of length and time to ponder about when trying to consider a new dimension we have yet to prove exists is like trying to discuss evolution with a highly religious individual where you can not get past the argument that God created everything.

[Ben Tilly]

Whatever physical dimensions we agree on, there is no question that there are plenty of reasons to think in larger numbers of dimensions than that. Let me give a ridiculously simple example - look at the space of possible configurations of the human body. Even if you grotesquely simplify the human body, you get a lot of parameters. Here are a few:

2 knees, each of which may be bent over some range of angles.
2 elbows, each of which may be bent over some range of angles.
2 shoulders, each of which has 3 dimensions of motion. (up/down, forward/back, rotate your arm bone)
2 hips, each of which has 3 dimensions of motion.

I'm up to 8 dimensions, and I haven't even started in on what your neck, spine, wrists, ankles, fingers, etc can do. Let alone the fact that our various bones do not all have the same length. Clearly, describing the configuration of a given human body requires a lot more than 3 dimensions! (And it isn't just a straightforward n-dimensional region, there are design limits because, for instance, your elbow will only bend so far, and your hand can't go into your body.)

This example may seem contrived, but it is not at all contrived if you're trying to model a human being in a computer. Or if you're trying to build a robot.

Similarly in many other modelling situations, by the time you've finished describing your design parameters, you're in a high dimensional system. And it isn't just abstract theory - I know of real optimization problems in economics and engineering which involved several thousand dimensions. An excellent example which I saw an article on over a decade ago is the design of soft drink cans. The goal: design a can which uses as little metal as possible but holds a fixed amount of fluid under pressure and will survive normal drops, contact with sharp objects, etc. Coca-Cola spent several million dollars on this optimization problem, and the number of dimensions in their highly non-linear mathematical models was huge. However their savings completely paid for the program.

So there are some good reasons to think about lots and lots of dimensions in the mathematical sense.

[PixyMisa]

You do mention something which agrees with something I have said, but I am sure others will disagree with you for that. Space can be defined in terms of the dimensions length, angle, angle.
That's a valid and frequently used co-ordinate system; yes. And it means that there are three dimensions of space.

But there is another confusion being made here and that is the difference between a dimension and a physical reality. Dimensions are an arbitrary creation of ours. We make up a definition for dimension.No.

So someone can arbitrarily come up with a definition of physical space, like defining it in three dimensions of length and that model may work pretty darn well. That is, until some people come along, thinking outside the box, using their imagination combined with experimentation, and they find that the 3 dimensions used to define space don’t actually quite work 100%. Those 3 accepted dimensions do not precisely define and measure space.No.

To help us understand physical existence we have developed the convention of organizing physical quantities in a system of dimensions. The International System of Units has chosen 7 base quantities each of which is regarded as having its own dimension.No. Look at the name you just wrote. International System of Units.

From these 7 dimensions which are sometimes referred to as fundamental dimensions, the International System of Units.Units. Not dimensions.

I did not make these definitions, a body of highly educated people did.And then you decided that they were dimensions rather than what they really are - units.

Why exactly they chose these quantities and dimensions as base I do not know, but they did.The history of each of the units in SI is documented, and in many cases, interesting. That doesn't make them dimensions.

Seems to me Luminous Intensity is a derived dimensionUnit.
but I have not spent that much time trying to figure it out. I for one do not plan on arguing with the community of scientists, engineers and such who selected these seven dimensionsUnits.

as the base upon which the built the SI system of units and measurement.

The whole point of this thread is to discuss for fun the possibility of dimensions which have either not been solidly proven of not proven at all. It is an exercise of imagination and reasoning.Then why are you so insistent that your mistaken interpretation of the word "dimension" is correct and that the work of leading physicists into multi-dimensional explanations of observed reality is wrong?

Some dimensions which we are trying to prove really exist relate to the leading edge of physics and the fact that space can NOT be perfectly described in 4 dimensions. We know that our 4 dimensional model of space is flawed and imperfect.No. It's incomplete. As far as it goes, it is extremely accurate.

But then there is also the fun of considering dimensions which can not be proven and for that matter are likely to never be proven. These are the dimensions needed for science-fiction. When a spaceship leaps from normal space into hyperspace and then back to normal space while having traveled a normal space distance at a speed many times greater than the speed of light, how might that dimensional space be described? What extra dimensions would be needed?One would suffice.

Both of these topics are fun to me.That's fine.

