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Old 04-03-2004, 06:00 PM
erislover erislover is offline
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The Role of Mathematics in Human Life; What Is Math?

It can hardly be said without understatement: math is a part of almost every human activity directly or indirectly. It is apocryphally said that every human (or even dog) "does" calculus when it catches a ball thrown at it... Really, I think that is (possibly) overstated, but surely we do a lot of math and mathematical approximation in our everyday life. A short list:
  • Estimating time to drive to various locations, near and (especially) far
  • Balancing or roughly balancing the amount of money in our accounts
  • Estimating the time it takes to pay off debts
  • Deciding what size bookshelf, or how many bookshelves of a particular size, to purchase
  • Counting calories
  • Determining what errors are acceptable
Really, the list seems endless. What strikes me about these things is not that they can be represented mathematically (as catching a ball) but that they are a direct and immediate application of mathematics and mathematical thought.

Let's return to the ball-catching or ball-throwing example, because it is slightly more complicated than simple arithmetic and, I think, illustrates important points. There are three ways to look at the situation. One is that we have inductively "got a feel" for where a ball will land given its apparent speed and angle, and we can explain a ball's motion given certain assumptions with math. Another is that we inductively "got a feel" for the math behind the motion itself, and have managed to formalize this motion with what is normally understood as math (that is, symbolic manipulation). Finally, the third possibility that I see is that we are actually doing the math (insert vague behaviorist "in some way" here as desired).

Mankind's philosophical relationship with math has been very peculiar over the years. We've come, at various times, to try and discern what math means in a subjective and objective sense, and some have discerned a complicated game (formalists) while others a near-divine intuition (platonists). Still others have attempted to divine other isms to encapsulate the mathematical experience.

I think they have fallen short. I think the most suitable way to approach mathematics is as a language in a Wittgensteinian sense: an activity, a way-of-doing. This activity has no natural or artificial boundries. Any attempt to define mathematics qua mathematics or mathematics as an activity will result in the unfortunate circumstance of excluding obviously mathematical behavior. If we adopt Hilbert's formalism, for example, balancing a checkbook and trusting that balance is a mystery. If we adopt mathematical platonism, we can be forced into a holier-than-thou stance where some of us have special access to an eternal realm, and balancing a checkbook properly is still a mystery.

Instead let us pursue mathematics as the grammar of certainty. Logic, set theory, number theory, algebra, the calculus, analytic geometry, ideal geometry: these, to us, are the language of certainty. To the extent that our activities or interests lie in certainty, our activities will tend towards mathematics. To the extent that I am certain of something, I can use mathematical speech or writing to show that certainty. A argument used as a tool for transferring certainty or knowledge has a symbolic form just as any word, sentence, or (public) thought. To the extent that my certainty can be shared, it is mathematical. (Contrast: "To the extent that I only feel certain, it cannot be shared.")

I do mean to partially dismiss the symbology of mathematics inasmuch as English does not demand a symbology, but I do not mean to dismiss the symbology in that it is somehow distinct or seperate or useless in general. Where homophones fail, symbology succeeds; and where the mind fails to grasp large propositions holistically, symbology aids in that task. But it is important to remember that English is not as it is written, and math is not as it is done on paper.

We, as humans, do math all the time, but we have not all learned to speak math. Those who have not developed the ability to do math as an activity of symbolic manipulation are no less mathematical than the fact that I can't speak French implies a failing on my part to speak a conversational language.

As with any language, the ability to master it (and I don't mean "get a PhD"!) opens doors, enables pursuits, and increases one's ability to assemble relationships and analogies. But also as with any language, its mastery comes from expediency or desire than a tabula rasa simply being written on.

Math per se is not a thing, nor is it strictly a tool for abstraction, a kind of representation. It is a language, and we learn it in the way we have found a need or desire to in our own daily pursuits. As a language, the meaning of math is in its use. For what does the symbol "this" mean? Well, we use it thusly. What does "x2 + y2 = 1" mean? Well, in these cases... and in these... and we treat it so.

The test for mastery of mathematics is the same as the test of mastery of a language: its use. We use this symbol as such, and those who use it otherwise are not violating reality but convention.

Mathematics, then, is not a part of, a result of, indicative of, or an ontology. The use of mathematics in science, for example, does nothing other than encode our certainty. Electrons aren't points, even if our mathematical theories of electrons never ever say otherwise, anymore than I am literally solving a calculus problem when I catch a ball. We encapsulate the non-psychological rules of certainty with mathematics. We are sure electrons behave this way, and I don't mean "we have a feeling of certainty"; I mean we explain electrons mathematically in order to demonstrate and transfer our certainty of how electrons behave.

Mathematics, then, is not a tool. It is not a metaphor, because if it were it would have to be "a metaphor for what it is" which is absurd (as if a sex scene was a metaphor for sex). The attempt to strain "tool" to include mathematics creates a container so big that everything is a tool. (And then what use is the word? What is is supposed to distinguish?) Math is not simply something we use to solve problems, because to say so we'd again return to the person throwing or catching a ball and suggesting, quite contrary to events, that the person is "really" doing calculus. The calculus equation in question requires the accelleration due to gravity, and then we'd be forced to suggest that the person "really" knows that value even if they cannot answer the question "what is accelleration due to gravity?" And that would abuse the verb "to know" which implies the ability to demonstrate (contrast: "to believe", which makes no presumption of demonstration). So we can't say math is a tool, or we're still left holding the bag without explaining how people catch a ball.

No, the person catching a ball is "doing math" inasmuch as they have a behavioral certainty in their actions (again, not "a feeling of certainty"). "I knew the ball was going to be there." Note that here the person demonstrates their knowledge by catching a ball enough times to satisfy the questioner--it is not required that he pull out a piece of paper. Note again the similarity to language, as we learn a language (say, from our parents), the test of our vocabulary is in a word's use, not in our ability to scribble down a sentence and mark its position, its position's name, et cetera.

As an activity, its test of compency or mastery is the performing of the activity itself in any way which that activity is used. Catching a ball, balancing a checkbook, estimating travel time: these are math just as much as proving the limit of an infinite series.

This is a testament to math's generality. It is an abuse of the mathematical experience to suggest that people don't know math because they can't perform the symbolic manipulations, just as it is an abuse of the English experience to suggest that people don't know English because they are illiterate.

