The 22-year-old grand master is this week playing Anand Viswanathan, the world chess champion, in what some argue is the most important game since Fischer defeated Russia's Boris Spassky in 1972, the height of the Cold War.
In the interview with the UK's Observer newspaper, Carlsen later spoke seriously of the risk of insanity in later life, arguing that Fischer, who ended life as in exile from the US, ranting against a Jewish conspiracy, would have had mental problems without chess.
"It was probably only the chess keeping him sane," he said. "He would have gone insane much quicker without it. His story is very different to mine. He had a difficult upbringing. Difficult relationship to his family. I have lived a much more sheltered, normal life. As normal as it could be, considering how much I travelled."
Carlsen also downplayed a stunt he played some years ago when he played ten lawyers from Harvard University blindfolded.
"When you think about chess all the time you are playing blindfolded anyway, sort of. But I can understand why other people find it freaky. One of the beauties of chess is that you don't need a board either to play or analyse."
He also stressed that he shouldn't be viewed as a genius.
"I'm just really, really good at what I do. I'm fortunate to do something I love, but I'm not a genius."
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Nonetheless, he did not seem short on self belief.
"In tournaments, my assumption is that I am the best player there. That is why I seek positions where computer analysis can't play that much of a role, or where I can analyse it better than a computer."