"Mathemagician" humancalculator video Message #21 Posted by Karl Schneider on 23 Dec 2007, 11:01 p.m., in response to message #18 by Meenzer
"Meenzer" 
Thanks again for the link to the video from 2005. Very enjoyable!
Viewers will notice how the "Mathemagician" (Dr. Arthur Benjamin of Harvey Mudd College) cautioned that the 8digit calculators would not be able to display squares of 5digit numbers with full accuracy. This reminds me of a fairlyrecent thread in which Palmer Hanson described how a TI55II of the early 1980's used a different technique for statistical summation: It maintained the running totals of the following: Number of data, the mean average,  and presumably a sum of squares divided by the number of data, calculated in a manner that minimized the likelihood of overflow.
(HP models maintain the number of data, sum, and sum of squares.)
http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv017.cgi?read=124700#124700
Palmer stated:
Quote:
There was a problem in the (TI55II) statistics routine such that if the user entered 4, 5, 6, 7, and 8 the mean would be displayed as 6 but the value in the machine was actually 6  1E10 ! This was caused by use of a different algorithm for statistics accumulation where, for example, the sum of the input values was not stored, but rather the current mean and the number of entries was stored. V8N1P2627 of TI PPC Notes).
The TI55II was an 8digit model. It might be that TI's reason for using this summation method was that the sum of squares would overflow with a single 5digit input datum, or quite likely with even a few 4digit input data.
Maintaining the running means of {4, 5, 6, 7, 8} may cause roundoff error in the summation, depending upon the order of data entry.
I concur also with "dbatiz" that Dr. Benjamin made two errors in squaring, in which several digits were incorrect. Still, his mental calculating prowess was very impressive. (Also note how his bow tie and cummerbund are decorated with numerals!)
 KS
Edited: 24 Dec 2007, 4:15 a.m.
