I challenge the student of mathematics

[coberst]

I challenge the student of mathematics

It appears to me that most people look on math as something with supernatural qualities. I challenge the student of math to develop and post short essays on Internet discussion forums about those fundamental aspects of math that you think people can and should comprehend.

What follows is something that I have posted regarding my idea of what ordinary citizens should know abut this very fundamental domain of knowledge.

Arithmetic is object collection

It is a hypothesis of SGCS (Second Generation Cognitive Science) that the sensorimotor activity of collecting objects by a child constitute a conceptual metaphor at the neural level leading to a primary metaphor that ‘arithmetic is object collection’. The arithmetic teacher attempting to teach the child at a later time depends upon this already accumulated knowledge. Of course, all of this is known to the child without the symbolization or the conscious awareness of the child.

The pile of objects became ‘bigger’ when the child added more objects and became ‘smaller’ when objects were removed. The child easily recognizes while being taught arithmetic that 5 is bigger than 3 and 3 is littler than 7. The child knows many entailments, many ‘truths’, resulting from playing with objects. The teacher has little difficulty convincing the child that two collections A and B are increased when another collection C is added, or that if A is bigger than B then A+C is bigger than B+C.

At birth an infant has a minimal innate arithmetic ability. This ability to add and subtract small numbers is called subitizing. (I am speaking of a cardinal number—a number that specifies how many objects there are in a collection, don’t confuse this with numeral—a symbol). Many animals display this subitizing ability.

In addition to subitizing the child, while playing with objects, develops other cognitive capacities such as grouping, ordering, pairing, memory, exhaustion-detection, cardinal-number assignment, and independent order.

Subitizing ability is limited to quantities 1 to 4. As a child grows s/he learns to count beyond 4 objects. This capacity is dependent upon 1) Combinatorial-grouping—a cognitive mechanism that allows you to put together perceived or imagined groups to form larger groups. 2) Symbolizing capacity—capacity to associate physical symbols or words with numbers (quantities).

“Metaphorizing capacity: You need to be able to conceptualize cardinal numbers and arithmetic operations in terms of your experience of various kinds—experiences with groups of objects, with the part-whole structure of objects, with distances, with movement and location, and so on.”

“Conceptual-blending capacity. You need to be able to form correspondences across conceptual domains (e.g., combining subitizing with counting) and put together different conceptual metaphors to form complex metaphors.”

Primary metaphors function somewhat like atoms that can be joined into molecules and these into a compound neural network. On the back cover of “Where Mathematics Comes From” is written “In this acclaimed study of cognitive science of mathematical ideas, renowned linguist George Lakoff pairs with psychologist Rafael Nunez to offer a new understanding of how we conceive and understand mathematical concepts.”

“Abstract ideas, for the most part, arise via conceptual metaphor—a cognitive mechanism that derives abstract thinking from the way we function in the everyday physical world. Conceptual metaphor plays a central and defining role in the formation of mathematical ideas within the cognitive unconscious—from arithmetic and algebra to sets and logic to infinity in all of its forms. The brains mathematics is mathematics, the only mathematics we know or can know.”

We are acculturated to recognize that a useful life is a life with purpose. The complex metaphor ‘A Purposeful Life Is a Journey’ is constructed from primary metaphors: ‘purpose is destination’ and ‘action is motion’; and a cultural belief that ‘people should have a purpose’.

A Purposeful Life Is A Journey Metaphor
A purposeful life is a journey.
A person living a life is a traveler.
Life goals are destinations
A life plan is an itinerary.

This metaphor has strong influence on how we conduct our lives. This influence arises from the complex metaphor’s entailments: A journey, with its accompanying complications, requires planning, and the necessary means.

Primary metaphors ‘ground’ concepts to sensorimotor experience. Is this grounding lost in a complex metaphor? ‘Not by the hair of your chiney-chin-chin’. Complex metaphors are composed of primary metaphors and the whole is grounded by its parts. “The grounding of A Purposeful Life Is A Journey is given by individual groundings of each component primary metaphor.”

