ajh@sdcsvax.UUCP (Alan Hu) (09/03/83)
On the subject of using CPU time to measure the effectiveness of a trick: It doesn't work. That's why these are "tricks" and not "high-speed algorithms". It might work for some of these algorithms, but, in general, humans think so differently from computers that what is fast for a human isn't necessarily fast for a computer. An example is the Tractenberg (sp) method of arithmetic. This gives a whole, new set of algorithms for arithmetic. Students of this method can do arithmetic at blinding speeds. It isn't efficient for computers, though, because some algorithms involve throwing information away. By not forgetting various bits and pieces, a person can concentrate on getting immediate answers. A computer would have to recalculate. (A person would have to recalculate, also. However, compared to a person, a computer can store things much faster, relatively, than it can recompute things. People can usually recompute simple problems faster than they can commit things to memory and reaccess them.) Also, many of these tricks are based on base 10, so a computer would have to do base conversion to use them. Along the lines of squaring a number which ends in 5, you can do something similar for a two digit number which starts with 5. You take the second digit and add 25. That gives you the first two digits. Now square the second digit. That gives you the other two digits. Example: 57 ** 2 = (25+7=32) (7*7=49) = 3249 The Tractenberg (sp) method would be quite interesting to some of you people. It has all sorts of neat ways of multiplying, dividing, etc., and checking your answers. I studied some of these, although I never mastered them. It did speed up my arithmetic back in the old Junior High Math Team Days. I think I've forgotten them all by now. The book from which I learned them went out of print. You might be able to find books on this method in used book stores, etc.