OPUS 4 DEJA VU ON A CRUMPLED EQUATION by Don Jenkins

BERTAUT-MADELUNG TRUNCATION SERIES AFTER 44 YEARS: D&#201;J&#193; VU ON A CRUMPLED EQUATION.<br /><br />The equations in question are real ones unlike the equations sometime displayed on telly which are often nonsense! The “artist” was involved in the mid-sixties in computing electrostatic interactions between the ions in crystal lattices. Ions in a lattice are positively and negatively charged, interactions between pairs of positive ions (cations) and pairs of negative ions (anions) are positive in magnitude whilst those between positive and negative are negative in magnitude. So starting from a given ion and advancing out into space the interactions alternate between positive and negative terms contributing to the Madelung series so created. Depending on how accurately one desires to calculate the total interaction, governs the number of terms in the series one needs to consider or where one “truncates” (stops) the summation.<br /><br />In 1969 the University of Warwick, along with the 7 other new Universities, had a new Burroughs 7600 computer and because the artist had these massive summations to compute he was able to use all the machines spare computing capacity by using it overnight. Because the computer was new and plugged into the wall, the University was nervous about leaving it running unattended overnight and so the artist was provided with a bed next to it in order that he could “babysit” it while it did his calculations! This meant his research advanced at a great rate; it also meant the University got an early upgrade from the U.K. Computer Board well in advance of the other contending Universities because literally all the capacity of the machine was used to the full!<br /><br />The equation - which calculates the truncation point and hence when to stop calculating the alternating terms - although “crumpled” is still as valid today as it was when the artist worked it out and published it in Chemical Physics Letters, 1971, volume 9, number 5, page 473.<br /><br />Interestingly in 1971 these calculations took days to complete on the computers of the day, whereas on a modern laptop they would nowadays take a matter of a few seconds and there is no need to sleep with them anymore!!!<br /><br />

Crumpled indeed! Sorry!