PDA

View Full Version : On Mathematics



Endymion
01-27-2006, 11:21 PM
this is an open debate and exploration. more philosophy than anything else.

There is a widening rift in the mathematical community as to a fundamental issue in regards to how one advances mathematics. It can be summerized by asking "Is math a science?" That is, is mathematics discovered or created? Does an equation exist before it is derived or proven? Can a computer do math (http://en.wikipedia.org/wiki/Computer-assisted_proof) simply by exploring every possibility and seeing what works? This particular point reached an unresolved head with the 4-color map problem (http://en.wikipedia.org/wiki/Four_color_map_problem), which has only been proven by having a computer check every possible case. Will math become an observational science?

endlesst0m
01-27-2006, 11:24 PM
this is an open debate and exploration. more philosophy than anything else.

There is a widening rift in the mathematical community as to a fundamental issue in regards to how one advances mathematics. It can be summerized by asking "Is math a science?" That is, is mathematics discovered or created? Does an equation exist before it is derived or proven? Can a computer do math (http://en.wikipedia.org/wiki/Computer-assisted_proof) simply by exploring every possibility and seeing what works? This particular point reached an unresolved head with the 4-color map problem (http://en.wikipedia.org/wiki/Four_color_map_problem), which has only been proven by having a computer check every possible case. Will math become an observational science?
i hope so...man, it sucks!

i was learning about "singularity" today in school, about computers taking over and all that jawn, this kinda reminds me of that.

Endymion
01-27-2006, 11:29 PM
i was learning about "singularity" today in school, about computers taking over and all that jawn, this kinda reminds me of that.
that's what's known as the technological sigularity. there are other sorts. http://en.wikipedia.org/wiki/Technological_Singularity

endlesst0m
01-27-2006, 11:32 PM
that's what's known as the technological sigularity. there are other sorts. http://en.wikipedia.org/wiki/Technological_Singularity

i was learning about that kind of singularity.

anyway, i fucking hate math...i especially hate algebra. it worthless for humans to do math when computers can. humans are VERY prone to making simple mathematical error while doing any given kind of math...computers definatly should do ALL math in the future, and math should just become an observational science.

Also, i fucking hate math!!!!!

Rocky-girl
01-28-2006, 12:10 AM
Yes I think Math is a great sciens. I have some problems with it, but I think that man can't live without math!

JohnnyNemesis
01-28-2006, 12:14 AM
Endy, I think the better question is

ARE YOU NERD?

Mota Boy
01-28-2006, 03:02 AM
4-color map problem (http://en.wikipedia.org/wiki/Four_color_map_problem)


Hah, I remember doing that to kill boredom during class or dinner (this would just lead into a very long story about my childhood if I was taking this parenthesis seriously).

Preocupado
01-28-2006, 05:10 AM
Math is created by men. Things happen, we notice it, and create something out of it. (i.e. maths)
Don't ask me why the human creature ever started to give attention to things.

0r4ng3
01-28-2006, 05:16 AM
The numbers are created. The math, the process of manipulating those numbers, is discovered.

At least, that's what I came up with in the past 2 seconds.

Paint_It_Black
01-28-2006, 08:06 AM
It's discovered. 2 + 2 = 4, both before you discovered it and after you discovered it, and indeed regardless of if we had ever discovered it. We just name the numerals and invent the little symbols.

TheUnholyNightbringer
01-28-2006, 08:08 AM
The way I see it, the mathematics exist naturally, but in an undefined form. All humans do is give definition to it. Think of it this way - a tree still existed before humans gave it a name. Just because it didn't have the name of "tree" doesn't mean it ceased to exist.

And yes, I think equations exist before they're proven or derived. The tectonic plate theory was correct before it was even discovered; it's the same with equations. It's rather arrogant of humans to think that something doesn't exist simply because we haven't discovered it yet.

killer_queen
01-28-2006, 09:54 AM
Math is definitely not a science. It's just a branch that people need to use to understand other sciences.
And of course it is discovered but when I think about all those analytical craps, graphics and the others it looks like it is discovered. Maybe because I don't undrestand them well.

wheelchairman
01-28-2006, 10:09 AM
Mathematics, like time, or accounting, are concepts we use to measure things that do not physically exist.

Mathematics started out in religious philosophy, like most sciences actually.

But I haven't studied math in 3 years, so I really don't care either way.

sKratch
01-28-2006, 10:32 AM
Some of the replies here make me sad. In any case, full reply coming later cause I gotta run now.

HeadAroundU
01-28-2006, 10:39 AM
It doesn't matter.
You are total geek.

HornyPope
01-28-2006, 02:01 PM
Some of the replies here make me sad. In any case, full reply coming later cause I gotta run now.

Yeah. I was going to say something smart too but then I realized i'm completly unaware of math beyond high school.

sKratch
01-28-2006, 02:26 PM
I think that various tenets of mathematics are inherent. If you have one apple, and your friend gives you another apple, you now have two apples. All we have done is create labels for certain mathematical processes. Numbers, as a concept, I think also exist inherantly. When it comes to differential and integral calculus, I'm not so sure. Part of me wants to say that because it's a manipulation of other more basic mathematics, and because so many processes are modeled almost perfectly by it, it's something that just exists. Also, it's always amazed me that calculus expanded to serve so many other purposes and have a much deeper meaning after its initial institution by Newton and Leibnez. This assumption may be incorrect, because I assume neither of these men saw calculus do most of the things it does today during their lifetimes. I guess I kind of strayed from the question, but whatever.

