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Does Math Really Exist?

Posted January 21, 2012 7:43 AM

From Forbes - Tech:

In the midst of a rather interesting discussion of the notion of Aristotle's Unmoved Mover, Leah Libresco went on a mild digression about the philosophy of mathematics that I couldn't let go of, and feel compelled to respond to.

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#1

Re: Does Math Really Exist?

01/21/2012 9:19 AM

It's an interesting question. Does Math exist independently of human thought? Does one-ness exist such that 1 plus 1 equals 2, if a conscious being is not there to describe it?

I feel (not sure 'feel' is really the best word) -- I feel that geometry is somehow even more fundamental than math. Snowflakes are six-sided due to the geometry of water molecules. Salt is cubic due to the geometry of sodium and chlorine atoms when mixed together. Calcite has a solid parallelogram-like appearance. All of these shapes are due to nature and have been around since the dawn of time, billions of years before Cro-Magnon walked around and began painting cave walls.

Perhaps there is something in the geometry of the quarks and gluons that when two protons come together, one of them has to become a neutron in order for the two baryons to remain together as a deuterium nucleus. And from that 'rule' all other elements are constructed.

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#4
In reply to #1

Re: Does Math Really Exist?

01/21/2012 11:23 AM

I think that in the absence of humans, math, geometry, color, sound, etc. would still exist.........................they just wouldn't matter. Snow flakes would still have six sides, but without humans around to designate the number six...............it would be meaningless.

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#21
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Re: Does Math Really Exist?

01/23/2012 6:30 AM
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#2

Re: Does Math Really Exist?

01/21/2012 10:02 AM

The old question: Did Michelangelo create the David or did he simply chip away the marble that surrounded the statue? Did Newton create calculus or did he discover it? Did Mandelbrot create fractals or did he discover them?

I have recently been interested in sunflowers and mathematical simulations thereof. I doubt anyone told the sunflower the formula for maximum packing, it would have discovered it by evolutionary processes, trial and error; but the mathematics exist. So did the math exist when the sunflower evolved to it's present form or not until the mathematicians attacked the problem?

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#10
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Re: Does Math Really Exist?

01/22/2012 12:02 AM

Sunflowers seem to have worked out what we call Fibbonacci numbers.

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

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#3

Re: Does Math Really Exist?

01/21/2012 10:48 AM

I had this conversation when string theory was new, so if the math says it is most likely...

As for being a human construct, crows count; so not entirely human

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#5

Re: Does Math Really Exist?

01/21/2012 10:33 PM

Math is. Therefore, we are.

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#8
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Re: Does Math Really Exist?

01/21/2012 11:44 PM

Do we need a "1" to be able to recognize a "0"?

Is "1+1=3"? or is that just evolution/natural selection at work?

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#6

Re: Does Math Really Exist?

01/21/2012 11:12 PM

My answer is "no!". It's an abstraction, a complex one, invented for convenience, much like the concept of Time.

You can't look outside your window and see time or math. Just like you can't see "compassion", "Love" or "Temperature", etc, etc, ad nauseum.

The problem, IMO, is that we are so used to referencing these abstractions in our day to day conversations that we've lost sight of their origins and actually believe they are real.

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#7
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Re: Does Math Really Exist?

01/21/2012 11:31 PM

Just like you can't see "compassion", "Love" or "Temperature"...

I don't need to see them. I have felt them.

/Btw, I don't need to see gravity. I can feel it now.

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#9

Re: Does Math Really Exist?

01/21/2012 11:45 PM

Math is an invention of mankind, which is just a model of things we observe. It has been very useful for allowing us to "solve" riddles of the universe in terms of how we observe them. We may have gone too far with string theory and brane theory, which to me seems to be modeling things we cannot observe.

Wall street sure found ways to make math useful in the last 10 years!

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#11

Re: Does Math Really Exist?