But to become bogged down by people who have such blinders on that they can not even realize that we have a plethora of known dimensions besides that of length and time to ponder about when trying to consider a new dimension we have yet to prove exists is like trying to discuss evolution with a highly religious individual where you can not get past the argument that God created everything.I don't believe that you've actually read anything anyone else has written.

There are real properties of matter that physicists are working to model as additional dimensions. These properties are mass - which is on your list, charge - which is related to current, "flavour", and "colour".

Temperature is a measure of energy, derived from mass, length, and time.
Current is a derived unit from charge and time.
Luminous intensity is a derived unit from mass, length, and time.
Amount of substance is just a number. A mole is simply 6.02x1023 of whatever you're counting.

The idea that there may be additional dimensions is a great insight, and physicists have been studying this since early in the 20th century. The only problem with your idea is that you are choosing things as your extra dimensions that just don't work.

Take a look at the Wikipedia article on the Standard Model (http://en.wikipedia.org/wiki/Standard_Model). The Standard Model describes all the different types of matter and the forces that unite them. This is the fundamental nature of the Universe; this is what you need to explain with your extra dimensions.

[Just thinking]

Just poking in here ...

I believe number 4 is in error --- it should be Electric Charge (coulomb)

[Oppressed]

Ben Tilly,

Well put.

PixyMisa,

To not realize the difference between “our arbitrary creation of terms and definitions” and “physical reality” seems to be another blinder you are wearing. While there are a great many things one can do in life while wearing so many blinders, if you participate in the effort to better our existing knowledge of physical reality or expand our knowledge of physical reality into new unknown areas, your blinders would be a grave hindrance.

Dimension is all about measuring something. The International System of Units which was developed was done so with a pretty large group of very educated people who looked at all our collective knowledge we have collected on describing our physical world and they made the decision to select 7 quantities and dimensions and call them the base from which all others would be derived.

They took a chosen quantity of a chosen dimension and defined that quantity as the base quantity and that dimension as the fundamental dimension.

From this all other dimensions they were defining could be derived, though you will find at some point an exception stated by them that there are in fact more dimensions than they list and that some of the dimensions they list can not be described by the 7 selected fundamental dimensions.

But, in general, all the other dimensions they define units of measurement for are derived from the product of these 7 dimensions, each with an associated power.

I’ve been trying to find a good web page I can direct you to about this and believe I have found it. Ben Tilly, please look at the following links and see if you think they support what I am stating here.

http://physics.nist.gov/cuu/Units/bibliography.html
http://www.bipm.org/en/si/si_brochure/chapter1/1-3.html

As far as Luminous Intensity being chosen as a fundamental dimension, in many ways how we chose to look at things is arbitrary, even if it is found to be a valid and provable way of looking at things.

By realizing this, we can discover that sometimes there are different ways of looking at something which are both found to be equally valid and equally provable.

If Luminous Intensity is arbitrarily chosen as being a fundamental dimension, then the non-fundamental dimensions are derived from Luminous Intensity, not the other way around.

If this choice works well for it’s intended use, helps us abstractly describe and understand our physical existence better and is found to be the best model for doing so, then choosing to accept and work the definition is an objectively wise choice.

[PixyMisa]

To not realize the difference between “our arbitrary creation of terms and definitions” and “physical reality” seems to be another blinder you are wearing.
What are you talking about? That's exactly what you're doing wrong.

Dimension is all about measuring something.Nope.

The International System of Units which was developed was done so with a pretty large group of very educated people who looked at all our collective knowledge we have collected on describing our physical world and they made the decision to select 7 quantities and dimensions and call them the base from which all others would be derived.Units. They defined, for pragmatic purposes, a standard set of basic units.

They took a chosen quantity of a chosen dimension and defined that quantity as the base quantity and that dimension as the fundamental dimension.No.

From this all other dimensions they were defining could be derived, though you will find at some point an exception stated by them that there are in fact more dimensions than they list and that some of the dimensions they list can not be described by the 7 selected fundamental dimensions.They didn't define dimensions, they define units.

But, in general, all the other dimensions they define units of measurementThey don't define dimensions at all. They do define units of measurement.

for are derived from the product of these 7 dimensions, each with an associated power.These are not dimensions. This has been explained to you far too many times.

Take temperature: It is simply a measure of energy, a function of mass, length and time. You already have mass, length and time on the list.

Same applies for luminous intensity.

Quantity is just a number.

Current is not represented by anything else on the list, but it is a function of charge (a fundamental physical property like mass) and time.