The boundry between natural language and mathematics is also not distinct, which is further evidence of my suggestion. For consider, where do we place the following proposition, "Twelve times twelve is one hundred forty-four." Is that a mathematical proposition, or an English proposition? Can we try and back away from the abiguity and suggest, "It is is a mathematical proposition in English"? But how did the certainty of math arrive in English if they do not have, as it were, a link? Is it merely a convenience that we have words in English for mathematical propositions? To me the answer is obviously no. Language as a behavior is not mere representation, or a tool, or an isomorphism of some kind. Mathematics is in various languages because it is a language and translation is possible, build on the bedrock of human activity.

Above, I noted, "Logic, set theory, number theory, algebra, the calculus, analytic geometry, ideal geometry: these, to us, are the language of certainty." Now we see why the question, "Certain of what?" can lead us down strange ontological paths like formalism and platonism: the question is somewhat improper, and the answer is simply, "Certain of whatever we're doing." It also shows why math itself is so certain, because any attempt to determine its certainty is circular. Math is certain because certainty (as a public phenomenon) is characterized by math (as an activity).

To those of you who have a position on "what math is", has my exposition made you rethink your stance? Do you agree with it? Disagree? Why?
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  #2  
Old 04-03-2004, 06:16 PM
Zagadka Zagadka is offline
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Quote:
Originally Posted by erislover
To those of you who have a position on "what math is", has my exposition made you rethink your stance? Do you agree with it? Disagree? Why?
Nope. Math is the same thing to me. Confusing and (thus) boring. 179-245 are the pages of a book to read, not whatever number it is. ;-)

On a more serious note, that was a rather epic post on maths. I would certainly define maths as a language in its own right. (Don't ask me why I always write it maths, I've been around Brits too long) On the other hand, just like you don't need to have a language to be able to think, I do not think that you need to understand math to, as you put it, "perform math" (in the case of the flying ball) - math is a language in that it allows expression of an idea (albeit, very specific ideas).

I would find a psychological study of this fascinating. A person who has no knowledge of maths or language being able to do basic calculations - I don't think that you need to know 1+1 = 2 to know that 2 apples are better than one, for instance.

I don't know what I'm getting at, and I'm nervous around numbers. Don't poke me with a + sign please.
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Old 04-03-2004, 06:23 PM
UselessGit UselessGit is offline
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Now that is a spectacular OP... hurrah for math!

Continue...
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  #4  
Old 04-03-2004, 06:31 PM
II Gyan II II Gyan II is offline
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erislover, have you read this?
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Old 04-03-2004, 06:36 PM
erislover erislover is offline
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I have not, II Gyan II. Sounds interesting.
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Old 04-03-2004, 06:51 PM
waterj2 waterj2 is offline
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Why was I so not surprised to see erislover's name under this particular thread title?

Actually, I was thinking along these lines just the other day, but, alas, came to no interesting conclusions.
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Old 04-03-2004, 06:57 PM
Milum Milum is offline
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II Gyan II : erislover, have you read this?
(Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being
by George Lakoff, Rafael E. Nunez, Rafael Nuñez)

erislover: I have not, II Gyan II. Sounds interesting.
If you have II Gyan II, please share your opinion.
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Old 04-03-2004, 07:09 PM
II Gyan II II Gyan II is offline
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Originally Posted by Milum
If you have II Gyan II, please share your opinion.
Well, I checked it out from my uni library alongwith other books, managed to read only the preface and half of chap 1 before I had to return it. I've reserved it again, so I'll let you know at the end of next week. But from what I did read, they indicate that math isn't transcendental or "objective", just our conception of the world. But I'll let you know after I'm done.
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Old 04-03-2004, 07:25 PM
II Gyan II II Gyan II is offline
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Quote:
Originally Posted by erislover
This is a testament to math's generality. It is an abuse of the mathematical experience to suggest that people don't know math because they can't perform the symbolic manipulations, just as it is an abuse of the English experience to suggest that people don't know English because they are illiterate.
I disagree with this part. You say math is the language of certainty and symbols and their manipulation is encoding that certainty. Surely someone capable of working with certainty can master the representations that correlate to it. To take your English example, someone who's illiterate, will most certainly, not know a great deal of vocabulary beyond the daily usage set of say, 1,000 words. They can't open a dictionary and they can't read philosophy (or Ulysses). What it comes down to is what does it mean to know something? Math and English are both vast and branched systems. A person doesn't have to know abstract algebra to be said to "know math". If you define what does knowing math mean, your statement can be better evaluated.
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Old 04-03-2004, 08:49 PM
The Tim The Tim is offline
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I agree with the OP - math is very language like and not some entity that exists beyond physical reality dictating it. I think that it doesn't fit the mold of spoken languagess, but that isn't what the OP requires of it.

My only issue with what was said is that you don't do calculus to catch balls or move. The physical stuff that enacts the motions does a lot of input/output mapping that can be described by calculus but there is no mental calculus being done. Not even at a subconscious level. If you want to claim it is math then even nonsentient things do math in this way, and I don't think that that was the intent of the OP.
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Old 04-04-2004, 12:01 AM
John Mace John Mace is online now
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Quote:
From the OP:

As an activity, its test of compency or mastery is the performing of the activity itself in any way which that activity is used. Catching a ball, balancing a checkbook, estimating travel time: these are math just as much as proving the limit of an infinite series.
A tad on the long winded side, and I'm not sure I even understand what the debate is, but the above statement I find confusing. Dogs are really good at catching balls. Are you suggesting that dogs are doing math when they catch a ball? If so, I would disagree.
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Old 04-04-2004, 12:37 AM
agiantdwarf agiantdwarf is offline
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The OP is a bit over my head, but I'll take a shot at it.

I disagree with what I think is the thesis of the post: math is the grammar of certainty.

I always thought that in modern math, you start out with a set of axioms, and as long as you can't derive a contradiction from them, it is as valid as Peano Arithmetic or Euclidian geometry.

