F# would probably be the best way to go, now.
Mar 12, 2010 at 3:02 PM
Mar 11, 2010 at 11:15 AM
I think there is a bi-directional correspondence between computation and energy transfers. If you think of computation as manipulations of symbols in the lambda calculus or in the pi calculus, then that involves clearing and storing "memory cells," usually represented as states of switches in a network. Ed Fredkin showed that you can't change states of memories without energy transfers (and the entropy growth that goes along with them, by the second law of thermodynamics!), so it's not possible to do computations without spending energy and growing the heat in the Universe!
Mar 11, 2010 at 10:15 AM
Hi Akopacsi -- The rough idea on time is this: Consider a path -- a 1-dimensional curve -- passing through points in space-time. Every point along that curve has a particular set of 4 coordinates: 3 space coordinates and 1 time coordinate, for any reasonable choice of coordinate systems. Now, parameterize that curve by the incremental distance along the curve: as you move from one point to another, you go a certain "distance" in 4-space, a distance measured by the "metric tensor," which is a generalization of the Pythagorean or Euclidean distance. Locally, that incremental distance is sqrt(dx^2 + dy^2 + dz^2 - dt^2) (notice the minus sign!). This distance measure is unique for a choice of metric tensor and is called the "proper time." It's a kind of cosmological average of proper times over the Hubble motion of galaxies along their curves that measures the age of the Universe backwards 13 or 16 billion years. Very rough idea, but hope that adds some clarity.
I'll take another look at "Rigs of Rods," one of my all-time favorite pieces of software!
Jan 08, 2010 at 8:44 PM
Fantastic, Curt! thank you.
Jan 06, 2010 at 8:53 AM
Erik and I have started cooking up the last batch on this topic. Will have something to video soon.
Jan 04, 2010 at 5:31 PM
Yes, Parmenio, there are plenty of people looking to model fundamental processes in physics as computations. Here's just one paper that I found in a few seconds of Binging : http://arxiv.org/abs/quant-ph/0312067
In general, arxiv.org is a fantastic place to watch for new stuff coming down the pike.
Jan 04, 2010 at 3:34 PM
Sorry you didn't like it, bigbag.
Jan 04, 2010 at 3:33 PM
Spivak is the classic -- very terse, very beautiful, very out-of-print Hubbard & Hubbard is loaded with examples and remarks and exercises.
Jan 03, 2010 at 6:53 PM
yes yes, we need to finish up
Jan 03, 2010 at 2:51 PM
yes, ShiNoNoir -- the best, current source I know is "Vector Calculus, Linear Algebra, and Differential Forms" (VCLADF) by Hubbard & Hubbard, http://matrixeditions.com/UnifiedApproach4th.html .