Can Science and Mathematics coexist?

[stone space]

Is Mathematics the "Queen on the Sciences", as it had been dubbed, or are the methods of Mathematics inherently in conflict with the methods of Science?

Can science and mathematics coexist?

20 Things You Didn't Know About... Math

snip------------

2. The great 19th-century mathematician Carl Friedrich Gauss called his field “the queen of sciences.”

3. If math is a queen, she’s the White Queen from Alice in Wonderland, who bragged that she believed “as many as six impossible things before breakfast.” (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)

snip-------------


http://discovermagazine.com/2012/mar/09-things-you-didnt-know-about-math

[DetlefK]

1. Considering that math is the language of science...

[Android3.14]

2. Mistitled, a little dated

Actual title is "20 Things You Didn't Know About... Math", and there is nothing in the article about math and science having any difficulty coexisting. It came out three years ago.

[cbayer]

3. In addition, I can't for the life of me figure out the connection to religion.

[stone space]

9. Not religion per say, but some do...

...see an inherent conflict between belief and science.

Since mathematicians take belief to the extreme, the possibility for conflict is certainly there, under that particular theory.

(A guy once explicitly claimed to me that teaching children to believe six impossible things before breakfast is a form of child abuse.)

[cbayer]

10. We often discuss the conflict (or lack thereof) between belief

and science. I could understand if you wanted to discuss the possibly conflict between math and belief, but this just seems to have no connection at all.

[stone space]

12. Given point (3) in the article, ...

...mathematics is unlikely to have a conflict with belief.

I could understand if you wanted to discuss the possibly conflict between math and belief

But if belief is in inherent conflict with science (a position that I do not maintain), then point (3) would also suggest the potential for conflict between mathematics and science.

[cbayer]

13. So you are saying that math relies on belief?

[stone space]

14. I like the description of mathematics as...

...the White Queen.

I think that it hits on a important and fundamental part of the nature of modern mathematics.

We really do believe six impossible things before breakfast (or at least six contradictory things).

It would be interesting to know just how much of the controversy between belief and science is really about belief per say, and how much of it is about a general hostility to religion, having little or nothing to do with belief.

Are folks who decry belief in general as being incompatible with science really serious, or is "belief" itself just a target of convenience for folks opposed to religion?

Some of the current arguments made in religion vs science debates mirror past controversies within mathematics, so I sometimes look to the history of my own subject in an attempt to understand them.

[cbayer]

16. I think it's about hostility in both directions.

Religion fundamentalists think that science is trying to destroy religion. Atheist fundamentalists think religion is trying to destroy science.

The fact that they challenge each other is not an argument that they are incompatible at all. It is important for both sides to accept the challenge and approach each other in a way that doesn't make them fearful.

In the end, I think that those who take the position that religion is opposed to science are just using belief as a target of convenience in their war against religion.

[trotsky]

19. "Atheist fundamentalists think religion is trying to destroy science."

Evolution is under assault in schools across the country. By religious groups. Do only "atheist fundamentalists" think this?

[Dont call me Shirley]

26. No, Agnostics think it too.

[gcomeau]

20. I think...

...you're missing the concept of a metaphor here.

Math does not in any way actually rely on "belief". Someone was just being clever with language to tell a bit of a joke.

[stone space]

21. Do you believe in Fermat's Last Theorem? (nt)

[gcomeau]

22. The question makes no sense.

There is nothing to "believe in" in Fermat's last theorem. It is a mathematical formulation. Either the math works out, or it doesn't. (And it has been proven for 20 years now, FYI... so it does.)

[skepticscott]

23. Very odd that someone who

claims to be a mathematician would frame the question in such a senseless way. You'd think that he either doesn't have a clue how mathematics really works, or that he was just trying to provoke a reaction.

[stone space]

25. Ok, I'll rephrase it.

(And it has been proven for 20 years now, FYI... so it does.)

Do you believe that the set theoretical assumptions that Wiles used in his proof of FMT 20 years ago are consistent?

Here's an article that discusses Wiles' set theoretical assumptions:

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9050242&fileId=S1079898600000810

If you can't access the published version, here's a pdf version of the same article that is not behind a paywall.

http://www.cwru.edu/artsci/phil/Proving_FLT.pdf

That is, do you believe in the existences of Grothendieck universes (essentially, strongly inaccessible cardinals), or at least do you believe that their existence does not lead to contradictions?

How about a whole Proper Class of Grothendieck universes?

[gcomeau]

29. Sigh.

I can see they are.

It's pretty obvious you're trying to apply a definition of "belief" that is so vague that it means "accept is true for any reason", and then draw a false equivalence between that and the far different definition of belief as applies to religion which means "accept based on faith". So that you can then declare that one is "belief", and the other is "belief", so they're the same thing!!!!


It's not going to work. They are very very different things, and math remains based on logical proofs not "belief".

[stone space]

30. How?

I can see they are.

[gcomeau]

31. The same way I can see 2+2 =4.

Only with slightly more effort. Stop playing dumb. It's annoying.

[stone space]

32. Divine revelation, perhaps?

The same way I can see 2+2 =4.

We're talking about levels of infinity (strongly inaccessible cardinals) that (provably) cannot even be proved consistent within commonly accepted set theories such as ZFC.

Only with slightly more effort. Stop playing dumb. It's annoying.

If it's so easy, do you have a proof?

If you do, then you should consider publishing it.

It would prove the inconsistency of our most cherished set theories like ZFC, and would bring the foundations of mathematics to its knees.

And mathematical logicians like myself would just love to see that happen!

It would be great fun!

[gcomeau]

33. Doing. The. Freaking. Math.

If it's so easy, do you have a proof?