I’ve been trying to find a good web page I can direct you to about this and believe I have found it. Ben Tilly, please look at the following links and see if you think they support what I am stating here.

http://physics.nist.gov/cuu/Units/bibliography.html
http://www.bipm.org/en/si/si_brochure/chapter1/1-3.htmlThe second page uses the term "dimension", but it doesn't mean what you think it does.

As far as Luminous Intensity being chosen as a fundamental dimension, in many ways how we chose to look at things is arbitrary, even if it is found to be a valid and provable way of looking at things.You can choose arbitrary units, as long as they are consistently defined; that's fine. You can't choose arbitrary dimensions to represent the Universe, because the Universe actually exists and actually has a set of dimensions. You can, again, choose your co-ordinate system as long as that co-ordinate system can me mapped onto the Universe itself.

If Luminous Intensity is arbitrarily chosen as being a fundamental dimension, then the non-fundamental dimensions are derived from Luminous Intensity, not the other way around.You can do that with a system of units, though starting with luminous intensity means that you have to exclude one of mass, length, or time, and it makes the maths hideous. Still doesn't mean the Universe has a luminous intensity dimension, of course.

If this choice works well for it’s intended use, helps us abstractly describe and understand our physical existence better and is found to be the best model for doing so, then choosing to accept and work the definition is an objectively wise choice.Since none of that is true, no physicist on the planet considers luminous intensity as a dimension in the sense of space, time, mass and so on.

For the last time, the idea of extra dimensions is sound. Your choice of possible dimensions is based on a misunderstanding of what a dimension is.

You can't have a Universe where you have dimensions of space, time, mass and temperature, because temperature is just kinetic energy, i.e. the movement of matter. It's mathematical nonsense; a property cannot simultaneously be fundamental and derived.

[Jimbo07]

Ben Tilly,

Well put.

PixyMisa,

To not realize the difference between “our arbitrary creation of terms and definitions” and “physical reality” seems to be another blinder you are wearing.

Oppressed, I think that you don't recognize here that Ben Tilly and Pixy Misa's takes are amenable and yours is not.

I don't know what your background is, but your confusion between dimensional analysis and spatial dimensions suggests that it's not college. This is perfectly okay, but you must be willing to understand, as you yourself have put it, "a pretty large group of very educated people who looked at all our collective knowledge," have come up with working models.

...

Even if you don't plan on doing a full college education (and more people in society don't than do), depending on your math background, you may be very interested in introductory courses in physics and linear algebra. Introductory courses are fun, because they often outline what is still on the fringes of the discipline (especially if you get a good prof, who likes dropping 'teasers').

...

A problem that you are trying to solve can be said to exist in a "space" (not outer space, a "space"). That space has a dimension. That is, it has a number of independent parameters that, together, can define a point (or solution to a problem, say) in that space. This is immediately obvious to everyone in our typical outer space, or 4D spacetime. Notice the different uses of the word "space" to represent a couple of different, if related, concepts? It's the same with dimension.

In 4D spacetime, to solve problems specifically related to that "space's" geometry, the dimension is said to be 4, and the dimensions are referred to as (x,y,z,ct). Note that these can be easily translated to spherical or cylindrical coordinates. On the other hand, solving problems with 'dimensional analysis' essentially refers to a different problem space.

That is, different disciplines are using different definitions, at different times, of the word dimension. From one of the earliest links, the word dimension does not have a single, authoritative use across all of the maths and sciences. It's not the only word that suffers from this.

Please understand that this is not closed-mindedness on the part of dogmatic internet goons (except maybe in my case :D). As Pixy Misa has pointed out, higher dimensionality to space time HAS been considered.

We've strayed far from the chance of any discussion of fiction, but we need to be on the same page for that, I think...

[Oppressed]

If you have access to a library look up the book "International vocabulary of basic and general terms in metrology". It might only be available in a technical library. You can also purchase it online.

This is the usual guide use for terms by the Bureau International des Poids et Mesures.

[Oppressed]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.

[PixyMisa]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.
Blink.

[Jimbo07]

Jimbo07,

I completed my University Degree in Electrical Engineering with two minors, one in math and one in physics in 1997.

Good.

Then you know that a set of N orthonormal vectors form the basis of a space of dimension N. This is true regardless of the space you are working in. In engineering mechanics these are your unit vectors.

You will also have performed 'dimensional analysis.' I have no idea from where the apparent confusion has arisen...

