Does mathematics have two transcendent attributes: truth and beauty? What makes math true? What makes math beautiful? Are there different kinds of mathematical existence? How can math combine idealized perfection and explanatory simplicity?Since the subject is Mathematics, it would have been nice if they interviewed some mathematicians. Yes, Witten has some very impressive mathematical accomplishments, but he was schooled in Physics and thinks like a physicist.Featuring interviews with Robbert Dijkgraaf, Edward Witten, Max Tegmark, Sabine Hossenfelder, and Jim Holt.
Inevitably these non-mathematicians say that Math is not truth because it depends on axioms, or because Goedel proved that truth is not provable. Their description of Goedel's work is usually something that Goedel himself would disagree with.
To show that math can be false because of faulty axioms, they point out that dropping one of Euclid's axioms gives rise to non-euclidean geometry, and that was actually useful in general relativity.
No, Math gives absolute truth, and these arguments miss the point. Euclidean geometry is just as true as it ever was. General relativity uses Euclidean geometry to model the spatial tangent space. Yes, different axioms give different theorems, and all those theorems are true for those axioms.
Another podcast in this series addresses Why the “Unreasonable Effectiveness” of Mathematics? | Episode 2203 | Closer To Truth. Again, the interviews are with string theorists and physicists, not mathematicians.
Roger,
ReplyDeleteAm posting while away from my m/c, (this palm-held device is, hardly, a machine!).
You say (don't have the ordinary "greater than" sign on this III Class non-m/c, and even if it were to have one, it would't make a diff):
"Yes, different axioms give different theorems, and all those theorems are true for those axioms."
Well, the point is, for reaching the Truth, you need those Axioms. Maths is a poor place to go looking for those. Very poor. Poorer than even Physics. ....Why?
The what precedes the how, that's why.
BTW: Good / engaging (but not too so) a piece for the opening music. Credit not listed. Any idea about the piece?
Best,
--Ajit
BTW, by "the Truth", I meant the most basic, the most fundamental truth... *The first* truth, as Aritotle might have put it.
DeleteBest,
--Ajit
Mathematicians and physicists blather about 'truth', and then promptly go dividing by zero and assigning mass to zero volume points to make their equations work. Failing basic arithmetic does not lead to cosmic insight, just incorrect answers.
ReplyDeleteMath is an abstract logical construct. It's based on rules, and It can't be perfect, nothing real is, and is only as true as the assumptions you apply it to.
As far as reality goes, GIGO is the one ring of all logical abstraction that rules all others, whether they admit it or not.
As far as fantasy physics goes... they can just go divide by zero or truncate infinities until they drop dead of their own entirely finite means, as apparently they lack the basic epistemology to know better.
Some actual cosmic perspective:
ReplyDeleteAs far a we can know, truth only has meaning to humans who are even remotely concerned about it (if at all), until we meet someone entirely other to argue about it with, this will not change.
The universe cares not at all for the labels we slap on it or the rules we dictate to it, except for the very small parts of it that are ourselves in the insanely tiny moment in which all of humanity has ever existed.