Author: Bob Durrett
Date: 17:51:32 01/05/04
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On January 05, 2004 at 20:05:01, Rolf Tueschen wrote: <snip> > >Often the third man can solve the insolvable between two great experts. Often it >needs a little catalyst and the two undertsand each other. > >Here we have a very simple puzzle. > >That you see no reason to rely only on statistical numbers, that is totally ok, >but this doesn't show how such 'other' information could be included into Elo >stats. > >Rolf ><snip> Thanks for trying to help, Rolf. : ) I'm afraid that the discussion has drifted into measure theory. I'm sure you use various measures in your line of work. Perhaps we are heading toward a discussion of how one thing can be used to measure many other things. Three things are of interest: (1) Measures of past chess performance, (2) measures used in estimates of future chess performance, and (3) measures of a chessplayer's ability to perform in the future. Generally, one may use a single thing to measure many other things. I cannot think of an example from Psychology, but here is one from Physics: Suppose one had an ordinary meter stick marked off in decimeters, centimeters and millimeters. This "ruler" can be used to measure distance, pressure, and temperature. All that is required is a one-to-one correspondence. Atmospheric pressure is often measured in centimeters. The height of a column of mercury is measured with the meter stick and then the one-to-one correspondence between distance and pressure is applied to get the pressure. In this case the pressure is expressed in centimeters. Similarly, the ordinary thermometer is commonly used to measure temperature. But what we are actually doing is measuring a distance, the length of the mercury column, and then using an approximate one-to-one correspondence between temperature and distance. In this case, however, the ruler is usually annotated with a different measure, degrees celsius. One thing can be used as a measure of many things and many different things can be used to measure the same thing. [ This just helps to keep scientists employed. : ) ] Although the numerical values labeled "rating" in the FIDE rating list is an excellent measure of past performance, it is also a measure used in the estimation of future performance. It is also a measure of chessplaying ability. Furthermore, it may be used to measure many other things like the chessplayer's IQ. Admittedly, a chess rating certainly is a very poor measure of IQ [because chess ratings and IQ are very poorly correlated] but it does at least make some sense because, for example, cretins do not play chess. Hang in there Rolf! Bob D.
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