'Chess Knightmare and Turing’s Dream' makes the claim that there is an upper limit to how good something can be at chess.

'My work also hints that the Elo rating of perfect play may be as low as 3600. This is not far-fetched: if Anand could manage to draw a measly two games in a hundred against any perfect player, the mathematics of the rating system ensure that the latter’s rating would never rise above 3500, and if Gelfand could do it, 3400'.

With standard time controls how close are we to playing in excess of 3600?

If we could get a player playing to a higher standard than this now that would disprove KWRegan claim. If however we can get a player that should be playing at a strength in excess of 3600 but can only play at that strength then we have a good indication he is right.

If you take the wikipedia ratings of 3250-3299 elo at 40 moves in 40 minutes we have Houdini 2.0c on a x64 4CPU has a rating of 3299, Rybka 4 has a rating of 3256.

By some estimates the large Rybka cluster with 296 cores would be 200 points higher that this rating. Though many suggest that this is an overestimate because a human player would do better than this rating difference implies. If this fairly small cluster is not this good a cheap supercomputer like the '10,000-core Linux supercomputer built in Amazon cloud' should be.

There is generally an increase in elo rating of 30-50 points a year. This improvement rate puts a standard computer near the 3600 figure very soon.

Another way to improve playing strength is combining a chess engine with a very good player. This advanced chess where the human makes strategic decisions, possibly just deciding between alternatives the computer finds nearly equal. Advanced chess with a great player seems to improve the engines rating by about 200 points. 'Experts have estimated that the best man-computer teams are able to achieve a performance rating of 3000 on the Elo scale (the world's strongest players are just around 2800'. This 200 elo improvement would put Houdini on a good desktop computer now at 3500. This means at the moment a strong grandmaster with a cluster of computers should be playing at a level of nearly 3700.

A computer could be set to play at an elo rating in the 2700s. If computer draws with the advanced cluster human combination even occasionally that would imply that 3600 really is the upper limit of the elo rating.

At this point we would start noticing that adding more computation does not make for better chess. This happened before with draughts but that was solved which is a different matter.

If in the next few years we find that more computation does not produce better chess is that a datapoint that suggests that adding more computing power will not always result in improved performance the way say 'When will computer hardware match the human brain?' implies it will?

It could be that some things have a level of complexity that is so great that we cannot get all the answers but also are not free form enough that we can keep improving. Chess could be the first in a complexity class of things that the opponent can block your progress no matter how much extra computation you add. Is chess easy enough to draw in that the best human player would draw one in a hundred games against the perfect opponent?