:boggled:

[Ziggurat]

To help us understand physical existence we have developed the convention of organizing physical quantities in a system of dimensions. The International System of Units has chosen 7 base quantities each of which is regarded as having its own dimension.

From these 7 dimensions which are sometimes referred to as fundamental dimensions, the International System of Units.

The symbol for the fundamental dimension of length is “L”
The symbol for the fundamental dimension of mass is “M”
The symbol for the fundamental dimension of time, duration is “T”
The symbol for the fundamental dimension of electric current is “l”
The symbol for the fundamental dimension of thermodynamic temperature is “Capital Theta”
The symbol for the fundamental dimension of amount of substance is “N”
The symbol for the fundamental dimension of luminous intensity is “J”

I did not make these definitions, a body of highly educated people did.


And you misunderstood them. The SI defines fundamental units, NOT fundamental dimensions. Most of these independent units are associated with "fundamental" dimensions (ie, meters are associated with length), but that is NOT true of amount OR luminous intensity. Amount is DIMENSIONLESS. It is a pure number, and numbers have no dimension. I've already told you that. Your persistence in ignoring this correction does not speak well for your comprehension skills.

Seems to me Luminous Intensity is a derived dimension, but I have not spent that much time trying to figure it out. I for one do not plan on arguing with the community of scientists, engineers and such who selected these seven dimensions as the base upon which the built the SI system of units and measurement.

Luminous intensity, as already mentioned, has dimensions which are derived from dimensions associated with other fundamental units. The Candela is considered a fundamental unit because there are aspects of the definition of the unit which make the unit independent of the other SI units, but the dimension is not fundamental. Units and dimensions are not the same thing.

The whole point of this thread is to discuss for fun the possibility of dimensions which have either not been solidly proven of not proven at all. It is an exercise of imagination and reasoning.

It is perhaps an exercise in imagination, but it is most certainly not an exercise in reasoning.

[Oppressed]

Jimbo07,

…and if I said Luminous Intensity was a dimension of space I would be wrong.

But that is not what I have stated. Space is part of our physical existence which we measure. In order to measure it, we have defined dimensions to do so. To measure space our most basic model uses 3 dimensions. When we measure space-time we use 4 dimensions.

But what constitutes a dimension is not just that of length and time. The dimensions of length are used to measure space but there are many other dimensions which are NOT used to measure space but are used to measure something else.

Ziggurat,

A very large body of very well educated people defined the list of dimensions as being “Dimensions”. You can follow some of the links I have previously given, contact them and explain to them they are wrong.

I quote: “
quantity dimension
dimension of a quantity
dimension
dependence of a given quantity on the base quantities of a system of quantities,
represented by the product of powers of factors corresponding to the base quantities
NOTES
1 The conventional symbolic representation of the dimension of a base quantity is a single
upper case letter in roman (upright) sans-serif type. The conventional symbolic representation
of the dimension of a derived quantity is the product of powers of the dimensions of the base
quantities according to the definition of the derived quantity.
2 Quantities having the same dimension are not necessarily quantities of the same kind.
3 In deriving the dimension of a quantity, no account is taken of any numerical factor, nor of its
scalar, vector or tensor character.
4 The dimension of a base quantity is generally referred to as ‘base dimension’, and similarly for
a ‘derived dimension’.
EXAMPLES
a) In the ISQ, where L, M and T denote the dimensions of the base quantities length, mass, and
time, the dimension of force is LMT –2.
b) In the same system of quantities ML–3 is the dimension of mass concentration and also of
volumic mass (mass density).
”

[Ziggurat]

Ziggurat,

A very large body of very well educated people defined the list of dimensions as being “Dimensions”. You can follow some of the links I have previously given, contact them and explain to them they are wrong.

I never said they were wrong, I said you were wrong. And I have no intention of digging through all your past links to refute every single instance that you misinterpreted one of your sources. What you have quoted in this post does not contradict anything I said.

[Oppressed]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

[calebprime]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

Oppressed, perhaps you could concede that you were using the word 'dimension' in a way that was confusing to some. It confused me--but then, I'm not that well-educated in science.

Now, can you move on? You've got these, err, parameters, aspects, qualities, factors, features, elements. How do you propose to philosophize with them?

I also note the word 'astral'. What are you going to do with that one?

[Molinaro]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.


From your link, I went to this (http://physics.nist.gov/cuu/Units/SIdiagram.html) page. There is a nice chart there listing the 7 base SI units.

