Maths doesn't exist without someone to codify it. And once someone lays down the rules to describe math, they begin to explore where those rules take them.Quote:
Originally Posted by Poopadoop
edit: remember, there are entirely useless maths.
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Maths doesn't exist without someone to codify it. And once someone lays down the rules to describe math, they begin to explore where those rules take them.Quote:
Originally Posted by Poopadoop
edit: remember, there are entirely useless maths.
Me too.Quote:
Originally Posted by Savy
Of course it does. The ratio of the circumference to the radius is pi, and that was true before someone figured it out.Quote:
Maths doesn't exist without someone to codify it.
Maths is like language. The word mountain describes something that it physical. The word itself is not the mountain, the word is merely the noise we associate with the physical object that is a mountain.
Without the word mountain, mountains still exist.
Great, maths is discovered.
Just like a wheel was always a wheel before someone created it.
Further, where there are two mountains... it doesn't require someone to be able to count for there to be two mountains there.
All we invented was the words to descirbe the concpets that we're trying to describe. The mountain exists, just as one and two exist. All we need to do is create the language to communicate these concepts.
No. Someone had to conceive the wheel, someone had to manipulate physical objects in order to create the object they conceive.Quote:
Originally Posted by a500lbgorilla
That is not what is happening with maths, nor with language. With language, we see something, then we create a word for it. We don't manipulate rock to create mountains so we can give it a name... mountains were discovered, not invented.
The wheel was invented becuase it wasn't "found" lying around, and then someone said "I'll call this the wheel".
How didn't Newton manipulate a thing to develop his understanding of mechanics?Quote:
Originally Posted by OngBonga
Newton didn't invent gravity, nor did he invent the laws of motion. He discovered the laws of motion, and observed gravity. He didn't even discover gravity, he just explained it (rather well but not nearly perfectly).
He invented how to describe gravity.Quote:
Originally Posted by OngBonga
And in the same vein, maths is both invented and discovered.
Just like how Goodyear invented a way to make wheels real.
No he didn't. He didn't invent the words he was using. He merely figured out how to apply the maths to his concepts, he solved the puzzle better than anyone else for a long, long time. But he didn't invent anything, with the possible exception of a slightly flawed intepretation of physical laws that already existed. I suppose that he was wrong means he did invent something! But, that's just pedantry.Quote:
Originally Posted by a500lbgorilla
There's a clear distinction between inventing and discovering. I know you like to wrestle with language and philosophy, but inventing something involves direct manipulation to create something that didn't previously exist, other than in theory.
The wheel actually isn't the best example, because it's possible that a circular piece of debris was found and used for the purpose, which would make it a discovery. Let's talk about the light bulb. That's a very clear "invention". Is it also a "discovery"? The discovery is what's going on inside the head. The invention is the creation of a concept, it's applying the discovery to the physical world.
Nobody is creating maths, just applying it or describing it.
Only the words used to describe maths are invented.Quote:
nd in the same vein, maths is both invented and discovered.
Mathematics is not a science.Quote:
Originally Posted by DietelByaneth
Mathematics is not based on experimental observations, but on propositions, or axioms. Mathematics supposes its axioms are true and draws logical conclusions based on those axioms. If an axiom causes inconsistencies, it is discarded from that corner of mathematics, which is reminiscent of scientific processes, but not enough. Whether or not those axioms represent anything which could be observed is not relevant. Only the internal consistency of the logical mathematical system is relevant.
In the sciences, for any statement to be considered "true" (true in quotes, because science doesn't produce true statements, only statements not yet shown to be false), it must match experimental observations. It is not enough that a statement adds or does not disrupt the logical consistency of the science's other statements.
Why are the mathematics axioms assumed true?
Because someone said if you assume a b and c then d, ohh shit e f g h i j too, maybe even x y and z.Quote:
Originally Posted by wufwugy
And no one has had a problem with a b or c at any point in time and we're onto zzzzzzz
Pretty much what Savy said.
Mathematical statements begin, "If you assume..." which is formally saying, "For the sake of the following discussion, that statement is absolutely true."
The thing is that math is very tight with its axioms. Simpler, more intuitive statements are preferred in most cases.
E.g.
Assume identity is not an absurd idea, i.e., that 'things' in the broadest sense, can be told apart, i.e. that if we were to talk about "this" thing, we would know that we're not talking about "that" thing, and vise versa, because we can tell these are different things.
That's more formally stated in mathematical axiom, but that's the gist of the fundamental principle which gives rise to all of algebra.
Whether or not this is true, or any reflection of reality is coincidental. That coincidental relationship can make humans more or less interested in studying it, but it doesn't change that the relationship between reality and numbers is not formally required in any part of mathematics.
I dunno, I think maths is sort of science. I think it's like a chess opening database compared to an endgame tablebase... science is the study of openings... it develops, and new openings become superior to what were once considered optimal. Maths is like the tablebase, working backwards, slowly figuring out all possible outcomes, starting with the most basic and becoming ever more complicated.
Either way, it's all doing the same thing... figuring chess out.
I thought you'd like this, wuf.
https://www.youtube.com/watch?v=3gBoP8jZ1Is
2nd video
https://www.youtube.com/watch?v=S4zfmcTC5bM
Cool, thanks.