01/22/2012 1:05 AM

Math is simply a more accurate way to convey a quantity of 'less' or 'more'.. any creature with a brain can do simple math to find 'more' food and water and is smart enough to live with 'less' predators etc.. a simple person or animal might pick fruit from the tree with 'more' hanging fruits, but only the most greedy And paranoid of the creatures feel the need to Accurately acccount each fruit available. Math is useful for description of atomic struture where the accuracy of 'more or less' electrons actually has significance. Math is a mere convince when trying to give significance through false accuracy of abstract concepts such as space and time. Why it's our burden to care is the question?

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#12

Re: Does Math Really Exist?

01/22/2012 2:54 AM

Here is just a starter on various viewpoints about this topic.

No guarantee that I am seeing this the right way, but to me it seems that mathematical truth is "out there", and is discovered rather than invented. But the discovery oftentimes takes as much ingenuity as invention would.

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#13

Re: Does Math Really Exist?

01/22/2012 6:33 AM

The fact that everything in the universe seems to obey to interaction rules that can be described by human arbitrarily assigned logical generalizations (that's my description of human math at this context) makes the question self (un)answered: Yes, as long as there 's human (or better) intelligence to interpret it. S.M.

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#14

Re: Does Math Really Exist?

01/22/2012 10:31 AM

Mathematics is just a language to describe relationships..Without humans the language might not exist, but the relationships certainly would..

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#17
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Re: Does Math Really Exist?

01/22/2012 11:59 AM

To that point, ref my earlier

Crows count, monkeys count, dolphins count; both up and down

That covers Identity, Abstraction, Addition and Subtraction

Either math exists or our ancestors 'invented' it and taught the beasts.

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#15

Re: Does Math Really Exist?

01/22/2012 11:33 AM

I can see it now....

Some middle schooler says, "Math does not exist; therefore I don't need to take this test. Bye!"

Then the teacher retorts, "It just became an essay test. Explain this in 1000 ± 100 words!"

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#16
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Re: Does Math Really Exist?

01/22/2012 11:58 AM

You've got it!!!!

Why try to understand math, when a little essay describing it, in your own words will do the trick? Somebody, give that teacher a raise!

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#18

Re: Does Math Really Exist?

01/22/2012 9:30 PM

i have posted the header of a book review below, (in 'read any good books lately'?) the very debate of this blog is central to the book. that other animals count seems a fairly convincing argument for the a priori existence of certain underpinnings of the cosmos. the book takes this to the point where an alien spaceship shows up with geometric proofs of A2 +B2 = C2 emblazoned on its' hull.

Anathem is a speculative fiction novel by Neal Stephenson, published in 2008. Major themes include the many-worlds interpretation of quantum mechanics and the philosophical debate between Platonic realism and formalism.

Those interested in the history of science have probably already read Stephensons' series of long historical novels, The Baroque Cycle.

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#19

Re: Does Math Really Exist?

01/22/2012 9:37 PM

and, if this is to be decided by a vote, i am definitely in the, 'math is out there', camp.

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#20

Re: Does Math Really Exist?

01/23/2012 3:26 AM

Maths physics and all science is just a tool to explain the physical world to ourselves.
If it works fine, if it doesn't then work up a new theory.
Maths is true and absolute as far as we know, at the moment within our limited understanding.
We inhabit a very small dot in the space time continuum thingy

How much maths does an Aborigine use when making a boomerang?
And how much maths does the aeronautics student use trying to analyse it?
The universe trundles on quite happilly without a formally expressed maths.
And cats just don't giveadamn.
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#22

Re: Does Math Really Exist?

01/23/2012 3:50 PM

I've always had a problem with math. And to prove its being a human invention, and like us not perfect, I'll point out what bothers me about it.
If you were to say that 3 people each can have 1/3 of a pie... Visually or graphically, that is no problem. But digitally or mathmatically 1/3=.3333333~ which to me is imperfect because of the infinity thing. We have to be content to round it off at some point. So I consider it flawed. At least the numbers or our description of it is somehow anyway.

