Why is mathematics so effective when describing nature?

[pboily]

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.

In a universe where an observer is often needed to "collapse the wave function", can it be said that logic exists on its own?

Shrodinger's Cat implies that if that were the case, you would need an original observer (I'll give you one try to figure out who that observer would need to be...)
As I have no need for that particular hypothesis, the other, less appealing notion (that a theorem exists only after it is formulated) merits some consideration. And that's the crux of the whole "debate."


But as I said, it's an informal debate: nothing like the Foundation crisis of 100 years ago. It doesn't really affect how we do mathematics.

 

[Sidhe]

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?

So long as they are paying you to do it and you enjoy it, why should you care what the others think?

And don't worry, in a hundred years someone will look at your work develop some general rule for some non deterministic theory that'll shed light on the non deterministic world of physics in some cleverly meaningful way and you'll achieve some short lived burst of fame long after your gone. It's a thankless task though, I mean who remembers who invented imaginary numbers? Can you remember without googling it?

 

[pboily]

So long as they are paying you to do it and you enjoy it, why should you care what the others think?

Because I'm not a robot? It would make my life a lot easier if I didn't have to deal with *******s, is all.

Imaginary numbers? Cardano is the first to use it in an application (The Cubic formula). Who gave them a first geometric interpretation? Buee, Gauss and that danish architect. Who made them popular? William Rowan Hamilton with his quaternions.

I'm not too worried about posterity: I was merely pointing out that most mathematicians (including myself) don't want our work to be seen to have a connection to the real world while we are still alive.... didn't you once refer to it as mental masturbation?

 

[Eran of Arcadia]

Shrodinger's Cat implies that if that were the case, you would need an original observer (I'll give you one try to figure out who that observer would need to be...)

Schrodinger? God? Chuck Norris?

(That's three . . . I can't count.)

 

[pboily]

well, that's only two, really. I mean isn't God just one of the manifestations of Chuck Norris?

Seriously, it is my opinion that if mathematics exist in vaccum (on their own), we need a primal observer (or God, if you will). Not necessarily someone to create the universe, but to "observe" the universe existing or coming into existence.

As it stands, I currently believe that mathematics do not exist in vaccum, and that the universe acts as its own observer. But I really have no idea.

 

[Eran of Arcadia]

well, that's only two, really. I mean isn't God just one of the manifestations of Chuck Norris?

Touché.

Seriously, it is my opinion that if mathematics exist in vaccum (on their own), we need a primal observer (or God, if you will). Not necessarily someone to create the universe, but to "observe" the universe existing or coming into existence.

As it stands, I currently believe that mathematics do not exist in vaccum, and that the universe acts as its own observer. But I really have no idea.

That is an interesting way of looking at it. Is that part of any deeper philosophy of the meaning of the universe?

 

[pboily]

I don't know Eran. I tend to like my philosophy light and fluffy. Most of the time, I navigate in foggy waters. I can formulate this belief, but I'd be hard pressed to justify it: muddy understanding of quantum phenomema (do they even apply to macroscopic constructs?) and all these things.

 

[Birdjaguar]

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.

Did "reason" exist before humanity?

If so, when did it arise and in what creature?

Humans use mathmatics to describe or characterize physical phenomena such as flight. We use all kinds of equations to do so. Birds have been flying for millions of years. Are those equations anything more than just our view/perspective of what birds do? Are they anything more than just flight seen through the filter of human reason?

 

[Ayatollah So]

IMHO, trying to place logical and mathematical facts in time is misguided. You can ask, Is there a number between 2 and 4? But you can't ask (without needless confusion), did the number 3 exist before anyone ever thought of it? Because that question tries to place a number in time, which is wrongheaded. It's a bit like the question "did you stop beating your wife yet?" - there seems to be a false presupposition involved.

 

[pboily]

MU ..............

 

[Birdjaguar]

IMHO, trying to place logical and mathematical facts in time is misguided. You can ask, Is there a number between 2 and 4? But you can't ask (without needless confusion), did the number 3 exist before anyone ever thought of it? Because that question tries to place a number in time, which is wrongheaded. It's a bit like the question "did you stop beating your wife yet?" - there seems to be a false presupposition involved.

If you look at the history of counting it took several very distinct steps:

1. Tallies – Simple counting (the addition of one more unit of something) that shows up in Paleolithic finds as notches in a stick or bone.

2.Concrete counting – One to one correspondence. A token that represents “one jar of oil” or “one measure of grain” illustrates this concept. Concrete counting begins to show up in trading by about 6000 BC. If I had 3 jars of oil and 2 sheep to trade you for something, I would have them counted as
1 jar of oil + 1 jar of oil + 1 jar of oil + 1 sheep + 1 sheep. quantities and objects were conceptually locked together as a single item. In modern society “twins” and “quartet” are examples of concrete counting. The amount and the object are locked together in the word: 2 babies and 4 musicians.