The only mention of the word dimension on that page is the following:

The reason is that in the SI, the quantities plane angle and solid angle are defined in such a way that their dimension is 1 -- they are so-called dimensionless quantities.

So, why are you talking about dimensions, when your link says they are base units?

[Ziggurat]

I have checked and confirmed through multiple resources to make sure that I am right.

http://physics.nist.gov/cuu/Units/bibliography.html

This site will give you links through which what I have said can be verified.

I did. And you're wrong. Note, for example, this statement (http://physics.nist.gov/cuu/Units/units.html):
"The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1."
Note that it doesn't say dimensions, it says units. Units are not dimensions.

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.

Your personal experience is beside the point. And your references don't say what you seem to think they say, so the fact that you use them as references is of no consequence.

[PixyMisa]

You can state I am wrong all you like, but I pull my information from 6 years of University level education, 10 years of professional engineering experience and references from the majority consensus of scientists and engineers around the World.
Here in Oz, dimensional analysis is a topic in highschool physics. That you apparently haven't even heard of it in six years of university and ten years of practice is something of a worry.

[Oppressed]

I feel like I am arguing with someone over religion.

This is first year college stuff, understanding the basic definitions of terms used in science and engineering.

The usual guide which contains the definitions used is the
"International Vocabulary of Basic and General Terms in Metrology" (VIM)
http://www.iso.ch/iso/en/prods-services/otherpubs/Measurements.PublicationList?CLASSIFICATION=MEASUR EMENTS#092001

I’ve read it more than once.

Look at “Table 1. Fundamental Dimensions” from the American Meteorological Society.
http://amsglossary.allenpress.com/glossary/search?id=fundamental-dimensions1

The table lists the fundamental dimensions I have at the beginning of this thread, which you say is wrong. Are you ready to tell the American Meteorological Society they are wrong? By the way, you can get to this page through the single link I gave you in my last response.

Look at SI brochure, Section 1.3 at the following link.
http://www.bipm.org/en/si/si_brochure/chapter1/1-3.html

I quote the first sentence “By convention physical quantities are organized in a system of dimensions.” Below is then given a table which lists 7 base quantities, the symbols for those quantities and the symbols for the associated base dimension.

This is from the Bureau International des Poids et Mesures. They, like the American Meteorological Society are defining the same set of base/fundamental dimensions which you are stating is wrong. Maybe you should also contact them and tell them to correct their mistake.

From the ISO VIM (DGUIDE 99999) “International vocabulary of basic and general terms in metrology (VIM)”. Find a copy and read it.

Chapter 1: QUANTITIES AND UNITS gives a good example of some general concepts of quantities.

In section 1.7 it explains about dimensions and gives some examples.

I quote from this book:

“The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity.”

“The dimension of a base quantity is generally referred to as ‘base dimension’, and similarly for a ‘derived dimension’.”

Again, this document is stating that which you are saying is wrong. This document is from the International Organization for Standardization also known as ISO. You can contact them and explain to them how they too are wrong.

[PixyMisa]

This is first year college stuff, understanding the basic definitions of terms used in science and engineering.
It's really highschool stuff. So why are you getting it so badly wrong?

Can you understand that current, temperature, and luminous intensity are derived from fundamental physical properties, including charge, mass, space and time?

If you have a problem with that statement, what is the problem? Stop pointing us at other examples of people using the term "dimension" to talk about units, and address the mathematics.

Again, this document is stating that which you are saying is wrong. This document is from the International Organization for Standardization also known as ISO. You can contact them and explain to them how they too are wrong.
We're not saying that they're wrong, we're saying that you're wrong. There are two meanings of the word "dimension" at work here, and they are not referring to the same thing.

[Oppressed]

PixyMisa,

And I am saying you are wrong and I cite references to support that, but then you do not accept those references.

Just what is your educational background? Mine has been questioned and I am responding.

The core of my studies was all about science and the use of science in engineering. I excelled in all elements of science. The only thing which ever pulled my grades down was classes like history or English composition.

I minored in physics I taking General Physics I, II and III, Modern Physics I and II, Electromagnetic Fields and Waves I and II, Special Theory of Relativity and Solid State Physics. With rare exceptions I earned As in all science and math related classes, the exceptions being when I only earned Bs.

I was a member of the honor society Eta Kappa Nu. I was and am a member of ISA and IEEE.

