Even a cursory understanding of, say, the trials our ancestors went through in the 1300s makes it obvious that he's wrong to project back his little exponential curve that far.
See http://www.revisedhistory.org/view-garry-kasparov.htm for details of Kasparov's beliefs. See http://en.wikipedia.org/wiki/British_Agricultural_Revolution and http://en.wikipedia.org/wiki/Medieval_demography for basic historical facts that show some basic flaws in Kasparov's arguments. (About his points on Roman numerals, they are indeed entirely unsuited to calculation. The Romans did all calculations using abacuses, numerals were just their way of writing down the answers for which purpose they are just fine.)
Not too far off from a modern algorithm, except that it lacks even basic optimizations like alpha-beta pruning, etc. and an incredibly fine-tuned evaluation function and a huge library of opening and closing moves.
http://uscfsales.wordpress.com/2011/07/01/an-“easy”-engine-f...
So what takes so long? I assume their process is roughly "consider all possible moves, decide how good they are". So if they only look one move ahead, that sounds to me like when they evaluate a potential position, it can take more than a few seconds and they do it without reading possible future moves. Which seems unlikely.
Am I misinterpreting "one move ahead"?
The article mentions they also played at 5-ply and it lasted 27 and 30 moves against Kasparov, which is probably better than most casual players would do.