Besides that, it leads to all the greed and envy

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#23
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Re: Does Math Really Exist?

01/23/2012 7:24 PM

You can solve your dilemma by switching to base twelve for this problem.

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#24
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Re: Does Math Really Exist?

01/24/2012 3:42 AM

Or simply accepting that 1/3 is just as valid an expression as a digital one. It's like the vast mass of people who think a digital display is somehow more accurate than an analogue one. Put a digital display on a cheap cr4p instrument and it magically becomes accurate, oh, and jack the price up while you're at it.
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#25

Re: Does Math Really Exist?

01/24/2012 5:51 AM

May be there are many kinds of mathematics like the many religions.

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#26

Re: Does Math Really Exist?

01/24/2012 10:59 AM

Asking whether or not mathematics exists is on par with asking: do the words 'red,' 'car,' and 'is' exist, and is their relationship in the sentence 'the car is red' a meaningful one?

Mathematics is a language (see Galileo). It has a specific vocabulary for a fairly narrow range of concepts (limit, group, space, quantity, etc.) and a grammar (in Greek, a logos). It exists only in so far as the objects/concepts that it describes exist and the observers that discuss them exist. To borrow from the Kantian model, mathematics is a phenomena born of the noumena of objects, concepts, observers, and interlocution.

(Philosophical full disclosure - this position is born of an amalgamation of belief in a knowable and obervable reality, somewhat limited ability to know on the part of human observers, a soft Wittgensteinian view of language, and a muted rational empiricism.)

In any discussion of language, we have to remember Humpty Dumpty's argument that words have no inherent meaning, but mean what the speaker wants them to mean (no matter how infuriating this is to Alice).

From Through the Looking-Glass by Lewis Caroll:

"I don't know what you mean by 'glory,' " Alice said.

Humpty Dumpty smiled contemptuously. "Of course you don't-till I tell you. I meant 'there's a nice knock-down argument for you!' "

"But 'glory' doesn't mean 'a nice knock-down argument'," Alice objected.

"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean-neither more nor less."

"The question is," said Alice, "whether you can make words mean so many different things."

"The question is," said Humpty Dumpty, "which is to be master that's all."

Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. "They've a temper, some of them-particularly verbs, they're the proudest-adjectives you can do anything with, but not verbs-however, I can manage the whole lot! Impenetrability! That's what I say!"

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#27

Re: Does Math Really Exist?

01/24/2012 8:47 PM

The more interesting question is, "Why does anyone care?" -- meaning, that each person who finds this an interesting question, ask themselves, why they find it so. It may not be so easy to answer.

But a clue is the fact that "philosophy" exists. And, as far as I can tell, philosophy can be boiled down to the common children's, one-word question, of "Why?" Some kids get fancy and expand it to 2 words, of, "How come?" It seems to be a built-in characteristic of our "nature." There was quite a long thread started by chrisg288 allied to this.

The most interesting subject of all is consciousness. Abstractions such as math, scientific laws (the interrelationship of objects detected by our senses), all arise in the mind of man. Whether they exist independently really doesn't matter. As the experience of being conscious is all any one of us really knows. We say we "know" this and that, but we really mean we experience this or that. Or "we" "think" this or that. Do you really exist because you think, a la Descartes? Truly, what is "awareness?" Can it be without thought? Some (mystics) might answer, "Yes." But unless one has experienced "awareness" without "thought" (and that state is said to become self-evident as one experiences it by "mystics"), the statement that one can, is about as useful as all the questions framed as, "Would... if man wasn't around to experience it."

I, also think, most of us, see some version of what we call consciousness in some animals, despite the effort of some to reduce animal action to a non-thinking machine. I would say it can't be proved to exist (or not) in animals, unequivocally, short of having a Spock-type mind meld with any creature, or life-form, in question. And even if you could, and afterward, "felt" you now "knew" it, how would you convince your neighbors? You'd have to do your best to try to teach them the same technique so they could try it out for themselves. Most people who have had pets don't doubt that some version of what we deem "consciousness" exists in animals. At least, most of the ones I've discussed it with.

