There’s a new TV show called “NUMB3RS” starting tonight, whose main character is a mathematican named “Charlie”, who solves crimes using mathematics. His motto is “Everything is Numbers”.
A secondary character is “Larry”, a Caltech physicist working on 11d supergravity. In one scene he shows up trying to get mathematical help from Charlie, whose graduate student sneers at him “Why don’t you do your own mathematics, like Ed Witten or Feynman?”.
Well I think the point I’m trying to make is – very little needed to be deduced at that point! Klein had his program, his problem, and his methods, and all that was lacking was *physical insight* into the meaning of the non-Euclidean geometry (which turned out to be Minkowski space) that *he himself*, with his particular sort of intuitionist brilliance, had created, and had used in this problem.
It’s *physical insight* more than anything else that’s needed to make progress in physics. Almost anyone can learn the math – even learn it “in the bones” so to speak – but physical insight is the rarest of all gifts it seems.
I am not sure the Classical Top is a good example of the difference between a physicist and a mathematician . My own opinion is that out of all physicists only Galileo , Newton, Maxwell ,Einstein and Feymann could have made the deductions that you alluded to in 1896!
I have been looking at the history of great discoveries in Physics, and it seems that the Great Man Theory does not stand up as well as it might. Essentially, many people have different models which turns out to be essentially the same, after mathematicial inconsistences are straighten out! (String Theory and Loop Gravity anyone?)
For example, the reason why we remember Maxwell rather than Riemann as the discover of Electrodynamicism, is that Riemann mixed in Gravity! i.e Riemann realised that if there was a link between Electric and Magnetic phenomena, this would lead to symmetry constraints on the physics. Physicists need an Einstein to explain this in terms that they could understand PHYSICALLY.
What does being classical have to do with it? It’s about representations of the rotation group via the complex plane (stereographic projection). Klein noticed that his problem – to describe the motion of the top subject to external forces – was much simplified if he introduced a non-Euclidean geometry with the fundamental quadric (in the sense of projective/metric geometry)
x^2 + y^2 + z^2 – t^2 = 0
Again, Klein goes to some lengths to disabuse his readers of any “metaphysical implication” in introducing a non-Euclidean geometry. Now, this was in 1896! Klein has basically all the mathematical elements for relativity not only in hand, but at work!
The irony of this is priceless – Klein had clarified the relation of affine, pseudoaffine, hyperbolic, and elliptic non-Euclidean geometry to each other – he’d written a classic book on the subject – he was past master of function theory and operations in the complex plane – yet he missed relativity – not only missed it, but turned it away when it knocked on his door – from the inside!!
The point is – being a good physicist is a completely different metaphysico-realistic setup than is being a good mathematician.
Poincare was great mathematician. Einstein was a great physicists. Someone said that Poincare was too much of a mathematician to discover special relativity which was in the air and although he discovered Poincare group. If a kind of cognitive complementarity is involved, the replacement Poincare-Einstein–>Witten-Witten would not make sense unless Witten enjoys a positive variant of multiple personality disorder;-).
I do no understand what SR has to do with the mathematical theory of the Top! This theory is ENTIRELY Classical!
I agree that Einstein was a good mathematician. However he was not a great one, unlike Ed Witten.
How do these rumors get started?
Einstein did NOT “often have a mathematician to help him with the hard stuff”. In fact the great mathematicians of the day, including Klein and Poincare, fell all over themselves getting things wrong. See for example Klein’s “Mathematical Theory of the Top”. The locus for this work is the complex plane under SU(2) – really SL(2,C), because the quadratic form arises:
x2 + y2 + z2 – t2 = 0
Klein EXPLICITLY mentions that the non-Euclidean geometry he is using should not be taken literally. In fact, it should be taken VERY literally because it’s Minkowski space. In other words, the greatest mathematician of the day was flat wrong about his OWN WORK!
GEEZ, save me from Einstein bashing!!
I actually liked the show. Sure the mathematics is over the top but hey it’s fiction! It seems as if they’re trying to make it educational and I only say this because they have the main characters narrate their thought process like a PBS special.
“Why don’t you do your own mathematics, like Ed Witten or Feynman?”
Perhaps this physicist guy is supposed to be more like Einstein since Einstein often had a mathematican who would help him with the hard stuff (like Riemannian geometry).
Would it have been more credible to the mathematician that number theory be based on some principle as posted here?
It would make sense to me, why string theory might be rejected, and a new method considered as a basis?
It’s not quite as bad as the ads made look. It’s still painful for math-savvy people to watch.
Not even close to PI, an excellent movie.
I bet it doesnt go longer that 3.1415… episodes 🙂
Step up, folks, and place your bets! How long until the show gets cancelled?
>But on the positive side, maybe one benefit is that >it will portray math as being ‘cool’ 🙂
Perhaps…but I’m not convinced…
Funny. Though the one advertisement I saw for the show made it look positively awful.
Made me think of the show called PI
Hey! I know! Let’s make a math show and call it numb2.71828rs? No, well, then how about numb2.718rs? NO, GEEZ! WELL IS NUMB3RS 0K WITH Y0U?!?
Amusing 🙂 But on the positive side, maybe one benefit is that it will portray math as being ‘cool’ 🙂