G'morning David, 

 DW> I agree that the process of analyzing this problem has been very
 DW> interesting. At the beginning of this thread, someone (? Mark)
 DW> mentioned that it used to take a whole day to find the first 100
 DW> triples. But, if people back then had thought about the problem as
 DW> thoroughly as we have done, I'm sure they could have found 100 triples
 DW> in an hour or two, using only pencil-and-paper calculations. The vastly
 DW> faster speeds that we can achieve now are only partly the result of
 DW> much better calculating technology. Another major factor is that we
 DW> have immensely more efficient algorithms than the trial-and-error
 DW> method that is the most obvious one to try. The latest version of the
 DW> program is thousands of times faster than my first attempt, which was
 DW> basically a hunt-and-peck effort.

The latter-day evolutionary psychologists would hold that people 
are thinking clearer these days as various algorithms become `part 
of the language' - but there are times when popular understanding 
of things established over the last 200 years drives me to 
despair..

 DW> Good computers are useful. But they are no substitute for clear
 DW> thought.

Amen.

:-))
 
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