Brian Beckman: On Analog Computing, Beckman History and Life in the Universe Redux
Mar 12, 2010 at 3:02 PMF# would probably be the best way to go, now.
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F# would probably be the best way to go, now.
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!
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!
Fantastic, Curt! thank you.
Erik and I have started cooking up the last batch on this topic. Will have something to video soon.
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.
Sorry you didn't like it, bigbag.
Spivak is the classic -- very terse, very beautiful, very out-of-print Hubbard & Hubbard is loaded with examples and remarks and exercises.
yes yes, we need to finish up
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 .