Therefore, math doesn't even have to be certain. It can totally contradict reality.
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Old 04-04-2004, 12:42 AM
erislover erislover is offline
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Quote:
Originally Posted by II Gyan II
Surely someone capable of working with certainty can master the representations that correlate to it.
Well, I believe it is possible, yes, if they have some kind of reason to. But most manage fine without it.
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To take your English example, someone who's illiterate, will most certainly, not know a great deal of vocabulary beyond the daily usage set of say, 1,000 words.
What makes you say that? Do you think we only had around one thousand words before we developed writing? Do you think ~1000 words is sufficient for getting along? In The Language Instinct, Stephen Pinker suggests that the average high school student knows more words than was used in all of Shakespeare's plays. Do you suppose this is only because they are literate? Certainly literacy increases a vocabulary... but is that to suggest that literacy of some words came before the words themselves? That would be strange.
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What it comes down to is what does it mean to know something?
For me, knowledge implies the ability to demonstrate whatever it is one knows in whatever way such things are (conventially) demonstrated.
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If you define what does knowing math mean, your statement can be better evaluated.
But the point is that such a thing cannot strictly be said. We can set certain boundries, but they will not be definitive. We can suggest math is simply the formalistic activity the educational system brings us up to think, yet this defies all the practical application of math. Is only discrete mathematics real because we humans have finite limitations? But then what are we doing when we show that there are an infinite number of prime numbers? Knowing anything includes an ability to demonstrate one's knowledge, through example or application, as the case may be. The engineer might build a model to show his grasp of the formulae, the grad student might elaborate on the consequences of a proof, the statistician must conduct proper polls and assert correlation at the proper times within certain bounds... yet these are all mathematical behaviors. Mathematics bleeds out from the core platonic ideal to the hopelessly mundane: figuring out if I brought enough cash to the grocery store so I don't attempt to purchase more than I can afford.
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Originally Posted by The Tim
My only issue with what was said is that you don't do calculus to catch balls or move. The physical stuff that enacts the motions does a lot of input/output mapping that can be described by calculus but there is no mental calculus being done. Not even at a subconscious level.
Precisely! I did not mean to suggest otherwise. Calculus is an activity dealing with equations, and how the whole changes with respect to the components. It is traditionally done on pencil and paper. We can use calculus to describe ballistic paths... like a thrown ball about to be caught. It is a testament to our own certainty in such activites. Yet though I know where the ball will land so I may catch it, I am not doing calculus. But my certainty is no less real because of that. Calculus is an artifact of certainty, it is a particular kind of certainty. We use the calculus to assure ourselves or others of things. It would not be surprising, for example, to play a game of catch than have someone suggest, "You know that we can predict where the ball will land? See here, I have this equation which demonstrates its path..." But why isn't it surprising that we can make such an equation? Because we are already certain of such things. That we may encode our certainty in such propositions is no more surprising than that the certainty was already there and demonstratable in another way. And since most humans are already convinced of the ballistics of thrown balls, there is no need for most of us to understand the other way we might suggest such a certainty (which is the activity of calculus).

But if we, as two students of math (hypothetically), are aware of this other certainty, can't we use it to demonstrate the path of other objects, like missles which travel farther than we can play catch?
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I think that it doesn't fit the mold of spoken languagess, but that isn't what the OP requires of it.
Well, spoken language doesn't fit spoken language. A great part of communication is nonverbal. But mathematics is highly verbal and linguistic in nature. It can encode information, represent concepts, demonstrate relationships... it is very grammatical, with a rigid syntax (which must be the case if it is to be the language of certainty). At its broadest, math is how we explain our certainty, what is reasonable, what qualifies as such and why. This is not purely verbal, but it does certainly have verbal components. (Such as the English sentence I gave as an example, was it a mathematical proposition or an English one?)
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Originally Posted by John Mace
Dogs are really good at catching balls. Are you suggesting that dogs are doing math when they catch a ball? If so, I would disagree.
I cannot strictly agree or disagree that dogs are doing math when they catch a ball. We do not usually suggest that animals have such a thing as certainty, or that they anticipate specific events, and so on. But I do not mean to say they do not, either. I am pretty uninterested in canine intelligence. While they might respond somewhat similarly to humans, the hallmark of math as a human activity (for me) is knowing where a ball is going to be. While the dog surely seems to know it, if dogs can be said to know anything, it is not open to questioning like a human so the sorts of claims we can make about it are far more speculative.
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Old 04-04-2004, 12:49 AM
erislover erislover is offline
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Originally Posted by agiantdwarf
Therefore, math doesn't even have to be certain. It can totally contradict reality.
I don't believe that's the kind of certainty most would be familiar with. We can depend on the results of formal mathematics whether or not we find any particular application for them. The testament of math's certainty is not its correlation to reality. That's why I reject the notion that math is just something that represents: it doesn't have to represent anything. Just like a perfectly grammatical English sentence doesn't have to mean anything: "The ice was boiling hot." There is no application for this sentence, and it contradicts reality, but is it not English because of that? We find a need, and address that need through the application of various behaviors. Once those behaviors are established, they can find themselves applied in other circumstances. Language is often used for reporting (states, events, feelings, cautions, etc) but we wouldn't suggest that non-reporting statements aren't a part of language (like a work of fiction, which may also totally contradict reality).
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Old 04-04-2004, 12:55 AM
agiantdwarf agiantdwarf is offline
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Quote:
Originally Posted by erislover
I don't believe that's the kind of certainty most would be familiar with. We can depend on the results of formal mathematics whether or not we find any particular application for them.
Well, what do you mean by "certain"? I thought you meant that if we prove something through mathematics, regardless of the initial assumptions/axioms, it corresponds with reality. This is simply not true.

Quote:
The testament of math's certainty is not its correlation to reality. That's why I reject the notion that math is just something that represents: it doesn't have to represent anything. Just like a perfectly grammatical English sentence doesn't have to mean anything: "The ice was boiling hot." There is no application for this sentence, and it contradicts reality, but is it not English because of that? We find a need, and address that need through the application of various behaviors. Once those behaviors are established, they can find themselves applied in other circumstances. Language is often used for reporting (states, events, feelings, cautions, etc) but we wouldn't suggest that non-reporting statements aren't a part of language (like a work of fiction, which may also totally contradict reality).
I totally agree. I wish your other posts would have been as clear as that.
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Old 04-04-2004, 01:09 AM
erislover erislover is offline
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Originally Posted by agiantdwarf
Well, what do you mean by "certain"? I thought you meant that if we prove something through mathematics, regardless of the initial assumptions/axioms, it corresponds with reality. This is simply not true.
That's what I tried to cover near the end of the OP. What we mean by certain is that it is mathematical. We are satisfied that the point is made because of limited induction (he's performed the behavior ten or twenty times without my assistance), because of its structure (it follows a logical argument), because of its relationship to pencil and paper math (applying a formula in certain new circumstances). The hallmark of certainty is math: math, in a very broad sense, characterizes certainty. It is larger than pencil and paper tricks, even though we can (and often do) use pen and paper tricks to explain why we can be so certain. Check my response to The Tim above, I think I was very clear there.
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I totally agree. I wish your other posts would have been as clear as that.
Well, it is a big subject and I tried to cover several different views. Not all of the post would apply to every person, you know what I mean?
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Old 04-04-2004, 01:16 AM
erislover erislover is offline
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agiantdwarf, let me add to a portion of my response to The Tim. I said, "It would not be surprising, for example, to play a game of catch than have someone suggest, "You know that we can predict where the ball will land? See here, I have this equation which demonstrates its path..." But why isn't it surprising that we can make such an equation? Because we are already certain of such things. That we may encode our certainty in such propositions is no more surprising than that the certainty was already there and demonstratable in another way. And since most humans are already convinced of the ballistics of thrown balls, there is no need for most of us to understand the other way we might suggest such a certainty (which is the activity of calculus)." But you see, in this case math is the language of certainty. It is the form, the grammar of it. To express to you that I know how a ball will travel through the air, I may express it with pencil and paper mathematics, or I may demonstrate it behaviorally (i.e.-by catching the ball). I hope that made it more clear!
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Old 04-04-2004, 01:41 AM
agiantdwarf agiantdwarf is offline
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Of course, there is no way to determine the truthfulness of anything in mathematics, since you always have to assume something. However, defining math by circular logic (math -> anything certain, certainty -> anything mathematical) isn't quite useful. It tells us nothing about the essential question in this thread: "What is math?"

