At 9:16 AM -0800 10/31/96, Hal Finney wrote:

First I am going to write a little bit about the lore of logarithms. I think today a lot of people don't know what they are. When I was a boy, in the 1960's, computers and even calculators were not widely available. Yet engineers in many fields needed to perform ... By the time I was in high school calculators were becoming fairly widespread, but we still learned how to use log tables to do multiplication and division. Whole books were published containing nothing but tables of the logarithms of numbers. You can still find these sometimes in used book stores. There were lots of tricks to

(These were the "Smoley" books, amongst others.) Sliderules were just becoming common when I was in high school.... Seriously, only a very few of us had and used sliderules...mine was a big synthetic K & E (Keuffel and Esser, as I recall). The raging "DOS vs. Mac" or "RISC vs. CISC" debate of that age was "aluminum" (the yellow Dietzgens) vs. the old standby, "bamboo." Plus some oddball circular sliderules. Those of us who used sliderules were sometimes characterized as "nerds"...perhaps this is why I today have such a strong reation to so many young programmers and engineers voluntarily calling themselves "nerds" and "geeks." (The deconstructive, postmodern theory is presumably that they are "reclaiming" the term, as with dykes and niggers reclaiming those hateful terms. I still reject this as crap.)

It's hard for people today, raised on throwaway and even virtual calculators, to understand the sense of power that came from using logs for calculations. Until we learned these advanced techniques the only accurate alternatives were the terribly tedious hand methods. Being able to get results by adding up a few numbers from a book was an amazing improvement.

And these tables were of course a major motivation for the development of computers, going back centuries. Mechanical computation of log tables, and even Babbage's work, was inspired by this. Ditto for artillery range tables, some of the earliest applications of the earliest digital computers. (Precomputation of values, aka "tabling," is of course still a modern topic. Some of the newer names come out of AI, compiler research, etc. For example, speculative execution. Not exactly a book of precomputed logs, but similar.) Recall that Fermi, von Neumann, and Feynman had a contest at Los Alamos in WWII, with some problem being computed by Fermi on sliderule, von Neumann on early versions of computers, and Feynman with log tables and adding machines. Feynman won, as I recall the story, but presumably only because von Neumann was not allowed to do it in his head. (The funny story goes that a problem was going around Los Alamos that goes like this: two trains are approaching each other on the same track, one train going 60 mph and the other going 40 mph. When the trains are 100 miles apart, a fly takes off from one train and flies 200 mph toward the other train, then turns around and flies back at the same speed, and so on, until the trains collide. How far does he fly? Von Neumann was asked this, glanced at the ceiling, and gave the answer (left as an exercise for the reader). The questioner said, "Oh, Dr. von Neumann, I'm glad you saw the trick and didn't try to compute the infinite series." Von Neumann replied, "You mean there's another way?") --Tim May "The government announcement is disastrous," said Jim Bidzos,.."We warned IBM that the National Security Agency would try to twist their technology." [NYT, 1996-10-02] We got computers, we're tapping phone lines, I know that that ain't allowed. ---------:---------:---------:---------:---------:---------:---------:---- Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay@got.net 408-728-0152 | anonymous networks, digital pseudonyms, zero W.A.S.T.E.: Corralitos, CA | knowledge, reputations, information markets, Higher Power: 2^1,257,787-1 | black markets, collapse of governments. "National borders aren't even speed bumps on the information superhighway."