sexta-feira, agosto 10, 2018

Sock Theory vs. String Theory: "When Einstein Walked with Gödel - Excursions to the Edge of Thought" by Jim Holt

My contribution to Holt’s Edge of Thoughts in the form of an article too:

An unauthorised and short version of physics.

How did scientists first deduce that the universe had hidden dimensions, dimensions that are curled up so tight we can't see them? Until recently SOCK THEORY was the ruling paradigm. It was thought that Theodor Kaluza and Oscar Klein deduced the existence of at least one additional dimension from well known tendency of socks to disappear and then re-appear in unlikely places. How else to explain the mysterious behaviour of hosiery? Latterly a new paradigm, STRING THEORY, has superseded sock theory. Leave a length of string or anything long, thin and flexible lying undisturbed for even a day and you will find it has somehow got itself tied into knots. This can only be explained if we assume at least one additional dimension. String theory also gave birth to QUANTUM FIELD THEORY. Richard Feynman found that if you stored several discreet pieces of string in a cupboard for an hour or so they would become inextricably entangled. Feynman realised that given half a chance everything would get ENTANGLED with everything else. String theory also gave rise to superstring theory which in turn morphed into the theory of branes. If you've read this far you're probably a P-BRANE.

Quantum theory is flawed and quantum proponents are in denial. String theory is in crisis (it has recently been described as dangerous nonsense). The Copenhagen interpretation is under attack (by recent experiments - even though this not allowed by Copenhagen). Neutrinos don't actually exist (did your Neutrino lose it's flavour on the bedpost overnight?).


NB (not part of the article above): The references to one of Gödel's Incompleteness theorems in Holt’s first article suggest a slight misunderstanding of the meaning of Godel's work. What Gödel showed was not that the axioms of mathematics must be taken on faith (this insight is much older and relatively harmless) but something more subtle. Gödel showed that in any reasonably powerful mathematics, there must be perfectly legal statements which cannot be proven within the framework of that system, but will require additional axioms to plug the gap. And that this more powerful system will in turn necessarily include legal statements that cannot be demonstrated to be true or false without resort to still more new axioms, and so on... In other words, that no systems of mathematics along the lines of the Principia of Whitehead and Russell can ever be self contained. Yet another way of saying this is that the mathematical backbone of thought is a convention or a construct, not a pure, freestanding Platonic ideal. This was a startling insight, because prior to this discovery it had been assumed by all who are equipped to assume such things (e.g., Hilbert, Russell, etc) that a proof of the completeness of mathematics would be positive, not negative. Mathematicians are Platonists in their souls - it's profoundly disturbing to find out that the universe is not Platonic. Turing's and Church's related insight (the discovery of well-formed problems which no computer program can solve) was even more unsettling and of far greater practical significance. (The strategy of reducing a new problem to the halting problem, and thereby demonstrating it to be unsolvable is routine even for undergraduates, and applies to a universe of problems that come up frequently in practical applications, which undecidability does not.) Godel's theorem is simply the formal-logic manifestation of the same drubbing that Einstein, Plank, Heisenberg, Turing, Darwin, Freud, Wittgenstein, Lyell, et al, gave in other fields to our formerly rather poetical understanding of the nature of knowing.

Gödel's incompleteness proof shows that axioms, formulated in the artificial language of Peano arithmetic (the five Peano's axioms that is), could not be reducible to logic. They required supplementing with other branches of mathematics such as set theory. Effectively that requirements for completeness and consistences in any logical system were violated - hence the need for supplementing logic with other constructs.

2 comentários:

Book Stooge disse...

re: string theory

so this theory, that has been touted as the be all and end all of everything, suddenly is wrong?

And scientists wonder why the general run of the mill Joe Public doesn't trust science. At least religious leaders will admit when they don't know the answer to something (well, the good ones anyway).

I know I've banged this drum before, but my goodness, "scientists" today sound, act and talk just like religious cultists throughout the history of the world. It does so much harm that I want to cry.

Manuel Antão disse...

The problem is not that the theory is wrong. The problem is that no one can prove it's even wrong let alone proving it's right...