Philosophy of math

mikau · 2005-11-29 18:17:38

What is math?

"Math is natures way of communicating with us" - Charlie Eps, Numb3rs

"Math is a gigantic can of whoopass in disguise" - Mikau

Whats your philosophy? What is math?

Last edited by mikau (2005-11-29 18:33:36)

mikau · 2005-11-29 18:24:02

"Math is the intelligence and order of the mind of God. This order enforced upon the world holds the physical word together. Without it, nothing could exist. God created the world, but first he created math, and built the world upon it." - Mikau

And btw, the idea of this thread is just to list lots of interesting philosophies about math. Not start a religious debate. If you do not believe in God, just ignore it, I'm not trying to preach or prove anything.

Last edited by mikau (2005-11-29 18:28:22)

MathsIsFun · 2005-11-29 20:16:42

OK, just so long as it doesn't get serious ...

Mathematics is the language of the universe ... whatever universe you want it be the language of!

Chaotic Neutral · 2005-11-29 23:38:19

This maths is the cornerstone of this universe, an entityless carcass which holds this world together.

The world is a mathemathic machine, running through it's complex mechanics powered by some unknown something that is time.We are a function of it, making our way following our endless parabola of the world field, determined by the terms "man" and the fractals of it.We do not just exist, we are "allowed" to exist by the model, and therefore we exist.

And who is god?Well, he's just the chief mechanic

mikau · 2005-11-30 04:31:43

:-)

Heres another one!

What is math?

Math is fun! :-D

Last edited by mikau (2005-11-30 04:32:00)

Chaotic Neutral · 2005-12-04 04:04:35

I think this great topic is underrated.

Last edited by Chaotic Neutral (2005-12-04 04:08:33)

mikau · 2005-12-04 13:21:04

You mean its been reviewed?

Ricky · 2005-12-04 13:29:33

If you want to get serious about the philosophy of math...

Imre Lakatos: http://en.wikipedia.org/wiki/Lakatos

Lakatos' philosophy of mathematics was inspired by both Hegel's and Marx' dialectic, Karl Popper's theory of knowledge, and the work of mathematician George Polya.
The book Proofs and Refutations is based on his doctoral thesis. It is largely taken up by a fictional dialogue set in a mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties of polyhedra. The dialogue is meant to represent the actual series of attempted proofs which mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Often the students 'quote' famous mathematicians such as Cauchy.
What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (If axioms are given for a branch of mathematics, however, Lakatos claimed that proofs from those axioms were tautological, i.e. logically true.)
Lakatos proposed an account of mathematical knowledge based on the idea of heuristics. In Proofs and Refutations the concept of 'heuristic' was not well developed, although Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs, and sometimes called his philosophy 'quasi-empiricism'.
However, he also conceived of the mathematical community as carrying on a kind of dialectic to decide which mathematical proofs are valid and which are not. Therefore he fundamentally disagreed with the 'formalist' conception of proof which prevailed in Frege's and Russell's logicism, which defines proof simply in terms of formal validity.
On its publication in 1976, Proofs and Refutations became highly influential on new work in the philosophy of mathematics, although few agreed with Lakatos' strong disapproval of formal proof. Before his death he had been planning to return to the philosophy of mathematics and apply his theory of research programmes to it. One of the major problems perceived by critics is that the pattern of mathematical research depicted in Proofs and Refutations does not faithfully represent most of the actual activity of contemporary mathematicians.

Pretty interesting stuff. I've only read his stuff on the philosophy of science though, not math.

ryos · 2005-12-04 18:40:14

"Philosophy and Math should not mix. Were it not so, Kepler's discovery of elliptical orbits would not have been controversial."

"Math is, more than any other subject, the training of the brain's logical and computational engines. For this reason, it's hardest to learn, requiring the most effort to master. For this reason, it's impossible to teach--every mind is unique, and must be trained in its own way; teachers of math must learn how to get out of students' collective way. For this reason, most people hate and fear math."

"Math is the tool that has built all societies."

All quotes by me .

I don't think Math should be called a science any more than engineering is a science. I don't see in it a natural law. Rather, it is a tool of our invention that allows us to describe and manipulate our world. It is the glue that holds all sciences together.

And, to mikau, I also think God is a mathematician. "The heavens, they are many, and they cannot be numbered unto man; but they are numbered unto me, for they are mine." -God

mikau · 2005-12-05 04:33:08

:-d

irspow · 2005-12-05 08:31:28

Math is a tool to communicate the logical progression of conceptual ideas. It is like any others science a figmant of the collective conscience. It is useless without a particular subjective viewpoint and set of assumptions. Gravity is no more of a true force than 1+1=2 unless we all agree to say it is so.

Chaotic Neutral · 2005-12-07 07:40:24

Why isn't logic a science?

The understanding of information fields between people can and should be brought down to formulas.

MathsIsFun · 2005-12-07 08:54:55

However, our "wetware" is a complex net of neurons that reaches conclusions based on incomplete data. Very important survival tool, but not good at hard logic.

So a cheap calculator can do something hopelessly beyond us. But the most advanced computer couldn't survive on a camping trip (without help!).

Chaotic Neutral · 2005-12-07 09:21:28

Ever noticed how our brain works?
It does not calculate with digits or binaries, but with "factors" and "factorial interactions".This intrigues me the most.If we could map this, and push this logic further than our brain can push it, we could "understand" many things.Einstein understood his theories because his brain could resonate up to those high factors, understand their integration, and allow enough room around it to explain it in plain words.

Could it be possible to construct a computer that would use the human brain code as operating module?
What is a brain-factor?Can it be defined (I hope no one will deny it's existence here)
Could it be mathematically noted?