The ideas for this post come from Philosophy in the Flesh. The quotes are from Where Mathematics Comes From by Lakoff and Nunez

[Twiler]

I don't think that most people consider mathematics to be supernatural in any way. Where did you get that idea?

[erlando]

It appears to me that most people look on math as something with supernatural qualities.

:confused:

No, they don't.

[Dancing David]

Coberst is just a spam bot, in the past there were occasional response to the posts in the threads, very few.
http://www.google.com/search?hl=en&source=hp&q=It+appears+to+me+that+most+people+look+on+math+a s+something+with+supernatural+qualities.+I+challen ge+the+student+of+math+to+develop+and+post+short+e ssays+on+Internet+discussion+forums+about+those+fu ndamental+aspects+of+math+that+you+think+people+ca n+and+should+comprehend.&aq=f&oq=&aqi=

[Raze]

I don't think that most people consider mathematics to be supernatural in any way. Where did you get that idea?

I don't believe he meant that literally. He seems to mean that when a barber is giving a dude a haircut, and then asks him what he does for a living, and the customer tells him he teaches math, the barber suddenly raises his eyebrows as if the customer is a necromancer preforming the arcane arts.

Figuratively speaking.

In other words, people associate math with some strange far off knowledge that only a few weird eccentrics ever understand. Mr. Oberst is right about that, I believe. The first thing you hear from someone not familiar with math when you speak about it is, "Oh, I never liked math, I just wasn't cut out for it." Even when the admission has NOTHING to do with the conversation or the point you brought up.



Oberst got his name from Bright Eyes (apparently- coberst = Coner Oberst), who writes/sings about philosophy, so predictably he will ask what he believes to be deep or profound questions. Sometimes they are. In fact, many times they are (at least as I have seen him on other forums). Other times they seem like a waste of time.

But he does occasionally respond. Not often though. Seems like he just thinks about stuff, comes to what appears to him to be an odd conclusion or an odd question, and then just dumps it on various forums, perhaps hoping to peak the interests of other inquisitive minds.

[Apathia]

He's Chuck Oberst.
He used to have a webpage septemberscholar.com
It's not available at the moment.

His musings, generally philosophical w/o woo-woo, and usually based on what he's currently reading, get a lot of hostile responses here.
But also some good discussion for those with his mature tastes.

Chuck,

if you check back in,

The ideas for this post come from Philosophy in the Flesh. The quotes are from Where Mathematics Comes From by Lakoff and Nunez

It's an excellent book. I have it and will someday get around to reading it.

This statement:
‘arithmetic is object collection’
reminds me of Doron Shadmi who up to just recently tried to propogate his "new paradigm" of Mathematics here.
(Last thread: http://forums.randi.org/showthread.php?t=125220)

One major angle on his approach is that it's based on the kindergarten conception of number.

He asserts that "Cardinality is a measure of existance (in groups)."

I'm not a proponent of his attempt to rework mathematics this way.
It's just that your post again reminded me with clarity of one of the foundations of his unique and off the map views.

[Lothian]

I challenge the student of mathematics

It appears to me that most people look on math as something with supernatural qualities. I challenge the student of math to develop and post short essays on Internet discussion forums about those fundamental aspects of math that you think people can and should comprehend.

What follows is something that I have posted regarding my idea of what ordinary citizens should know abut this very fundamental domain of knowledge. I suggest that if you want ordinary people to understand math ideas you don't talk about fundamental domains, sensorimotor activities, conceptual metaphors, neural level, symbolization, conscious awareness, entailments, subitizing, cardinal numbers, cognitive capacities, exhaustion-detection, Combinatorial grouping, Metaphorizing capacity, & Conceptual-blending capacity.

[coberst]

I suggest that if you want ordinary people to understand math ideas you don't talk about fundamental domains, sensorimotor activities, conceptual metaphors, neural level, symbolization, conscious awareness, entailments, subitizing, cardinal numbers, cognitive capacities, exhaustion-detection, Combinatorial grouping, Metaphorizing capacity, & Conceptual-blending capacity.

