The true part of my last letter yesterday was
[It's been a long day!]
The feeling that I'd expressed too strongly my criticisms of Jud McCranie's proposed attack on the kissing number problem somehow convinced me that they were wrong, and led me to apologise. In fact, they were quite valid, except that I think I mistakenly described the number of cases for each sphere (after the first few) as "a 3-dimensional continuum", when it's really only 2-dimensional. Jud's method is indeed fallacious. In 3 dimensions, it would probably get the correct kissing number of 12, and so maybe leave the fallacy undetected, but almost certainly the fallacy would be made manifest in the 4-dimensional case by the fact that it would "prove" the kissing number to be < 24. John Conway