Philosophy proper, being logical trains of thought, presented as arguments or proofs are a fine demonstration of the effects of consciousness but do not get one any closer to understanding consciousness. Whether "math" exists apart from consciousness, is this type of inquiry.

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#28

Re: Does Math Really Exist?

01/25/2012 12:44 AM

If math exists and is absolute, my question is: how may numbers are there between 0 and1?, answer; "infinite". If you agree with me then you'll also ask; how then do you get to one, or is there realy a 1. to me math is an illusion, a philosophy made real by belief, if you can believe otherwise you can nullify its existance.

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#29
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Re: Does Math Really Exist?

01/25/2012 12:50 AM

Simple algebra can easily leap over infinity, although it takes some care.

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#30

Re: Does Math Really Exist?

01/30/2012 8:31 PM

Math does not Really Exist. But the things math describes do. Math is a tool and a language for describing the way things combine, separate, grow, decay, exist, etc.. but the actual way in which things combine, separate, grow, decay, exist, etc.. does exist. For instance man invented "rock" both the idea and the word, but the object upon which the idea was found and later described with language does in fact exist. The object does not require the observation and descriptions of man in order to be. Man needs the idea and the word in order to quantify, think about, and eventually manipulate the rock in a meaningful and beneficial way.

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#31
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Re: Does Math Really Exist?

01/30/2012 8:38 PM

By your logic, the language you just wrote that in, does not exist.

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#32
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Re: Does Math Really Exist?

01/30/2012 8:57 PM

Correct I saw this post a bunch of neurons fired off in my head and because everybody that speaks English has come to a mutual understanding of what combinations of symbols will cause what neurons to fire off we can create similar responses in each other. If you are not convinced that language is not real try putting a rock in front of a book. It will have no response. You may say but it is not living to which i will reply ok put an untrained animal or even a baby in front of two books that are almost the same except for the words printed in them and gauge there reactions. Repeat this experiment 1000 times and compare results. You will find that until you train an animal or person to fire off certain neurons in response to certain symbols that the symbols don't relay exist or affect them except to say that the ink and paper exist. No one looks at a bunch of fallen toothpicks and tries to read them, at least not with any agreed upon or relevant meaning (Fortune tellers have similar practices for telling the future but the results have not shown to be statistically relevant in any way when dealing with random events.) The language is just a mutual understanding we have come to as a people.

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#33
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Re: Does Math Really Exist?

01/30/2012 9:40 PM

Ah ye ode "Cogito ergo sum" with a touch of "If a tree falls in a forest and no one is around to hear it, does it make a sound?"

I have always felt if that tree became the paper of pay checks in the philosophy department it would result in a full revision.

Now the peanuts are contending the numbers on the check are 'not real'?

Sounds to me quite like a 'viable solution' for 'inside the box' pseudo intellectual verbal masterbators

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#34
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Re: Does Math Really Exist?

01/30/2012 9:53 PM

I don't think the debate is well titled I don't think any one is arguing whether or not the idea of numbers and math exist. We are debating whether it is more than an idea. Out side of a computing machine whether it be man made or natural numbers are at best hard to find at worst impossible. So here is my challenge name one place in which math and numbers exist out side of a computing device... I can't think of any and if they do then why did it take humans so long to recognise them especially the more abstract ones such as 0 and negatives. I don't think it took man long to recognise that he was surrounded by objects which he later named rocks. That concept was easy because it dealt with real objects.

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#35
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Re: Does Math Really Exist?

01/31/2012 6:57 AM

Music, measurement, naming and barter

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#36
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Re: Does Math Really Exist?

02/01/2012 5:23 PM

I guess we're going to have to agree to disagree because everything you just named I believe only exist inside of a thinking machine (brain, computer, calculator, etc) which gets back to my point that math and numbers only exist inside of the interpreted electronic, mechanic, chemical or bio-electronic pathways of thinking machines.

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