I apologize I thought that this group might be above average.

[Lothian]

I apologize I thought that this group might be above average.You said you want to wirte essays for ordinary people.

In my experience ordinary people get turned off by simple ideas expressed in academic terms but respond well to complex ideas put across in plain English.

[erlando]

I've read the post again (took me a couple of tries). It is quite interesting. I apologize for my earlier post :o.

I know a lot of "ordinary citizens" who wouldn't understand a word of it though.

[Dancing David]

I apologize I thought that this group might be above average.

Considering the uncited, lack of evidence and old fashioned nonsense you have posted in the past...

[Cuddles]

I apologize I thought that this group might be above average.

Yet you've spammed exactly the same post around at least 7 other websites. Did you think they were all above average?

[ServiceSoon]

I don't know anything about coberst's past encounters with JREF, but why would posting this topic on different websites be viewed in a negative light or considered as spamming? Do you think you solved a mystery?

Message boards are SPAM=unsolicitated messages. The difference between email SPAM and message board SPAM is you have a choice to ignore or discuss. I can't see anything in the OP which leads me to believe that this post is made for monetary purposes.

Coberst obviously spent a lot of time creating this OP. If they are truly looking for input then it makes sense to discuss with as many people (websites) as possible.

[Raze]

Some of you guys are a bit too quick to judge. Skepticism isn't about mindlessly dismissing everything you see. It's about carefully and methodically examining what is before your eyes.

It seems quite clear to me that Mr. Oberst here has a legitimate concern. Instead of dismissing him, try answering the question.



As to why he would post exactly the same thing on many places... well, isn't it obvious? If I have a question haunting me in a math class, you can be sure that I'm going to post it in as many math forums I can, knowing that each post increases my chances of getting a good answer.

Likewise with Mr. Oberst here.

[Beerina]

"Mathematics a virtual world of virtual objects", check.



I can't leave it just at that sarcasm, though. All mentality that isn't just evolved, hard-wired, instinctual response is part of a "virtual world", an evolved analyzis/planning capability of animals that allowed faster adaptation to the environement -- even faster than sexual reproduction with controlled gene swapping and re-juggling.

Mental model complete with "oops/random attempt/try again" of everything from snails through dogs and humans, up through detailed analysis of only humans, "adapts" the organism faster through behavior changes driven by this mental model rather than evolved, instinctual changes. And has the bonus feature of being able to be "passed on" to children without having to be encoded in the genes first, either.


Yeah, the idea kinda skips that whole second part. :-/

[Apathia]

Some of you guys are a bit too quick to judge. Skepticism isn't about mindlessly dismissing everything you see. It's about carefully and methodically examining what is before your eyes.

It seems quite clear to me that Mr. Oberst here has a legitimate concern. Instead of dismissing him, try answering the question.



As to why he would post exactly the same thing on many places... well, isn't it obvious? If I have a question haunting me in a math class, you can be sure that I'm going to post it in as many math forums I can, knowing that each post increases my chances of getting a good answer.

Likewise with Mr. Oberst here.

When I was a teen back in the day when Western Civilization was dealt a death blow by Woodstock (according to my mother),
there were a couple of elderly men in our neighborhood, whose pastime was to write letters to newspapers and submit their ideas here and there.

At the time it seemed a sad sort of exercise that at least gave them something to occupy their minds to hold back senility.

Now I'm a senior myself, and I understand the inclination, though I find myself more inclined to write out my "wisdom" in private.

Now that we've got the Internet, there are lots of seniors who find it a better venue to share the wealth of age, ot at least the musings they didn't take time for in their youth.

Given my age, I'm not as inclined to accuse Coberst of spamming.
I hope his found like minded people to share his thoughts with.

I do wonder why he posts here given that most at the JREF respond as if he were an insufferable "woo."
Perhaps he has found some intelligent respondents here to make the flack worth it.

[Eyeron]

Well, Pythagoras was a mystic. Some people worship the Tetractys as a mystical symbol:

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

[JoeTheJuggler]

I don't think that most people consider mathematics to be supernatural in any way. Where did you get that idea?