JohnnyNemesis
01-28-2006, 02:28 PM
Stray all you want; your thoughts on the subject are still very interesting, which says a lot coming from me, since my knowledge of this discipline is horrible.

T-6005
01-28-2006, 11:12 PM
I strongly believe in human lateralist thinking.

Which, in other words, means that I believe that rules exist in nature before we are there to define them, but that we have to define them before understanding their intrinsic workings.

Betty
01-29-2006, 11:57 AM
It's tricky to think of what else to add to this. I pretty much agree with the majority in that I still think the concepts of numbers and arithmetic existed before we defined them. Which is what I think of most things - screw the philosophers.

But in terms of using more advanced math to model systems - it can get interesting. Apparently you can use both calculus or matrix algebra to define quantum theory, although I have never done the latter. I'd imagine we could come up with an entirely different method to manipulate numbers and model systems. So whether it's something that fundamentally exists...? I was trying to think of interesting things that came up in math, since I'm far from being a mathematician, and the best I could come up with is the natural logarithm.

wheelchairman
01-29-2006, 12:18 PM
How do concepts exist before we concieve them?

That's just what I don't get. It seems like math is a part of language and grew with it. In front of me is 1 laptop. Without me thinking this, there are only things that "are". They are not labelled, nor recognized. Unless someone else labels them. Labels exist for us, and possibly for animals, I don't know how they think.

Betty
01-29-2006, 08:31 PM
But as Stephan said: one item and one item always make two items. The fact that we show that via numbers and addition is how we interpret it, but it's a fundamental reality.

wheelchairman
01-29-2006, 09:48 PM
But as Stephan said: one item and one item always make two items. The fact that we show that via numbers and addition is how we interpret it, but it's a fundamental reality.
Wouldn't that just make math a means of intepretation?

sKratch
01-29-2006, 10:13 PM
A means of interpreting something that already exists. *sexes Michelle*

wheelchairman
01-29-2006, 10:17 PM
No one's arguing that they don't exist. I'm just saying it's an interpretation, no different than language.

I just don't think that the interpretation is transcendent of all things.

I really don't know though. I can't sleep and this is all a mess right now.

Betty
01-29-2006, 10:19 PM
I'm totally impressed at the lack of Brits posting in this thread. Cause I had been a little weary upon seeing the title of this topic.

Betty
01-29-2006, 10:21 PM
It's totally different Per.

You can't compare mathematics to language.

But I believe what we're saying, is that at least at a fundamental level, mathematics is a correct interpretation of a reality that already exists. It is not something we just pulled out of thin air as humans.

T-6005
01-29-2006, 10:35 PM
But I believe what we're saying, is that at least at a fundamental level, mathematics is a correct interpretation of a reality that already exists. It is not something we just pulled out of thin air as humans.
That's what I thought as well.

sKratch
01-29-2006, 11:23 PM
I'm totally impressed at the lack of Brits posting in this thread. Cause I had been a little weary upon seeing the title of this topic.
Haha we're on the same wavelength here. As soon as I saw you had replied I knew I had a friend here to battle the enemy if it came down to it.

Betty
01-29-2006, 11:31 PM
... the things you get way too excited about when you've had a few beers ...

But I'm ready to do battle anytime.

wheelchairman
01-29-2006, 11:31 PM
I'm lost again, how are the Brits involved?

Endymion
01-30-2006, 12:49 AM
ok, so how about real numbers? integers, sure, you can say that they have a basis in reality. but the reals? even better, the uncomputable reals? on what physical footing are they? sure, you can all them a logical extension of the math that comes "naturally", but it definitely is fully removed from the physical universe.

Betty
01-30-2006, 01:29 AM
I'm not overly familiar with "uncomputable reals", but if they're all a part of the infinite number line, could you not represent them as being the result of an infinite fraction? Or is it just the whole concept of infinity that throws it? And how come you can't find an infinite number of algorithms to compute these numbers anyway? In a theoretical sense as opposed to an realistic sense.

Endymion
01-30-2006, 02:11 AM
this is where the work of chaitin and others in the area of theoretical computer science/math really gets cool.

first, do you know the proof by diagonalization for there being an uncountably infinite number of reals? the proof goes like this: assume that there are a countably infinite number of reals. order them and put them one-to-one with the integers (which you can do since we're assuming them to be countably infinite). now, construct a new number by doing this: the i'th digit of our constructed number is a 2 if the i'th digit of the i'th number of our ordered list of reals is any number other than a 2, and a 3 if it's a two. thus, our constructed number now differs from eacy of our enumberated list of reals in its i'th digit. thus, we did not have all the reals enumerated. meaning, the reals are not countably infinite. this dates back to cantor etc, but still awesome.

now, on the other hand, the set of syntacticly valid programs in a particular language (any language. make one up. or french psudo-code. or mathematical equations. it doesn't matter) is countably infinite. texts can be ordered by length and alphabetically within ones of the same length. with a countably infinite set of programs possible, only a countably infinite number of outputs are possible. these outputs can always be taken to be a real number. thus, it is only possible to ever be able to utilize a countably infinite number of reals--the others can not be expressed (though of course they exist, they just can not be uniquely identified)!

this also leads to a proof of a weak form of turing's halting problem. we've got all our countably infinite outputs here, so why don't we just diagonalize across them and get a new number, like we did before? well, we can't because there's no way to be sure that our i'th program will output an i'th digit! that's a somewhat weak form of the halting problem, which is a more general statement than godel's incompleteness.