Maybe I'm still misunderstanding you?
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Old 04-04-2004, 01:55 AM
erislover erislover is offline
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Quote:
Originally Posted by agiantdwarf
Of course, there is no way to determine the truthfulness of anything in mathematics, since you always have to assume something. However, defining math by circular logic (math -> anything certain, certainty -> anything mathematical) isn't quite useful.
Certainty is characterized by math, the second part of your parenthetical. If we were to ask the question, "Is math certain?" then we'd run the circle. Which is why math is always certain. As my sig notes, "If a blind man were to ask me 'Have you got two hands?' I should not make sure by looking. If I were to have any doubt of it, then I don't know why I should trust my eyes." How do we get to be certain about math, say, pencil and paper math? I mean to say, how would I go about introducing doubt in your mind about the mathematical statement 1+1=2?
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It tells us nothing about the essential question in this thread: "What is math?"
The grammar of certainty!
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Old 04-04-2004, 04:32 AM
Aeschines Aeschines is offline
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Not in agreement....

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Originally Posted by erislover
A short list:
  • Estimating time to drive to various locations, near and (especially) far
  • ...
  • Determining what errors are acceptable
Really, the list seems endless. What strikes me about these things is not that they can be represented mathematically (as catching a ball) but that they are a direct and immediate application of mathematics and mathematical thought.
I think we need to distinguish between 1) Mathematics as consciously understood; 2) neurological functions that can be seen as a response to properties that are governed by the rules of number (e.g., seeing which object is farther without actually measuring); 3) and combinations of the first two.
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Let's return to the ball-catching or ball-throwing example, because it is slightly more complicated than simple arithmetic and, I think, illustrates important points. There are three ways to look at the situation. One is that we have inductively "got a feel" for where a ball will land given its apparent speed and angle, and we can explain a ball's motion given certain assumptions with math.
Yes, we've got a feel. It's neurological. So does a dog, as another poster pointed out. This is not related to a conscious understanding of mathematical principles.
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Another is that we inductively "got a feel" for the math behind the motion itself, and have managed to formalize this motion with what is normally understood as math (that is, symbolic manipulation).
No way. It's pure neurology combined with trial and error that let's us accomplish the task.
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Finally, the third possibility that I see is that we are actually doing the math (insert vague behaviorist "in some way" here as desired).
I find these three possibilities not to be distinguished very well; I really can't see the difference between one and two.
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If we adopt Hilbert's formalism, for example, balancing a checkbook and trusting that balance is a mystery. If we adopt mathematical platonism, we can be forced into a holier-than-thou stance where some of us have special access to an eternal realm, and balancing a checkbook properly is still a mystery.
You are describing the "problem" with either approach in emotional, pejorative terms and have not successfully argued against either.
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Instead let us pursue mathematics as the grammar of certainty. Logic, set theory, number theory, algebra, the calculus, analytic geometry, ideal geometry: these, to us, are the language of certainty. To the extent that our activities or interests lie in certainty, our activities will tend towards mathematics.
This is not making sense. Mathematics is, at base, the incontrovertible rules of pattern, a subset of which is the rules of number. It is true that our understanding of these principles is certain, since they are provable. Yet we may be certain of other things that are not provable: I am certain just looked to the left now, but I can't prove it, etc.
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To the extent that I am certain of something, I can use mathematical speech or writing to show that certainty.
Backwards. If I use the rules of mathematics and I have done my calculations correctly, I can be certain that the result is true. Certainty is not something that is; it arises for a reason (memory, calculation, etc.). Also, "certainty" (a mental state) needs to be distinguished from "certainty" mean "true."
Quote:
A argument used as a tool for transferring certainty or knowledge has a symbolic form just as any word, sentence, or (public) thought. To the extent that my certainty can be shared, it is mathematical. (Contrast: "To the extent that I only feel certain, it cannot be shared.")
This has quickly become a semantic hash. I don't know what you mean by "share"--I can "share" my certainty about having looked to the left simply by telling you so. Perhaps you mean "compel" someone to share that mental state of certainty. We would then be getting into some heavy-duty epistomology....
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The test for mastery of mathematics is the same as the test of mastery of a language: its use. We use this symbol as such, and those who use it otherwise are not violating reality but convention.
Wrong. If someone tells me that pi = 3.15 even, that person is flat-out wrong.
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The use of mathematics in science, for example, does nothing other than encode our certainty.
No. Reality itself must obey the rules of pattern, which is what mathematical symbols encode.
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Electrons aren't points, even if our mathematical theories of electrons never ever say otherwise, anymore than I am literally solving a calculus problem when I catch a ball. We encapsulate the non-psychological rules of certainty with mathematics. We are sure electrons behave this way, and I don't mean "we have a feeling of certainty"; I mean we explain electrons mathematically in order to demonstrate and transfer our certainty of how electrons behave.
No. We have a mathematical model for how electrons behave. We do not have, at first, a vague certainty about electrons that we must encode. Also, our mathematical model of how electrons behave bears no resemblance whatsoever to our neurological ability to catch a ball.
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No, the person catching a ball is "doing math" inasmuch as they have a behavioral certainty in their actions (again, not "a feeling of certainty"). "I knew the ball was going to be there." Note that here the person demonstrates their knowledge by catching a ball enough times to satisfy the questioner--it is not required that he pull out a piece of paper.
Neurological ability. If I put a 20 kg weight in your right hand and a 10 kg weight (that is the same size and shape) in your left hand, you and most people will be able to tell me which is heavier. Because all of Reality is based upon the principles of pattern and number, it's no coincidence that your neurons are able to calculate correctly which is heavier (that is, it's no coincidence that they are right). But there is no "understanding" of number implied in perceiving which is heavier, just as the sun does not need to calculate how much to gravitate the planets.
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This is a testament to math's generality. It is an abuse of the mathematical experience to suggest that people don't know math because they can't perform the symbolic manipulations, just as it is an abuse of the English experience to suggest that people don't know English because they are illiterate.
Bad example. Mathematical symbols are, as you said, a kind of language. Those who don't know how to use those symbols may still be able to count verbally or on their fingers and use mathematical language to some extent. But if they know nothing, then, yes, indeed they don't know mathematics. The neurological abilities remain, of course.
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To those of you who have a position on "what math is", has my exposition made you rethink your stance? Do you agree with it? Disagree? Why?
I'm afraid the exposition didn't make much sense. I'm essentially a Platonist and have yet to understand what is wrong with my stance.
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  #21  
Old 04-04-2004, 11:02 AM
John Mace John Mace is online now
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Originally Posted by erislover
I cannot strictly agree or disagree that dogs are doing math when they catch a ball. We do not usually suggest that animals have such a thing as certainty, or that they anticipate specific events, and so on. But I do not mean to say they do not, either. I am pretty uninterested in canine intelligence. While they might respond somewhat similarly to humans, the hallmark of math as a human activity (for me) is knowing where a ball is going to be. While the dog surely seems to know it, if dogs can be said to know anything, it is not open to questioning like a human so the sorts of claims we can make about it are far more speculative.
