Is math evidence?

[Fishteacher73]

Mathematics is a wonderful tool to support and explain various phenomenon. But it can help perdict out comes with probability, but is only absolute when concerned within itself. So I was wondering what we thought about certain ideas that are only supported mathematically. Is the math alone enough evidence to support such ideas?

[Smokinjoe9]

But it can help perdict out comes with probability, but is only absolute when concerned within itself. So I was wondering what we thought about certain ideas that are only supported mathematically. Is the math alone enough evidence to support such ideas?

 

Why should it be, I think not..I think if we believe math alone is enough evidence then we will miss the big one......

[sanctus]

no take the string theory,as far as I know there are different versions of it , all construcetd on math evidence. But experiments will show the one, if any, which is right.

[TJTodd]

Maybe I am not understanding this correctly, but I think that it could. Just because human conversational vocabulary cannot describe whats is being explained in mathematics, but the math can explain portions of other math. Why wouldn't it work?

[C1ay]

I think the question is a little broad. Math is certainly evidence enough to prove something like Fermat's Last Theorem. On the other hand I think it would take quite a bit more than math to settle the Freewill vs Determinism debate.

[paultrr]

no take the string theory,as far as I know there are different versions of it , all construcetd on math evidence. But experiments will show the one, if any, which is right.

 

In physics one has math underlining the explination of a theory. But in generally it takes far more than math to show a theory is correct. In math the math alone can prove itself. Other areas of science tend to vary a bit on this. In general, the search for a GUT has sometimes been linked with the idea of one set of equations that explains everything. However, the search is actually for far more than just a set of unified equations alone. On equations alone one would expect String Theory to be proven out. The problem is finding equations that not only generate the vacuum or spacetime we live in, but also one that has experimental and observational evidence backing it up. We had a problem with the standard model where untill we applied renormalization we always got infinite answers out of the equations. Now with String theory we get another sort of infinite answer in the way of different potential spacetimes. So here one would not see math as proving anything except that the equations appear to have the property of what we are after and are unique. What we need is equations that yield exactly what we observe out there in nature. You might say that math helps explain what is possible and how something works via the equations. But it's the observational lessons we derive out of nature directly that tell us if something is actually correct or not.

 

I have a friend with a math background that for years has tried to figure things out in a physics perspective. He can do the math all day. But some of his suggestions just run opposite of what nature shows is real. What he lacks is that understanding that it takes more than math for something to be correct. Yes, I've tried to explain this. For some reason it never seems to sink into him.

[Biochemist]

...Is the math alone enough evidence to support such ideas?

Yes.

 

Assumptions are everything, even in empicial experimentation. In the same vein, a math proof has assumptions in beginning conditions, and it has an output. The elements are essentialy identical to a physical experiment, except the "methods" are more explicit. A math proof can stand in for experiment, and support theory just like an experiment. Likewise, a math proof can be refuted because the assumptions are invlidated. (Or the math could be wrong, but I assume that those are rarely published.)

[Fishteacher73]

In a pure math, I think It stands self evident. The issues arise in my mind when various constants are plugged in "to make the math work". This seems IMO to not be the same as basic mechanical physics. This cut and paste idea with patches over the holes I feel is not absolute proof.

[Biochemist]

...This cut and paste idea with patches over the holes I feel is not absolute proof.

Agreed.

[infamous]

I think the question is a little broad. Math is certainly evidence enough to prove something like Fermat's Last Theorem. On the other hand I think it would take quite a bit more than math to settle the Freewill vs Determinism debate.

 

Good point C1ay; There are also questions about things like infinity, can math really explain such a concept? One can get paradoxical answers regarding the notion of infinity if they choose to stretch the limits of mathematics. The mental concept of infinity, I believe is outside the limits of mathematics.

[Qfwfq]

Yes.

No.

[Buffy]

No.

I agree with Q. Math proves math, except where Kurt Goedel's Incompleteness Theorem holds. Otherwise its simply a great way of modeling reality, but its only a model....

 

Integratedly,

Buffy

[Qfwfq]

I don't agree quite completely with B. :shrug:

 

Math proves math, including Gödel's Theorem.

 

Math has nothing to do with reality, although, with a bit of poetic license, it can be used for modeling it. Math is also a language and an instrument but, essentially, it's a game having only itself as an aim.

 

43 + 78 = ?

 

Given a staight line and a point not on it, how many staight lines are there through that point that don't intersect that line?

[paultrr]

I would also add, that both in preprints and in published articles on occasions math errors get through. Usually an initial theory may be offered that is backed up with some recent observation and math. But in general, the acceptance of any theory waits for both observational and experimental evidence. Its one reason one always hears mention of what are the predictions of such a theory. Its the predictions one can use to test a theory. Some theories have virtually the same results as current ones. In this case one must look to the small differences to check a theory out. Reality is the judge. Not the math.

[Qfwfq]

Apart from errors, math, based on logic by adding whichever axioms you please, is a pure matter of consequentiality. Modus ponens:

 

A => B

 

A is true.

 

If the above implication is apodictally proven AND you know A is true, you also know B is true. If you're sure there is no error in the implication, then you're exactly as sure of B as you're sure of A. If A is true in the sense of observation of reality, so is B.

[Buffy]

I don't agree quite completely with B. :shrug:

 

Math proves math, including Gödel's Theorem.

No, we do agree! You slightly misunderstood me! Math certainly proves Goedel's Theorem, but math can't prove anything that Goedel says you can't!

 

Cheers,

Buffy

[Qfwfq]

but math can't prove anything that Goedel says you can't!

:shrug:

 

Gödel's Theorem doesn't say what math can and can't prove, it shows something more fundamental. Choose your axioms and there will be asserts that you can neither prove nor disprove. Given one of these, add an axiom so that it becomes either true or false, but there will still be such a thing as asserts that can be neither proven nor disproven etc........