Particularly in classes relating to spatial understanding I did particularly well in. Vector Dynamics for example. Another example was Electromagnetic Waves where I had to learn how to model dynamic fields of energy in 3 spatial dimensions and show how a charged mass would be effected traveling though the fields, taking into account field gradients and curl, and being able to translate the model between Cartesian, Cylindrical and Spherical coordinates systems.

I’ve done a whole heck of a lot of study and work with dimensions, graduated with honors and am currently a Senior Systems Engineer. Four of my professional years of experience were in research, the last six being in industry which pays better.

I know what a dimension is, but apparently you do not.

[PixyMisa]

And I am saying you are wrong and I cite references to support that, but then you do not accept those references.
Those references do not address the point. Instead of Googling the word "dimension", perform a dimensional analysis on temperature, luminous intensity and current, with reference to the Standard Model of physics.

Just what is your educational background? Mine has been questioned and I am responding.
I'm a Computer Science dropout. But I was awake during highschool physics class.

The core of my studies was all about science and the use of science in engineering. I excelled in all elements of science. The only thing which ever pulled my grades down was classes like history or English composition.
Good for you. In that case, you'll have no trouble with the little task I set you above.

I minored in physics I taking General Physics I, II and III, Modern Physics I and II, Electromagnetic Fields and Waves I and II, Special Theory of Relativity and Solid State Physics. With rare exceptions I earned As in all science and math related classes, the exceptions being when I only earned Bs.

I was a member of the honor society Eta Kappa Nu. I was and am a member of ISA and IEEE.

Particularly in classes relating to spatial understanding I did particularly well in. Vector Dynamics for example. Another example was Electromagnetic Waves where I had to learn how to model dynamic fields of energy in 3 spatial dimensions and show how a charged mass would be effected traveling though the fields, taking into account field gradients and curl, and being able to translate the model between Cartesian, Cylindrical and Spherical coordinates systems.

I’ve done a whole heck of a lot of study and work with dimensions, graduated with honors and am currently a Senior Systems Engineer. Four of my professional years of experience were in research, the last six being in industry which pays better.
That's all very nice. Unfortunately the facts don't agree with you.

As I said, analyze how current, temperature, and luminous intensity relate back to the standard model. You'll quickly find that they are not in any way fundamental. They are defined as fundamental units under SI for convenience, not because they are intrinsic properties of matter. Particularly luminosity, which has some significant fudge factors in it.

[Fredrik]

Oppressed, you have convinced me that you're not the only one using the word "dimension" as a synonym for "unit", but it's still not a good idea to do so. The reason the sources you cite can get away with it and you can't is that they're not doing it in a text about dimensions of space-time. The word "dimension" means something else entirely in that context, and you seem to know that, so you should have been able to anticipate that you would cause a lot of confusion.

These are examples of what I consider appropriate uses of the word "dimension" in the context of units:

1. Grams and ounces are two different units of mass. The quantity x = 100 grams = 3.527 ounces has dimensions of mass. (I think most physicists use the plural form here, I don't really know why). Note that in this context a dimension is a class of units.

2. If we didn't know that the volume of a sphere is 4*pi*r3/3, where r is the radius, we could still estimate its order of magnitude using dimensional analysis: A volume has dimensions of length3, and the only length needed to specify the size of a sphere is its radius, so we estimate the volume as r3. (This estimate is wrong by a factor of about 4 and probably isn't very useful, but that's beside the point).

In the context of manifolds (like space-time) the definition is quite different. A manifold is equipped with a set of functions (called charts by mathematicians and coordinate systems by physicists) that map open subsets of the manifold into the set Rn (i.e. the set of ordered n-tuples of real numbers). The number n is called the dimension of the manifold.

By the way, the prefix "hyper" often means something else too. For example, a "hypersurface" in an n-dimensional manifold is an (n-1) dimensional submanifold. You can think of space as a hypersurface in space-time.

The question you've been asking in this thread (if I understand you correctly) is this: If we take a space-time manifold with more than four dimensions as a model of our own universe, and imagine an experiment that measures the magnitude of a displacement into one of the "extra" dimensions, would the result be in meters, seconds or some other unit?

(You're asking about the dimensions of dimensions, with the first "dimensions" not meaning the same thing as the second. No wonder people get confused, or think that you have confused two very different meanings of the word).

[Molinaro]

Well said Fredrik.

If we take a space-time manifold with more than four dimensions as a model of our own universe, and imagine an experiment that measures the magnitude of a displacement into one of the "extra" dimensions, would the result be in meters, seconds or some other unit?