It's unclear to me how central this is to your thesis, but I think you need to consider whether a human is really doing anything different than a dog when the human catches a ball. I'd say that, lacking clear evidence otherwise, one must assume that the human is not doing anything special.
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  #22  
Old 04-04-2004, 12:36 PM
erislover erislover is offline
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Originally Posted by Aeschines
I think we need to distinguish between 1) Mathematics as consciously understood; 2) neurological functions that can be seen as a response to properties that are governed by the rules of number (e.g., seeing which object is farther without actually measuring); 3) and combinations of the first two.
Governed by the rules of number? Well that's taking a pretty strict view of reality, isn't it? How do you suppose we would come to find that something is "governed by the rules of number"? Would we have to know math first? But that would be strange...
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[Knowing where a ball will be] is not related to a conscious understanding of mathematical principles.
Why? Because the ball isn't "governed by rules of number" or because the person doesn't know enough symbolic math to express it on paper?
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No way. It's pure neurology combined with trial and error that let's us accomplish the task.
Trial and error, yes, my use of "induction" indicated this process. The point is: when do we know we've succeeded? Are we setting roughly logical constraints on ourselves? "Hmm, every time I touch this, I get burned. He's like me; if he touched this, he'd get burned, too." Is this person developing a neural response, or is he doing logic, thinking logically, even if no one has ever explained implication, identity, and various logical deduction tools to him so that he may satisfy himself of the modus ponens? Why would you think the two are necessarily distinct?
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I find these three possibilities not to be distinguished very well; I really can't see the difference between one and two.
The last is, there is an isomorphism between neural functions and mathematical rules as done formally.
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You are describing the "problem" with either approach in emotional, pejorative terms and have not successfully argued against either.
Trusting math is not "emotional". Again: how did we come to suggest there are rules of number?
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This is not making sense. Mathematics is, at base, the incontrovertible rules of pattern, a subset of which is the rules of number.
A pattern? A pattern of what? Of thrown balls governed by gravity? Of objects dropped from tall buildings? Of the relationship between cause and effect?
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It is true that our understanding of these principles is certain, since they are provable. Yet we may be certain of other things that are not provable: I am certain just looked to the left now, but I can't prove it, etc.
I am asking you to distinguish public certainty, i.e.-knowledge, that is, what we can demonstrate to others' satisfaction, from a feeling of certainty which can by definition only assure the person who feels it.
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Backwards. If I use the rules of mathematics and I have done my calculations correctly, I can be certain that the result is true. Certainty is not something that is; it arises for a reason (memory, calculation, etc.). Also, "certainty" (a mental state) needs to be distinguished from "certainty" mean "true."
Yes! Exactly.
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This has quickly become a semantic hash. I don't know what you mean by "share"--I can "share" my certainty about having looked to the left simply by telling you so.
Yes, that is one kind of sharing. But sharing knowledge means exhibiting public behavior in such a way that someone else will come to know what you know. This is a subset of all sharing (ie public) behavior.
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Perhaps you mean "compel" someone to share that mental state of certainty.
No one is compelled to be certain of something. They may reject all conventions. Intuitionists, for example, aren't certain of any result derived from the law of the excluded middle. My personal satisfaction with that rule does not compell them in any way.
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Wrong. If someone tells me that pi = 3.15 even, that person is flat-out wrong.
Heh! They are, aren't they? Because the proposition about pi is a mathematical one. It must be certain, if anything is to be certain, because math is how we express certainty.
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No. We have a mathematical model for how electrons behave. We do not have, at first, a vague certainty about electrons that we must encode.
Then where did the model come from?
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Also, our mathematical model of how electrons behave bears no resemblance whatsoever to our neurological ability to catch a ball.
Sure, and my typing English has nothing to do with my neurological activities, either.
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Neurological ability. If I put a 20 kg weight in your right hand and a 10 kg weight (that is the same size and shape) in your left hand, you and most people will be able to tell me which is heavier. Because all of Reality is based upon the principles of pattern and number, it's no coincidence that your neurons are able to calculate correctly which is heavier (that is, it's no coincidence that they are right).
All reality, except my neurons? Oh, wait, I see, it is no coincidence that my neurons can "calculate" correctly. Interesting that you seem to be agreeing with me here, though I would not use those words.
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But there is no "understanding" of number implied in perceiving which is heavier, just as the sun does not need to calculate how much to gravitate the planets.
How we test for understanding of number is different than how we test for understanding of heavier. Yet the inductive or deductive processed used is logical ie mathematical in nature. When we begin to speak that language, the language which tells us such things are sure, we are able to express more and investigate more.
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  #23  
Old 04-04-2004, 12:42 PM
erislover erislover is offline
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Originally Posted by John Mace
...but I think you need to consider whether a human is really doing anything different than a dog when the human catches a ball.
And I'm saying: I think you need to consider whether a human is "really" doing anything different when tracking the path of a ball than describing its path on paper with formulae. Why does that work? Why are we sure of it? What are the limits, and why are we sure of those? How do we express this certainty so that others may share it?
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I'd say that, lacking clear evidence otherwise, one must assume that the human is not doing anything special.
Clear evidence like the whole of mathematical investigation, ballistic missles, or trebuchets? Or did you mean something else?
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  #24  
Old 04-04-2004, 01:13 PM
erislover erislover is offline
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I think I see a way to make myself at least marginally more clear. For the example that keeps coming up, a thrown ball. I get the feeling that my objectors are picturing me suggesting that the person is actually "somehow" doing calculus or algebra in his head, when that implies a certain psysiological activity. I do not mean to imply that at all. In fact the last I heard, animals catch things like balls by following, apparently, a very simple routine that seeks to keep certain distances the same (like where the ball is in one's field of vision). That's all very interesting scientifically, but that is really not where I'm going. I'm saying, as a person, I know where the ball will land. One way to demonstrate that certainty is to catch a ball thrown at various angles and speeds to someone's satisfaction--and what satisfies this other person is logical in nature. Another is to plot the course of the ball as with analytic geometry, work backwards from accelleration to a position plot with integral calculus, record a bunch of data and find a function that best fits it, etc. In either case, the person is satisfying mathematical interests, one on a broadly logical matter, another on a narrowly symbolic matter. Thermostats and dogs, as a rule, do not try to convince me of anything, as far as I can tell.
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Old 04-04-2004, 01:21 PM
Cabbage Cabbage is offline
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I've admittedly only skimmed this thread, and I don't really intend to enter the debate, but I do have a couple of things that I thought could be added. In all honesty, I don't know that they're particularly relevant to the debate (in the sense that anyone's arguments will hinge one way or the other based on this), but I definitely think they are of general interest.

