From: "David Grosof on behalf of David Grosof To: "jeevacation®gmail.com" <jeevacation®gmail.com> Subject: Multi-dimensional cryptography Date: Thu, 10 Sep 2009 21:38:13 +0000 Attachments: ThesisSaul_sgphdlOMB.pdf Hi, Following up on our phone chat about multi-dimensional cryptography, I wanted to share one, perhaps obvious if essential, clarification, and to point out to you a mathematical development that is highly relevant. Clarification. An arbitrary Rube Goldberg machine does not necessarily communicate information in a channel, howsoever many physical subsystems and kinds of force are harnessed. The mechanism has to communicate something about a subset (usually one) from a larger set of possible messages. It's not enough to have a complicated way to build and assemble a printer that prints "The plane arrives at 7"; there has to be a way of using the mechanism(s) to communicate alternate messages as well. I am a huge fan of Gregory Bateson's useful maxim, "Information is a difference that makes a difference" from the early, brilliant chapters of his book Man and Nature. Interesting Math Let's pursue the analogy to DNA some more. In the simple central-dogma version, the DNA sequence specifies an amino acid sequence, which, in certain physical circumstances normally prevaliing in a cell, circumstances of pH, osmolarity, ribosomes, energy in the form of ATP, and more, that when fabricated will fold up to do something amazing -- including the encoding of neuronal, immune or endocrine signals in one fashion versus another way (!). If those circumstances don't prevail, it won't fold up in a particular way and be integrated into cellular function normally. The relevant math of programmable assembly includes an interesting, strong claim (loosely expressed herein): an edge-connected string of tetrahedra can be folded up to produce any arbitrary 3-D shape (above the resolution limit set by the size of the unit tetrahedon). I attach my company co