That is exactly what Oppressed has been trying to ask.

[Cuddles]

Just poking in here ...

I believe number 4 is in error --- it should be Electric Charge (coulomb)

Not necessarily. As I said earlier, the exact choice of fundamental units is not fixes, several different systems are possilble. For the SI system either current or charge must be fundamental, and the other can be derived from a combination of the other fundamental units. The convention is to use current simply because that was discovered and measured first. Knowing what we do now, charge seems a more logical choice, but without any overriding need to change anything conventions tend to stick. It's a similar situation to that with the direction of current in electronics - the charges actually move in the opposite direction but because the convention was established before people knew that it has stuck, and there is no need to change it.

It reality there are really six fundamental units. Length, time, mass, current (or charge), colour charge and flavour. Colour and flavour have to be included because they are the equivalents of mass and charge for the other fundamental forces and cannot be derived. Temperature can be a tricky one, depending on how you define it and the system you use it can be fundamental, derived or dimensionless. In general use it is a measure of kinetic energy and so can't really be considered fundamental. Moles are often counted as a fundamental unit and it can be useful to think of them as such, but they are not actually a unit any more than the number "one" is a unit. A mole is a number, nothing more. Luminous intensity is definately not a fundamental unit because it is defined in terms of power. However, it is often mentioned as one because in the areas it is used it is often more useful to consider it as a fundamental and derive other quantities from it.

[PixyMisa]

Fredrik - yep. The problem is that he asked that question, and then proposed a whole bunch of impossible answers. That's how the argument arose.

[Just thinking]

Not necessarily. As I said earlier, the exact choice of fundamental units is not fixes, several different systems are possible. For the SI system either current or charge must be fundamental, and the other can be derived from a combination of the other fundamental units. The convention is to use current simply because that was discovered and measured first. ...

Well, I'll bet weight was discovered (realized) before mass as well. ;)

You're right in that temperature is a tricky one -- I think it more of a measurement of convenience rather than an actual dimensional unit, like hours or days as opposed to time. (Same for moles.) A way of describing the average amount of heat energy over a system as well as determining which way heat energy will flow between systems of different temperatures.

But anyway ... we do now know that the fundamentals include charge and mass, not current and weight.

[Jimbo07]

Jimbo07,

…and if I said Luminous Intensity was a dimension of space I would be wrong.

But that is not what I have stated. Space is part of our physical existence which we measure.

This isn't what I was talking about. I don't want to get into a pissing match about which units are fundamental. I'm afraid there's too much unwarranted animosity in this thread already.

I was talking about "A" space as a theoretical construct in which we solve problems. I wasn't talking about space-time. Space-time IS a vector space, but not all vector spaces are space-time... right?


In order to measure it, we have defined dimensions to do so. To measure space our most basic model uses 3 dimensions. When we measure space-time we use 4 dimensions.

Yes. You're right. When we measure space-time, we use 4 dimensions. Various cosmological models (in which I'll admit, I'm not proficient) suggest more dimensions of space (or time? I don't know). I am completely unqualified to speak to the validity of String Theory, say.


But what constitutes a dimension is not just that of length and time. The dimensions of length are used to measure space but there are many other dimensions which are NOT used to measure space but are used to measure something else.

Not in this context of the use of the word dimension.


A very large body of very well educated people defined the list of dimensions as being “Dimensions”. You can follow some of the links I have previously given, contact them and explain to them they are wrong.

They are not wrong... in their context. As an engineer (and if you're anything like me, you'll crave precision in terminology), you'll recognize that different disciplines will use different things according to their own conventions/traditions. It's not the same, but consider, for example, the complex coefficient. From your electrical background, you'll know it's 'j,' but from your physics background, you'll know it as 'i.' Different disciplines, same concept and context, but different terminology. Similarly, in this thread you have different disciplines, same terminology... but different context.


3 In deriving the dimension of a quantity, no account is taken of any numerical factor, nor of its
scalar, vector or tensor character.

This quote is so important, and should make it very clear that this interpretation is different than the interpretation of the word 'dimension' when used in terms of vector spaces.

I feel like I am arguing with someone over religion.

I'm very sorry for anything I've said to inflame this thread, and I'm sorry if I've been insulting in any way, but you have to admit that comments like this don't help.


This is first year college stuff, understanding the basic definitions of terms used in science and engineering.

I agreed, but thought you had it the other way around.