The first is the article Do Dogs Know Calculus?, by Timothy Pennings. To summarize, I'm sure anyone who has taken calculus at one time has seen the following problem: You're on one side of a river, and you need to get to a point on the other side (not neccesarily the point directly opposite). You can run on land at some given speed, and you can swim at some given (slower) speed. If you run along the bank of the river, then jump in and swim directly to the intended point, at what point should you jump in the river, in order to minimize the time taken? Well, this guy Pennings performed an (informal) experiment of throwing a ball into Lake Michigan, to have his dog fetch it. The point(s) at which the dog jumped in the lake were remarkably close to the "optimal" point!

The other is something I read some time ago (sorry, no cite, this was 10 or 15 years ago, and I don't remember what the source was). The article stated that ball players (and presumably people and dogs in general), catch fly balls by chasing it in such a manner so that the ball (in flight) appears (to them) to travel in a straight line.
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  #26  
Old 04-04-2004, 01:28 PM
Kimstu Kimstu is offline
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erl: Are we setting roughly logical constraints on ourselves? "Hmm, every time I touch this, I get burned. He's like me; if he touched this, he'd get burned, too." Is this person developing a neural response, or is he doing logic, thinking logically [...]

Well, consciously verbalizing your reasoning as informally logical propositions isn't quite the same thing as unconsciously following neural signals that help you catch a ball.

Sure, you could make the same sort of logical chain for ball-catching, along the lines of "Hmm, when it goes up higher it takes longer to come down, when the upward curve is steeper it doesn't go as far as when the curve is shallower", etc. etc. That still wouldn't be calculus, as you note, but it would indeed be conscious logical reasoning. But you don't need even that much conscious reasoning to successfully catch a ball, and neither does a dog.
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  #27  
Old 04-04-2004, 01:39 PM
II Gyan II II Gyan II is offline
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Originally Posted by erislover
Well, I believe it is possible, yes, if they have some kind of reason to. But most manage fine without it.
You're saying that ability to correlate symbolic manipulation to neurological certainty is indicative of choice. I'm saying it's indicative of ability.

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What makes you say that? Do you think we only had around one thousand words before we developed writing? Do you think ~1000 words is sufficient for getting along?
Depends on the culture. Before agriculture, I would say, easily. Today, around 5-7,000. How many times have you heard eudaemonia or catapedaphobia?
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  #28  
Old 04-04-2004, 01:40 PM
erislover erislover is offline
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Originally Posted by Kimstu
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Originally Posted by erislover
Are we setting roughly logical constraints on ourselves? "Hmm, every time I touch this, I get burned. He's like me; if he touched this, he'd get burned, too." Is this person developing a neural response, or is he doing logic, thinking logically [...]
Well, consciously verbalizing your reasoning as informally logical propositions isn't quite the same thing as unconsciously following neural signals that help you catch a ball.
Yes, this is very good! This is an observation I think is critical. But now I want to suggest: yet I can become conscious of my ability to catch a ball. How do I satisfy myself and others of this ability, consciously? "Trial and error" is an inductive test, failing to "match" mathematical induction because it is impossible for us to enumerate the entire set of thrown balls (something else we intuitively knew but came to formalize in various ways). "Doing math" is meant to imply "of or being certain in a public way", that is, a way which could transfer certainty. Symbolic math, done on paper, is the tip of the iceburg, and we got to do symbolic math by investigating our own certainties.
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But you don't need even that much conscious reasoning to successfully catch a ball, and neither does a dog.
You are absolutely right. Mathematics, as a field of interest, has taken on a life of its own, much as has linguistics, or history, or natural investigations (ie science). Yet we cannot break math away from its source, what caused us to create the symbology, why we find it so important (and so sure), without losing the essence of math itself as a language of certainty.
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  #29  
Old 04-04-2004, 01:47 PM
erislover erislover is offline
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Originally Posted by II Gyan II
You're saying that ability to correlate symbolic manipulation to neurological certainty is indicative of choice. I'm saying it's indicative of ability.
I'm saying that the recognition that I have that ability, and how I demonstrate to others that I have that ability, is mathematical in nature.
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Depends on the culture. Before agriculture, I would say, easily.
I do not see any reason to accept this at face value, largely because the written word, which did serve to increase vocabulary, came from the spoken word, which was logically and historically prior.
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How many times have you heard eudaemonia or catapedaphobia?
Why would that be a test of how many words one knows?
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  #30  
Old 04-04-2004, 01:54 PM
erislover erislover is offline
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And anyway. II Gyan II, I don't see whether it matters that hunter gatherers have a much smaller vocabulary than, say, a medieval knight or a twentieth century high school student. The point is that our investigations into life, and our ways of living, gave, imposed, or otherwise was correlated with our increase our vocabulary. Our investigation into farming, consciously directed or intrinsic ability based on contextual need, led us to words about agriculture. Our investigation into certainties led us to mathematics; i.e.-mathematics is the language of certainty. But language is also an activity, and so doing math is the the use or transfer of such certainty.
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  #31  
Old 04-04-2004, 02:03 PM
II Gyan II II Gyan II is offline
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Originally Posted by erislover
I do not see any reason to accept this at face value, largely because the written word, which did serve to increase vocabulary, came from the spoken word, which was logically and historically prior.
Because the written word codifies and preserves in memory the spoken words. If I give you 3000 words to orally remember, odds are, you will remember barely a fraction of them. You'll remember those which are most relevant in your daily activity. When you can sustain a precise recollection via writing, then you have the leisure and ability to pick up where you left off. Which allows greater and refined expansion, not feasible before.