I can't answer for him, but I remember my decision to give up on the TV show NUMB3RS when the guy figured out why his mathematical model for catching the bad guy wasn't working: he'd forgotten to account for the Heisenberg Uncertainty Principle. Since the bad guy knows we're after him, we have to change our formula to account for that. . . .

[Raze]

[...]

I do wonder why he posts here given that most at the JREF respond as if he were an insufferable "woo."
Perhaps he has found some intelligent respondents here to make the flack worth it.

Well, in my humble opinion, that kind of behavior usually signifies a lack of wisdom.

[Apathia]

Well, in my humble opinion, that kind of behavior usually signifies a lack of wisdom.

I usually think I'm wiser in not starting threads here about my own personal philosophical journey.

There's a social wisdom called in Japanese, "kejime."
You know the right context to share feelings and your significant thoughts.

It turns out that some people in this thread have responded to Coberst's ideas, but he hasn't replied to them.
So, I suppose he's not coming back here.

I'd engage him on the op, but I need to read that book first.

[Dancing David]

I don't know anything about coberst's past encounters with JREF, but why would posting this topic on different websites be viewed in a negative light or considered as spamming? Do you think you solved a mystery?

Message boards are SPAM=unsolicitated messages. The difference between email SPAM and message board SPAM is you have a choice to ignore or discuss. I can't see anything in the OP which leads me to believe that this post is made for monetary purposes.

Coberst obviously spent a lot of time creating this OP. If they are truly looking for input then it makes sense to discuss with as many people (websites) as possible.

I have tried to engage in debate with this character, that is why I state as I do, this is spam.

You will note that at least one poster did respond to the content of the post and what response did they get?

[Dancing David]

Sorry, I am not going to read Where mathematics Comes From and if I tried to engage Cobert in the discussion of neurology versus abstracted thinking about thinking, I know where taht will end. From at least teh wikipedia page it looks like your usual meta-cognitive book.

It would appers that it is not based in neurological studies and make little reference to actual demonstrations and behavioral cognitive science. Now the wiki could be wrong but it seems to be mainly about meta-cognition with little reference to biology.

I do not mind philosophy in the least but it should not be confused with science.

[coberst]

I don't know anything about coberst's past encounters with JREF, but why would posting this topic on different websites be viewed in a negative light or considered as spamming? Do you think you solved a mystery?

Message boards are SPAM=unsolicitated messages. The difference between email SPAM and message board SPAM is you have a choice to ignore or discuss. I can't see anything in the OP which leads me to believe that this post is made for monetary purposes.

Coberst obviously spent a lot of time creating this OP. If they are truly looking for input then it makes sense to discuss with as many people (websites) as possible.

The first person to make any kind of sense. It is delightful to read.

[coberst]

When I was a teen back in the day when Western Civilization was dealt a death blow by Woodstock (according to my mother),
there were a couple of elderly men in our neighborhood, whose pastime was to write letters to newspapers and submit their ideas here and there.

At the time it seemed a sad sort of exercise that at least gave them something to occupy their minds to hold back senility.

Now I'm a senior myself, and I understand the inclination, though I find myself more inclined to write out my "wisdom" in private.

Now that we've got the Internet, there are lots of seniors who find it a better venue to share the wealth of age, ot at least the musings they didn't take time for in their youth.

Given my age, I'm not as inclined to accuse Coberst of spamming.
I hope his found like minded people to share his thoughts with.

I do wonder why he posts here given that most at the JREF respond as if he were an insufferable "woo."
Perhaps he has found some intelligent respondents here to make the flack worth it.

The reason I did this is because society cries out in need of greater intellectual sophistication. What better place to start than by helping them to acquire a more sophisticated view of math?

[Apathia]

The reason I did this is because society cries out in need of greater intellectual sophistication. What better place to start than by helping them to acquire a more sophisticated view of math?

Ah. Pardon my misunderstanding of your personal motives.

I confess I'm not of the intellectual caliber myself to contribute to this goal.

