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Tue Feb 24, 2015, 10:45 AM

 

Can Science and Mathematics coexist?

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

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Reply Can Science and Mathematics coexist? (Original post)
stone space Feb 2015 OP
DetlefK Feb 2015 #1
Android3.14 Feb 2015 #2
cbayer Feb 2015 #3
stone space Feb 2015 #9
cbayer Feb 2015 #10
stone space Feb 2015 #12
cbayer Feb 2015 #13
stone space Feb 2015 #14
cbayer Feb 2015 #16
trotsky Feb 2015 #19
Dont call me Shirley Feb 2015 #26
gcomeau Feb 2015 #20
stone space Feb 2015 #21
gcomeau Feb 2015 #22
skepticscott Feb 2015 #23
stone space Feb 2015 #25
gcomeau Feb 2015 #29
stone space Feb 2015 #30
gcomeau Feb 2015 #31
stone space Feb 2015 #32
gcomeau Feb 2015 #33
stone space Feb 2015 #34
gcomeau Feb 2015 #35
stone space Feb 2015 #36
gcomeau Feb 2015 #37
stone space Feb 2015 #38
gcomeau Feb 2015 #39
stone space Feb 2015 #41
okasha Feb 2015 #42
skepticscott Feb 2015 #45
stone space Feb 2015 #4
Android3.14 Feb 2015 #5
trotsky Feb 2015 #6
cleanhippie Feb 2015 #7
cbayer Feb 2015 #8
okasha Feb 2015 #43
cbayer Feb 2015 #46
stone space Feb 2015 #11
edhopper Feb 2015 #15
cbayer Feb 2015 #18
AtheistCrusader Feb 2015 #17
pinto Feb 2015 #24
Agnosticsherbet Feb 2015 #27
stone space Feb 2015 #44
PoliticAverse Feb 2015 #28
Iggo Feb 2015 #40

Response to stone space (Original post)

Tue Feb 24, 2015, 11:09 AM

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

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Response to stone space (Original post)

Tue Feb 24, 2015, 11:33 AM

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.

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Response to Android3.14 (Reply #2)

Tue Feb 24, 2015, 11:34 AM

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

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Response to cbayer (Reply #3)

Tue Feb 24, 2015, 11:55 AM

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.)

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Response to stone space (Reply #9)

Tue Feb 24, 2015, 12:02 PM

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.

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Response to cbayer (Reply #10)

Tue Feb 24, 2015, 12:07 PM

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.

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Response to stone space (Reply #12)

Tue Feb 24, 2015, 12:14 PM

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

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Response to cbayer (Reply #13)

Tue Feb 24, 2015, 12:29 PM

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.









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Response to stone space (Reply #14)

Tue Feb 24, 2015, 12:37 PM

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.

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Response to cbayer (Reply #16)

Tue Feb 24, 2015, 02:05 PM

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?

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Response to trotsky (Reply #19)

Thu Feb 26, 2015, 04:33 PM

26. No, Agnostics think it too.

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Response to stone space (Reply #12)

Thu Feb 26, 2015, 01:29 PM

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.

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Response to gcomeau (Reply #20)

Thu Feb 26, 2015, 01:30 PM

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

 

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Response to stone space (Reply #21)

Thu Feb 26, 2015, 01:34 PM

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.)

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Response to gcomeau (Reply #22)

Thu Feb 26, 2015, 03:06 PM

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.

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Response to gcomeau (Reply #22)

Thu Feb 26, 2015, 04:29 PM

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?



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Response to stone space (Reply #25)

Thu Feb 26, 2015, 04:38 PM

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".

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Response to gcomeau (Reply #29)

Thu Feb 26, 2015, 04:40 PM

30. How?

 

I can see they are.




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Response to stone space (Reply #30)

Thu Feb 26, 2015, 04:41 PM

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

 

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

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Response to gcomeau (Reply #31)

Thu Feb 26, 2015, 04:52 PM

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!





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Response to stone space (Reply #32)

Thu Feb 26, 2015, 04:58 PM

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.

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Response to gcomeau (Reply #33)

Thu Feb 26, 2015, 05:04 PM

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.

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Response to stone space (Reply #34)

Thu Feb 26, 2015, 05:08 PM

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.

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Response to gcomeau (Reply #35)

Thu Feb 26, 2015, 05:18 PM

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.)

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Response to stone space (Reply #36)

Thu Feb 26, 2015, 05:20 PM

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.

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Response to gcomeau (Reply #37)

Thu Feb 26, 2015, 05:25 PM

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.





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Response to stone space (Reply #38)

Thu Feb 26, 2015, 05:29 PM

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

 

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Response to gcomeau (Reply #39)

Thu Feb 26, 2015, 06:18 PM

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


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Response to stone space (Reply #36)

Thu Feb 26, 2015, 10:41 PM

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."


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Response to okasha (Reply #42)

Fri Feb 27, 2015, 06:35 AM

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.

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Response to Android3.14 (Reply #2)

Tue Feb 24, 2015, 11:38 AM

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.





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Response to stone space (Reply #4)

Tue Feb 24, 2015, 11:40 AM

5. It's a silly question

 

Your response makes little sense.

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Response to Android3.14 (Reply #5)

Tue Feb 24, 2015, 11:53 AM

6. Thus, goats.

They at least make sense.

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Response to Android3.14 (Reply #5)

Tue Feb 24, 2015, 11:53 AM

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

It's nonsense.

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Response to stone space (Reply #4)

Tue Feb 24, 2015, 11:54 AM

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?

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Response to cbayer (Reply #8)

Thu Feb 26, 2015, 11:10 PM

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.

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Response to okasha (Reply #43)

Fri Feb 27, 2015, 09:44 AM

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.

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Response to Android3.14 (Reply #2)

Tue Feb 24, 2015, 12:03 PM

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

 

Mistitled, a little dated

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

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Response to stone space (Original post)

Tue Feb 24, 2015, 12:35 PM

15. Oh, bother

[img][/img]

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Response to edhopper (Reply #15)

Tue Feb 24, 2015, 12:49 PM

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

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Response to stone space (Original post)

Tue Feb 24, 2015, 12:49 PM

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.

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Response to stone space (Original post)

Thu Feb 26, 2015, 03:23 PM

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.

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Response to stone space (Original post)

Thu Feb 26, 2015, 04:33 PM

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.

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Response to Agnosticsherbet (Reply #27)

Fri Feb 27, 2015, 12:05 AM

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.











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Response to stone space (Original post)

Thu Feb 26, 2015, 04:33 PM

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

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Response to stone space (Original post)

Thu Feb 26, 2015, 05:52 PM

40. Oh, jeezus.

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