Limits To Science: God, Godel, Gravity

[n2doc]

By Johannes Koelman | November 12th 2010 07:22 PM


Stupid physicists, they are doomed. Spending their whole lives searching for a theory of everything, not knowing that some eighty years ago this was proven to be logically impossible.

The internet is full with sentiments like the above. Many such posts refer to Stephen Hawking's 2002 Dirac lecture Gödel and the End of Physics.

With the publication of his new book 'The Grand Design', the Oracle of Cambridge is again adding to the confusion. However, due to all the fuzz surrounding a much less interesting claim by Hawking this issue has not received any attention whatsoever.

What is Hawking telling us? In his Dirac talk he states:

"Up to now, most people have implicitly assumed that there is an ultimate theory, that we will eventually discover. Indeed, I myself have suggested we might find it quite soon. However, M-theory has made me wonder if this is true."
more

http://www.science20.com/hammock_physicist/limits_science_god_godel_gravity

[Joe Chi Minh]

1. A fascinating article. "Stating that Godel (or Turing, or gravity) implies

the logical impossibility of a TOE, is the same as stating that because of the incompleteness theorem an axiomatic logic can not be constructed. This is simply wrong. Axiomatic logics can be constructed, but given an axiomatic logic not every result can be derived. Similarly, Gödel nor gravity prevents us from constructing a TOE, but gravity does prevent us from turning this TOE into a crystal ball." - Johannes Koelman.

I wonder if, by his many references to "incompleteness" he is referring to "paradoxes", which, of course, are, a priori, unfathomable mysteries, no less gratuitous and arbitrary than the Divine Mysteries of Christianity. I think "counter-intuitive" is a misnomer, for what is, in fact, "counter-rational". There was a distinctly penumbral quality about the Enlightenment.

Unfortunately, the non-theist or deist of our modern, secular science, even working at the sub-atomic level, represses such a thought with visceral antipathy. They are as reluctant to countenance a reconciliation of science with religion, as the Vatican of Galileo's day was fearful of a vitiatation of their own high-priestly status by Galileo's discovery. A turf war, basically. Allowing the possibility of divine creation, even the Intelligent Designer of Einstein's theism, would certainly knock the notion of a TOE on the head very sharply. A TOE without a leg to stand on.

The "promissory note" rules! "One day, my son, an understanding of this whole universe will be yours... or at least your grandson's."

[Sofla]

2. Here's what 'incompleteness' means

Here is what is meant by 'incompleteness,' as in 'Godel's Incompleteness Theorem':

The original question was a kind of 'Holy Grail' for mathematicians, seeking to find whether some finite number of postulates could logically lead (semi-mechanically, maybe by using computers instead of mathematicians) to every TRUE statement about mathematics. (This was inspired by Euclid's geometry theory, where he used a handful of definitional postulates or axioms (e.g., any two points determine a unique line through them, parallel lines never meet, etc.) to prove a large number of theorems (true statements) about geometry.)

Godel was able to prove the opposite of this speculative programme: his proof showed that if there are a finite number of postulates, and they are all consistent with each other (i.e., no two postulates contradict each other), then there will always be some true (mathematical) statement (theorem) that cannot be derived from the postulates themselves. Which is to say, even if one could find ALL the logical deductions available from any finite and self-consistent (non-self-contradictory) set of postulates, while such a set of deducible theorems might be very large, it would be INCOMPLETE (in that there would still be provably true statements not contained in this listing of all the logically sound implications and deductions available from such a process).

Your idea of incompleteness being related to paradoxes is not really true in this case (see above), but curiously, Godel's proof uses a paradoxical, self-contradictory statement in a key part of the proof! It's been too long since I've studied this to be more specific, but maybe Wiki can fill this in a little better (haven't looked to see what they say on this).

[Joe Chi Minh]

3. Thank you for your explanation. I won't try Wiki, though, it would all be too

technical for me.

But you can see my point about paradoxes, can't you? Consciousness that paradoxes differ absolutely from the broader, generic kind of mysteries - which latter are, in principle at least, susceptible to solution - seems to be universally repressed by secular physicists, while they quite appropriately, pragmatically exploit them as markers, incorporating them in the big picture.

I had a similar problem with the symbol for infinity. I'm still outraged at the thought that we were expected to countenance infinity's being bandied about, like some piffling taradiddle!

"Which is to say, even if one could find ALL the logical deductions available from any finite and self-consistent (non-self-contradictory) set of postulates, while such a set of deducible theorems might be very large, it would be INCOMPLETE (in that there would still be provably true statements not contained in this listing of all the logically sound implications and deductions available from such a process)."

That sounds rather like not being able to disprove a negative! The task would be all together too mighty...!

I might add that I feel honoured to be the first recipient of a post from you on DU. It was kind of you.

[Joe Chi Minh]

4. I did google some questions, and it seems they use the word,

"contradiction", for "paradox".

I suppose mathematics should inevitably reflect the fact that we'll never have a complete understanding of the physical universe. I said as much in a post to the "surfer dude", though for years I had imagined mathematics as the perfect discipline, not considering that, due to its correspondence with the physical world, its scope would be finite, even in terms of physics.

Establishing the proper reference-frame of light would be a start, but for some reason the fact that it is clearly exogenous to our space-time seems to have been overlooked or ignored by the scientific community. Well, perhaps that is actually more sensible than trying to understand the Big Bang, as I believe the nexus between the two is close, to say the least. Still, I would imagine the mere fact of trying, conjecturing, is a useful exercise of the imagination.

Not that I'm knocking the work of theoretical physicists, in principle; merely lamenting that, as Einstein oberved, scientists don't make good philosophers.

[bananas]

5. He really doesn't understand the problem

His two diagrams make it clear that he really doesn't understand the problem.
Diagram two should have an infinitesimally small yellow dot.

Or, diagram one and two could be earthrise and pale blue dot
http://en.wikipedia.org/wiki/Earthrise
http://en.wikipedia.org/wiki/Pale_Blue_Dot

[jancantor]

6. Speaking of Godel

When I was in high school, a friend turned me on to the book Godel, Escher, Bach and I credit this book with helping stoke intellectual curiosity about science and the world around me, and a search for meaning for the rest of my life. It's a great book to read, especially to get for your high school or junior high kids imo.