Why is mathematics so effective when describing nature?

[Marshy]

It occurred to me recently that there are two schools of thought on the effectiveness of mathematics in science. The first school views the power of this abstract language that we use to describe the universe as highly improbable, perhaps almost mystical.
The second point of view is that maths works in science because we have constructed it to do so.

In the blue corner of this heavy-weight bout we have Einstein,
"How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?".

In the red corner we have Russell,
"It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance."

I lean towards Russell. Any thoughts?

 

[El_Machinae]

"When all you have is a hammer, every problem looks like a nail"

I think it's a example of force-fitting. Mathematics is a way of thinking that's been useful to us for years. And we use this tool for more and more purposes.

 

[Perfection]

Well, if we assert that the universe behaves in a logical and coherant manner then mathematics of some sort should describe its behavior.

 

[Erik Mesoy]

Both.

Since the universe is probably non-sentient, it won't go out of its way to upset us, meaning we can describe it effectively. Then our descriptions grow better over time.

Of course, funny stuff happens when you have things such as difference equations. A tends to get involved when you're working out a series restricted to Z and the solution involves using complex fractions.

 

[Marshy]

Well, if we assert that the universe behaves in a logical and coherant manner then mathematics of some sort should describe its behavior.

This summarises my position. But what do you (the casual reader, not just Perfection) think of the Platonic position: that the world of mathematics exists independantly of us. Well I'm not 100% sure that this is the best description of the Platonic philosophy, perhaps someone could do a better job?

If we believe the Platonic viewpoint then surely there must be something almost mystical about the effectiveness of mathematics?

 

[Heretic_Cata]

Well, if we assert that the universe behaves in a logical and coherant manner then mathematics of some sort should describe its behavior.

Nicely put : IF.

In a way math is just like (not all) religions in the middle ages they both think they are smart a$ses that think they can explain everything but in fact what they do is just say a point of view (be it usefull or not).

 

[Eran of Arcadia]

No, God did it all.

Seriously, though, I think that mathematics is just a way of describing the form that the universe takes; we constructed mathematics to explain the universe, not the other way around.

 

[warpus]

Mathematics is based on pure logic.

It is a very useful tool for describing models that approximate the way the Universe behaves because the laws of the Universe also operate according to pure logic.

 

[JerichoHill]

It is useful. It works. It is helpful.

Why should I care otherwise?

 

[Urederra]

I think the word you are looking for is physics, the link between math and the universe.

 

[pboily]

Nicely put : IF.

In a way math is just like (not all) religions in the middle ages they both think they are smart a$ses that think they can explain everything but in fact what they do is just say a point of view (be it usefull or not).

HC, we tend to hate the notion that any of what we do can explain (or be used for anything). Engineers, scientists, economists, psychologists (all professions that use mathematical tools) might labour under the delusion that they see the universe for what it is, but we do mathematics for two reasons (if even that): 1. beauty. 2. logical training.

For better or worse, mathematicians don't care about the results.

If somebody else uses the material: great. If not, well, I doubt if there are more than 20 people in the world (including myself) who care about what I'm working on, let alone think it can explain anything.

If you can show me an honest to goodness mathematician who thinks that what he or she is doing explains the world around us, I'll show you someone who is not an actual mathematician.

Otherwise, it sounds an awful lot like you are parotting somebody else's notions (and mis-directing your 'venom' at that).

 

[pboily]

No, God did it all.

Seriously, though, I think that mathematics is just a way of describing the form that the universe takes; we constructed mathematics to explain the universe, not the other way around.

You don't subscribe to the theory that God is the ultimate mathematician? Were I a believer, I think I would. Anyways...

There is a (semi-hidden and highly informal) debate amongst (some) mathematicians: do mathematics need somebody/something to formulate them in order to exist? That is, does a theorem exist before it can be expressed/proven? Or does a theorem spring into existence once it is expressed/proven?

 

[Eran of Arcadia]

You don't subscribe to the theory that God is the ultimate mathematician? Were I a believer, I think I would. Anyways...

God is the ultimate mathematician, and evolutionary biologist, and particle physicist, etc. But that doesn't mean He created mathematics as such; He just knows how to use the rules to get results. But of course, He doesn't tell us all this stuff directly, so scientists get to figure it out.

 

[sanabas]

we do mathematics for two reasons (if even that): 1. beauty. 2. logical training.

If you can show me an honest to goodness mathematician who thinks that what he or she is doing explains the world around us, I'll show you someone who is not an actual mathematician.

Damn straight. What are you working on, BTW?

 

[warpus]

There is a (semi-hidden and highly informal) debate amongst (some) mathematicians: do mathematics need somebody/something to formulate them in order to exist? That is, does a theorem exist before it can be expressed/proven? Or does a theorem spring into existence once it is expressed/proven?

Surely the logic behind the theorem has existed before humans could even speak - but we did not know of it until it was written down (and proved) by a Mathematician.

 

[Ayatollah So]

In the red corner we have Russell,
"It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance."

I lean towards Russell. Any thoughts?

Heck, I think Russell doesn't even go far enough. Or maybe he does, and you just didn't quote it. But the next point is that if there were multiple universes with radically different natural laws, you would expect the intelligent inhabitants of each to seize upon whichever mathematical theorems and domains were useful in their universe. Not only would they favor the useful and disregard the rest, they would be less likely even to conceive of the rest. People are part of the universe too, and our brains spent a long time adapting to the patterns in our environment prior to anyone's doing mathematics.

 

[Erik Mesoy]

non/Euclidean geometry, anyone?

 

[Heretic_Cata]

HC, we tend to hate the notion that any of what we do can explain (or be used for anything). Engineers, scientists, economists, psychologists (all professions that use mathematical tools) might labour under the delusion that they see the universe for what it is, but we do mathematics for two reasons (if even that): 1. beauty. 2. logical training.

Well i have to admit i did love studying math for the 12th grade high-school exam, even tho it really had no point. That math is fun. The math we are studying at the univ now sux.

For better or worse, mathematicians don't care about the results.

If somebody else uses the material: great. If not, well, I doubt if there are more than 20 people in the world (including myself) who care about what I'm working on, let alone think it can explain anything.

If you can show me an honest to goodness mathematician who thinks that what he or she is doing explains the world around us, I'll show you someone who is not an actual mathematician.

Otherwise, it sounds an awful lot like you are parotting somebody else's notions (and mis-directing your 'venom' at that).

Yea i think i misdirected my venom. Most of my math teachers are with their heads far above the clouds and really don't care about explaining stuff in the universe; they are in math-world.
I was (probably ?) aming at other people that "USE" math (physicists, chemists, stuff), but mathematecians don't use math they "MAKE" math.

Sorry if i may have ofended you; i picked on math because it is used in too many domains that think they can explain everything.
(i do have a history of misdirecting my anger ... i just have to much of it and i spread it around everywhere)

 

[pboily]

Damn straight. What are you working on, BTW?

Self-sustaining patterns (specifically, the so-called "spiral waves" of excitable media). Mostly existence results. Physicists and engineers think it's useless because we can't tell them anything about the exact location, frequency of rotation, speed to transition, etc... of the event, and (some) mathematicians look down their nose because we're not doing co-homological algebra.

The moral of the story: there are *******s everywhere.

What about you? Are you a professional mathematician (or do you aspire to become one), or a skilled enthusiast?

 

[pboily]

@Cata: offended? no. But I'm happy with your "clarification".