The proof you linked is the proof. Hence why it's referred to as a proof.

Are you disputing it? Because I'm sure the entire mathematical community would be fascinated to see your work.

[stone space]

34. You are the one claiming...

...that the existence of a Proper Class of strongly inaccessible cardinal numbers is consistent with ZFC, not me.

If you can prove your claim within ZFC, then you can also prove that 0=1 within ZFC.

In fact, you'll be able to prove anything you want from there, since your proof will show that ZFC is inconsistent.

[gcomeau]

35. I simply pointed out the proof existed.

If you want to dispute it go ahead and do the work to show it's wrong.

[stone space]

36. That wasn't the question.

My question was whether or not the assumptions made by Wiles in the proof are consistent.

He assumes the existence of a Proper Class of strongly inaccessible cardinal numbers.

This is a statement known to be unprovable in standard set theories such as ZFC.

Now, you claim that you can just "see it".

And that seeing it is as easy as seeing that 2+2=4.

But I can prove that 2+2=4 in ZFC.

Hell, I can prove that 2+2=4 in Robinson's Q. That's how trivial the statement is.

I'm not discounting your "vision".

But a proof of your assertion within some standard set theory like ZFC would be nice. (Particularly nice in this case, since it would mean that ZFC is inconsistent and would bring mathematics as we know it to its knees.)

[gcomeau]

37. If. You. Want. To. Dispute. The. Proof. Do. The. Work.

Feel free. I'm sure many people will be fascinated to see your effort.

[stone space]

38. How can I dispute your work?

Your claim is based on a vision.

You don't provide any work.

And I can't dispute your vision.

I'm a mathematician, not a theologian.

You claimed a vision.

You could just "see it".

Easily.

That's cool, but you need more than a vision if you want to convince a mathematician.

Some indication of a proof would be nice.

[gcomeau]

39. I didn't write the proof you linked. And now you're *really* playing dumb. -eom

[stone space]

41. I didn't link to a proof.

39. I didn't write the proof you linked. And now you're *really* playing dumb. -eom

[okasha]

42. Allow me to translate gcomeau's responses

into everyday language. What he means to say is that he has no freaking idea what you're talking about and is waving his hands frantically to avoid saying "I dunno."

[skepticscott]

45. Nice try, but gcomeau had it pretty well nailed in post 29

This is all just a silly attempt by stone space to draw a false equivalency between acceptance of the validity of a mathematical proof and religious "belief". And when he got called out on it, he tried to distract from the fact by spewing out jargon like a cornered octopus spewing out ink.

[stone space]

4. I think they can coexist quite well.

It came out three years ago.

Mathematics has been around a long, long time.

Three years is nothing to us.

[Android3.14]

5. It's a silly question

Your response makes little sense.

[trotsky]

6. Thus, goats.

They at least make sense.

[cleanhippie]

7. Congrats. You're seeing what everyone else sees, too.

It's nonsense.

[cbayer]

8. I feel fairly certain that you are trying to make a point here that

ties in with religion

Is there some reason you don't just state it?

[okasha]

43. My math is limited.

Since I began working in ceramics, I 've used some basic algebra to interpolate glaze formulas, but that's as far beyond plain old arithmetic that my left brain gets on your average Tuesday.

However. I do think I get where stone space is going with this. Thanks to an enthusiasm for science fiction, I know that there are, for instance, a number of non-Euclidian geometries that not only do not describe our experiential universe but are in conflict with each other in their references to such things as the curvature of space, black holes, multiverses, etc. There's an anology with religion in the varying systems and their methodologies. Yet math is not inconsistent with science, even in areas where no proof exists. By the same token, varying faiths, while not consistent with each other and not subject to a true/false dichotomy, are not inconsistent with science. They're different universes, and the languages that describe them are different.

[cbayer]

46. As the thread has evolved, I have gotten a somewhat better understanding

of what he was going for. I think you've pretty much got it in this post.

It's about belief without evidence.

[stone space]

11. You copied the title from the OP, right?

Mistitled, a little dated

Actual title is "20 Things You Didn't Know About... Math", ...

[edhopper]

15. Oh, bother

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[cbayer]

18. Ah, that's my childhood alter-ego.

[AtheistCrusader]

17. I'm guessing you enjoyed Anathem.

As to your question, math is a cornerstone to the foundation of science. Be hard pressed to 'do science' without math.

It sounds like you're alluding to pure math that may have a conjecture, but no as-yet discovered proof or practical application. I don't see a problem, since to presuppose any particular pattern MUST have a use, presupposes a designer. I don't, so I don't have a problem with interesting and unreal mathematical conjectures with no apparent proof. One may be found, or not. It may have a use in reality or not.

[pinto]

24. Math is fundamental to much of science (no pun intended). Don't see the connection w/ religion here.

Unless it's about the somewhat similar, shared history of internal debates, disputes, challenges and rebuttals, etc. A stretch, imo, but I guess the analogy could be made.

[Agnosticsherbet]

27. Math and Science are the inextricably bound together.

If math were suddenly proved to be just so much hot air, Science as we know it would fall apart.

[stone space]

44. Somehow, I suspect that science would weather the storm.

Science as we know it would fall apart.

As would many parts of mathematics.

If math were suddenly proved to be just so much hot air

Although which ones and how well would no doubt depend on the nature of the contradiction and in what system it occurred.

If history is any guide, old ideas seemingly destroyed by contradiction would be reformulated and reborn anew, and be given a new life in a different light.

[PoliticAverse]

28. I refuse to believe in 'imaginary numbers' until someone can proove they are real... n/t

[Iggo]

40. Oh, jeezus.