With Houdini, anyone can be a genius. Not to take anything away from Stockfish, which is also quite good.
Carlsen is now, in my eyes, as strong or very nearly as strong as Fischer was in 1972: http://www.2700chess.com/ Now the 2900 barrier is the only thing that is stopping him from being the most dominating player in the history of the game. I just hope he continues to have fun playing this beautiful game.
Comparing chess players from different eras is futile. The play has evolved as the game's mysteries continue to be revealed with the use of computers and those solutions widely disseminated. Fischer's opponents were lucky he quit when he did because he would have dominated for years. But the player who dominated his era more than anyone else is Paul Morphy.
It used to be futile, but now with the advent of computers, we can check how error free, or how complex, the positions of past and present players past had to deal with. Fischer found no problem comparing players from different eras, and he blatanly said that if Morphy was alive in his (Fischer's) day, he would beat everyone. I agree with him that it is very possible to compare players from different era. There is no question that if Fischer played with his knowledge against a modern top player with their knowledge, Fischer would likely be the underdog. But, if you gave the young Fischer 2 years to study the game today, in two years time Carlsen or Kasparov, __anybody__ would be in grave danger of not being the best player in the world against a prime modern Fischer. Would that be true of Capablanca? Or Lasker, or Alekhine? I don't know, but I have zero objections of saying this about Fischer. Carlsen has to be about 2925, and dominate the best players in the world for five years, before I consider him the best player ever. In my mind he is not yet better than even Kasparov, who even at 50 if he came out of retirement could school Carlsen. On the other hand, I know of no one who has written more masterly chess books than Kasparov. What will Carlsen's "My 60 memorable games" look like?
Of course you can analyze the recorded games of players to reveal how close to the "truth" the moves are. The point of futility is the comparison whether Player A from one era is/was stronger than Player B from a different era given the knowledge and resources available at the time. Agree all you want, Fischer had strong opinions about the game and was fallible. I'm not saying Morphy wouldn't dominate if he was born into this era but that we cannot ever know. Morphy dominated in an era where there was no defense and the sacrificial attack ruled. He had MAD SKILLZ, though. You are saying Fischer would be stronger than Capablanca, Lasker, and Alekhine if they were transported to the current era. That is pure speculation on your part.
Here is what isn't speculation: Houdini, Stockfish, Rybka, Fritz, etc. would dominate all of them. The engines have revealed that even the best human players are not that good at chess. Competitions amongst humans are the chess version of the Special Olympics.
Funny how two people can see things in such different light. Where you see the chess players vs computers as "special Olympics", I see Hercules vs a Lion. The problem is that it is more like Hercules against a Bulldozer. All of humanity is a "special olympics". If the ancient greeks looked at a cheetah, what is the point of having a foot race between human beings? If the ancient greeks saw a chimpanzee, what is the point of having two people wrestle? Or a gorrilla in the heavy weight section that could disassemble you from your sockets? What is the point of having a swimming race between human beings when a dolphin can spot Mike Phelps the entire pool length? If this was the attitude of the ancients, we would never have an Olympics, and you wouldn't even have your poor analogy. You see, I am more amazed by the fact that a human being can keep up with a machine that can "see" 200,000,000 positions a second. To me that is the real amazement, not that a computer is say 200 to 300 points stronger than the strongest human player. If we wanted to put chess out of the reach of computers, we could turn Chess into Go very easily. The best human players would stay the same, but computers would go back to being second rate amateurs.
You are right. It is funny. Running, wrestling, and swimming comparable to playing chess? Really now, and you say my Special Olympics analogy is poor. Why not compare chess to something that fits, like a mental activity? How about mental arithmetic? There used to be contests between humans for that. Do you think the calculator could have had something to do with its demise? Chess is a game that tests short-term calculation and memory using 32 pieces moving around 64 squares. It has been in its current form for 500 years and is close to being played out. Openings now go 30+ moves deep and the sharpest lines peter out to a draw. Six-men endgame tablebases are freely available. For non-chess enthusiasts, this means that every position with 6 pieces or fewer left on the board has been solved. Yet chess is still a fun game. I play 5m speed chess twice a month with a group of guys for $1 a game and the competition is fierce. I'm sure I'll play in a rated tournament this year at the club. I am the second highest rated player there, but in terms of the level of play, it is the Special Olympics of chess, just like it is among the Grandmasters. The engines prove this. You may not like admitting it, but humans aren't that good at chess. It's not a big deal. Get over it.
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One of the first things I do when I learn a new programming language (or while trying to learn it) is to write a little legal chess move generator in the idiom of the language. Given my recent interest in Clojure, I am going to attempt it. The exercise will not be to make if the fastest chess "engine" imaginable. In this case, instead, I will be building a chess DSL (Domain Specific Language) in Clojure, then describing the rules of Chess game to the machine in this Chess DSL. Maybe a proper name for it would be Chessure.