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Why would that be a test of how many words one knows?
I'm not debating your particular ability to remember words, given that you are literate. Your original statement was "it is an abuse of the English experience to suggest that people don't know English because they are illiterate". Like I asked earlier, what it does mean to know something? If someone illiterate wanted to express the concept signified by eudaemonia, they would have to express it as best they could with existing vocabulary and hope that the receiver grasps the essence. Do they know English, in this case?
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  #32  
Old 04-04-2004, 02:07 PM
The Tim The Tim is offline
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I think I can explain what erislover is trying to get at. Math isn't a magic sky pixie. Math is a mode of expression of facts of the universe but it isn't a required fact of the universe anymore than English is. There is no secret reality of computation where the math is being done to create what we see.

What this means is that math is a language. My minor quibble is that it isn't a language like English, and I mistakingly used spoken language when I suppose social language would be closer to what I meant and not as loaded with regards to the debate. Math is a language that describes principles we hold to be required principles that we are certain of. Social languages are those that describe our social reality. I think that it is entirely possible that eventually math could develop to the point where it could be a social language as well. People could think in an endless stream of math about everything happening during their day. Math is not like that yet and I don't think that math is wired up in the brain in the same way that social languages are. I think it is wired with similar tricks and exploitations of existing structures that language uses but the structures in question differ.
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  #33  
Old 04-04-2004, 02:19 PM
II Gyan II II Gyan II is offline
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Originally Posted by The Tim
I think I can explain what erislover is trying to get at. Math isn't a magic sky pixie. Math is a mode of expression of facts of the universe but it isn't a required fact of the universe anymore than English is. There is no secret reality of computation where the math is being done to create what we see.
I somewhat agree with this. But I disagree that math is not necessary. The mind is not a tabula rasa, but it doesn't come inbuilt with the neurological correlate of the solutions of a quadratic equation. The symbological expression of math can induce new understanding. So, someone who isn't well versed with symbolic manipulation can possess deficiencies in the ultimate fact and thinking process.
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  #34  
Old 04-04-2004, 02:19 PM
erislover erislover is offline
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Originally Posted by II Gyan II
Because the written word codifies and preserves in memory the spoken words. If I give you 3000 words to orally remember, odds are, you will remember barely a fraction of them.
Right out like that, perhaps. It depends on the context: the meaning of a word is its use, not that it is presented in a list, whether spoken or written.
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Which allows greater and refined expansion, not feasible before.
Fine. Can we get to the point where this relates to my OP?
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Your original statement was "it is an abuse of the English experience to suggest that people don't know English because they are illiterate". Like I asked earlier, what it does mean to know something?
Like I answered earlier: an ability to demonstrate one's knowledge. If the test of "knowing English" to you is that someone can express the concept of eudaemonism, first you must explain just what that concept is; that is, you must teach it to them. Then they will attempt to show that they know the concept by pointing out instances, using it in a long sentence, deriving other things from the thought, etc, to the point where its use is best served as a word rather than a phrase or sentence, at which point etc. etc.... When do they "know" about eudaemonism? Doesn't it depend on who is asking, and when and why they're asking?
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If someone illiterate wanted to express the concept signified by eudaemonia, they would have to express it as best they could with existing vocabulary and hope that the receiver grasps the essence. Do they know English, in this case?
I would say so. The test of "knowing English" is not, for me, a vocabulary matter any more than the test of "thinking logically" is being able to construct any particular symbolic tautology. A greater vocabulary lends itself to a greater application of language. There is no special cut-off point where we say, "There! Now he knows." He meets the questioner's explicit or implicit (unconscious) conditions. The socialization of these conditions, and their application and character, results in a language, a way of doing, a way of living, thinking, speaking, and lastly: writing.

The Tim, very well said.
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Math is not like that yet and I don't think that math is wired up in the brain in the same way that social languages are.
No, I don't think so either, but that is a matter for natural science to investigate. Whether we are wired for it or not is outside the scope of this thread, at least as I intend it. I won't discourage such thought, though.
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  #35  
Old 04-04-2004, 02:22 PM
II Gyan II II Gyan II is offline
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Originally Posted by erislover
When do they "know" about eudaemonism?
I can't ever "know" if they know about eudaemonism. Just make a guess and be internally satisfied.
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  #36  
Old 04-04-2004, 02:26 PM
erislover erislover is offline
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Originally Posted by II Gyan II
I can't ever "know" if they know about eudaemonism. Just make a guess and be internally satisfied.
Well then no one "knows" anything and the word "know" is useless. I prefer to keep my words useful, if you don't mind.

They know when they can demonstrate it to me in a way that either would let me know, or would satisfy me that they know. This is the point I am attempting to drive home, not some strictly analytical binary-valued state of "knowing", but a social phenomenon involving the investigation, conscious or otherwise, of our knowledge and certainty.

If that does not encapsulate the word "know" for you, perhaps you could do me the favor of telling me what word or concept it does match for you so that we may continue.
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Old 04-04-2004, 02:38 PM
II Gyan II II Gyan II is offline
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Originally Posted by erislover
Well then no one "knows" anything and the word "know" is useless.
True for the first part and kinda true for the second part. At the very least, you have to know your memory and brain is functioning according to your assumption. But if it isn't, how would you "know"? . The solution is make an assumption and hold that as truth, i.e. axioms.


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They know when they can demonstrate it to me in a way that either would let me know, or would satisfy me that they know.
This is what I said earlier: Just make a guess and be internally satisfied.
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Old 04-04-2004, 02:50 PM
erislover erislover is offline
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Originally Posted by II Gyan II
True for the first part and kinda true for the second part. At the very least, you have to know your memory and brain is functioning according to your assumption. But if it isn't, how would you "know"?
Well I think this is an abuse of the word. Honestly. I distinguish the feeling of certainty, which satisfies me and me alone, from the phenomenon of certainty, which satisfies me and those in my environment, to some degree.
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This is what I said earlier: Just make a guess and be internally satisfied.
But I am not guessing someone knows. I say that they know; I attribute the ability to demonstrate mastery of the concept because I have just seen them demonstrate the mastery of a concept in such a way that those who were interested in such satisfaction would also be satisfied. I'm not guessing anything.
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  #39  
Old 04-04-2004, 02:54 PM
II Gyan II II Gyan II is offline
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I'm not guessing anything.
Unless you get in their heads and become them, how do you know?
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  #40  
Old 04-04-2004, 03:05 PM
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To quote my abstract algebra teacher, "This isn't math, this is religion."