3. Abstract counting – Numbers separated from objects. “Twoness” is independent of any particular object and may be associated with many items and used mathematically. 2+4 = 6, but twins cannot be added to quartets. The earliest record of abstract counting was in about 3100 BC in Uruk Sumeria.

So back to your post. The "number" three did not exist as far as people were concerned prior to about 3100 BC.

 

[sanabas]

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.

Sounds interesting.

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

Delinquent uni student. In theory I want to do maths teaching, which may be sidetracked by something interesting for an honours or PhD project. In practice, passing uni is getting in the way. I tend to teach myself stuff when I find it interesting, and get incredibly bored with actual classes. I think I need to do a class with someone that I'm tutoring for that class, as I tend to be reasonable at teaching myself stuff so I can teach it to someone else.

 

[batteryacid]

Mathematics is not pure and without flaws, as Gödel prooved (A "Landsmann" of mine I´m proud of)!
Mathematical sentences exist, that are equal to the "This sentence is not true" paradoxon, so mathematics and pure logic are equally flawed as language- but actually this is a good thing, as otherwise all mathematics could be done by an automaton and no human intuition would be needed!

And to the idea of some kind of space where pure mathematics and numbers exist:
There is ALWAYS a human beeing with his own pirctures of reality in his head who brings nimbers and equations together to describe what he observes

Q: Is there a universe with no entity to observe it?
A: If its, empty, who cares?

 

[Leifmk]

Mathematics is not pure and without flaws, as Gödel prooved (A "Landsmann" of mine I´m proud of)!
Mathematical sentences exist, that are equal to the "This sentence is not true" paradoxon, so mathematics and pure logic are equally flawed as language

No, that's not quite it.

What Gödel's incompleteness theorems show is, basically, that any formal system rich enough to do math in (i.e. one that allows you to define the natural numbers) will contain true statements that cannot be proved within the system (and therefore false ones that cannot be disproved). I.e. "this statement cannot be proved to be true", not "this statement is false". That is, a formal logic system cannot be used to prove its own consistency.

 

[El_Machinae]

A staple of science fiction is that aliens would use math as a common ground to communicate with us. Anyone reading this thread now realises that's a huge assumption.

What I like about math is how one can 'get' math. You can get the 'theme' of an operation intuitively once you understand it. That means that you can look at problems and immediately get approximate solutions.

I've loved that fact since the beginning. This belief of mine also allows me to determine my 'level' of math, because at some point I hit a wall - where I can perform operations but don't 'get' the intuitive meaning of the operations.

If I recall an article correctly, we're hitting a wall in math theory. The mathematicians can only 'get' so much ... and super-computers can do the operations for the next level of understanding, but people don't 'get' that level, we can just crunch the numbers.

 

[sanabas]

A staple of science fiction is that aliens would use math as a common ground to communicate with us. Anyone reading this thread now realises that's a huge assumption.

I don't think it's too huge an assumption. The problem would be the language & symbols used to define axioms and operations.

 

[pboily]

If I recall an article correctly, we're hitting a wall in math theory. The mathematicians can only 'get' so much ... and super-computers can do the operations for the next level of understanding, but people don't 'get' that level, we can just crunch the numbers.

you don't happen to remember the name of the article and where you read it, do you?

 

[batteryacid]

I don´t think that language or symbols are a problem- It´s easy enough to illustrate mathematics and numbers by universally understandable things like breaking down everything to relations between lines or to relate everything to universal frequencies, like some hydrogen transision freqency or something similar.

1 apple and 1 apple always gives 2 apples, independendly of symbols and languages - thinking about it...- we should send them some apple-math books to establish contact

 

[Marshy]

If I recall an article correctly, we're hitting a wall in math theory. The mathematicians can only 'get' so much ... and super-computers can do the operations for the next level of understanding, but people don't 'get' that level, we can just crunch the numbers.

I think that this really only applies to a very small subset of mathematics, particularly numerical analysis. Most of the pure mathematics research done today has no connection with computing. It deals with the properties of abstract structures.

The objects that mathematicians deal with are generally not the sort of objects that one can compute with. Take for example the ordinals.
They are argueably the most fundamental objects in mathematics. But beyond the countable ordinals they are necessarily "non-computable" or "non-describable". A mathematician who deals with these objects daily can gain a good intuition about these objects that can serve him well. There is no way to test or investigate the propeties of uncountable ordinals using a computer (or least none that I've encountered ).

 

[King Flevance]

I believe mathematics are a set of principles contained within the universe. We have just recognized the system because of its repetative nature occuring over and over. I don't think humans "invented" mathematics. I think we discovered it. But there is still many formulas we have yet to discover involved in the idea of mathematics. This is when something happens and we go "How is that possible? it can't be explained through mathematics!" I believe it can, we just don't have enough of the constant variables put in the equation. (too many "X" factors)