Math and the mysterious

[PrayingMantis]

"The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it."

Taken from this article, written by Eugene Wigner, winner of the Nobel prize for physics in 1963.

Discuss.

[Borodog]

I think it's a bit of an anthropic principle cannard. If mathematics weren't useful in describing the world, it never would have been developed.

[gumpzilla]

A couple of things:

1) Borodog makes an excellent point.

2) Wigner is a stud.

3) Above and beyond the issue of mathematics, I think there is an underlying implication in Wigner's statement that it is not a priori obvious that the world had to behave in such a regular, systematic way that could yield to human explanation at all. (I didn't read the article, perhaps he makes this explicit.) And as far as I know, there is no rational explanation for that.

[benkahuna]

There is order in the world and an orderly manner of thinking is useful to describe the world.

That math is useful is unsurprising. The orderliness of the world is the profound thing. Math is just the vehicle.

[Borodog]

[ QUOTE ]
3) Above and beyond the issue of mathematics, I think there is an underlying implication in Wigner's statement that it is not a priori obvious that the world had to behave in such a regular, systematic way that could yield to human explanation at all. (I didn't read the article, perhaps he makes this explicit.) And as far as I know, there is no rational explanation for that.

[/ QUOTE ]

I invoke the anthropic principle again. If the world were not orderly, life could not develop. Any kind of self-replicating system needs a consistent set of rules to follow for the process to be repeatable, a prerequisite of life. If the world were not orderly, we wouldn't be here to worry about it. So the fact that the world is orderly is not profound at all.

[benkahuna]

I think existence itself is profound, if that helps. It's very easy to take for granted if you don't think our existence is anything special. Then it becomes obvious. And I agree with you, orderliness in the universe can not be disentangled from the universe itself, which is why I find the orderliness profound.

I think we agree on the nature of things, just have different definitions of profound.

[sweetjazz]

[ QUOTE ]
I think it's a bit of an anthropic principle cannard. If mathematics weren't useful in describing the world, it never would have been developed.

[/ QUOTE ]

This doesn't directly contradict what you wrote, but there are areas of math that were studied purely out of interest (without applications to the real world) that were later used to describe the universe. One example is group theory (the study of symmetries) which has been very useful in molecular chemistry. Another example is the discovery of non-Euclidean geometry (which took place in the mid 19th century), a result that was purely of theoretical interest until Einstein discovered in the early 20th century that space-time is a naturally occurring non-Euclidean geometry.

So the mystery of why mathematics can be used to explain and describe natural phenomena may still remain.

[tek]

Fibonacci numbers rule.

[PrayingMantis]

[ QUOTE ]
I think it's a bit of an anthropic principle cannard. If mathematics weren't useful in describing the world, it never would have been developed.

[/ QUOTE ]

First, I'm not sure exactly what you mean by "cannard". (BTW the term, or concept of "anthropic principle" was first used maybe 10 years after this particular article was written). In any case, I agree that the "anthropic princlple" is actually a very rational attempt for an explanation of such problems, but in fact it is a kind of axiomatic argument. You can invoke the "anthropic princple" to explain any piece of evidence, "mysterious" as can be, and therfore it isn't "rational" in any real sense. I truely believe that Wigner would not accept it as a rational explantion for the problem he presents, but only as some more "sophisticated" version of an explanation of the form: "what is - must be (because we are to watch it)", which you can't say is more rational than saying "this is what krishna decided", or something to that effect.

I think that the deep point that Wigner is trying to make here, is that the connection between math (as we know it and use it) and phenomena is not obvious at all, as opposed to some suggestions on this thread. The argument that the universe has "order", and so "does math", and therefore they "fit", also doesn't hold and it's really the easiest way out of the question. If you read Wigner's article you can see why he choosed to use words such as "mysterious", and "no rational explanation" (and also "miracle", later on in the article). The fact the such a prominent scientist has chosen to use these specific words (it was a very provocative statement by him) should also be considered.

[Trantor]

[ QUOTE ]
[ QUOTE ]
3) Above and beyond the issue of mathematics, I think there is an underlying implication in Wigner's statement that it is not a priori obvious that the world had to behave in such a regular, systematic way that could yield to human explanation at all. (I didn't read the article, perhaps he makes this explicit.) And as far as I know, there is no rational explanation for that.

[/ QUOTE ]

I invoke the anthropic principle again. If the world were not orderly, life could not develop. Any kind of self-replicating system needs a consistent set of rules to follow for the process to be repeatable, a prerequisite of life. If the world were not orderly, we wouldn't be here to worry about it. So the fact that the world is orderly is not profound at all.

[/ QUOTE ]

Accepting this as true, arguendo, it doesn't explain why the "sytem" of sytematic nature of the universe is the same "sytem" as the sytematic nature of mathematics.