[Dancing David]

Now I am not sure about the embodied mind of George Lakoff, as I have found a good source and so i am not sure that I can agree with it or not some parts sound very reasonable. But this stament about math i do disagree with:

"Early in 2001 Lakoff told the AAAS: "Mathematics may or may not be out there in the world, but there's no way that we scientifically could possibly tell." "
http://www.reference.com/browse/wiki/George_Lakoff
Now I really don't see how numbers such as pi ot e are inherent in biology or social norms, nor is the Pythagorean theorm.

Now his argument seems to be the standard 'we are constrained by our biology' sort of presentation.

So how is the ratio of the circumfrence of a circle to it's radius constrained by the 'metaphors' of our cognition. (I would call it pattern matching myself.)

[technoextreme]

"Early in 2001 Lakoff told the AAAS: "Mathematics may or may not be out there in the world, but there's no way that we scientifically could possibly tell." "
Wow he never met an engineering now did he. Entire field of control theory is math and dynamics.

[Dancing David]

Well and calculators show that math is not a product of biology. As do slide rules.

[!Kaggen]

So how is the ratio of the circumfrence of a circle to it's radius constrained by the 'metaphors' of our cognition.
below
I do not mind philosophy in the least but it should not be confused with science.

Commonly known as the metaphysical argument for the a priori existence of scientific laws.

I would also call it pattern matching ;)

[GreyICE]

Look to science and engineering.

Most useful mathematical concepts can be expressed by showing how they allow practical problem solving in the real world.

Not to put too fine a point on it, but those that don't are fair game for remaining 'arcane.' It's a point that those bent on condemning the stupidity of the 'average american' often miss, but not everyone has a burning need to know everything. In point of fact, it is physically impossible to know 'everything' even about a limited subset of everything (i.e. it is quite impossible to know everything about mathematics).

Also, while you might insult us by claiming that we cannot understand what you are saying, there is a difference between failing to interpret your jargon-laiden post, and claiming that the average person will dismiss anything that obtuse as unworthy of their time. After all, if you can't take the time to communicate clearly to your target audience, they owe you no time to understand your ramblings.

[Dancing David]

below


Commonly known as the metaphysical argument for the a priori existence of scientific laws.

I would also call it pattern matching ;)

I would not say that I assume them to preexist, they just happen to be there, if the univesre was not acting in a similar fashion at different places in space and time, then the scientific method would not have the power that it does. And calculators would not give the samer answers.

All my arguments are post fact and ad hoc. I can easily imagine thought spaces where the universe does not behave consistently. I do not assume it prior to the facts.

[six7s]

I apologize I thought that this group might be above average.forums.randi.org: the Lake Wobegon of the interwebs

[Apathia]

forums.randi.org: the Lake Wobegon of the interwebs

Click & Clack

Snort!

[Dancing David]

Click & Clack

Snort!

Don't drive like Apathia!

[!Kaggen]

I would not say that I assume them to preexist, they just happen to be there "The Given" ;) which you perceive and then invent a language to describe in order to have knowledge thereof. Ignoring the "just happen to be there" makes no difference to validity of scientific laws. However I believe it makes a big difference to our ability to act into the future. It does mean that the human, that means everything that makes us human, needs to be accounted for in science. For this reason I tend to agree with the OP in that in order to understand things such as mathematics origin we need to take a closer look at the inventor thereof, the human.

if the univesre was not acting in a similar fashion at different places in space and time, then the scientific method would not have the power that it does.
And calculators would not give the samer answers.

Yes, the language we use to describe "the Given" happens to describe "the Given" very well. This is obviously no accident as it has taken humans years, much thought and much experimentation to come up with the language which describes "the given" so accurately and universally.


All my arguments are post fact and ad hoc. I can easily imagine thought spaces where the universe does not behave consistently. I do not assume it prior to the facts. Yes, the scientific method helps control the imagination.
However it does not mean that imagination is inaccurate merely exciting.
Exciting enough to describe the universe as acting and behaving with powerful scientific laws :eek: