If the universe was "made of mathematics," then there would necessarily exist a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that not only does a Grand Unified Theory not exist, but that the formulation of one is impossible (http://www.hawking.org.uk/godel-and-the-end-of-physics.html).
The author stresses that all of reality is mathematical in structure, but this is at odds with the fact that all mathematical systems containing self-reference are necessarily incomplete. Physics is a self-referential system.
If the structure of the universe is mathematical, it is probably a very different math than humans are used to. Insert your favorite flavor of metaphysics here!
Suppose we discover our universe is a simulation. This would imply that the universe is Turing-computable. Would there not therefore exist a "Grand Unified Theory" that simply described, with absolute precision, the operation of the simulator? Or would it be impossible to produce such a specification?
So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state was possible or not?
Then all you have to do is demonstrate that we live in such a universe, and all the philosophers can retire because we've found the ultimate answer to the ultimate question.
I think we all know exactly what the Gödel number for our universe would be...
Comments
If the universe was "made of mathematics," then there would necessarily exist a Grand Unified Theory. But, Hawking asserts that Gödel's Theorems imply that not only does a Grand Unified Theory not exist, but that the formulation of one is impossible (http://www.hawking.org.uk/godel-and-the-end-of-physics.html).
The author stresses that all of reality is mathematical in structure, but this is at odds with the fact that all mathematical systems containing self-reference are necessarily incomplete. Physics is a self-referential system.
If the structure of the universe is mathematical, it is probably a very different math than humans are used to. Insert your favorite flavor of metaphysics here!
Hmm. That's an interesting counterpoint.
Suppose we discover our universe is a simulation. This would imply that the universe is Turing-computable. Would there not therefore exist a "Grand Unified Theory" that simply described, with absolute precision, the operation of the simulator? Or would it be impossible to produce such a specification?
So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state was possible or not?
Then all you have to do is demonstrate that we live in such a universe, and all the philosophers can retire because we've found the ultimate answer to the ultimate question.
I think we all know exactly what the Gödel number for our universe would be...
420?
My money's on 69.
Rudy Rucker had some interesting conversations with Gödel about a deterministic universe in which (because time is illusory) backward time travel exists: http://www.rudyrucker.com/blog/2012/08/01/memories-of-kurt-g...
Thankyou - fascinating account.
I particularly like how, in describing Gödel's office, he mentions "On the empty desk sat an empty glass of milk." The paradox seems appropriate.