Apr 19
physics
Discuss some ideas in the physics of information.
This stuff is by and large full of deep theoretical
physics, so most of what we can do here is hand waving.
some sources:
From wikipedia's "holographic principle":
In his 2003 article published in Scientific American magazine,
Jacob Bekenstein summarized a current trend started by
John Archibald Wheeler, which suggests scientists may
"regard the physical world as made of information, with
energy and matter as incidentals."
some of the ideas are:
- deep connection between physics entropy & information entropy
- physics is deterministic (even quantum wave equations) & reversible, so information is "conserved"
- does then matter flowing into a black hole destroy information?
- "black holes have no hair"
- hawking radiation - no information content?
The full theoretical physics of all this seems to be tied up in
a complete theory of quantum gravity ... which we don't have.
So there's a fair amount of wiggle room out there.
zero knowledge proofs
Google that for lots of references.
The typical approach is to split the "knowledge"
somehow into two pieces, both of which together
reveal the secret. Then in an interactive
dialog between a "prover" and a "verifier"
- the prover digitally signs the 2 pieces, and offers to show either to verifier
- verifier picks either and is shown that it is correct, but does *not* get to see the other half
- repeat many times, with probability of "prover is guessing answer" dropping by 1/2 on each iteration
Do this for the hamilton circuit of a graph. The two pieces can be
- relabeling (isomorphism) of vertices, and
- traversal sequence in terms of new labels
Class exercise : prove that you've solved a sudoko ... without revealing the solution.