Last edited by Chaotic Neutral (2005-12-07 09:25:09)

MathsIsFun · 2005-12-07 17:30:30

I have done some research on that subject in my own humble way, and I like to think that we can model brain function on silicon.

Interestingly, what is needed is a true random number generator, or else the machines thinking could be labeled "static".

"Neural Networks" is the subject.

mathsyperson · 2005-12-07 18:55:47

People are close to achieving true randomness by building a computer that counts the number of atoms in a radioactive sample that decay at any given time.

ryos · 2005-12-07 19:00:32

Chaotic Neutral wrote:

Why isn't logic a science?

My dictionary defines science as "The intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment" (emphasis mine).

Science involves logic, but logic is not science.

Rod wrote:

So a cheap calculator can do something hopelessly beyond us. But the most advanced computer couldn't survive on a camping trip (without help!).

Or another example, something we do constantly: image recognition. This is very, very hard to get a computer to do reliably, and is one of the things holding robotics back.

Our brains are broken in odd ways. We have a brain that stores every input it ever receives, and then promptly forgets where. Its autonomous function processing is incredibly powerful--when we train it to do things, it can do a large number of them at the same time. One example is sight-reading music. But, our higher function processing is annoyingly modal (to use a computer nerd term) - that is, only one task fits in there at a time.

I don't know how they came up with the oft-quoted figure that humans only use 10% of their brains, but it feels true to me.

Chaotic Neutral · 2005-12-08 00:47:27

Gentlemen, forget those random generators.Everything works with starting values, even the human brain.
Proof: think about a random word.The word that comes up into your imagination isn't completely random, it is a word that you associate with the theme you was thinking on by now.If it wasn't directly associated, then it was indirectly associated (for example, the word wolf somehow reminds me about motorcross, probably something that has happened in the past).But you will NOT come upon a completely random word.
This means, the human brain is not randomizing.
Which means it isn't randomized.
Which means, to simulate it you just have to copy the structure and add hormonal simulators (feelings) to it.
As the "free will" of a human being is directed by the amount of chemicals playing in it's blood, interacting with the analytical function and memory.
Proof: how even the most gallant gentleman can turn into a dirty pig upon the sight of a naked lady.The sexual hormons will affect the "free will", making the person thinking about only one thing: how to get that lady.

Jims · 2005-12-08 04:48:21

Give her some clothes. Why else would he be a gentleman?

Philosophy of math:
Interpreting order from chaos.

Chaotic Neutral · 2005-12-08 05:26:02

In that case his sense of honor would be bigger than his wanting of sexual pleasure. Still no counterproof.

And what chaos? Where? According to who?

What you call chaos is chaos because it's chaotic to you.
What policemen call "chaos on the streets" is in fact an organized crime hierarchy better organized than any social structure known to men.

Jims · 2005-12-09 04:00:56

What counterproof?

Your definitions seem bitter.

Would you have us, interpret ohaos from crder then?

Is there even a difference for you?

Jims · 2005-12-09 04:17:17

regardless,

Significance of numbers and mathematics:

Instead of an apple being just an apple, it becomes 1 apple.
To trade 1 apple for 1 banana ... 3 for 3 ... a dozen for a dozen.
Rather than, "all of what I have for all of what you have".
Which may seem balanced without numbers.
(and that's all ignoring quality ... before even getting to the market)

To cook:
"set it and forget it" rather than the art of BBQ

In manufacturing:
Interchangable parts instead of "eye-balling" each component to size or custom fit.

Maths eliminates guess work. (well, sometimes it is guess work ... or best-option work)
It simplifies into a repeatable process.

Seeing that mathematics is a language, used to read reality ... Math, being an expandable application, can account for items within it's own level of calculability ... The further we advance the art of numbers, the more we could say that whatever we apply that math to is, by extension, mathematics.

Last edited by Jims (2005-12-09 08:15:01)

Chaotic Neutral · 2005-12-09 04:29:47

What is so bitter about my definitions?Excuse me, I do not understrand the meaning of that word in context, do you mean bitter as in "pessimistic" or bitter as in "weak, bad,insufficient"?

Take the tangens(sp) of a corner.I am not so interested in what the tangens is at known values (30 degrees root 3/3 and so on) but what really does intrigue me is: we all know that the tangens of 90 degrees is ∞, but if you subtract a number so small that it lies somewhere in the end of the endless PI tail of it, it would be a existing number, almost endlessly far but still existant.That is what truly intrigues me, what does TRULY happen at those edges where traditional maths says that it SUPPOSES something is like that.Those edges beyond all numbers and known defenitions.Perharps it's just my childish ignorance and curiosity playing in me.

I interpret chaos as it is, as I consider there is no order and chaos, only defined and undefined things according to mankind.Your apple is only for us 1 apple, it is in fact no more than a part of "1 ecosystem" which is a part of "1 galaxy" which, at the end, is a part of "1 plane of existance".
So to me, there isn't a difference between order and chaos, they are for me as relative as random, up, beautiful....

Last edited by Chaotic Neutral (2005-12-09 04:35:15)

Jims · 2005-12-09 08:00:02

as in taste buds
Now if you want to reorder language, that's your perogative.
Forget Webster.

Read carefully:

Interpreting order from chaos.

Last edited by Jims (2005-12-09 08:07:34)

MathsIsFun · 2005-12-09 09:23:54

It's a good definition ... but in the last few decades Mathematicians have been interpreting chaos from order! (Mandelbrot et al)

However, being able to define chaos is (in a sense) creating order.

I believe that "randomity" is one of the basics of nature. Possibly more fundamental than space and time.

If the universe were Newtonian (totally definable and mechanical) then we could write a set of equations (a large set, but still possible) that completely defined the universe from beginning to end. So it would be a static universe.

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#1 2005-11-29 18:17:38

Philosophy of math

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Re: Philosophy of math

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