Stephen Hawking, Theory of Everything, and Goedel’s Incompleteness theorem

This post has the following readability test scores:

Flesch Reading Ease: 63.63
Flesch-Kincaid Grade Level: 8.00
Automated Readability Index: 9.00

For more info about readability tests, check out my post about those here.

Whew, it’s been a while since my last post. Work and a project (during and continuing till after the end of a semester) kept me really busy.

Anyway, this post is about the webpage containing prof. Stephen Hawking’s talk about his latest (AFAIK) stand on the search for the theory of everything, how Kurt Goedel’s incompleteness theorem/s influenced his opinion/view.

The speech in text format (1st reference link below), as you may immediately notice, is quite messy and seems to be unedited. I think that the speech laid out in the web page was just a speech-to-text conversion of prof. Hawking’s speech, which by the way you can download, so you can listen to his very iconic “electronic” voice. This speech-to-text conversion is quite evident I think since the starting letter of each sentence is not capitalized, and difficult words (at least for an American English speech-to-text program) such as Laplace (for the French mathematician) turn out to be spelled as Le-plass, which is what you would most probably get if you spoke into a speech-to-text synthesizer just like prof. Hawking’s.

As you may well know, a theory of everything (ToE) in physics aims to unify the four basic forces in the known universe, and which can, in theory, be used to predict anything that ever happened or will happen in the universe. My previous weblog post further clarifies this theory, or the search for it. I found the 1st reference link below when I Googled for “Stephen Hawking Theory of Everything”, hoping that I would be further enlightened about how the man labelled as “the brightest theoretical physicist since Albert Einstein” is going about searching for the ToE. I never expected that he would give up, in a sense, which for a while made me feel uncomfortable, though the feeling eventually disappeared. What made me feel uncomfortable was not because the universe is full of uncertainty and randomness we can’t explain (or at least not yet for some). What made me feel uncomfortable was that the man who so passionately sought for the ToE from his books and studies in the 70s and 80s (an example is the 2nd reference link below) has given up the search for the ToE.

But as I re-read the speech, Goedel’s incompleteness theorem hits the point in between the eyes. The great professor starts out (as he usually does) by discussing briefly the ideas that will prove to be necessary for his lecture’s whole point, including Quantum Chromodynamics (QCD), scientific determinism, Newton’s gravitational law, wave functions, etc. This is a style which I think he is famous for, and which is why his lectures are very popular and well sought after. His funny and comical inserts pop out once in a while to stir things a little bit.

Essentially, the gist of his lecture (as it would seem to me) is that there cannot be a single ToE, one which, as I’ve mentioned previously, will let us know what exactly happened at a specific point in our universe’s history, or what will happen to its future. The ToE should be able to tell you what you were thinking last night, or what you will think tomorrow night. Yes, the ToE is the theory of all theories. The problem however is that the human brain, as prof. Hawking puts it, is composed of so many parts made up of so many particles that we couldn’t possible compute what you’ll be thinking the next minute, even with the most powerful computers in the world today.

Prof. Hawking admits that until he realized the implication of Goedel’s incompleteness theorem, he implicitly assumed that a ToE will be found, probably relying on what can be referred to as “scientific intuition”. According to prof. Hawking, the positivist philosophy of science is that every good physical theory is a mathematical model, which he probably gets from Karl Popper and other positivist thinkers. And since, according to Goedel’s incompleteness theorems, there are mathematical results that cannot be proven, then so must there be physical theories that cannot be proven as well, including the ToE. Goedel’s incompleteness theorems essentially say that, as mentioned by prof. Hawkings himself, math is either inconsistent or incomplete. The professor bets his money (as he did in a previous debate with Kip Thorne decades ago) on the incomplete part of mathematics. Goedel’s theorems are proved using self-referring statements such as

“This sentence is false”

If the statement is true, then (the idea it implies) it is thus false. If the statement is false, then it is the opposite, meaning the idea the statement implies is true. Another would be to apply Bertrand Russell’s paradox on the barber paradox:

In a town which has a rule that the (only) barber shaves only all men that do not shave themselves, and doesn’t shave those who shave themselves. One can then ask, does the barber shave himself? If he does, according to the rule, he shouldn’t. If he doesn’t shave, according to the rule, he must shave himself.

Lastly, prof. Hawkings apologizes if anybody got/gets disappointed on his current view about the ToE. As I’ve said, I was initially disappointed, but considering his rationale about the search for the ToE, I turn out to be fine, though I still think he still leaves room in himself in case he makes a wrong prediction (just as he did in the 2nd reference link) that we might find the ToE in this decade. In his lecture in the 1980s regarding the discovery of the ToE, he said that we may find the ToE, and he’ll give another lecture about the ToE and where we stand 20 years later (which is now). Well, he did tell us where we stand, or at least what his view of where we stand in the search for the ToE. He also said then that once the ToE is found, physicists will lose their jobs, and physics will end. But according to his latest lecture, thanks to Goedel, mathematicians he said will always have a job, and most probably physicists too.

References:

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14 Responses to “Stephen Hawking, Theory of Everything, and Goedel’s Incompleteness theorem”

  1. Jimbob Says:

    im am so confused with everything on the page

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