G'morning Mark, 

 MM> Ah me ... took a whole term to derive the principal
 MM> components of a 10 item table of correlations,
 MM> doing everything by hand and mechanical adding
 MM> machine as a fulltime student  ...   and now, on
 MM> this old Pentium, I routinely do a much fuller
 MM> multivariate analysis of 3 or 400 variables in
 MM> seconds.... :-)

 ml> i have experianced almost the same type of thing... i wrote a program
 ml> years ago to find what i call Pythagorean Triples... they are the
 ml> A, B, and C in A^2+B^2=C^2... 3 4 5 being the first set...

Diophantine or whole number triplets ?

 ml> back then, it took many hours for those up to 100 to be
 ml> found... on today's machines, that run is over in
 ml> seconds... i've adjusted the program over the years and run
 ml> it every once in a while just for fun and it still takes
 ml> only seconds for it to find the triples up to the highest
 ml> it can count in that language...

Mind-boggling stuff - my factor analyses seek the eigenvalues from 
square matrices of correlations repeatedly - which means a 100 
cell matrix for 10 items and 160,000 for 400.  On the old IBM 1800 
series mainframes under Fortran with Assembler modules in the mid 
60's you could write off 30 minutes for a 20 item analysis;  to 
have your desktop repeat the same work in under a second is 
totally amazing....

:-)
 
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