...seriously, now, I think math is a simplified way of looking at the world. From the most basic counting numbers (1 = "one of something") to calculus (the ball problem) to the really abstract linear analysis business (the rules of math itself). The simpler the thing we're analyzing, the simpler the math, and the more complex, the more equations. And besides, there's also statistics, probability, and fuzzy logic, all of which are branches of math that deal with uncertainty.

A football player can throw a football without knowing that the spin stabilizes the fall flight; a physist can describe all the relevant equations, but not be able to throw worth beans. However, a pilot better know at least some aerodynamics if he wants to fly a plane, or he wouldn't know how to deal with all the variables involved. (Of course, nowadays computers are doing most of the number-crunching for us, but I digress.)
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  #41  
Old 04-04-2004, 03:54 PM
The Tim The Tim is offline
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About the literacy sub-thread that's appeared it is sort of missing a point about social languages - they exist in both formal and informal modes. Formal English is written English. Formal speaking sounds like it is written, or at least it does ideally. Illiterate individuals have only indirect access to formal language. They have a full grasp of the informal language and can describe the world adequately. To think otherwise is to be profoundly ignorant of linguistics. In many cultures with writing the formal language is written language. Writing allows for complicated sentences that would be nearly impossible to come up with on the fly. These are sentences that take full advantage of recursion because it is possible to look back over a written sentence or to read it slowly.

The formal language of languages without writing involves special vocabularly, structures and patterns that require specialized knowledge of the formal language. It is optimized to be done without notation and so doesn't produce longer utterances, merely denser ones that can only be decoded by those who have a grasp of the formal language.

I'd recommend Doing Our Own Thing by John H. McWhorter for an interesting take on this issue.

I'm sure somewhere in my post there is something that applies to the main point of the thread.
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  #42  
Old 04-04-2004, 04:16 PM
II Gyan II II Gyan II is offline
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Originally Posted by The Tim
They have a full grasp of the informal language and can describe the world adequately.
Define 'adequately'. Is the scope of 'the world' the same for both formal and informal language?
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  #43  
Old 04-04-2004, 05:12 PM
The Tim The Tim is offline
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I mean that they can describe everything that occurs to them in their daily lives, can refer to hypothetical situations and can come up with new expressions to describe new experiences. They will be no more at a loss for words than any other speaker of the language.

As for the scope of the world I would say that in most cases there is a strong correlation with those who have a wider range of intellectual experiences and those who have learned the formal level of their language. In this regard more esoteric experiences are likely to have more representation in the formal level than the informal level. It doesn't mean the informal language user cannot experience an equally wide intellectual world it just means they do not sound as educated when discussing them.
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  #44  
Old 04-04-2004, 06:16 PM
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Originally Posted by The Tim
I mean that they can describe everything that occurs to them in their daily lives, can refer to hypothetical situations and can come up with new expressions to describe new experiences. They will be no more at a loss for words than any other speaker of the language.
How would you go about verifying this?
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  #45  
Old 04-04-2004, 06:33 PM
The Tim The Tim is offline
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Linguists interested in language use in a natural setting get people to agree to carry around tape recorders on their person, most of these studies seem to have been done in Britain which seems to have laxer rules about recording people who aren't entirely aware of it. Combine this with anthropological data on cultures without writing to get a full empirical look at it.

However it seems that this isn't all that is required to verify it. Formal language is developed by a culture, taught as a specific additional skill to the informal language and not mastered by all members. Not even literate individuals are masters of the formal language of their native language. It is rare to encounter individuals that cannot employ language for their daily needs and then some. People enjoy talking a great deal and about a great deal of issues even if they do not delight in the formal language. These facts imply that the formal language is not required for function.

My question to you is what is a concept that a literate person can express that an illiterate person cannot? What concept requires the ability to produce long sentences with numerous nested clauses in order to be expressed?

Think about having a philosophical discussion with your friends in person. If you wrote down a transcript of what was said would it look like a thread in Great Debates?
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  #46  
Old 04-04-2004, 06:40 PM
II Gyan II II Gyan II is offline
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Quote:
Originally Posted by The Tim
My question to you is what is a concept that a literate person can express that an illiterate person cannot? What concept requires the ability to produce long sentences with numerous nested clauses in order to be expressed?
I wouldn't know, I'm literate.
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  #47  
Old 04-04-2004, 06:45 PM
Milum Milum is offline
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Does man select coincidental numbers to explain the Universe or do numbers dictate and reveal the absolute explanation of the mechanisms of the Universe to man?

Simple. Does one and one equal two? Of course not. First of all we must delimitate the existence of "twoness" in the Universe. And we can't.

Oh well...
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  #48  
Old 04-04-2004, 07:33 PM
erislover erislover is offline
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Quote:
Originally Posted by II Gyan II
Unless you get in their heads and become them, how do you know?
I don't use the word "know" like that. Psychic phenomena has never been a requirement for knowledge for me. Guess I'm just funny like that.

In your comments to The Tim:
Quote:
I wouldn't know, I'm literate.
I don't think that's quite right. The question is, what is so peculiar to written English that only written English can express it? That there is no verbal counterpart? Where there can be no verbal definition? Being literate is a requirement for answering the question, not a hindrance!
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  #49  
Old 04-04-2004, 09:29 PM
II Gyan II II Gyan II is offline
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Originally Posted by erislover
I don't use the word "know" like that. Psychic phenomena has never been a requirement for knowledge for me. Guess I'm just funny like that.
Well, that is certainly funny. What do you mean by 'know' then?


Quote:
In your comments to The Tim:I don't think that's quite right. The question is, what is so peculiar to written English that only written English can express it? That there is no verbal counterpart?
The question isn't about having a verbal counterpart. Ultimately all written English has to be pronounced. The limitations of verbal usage, memory and interaction is what (IMO) would constrain the illiterate.

Quote:
Being literate is a requirement for answering the question, not a hindrance!
But it is. I can't ever know whether I can, with certainty, adopt the perspective and framework of an illiterate. I can guess, but I wouldn't know.
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  #50  
Old 04-05-2004, 02:44 AM
erislover erislover is offline
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I believe I have answered the "what is it to know" question enough times already, actually.
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