I quote the first sentence “By convention physical quantities are organized in a system of dimensions.”

Note the words "By convention."


Again, this document is stating that which you are saying is wrong. This document is from the International Organization for Standardization also known as ISO. You can contact them and explain to them how they too are wrong.

Again, for their context, they are not wrong. However, I'm not aware that ISO has any jurisdiction (or current interests) in regards to cosmology. I assumed that you were interested in cosmology when you started with the OP.

PixyMisa,

And I am saying you are wrong and I cite references to support that, but then you do not accept those references.


The references cited don't support the OP. Check the references I cited. I'm also willing to go offline to cite print textbooks.


Just what is your educational background? Mine has been questioned and I am responding.

You did. I believe you are the real deal, because by-and-large you've been civil (and besides, nobody other than a member of the ISA would admit to being a member, or even know what ISA is :D).

Without getting into a credentials smackdown, I'll simply say that the program I just finished is VERY similar to what you've described yours as.


I minored in physics I taking General Physics I, II and III, Modern Physics I and II, Electromagnetic Fields and Waves I and II, Special Theory of Relativity and Solid State Physics. With rare exceptions I earned As in all science and math related classes, the exceptions being when I only earned Bs.

In my neck of the woods, this is called Engineering Physics.


I know what a dimension is, but apparently you do not.

Much like the "religion" quote, this is inflammatory, and coupled with the confusion over the use of the term "dimension" led me to question your education.

I am sorry.

Mea Culpa.

In the context of things like cosmology, I still think you might be wrong. ;)

ETA: See Fredrik's post.

[Oppressed]

LOL

Well, at least I better understand why PixyMisa does not understand this. Lower level classes in science often simplify definition and then make statements about how the simple definition is a rule when if fact it is a narrowed view of a greater view, narrowed to make the subject easier to understand.

Fredrik,

Dimension is absolutely not a synonym for unit. Dimension does not equal unit.

Is about observing something and then developing a means of measuring it, for example, length. If you want to measure the distance between two points where do you begin? To measure it, you are going to count/measure the quantity of something. But what is that something? You can place your foot down in front of the first point, heading towards the second point and then place your other foot in front of the first, touching toe to heal and continue until you get to the second point. Now you have counted/measured out the distance in feet. But feet of what?

Feet is a unit of measure. Length is the dimension in which the unit feet is used to measure. A dimension has no units. In order to measure a dimension we define units of measure in that dimension that we can count.

As far as what is base, fundamental, derived and so on, I am not sure I always agree with or perfectly understand why some definitions are chosen. To be honest about it, sometimes I have worked some definitions out so I understand something and then have forgotten the proof I went through.

Why did the people putting together choose “Electric Current” as a base dimension? It is a dimension, I do not question that. But why do they define it as a base dimension which has led others to call it a fundamental dimension? I’m not sure why, I just know that they have done so.

Is not electric current the amount of charge that passes through the surface in the time T? So that I=Q/T? But, then Q=I•T. A lot of things depend upon our point of view and can result in more than one point of view being correct. This is actually one of the reasons for trying to standardize our terminology for measuring the dimensions of our physical existence that we observe, so that we can discuss something from the same point of view.

In the SI system electric charge is given the unit of coulomb “C” They define coulomb as a derived unit of measure “coulomb = ampere • second” The dimension of coulomb is derived from the dimension of “Electric Current” • “time”.

In the SI system electric flux, flux of displacement and quantity of electricity are also given the unit of measure of “coulomb = ampere • second”, but there are differences between them which result in their separate definitions.

As Cuddles points out, there are things which are defined as base or fundamental which we would probably change except that using it is so entrenched in our every day use that rather than use a less logical chose for a base dimension because it is not worth the cost and effort to change. We can and do call something a base dimension and do so successfully even though we have learned that maybe that dimension might better be defined as derived. Again, it is possible to view things from more than one point of view and have both viewpoints be correct.

As for the dimension of “Amount of Substance” and the corresponding unit of “moles”, that is definitely the one dimension I question the most as being called a dimension. And yet it has been defined and that definition has been accepted by a very large body of educated people, many of them being much smarter than I.

To understand it I had to go back to the understanding of what dimension really stands for, that is for measuring out of something.

The dimension of “Amount of Substance” has the dimension of the substance being measured out.

[PixyMisa]

LOL

Well, at least I better understand why PixyMisa does not understand this.
What is it that I don't understand?

You are saying that Ampere is a unit and cur