...even if you cannot prove it ? This was the question posed by Edge.org to a number of scientists, intellectuals, and thinkers of various hues. There have been numerous comments on this article, and a spread in the NYT, but what I found interesting was the choice of people interviewed. There were extremely few computer scientists in the bunch, and not a theoretician among them ! John McCarthy thinks that the continuum hypothesis is false...
Any thoughts on what statements we believe to be true, even if we can't prove them ? P ? NP is not included :)
1) Does a single mathematician count?
ReplyDeletehttp://www.edge.org/q2005/q05_8.html#devlin
He states obliquely that he believes the Riemann Hypothesis.
2) OK how's this: I believe but can't prove that Graph Isomorphism is strictly between P and NP.
Posted by Mitch
Regarding Freeman Dyson's answer:
ReplyDeletehttp://www.edge.org/q2005/q05_9.html#dysonf
I'm not convinced that his statement is unprovable. In fact, I believe that can be proved. But I can't prove it at the moment.
Posted by Anonymous
Wow, thank you so much for posting that. I need to drop by Edge more often.
ReplyDeleteI kind of bought Dyson's explanation that it can't be proven b/c of the randomness factor, but I'm not a mathematician and am more than willing to believe people, especially Professor Dyson, whom I've found to be as kind as he is smart.
That aside, though, strictly speaking the question was "What to do you believe to be true even though you cannot prove it?" not "even though it's not provable." Which, I think, is a good point when we are discussing life with each other and assessing each other's beliefs. Just because I can't prove something, especially right here, right now, doesn't mean it isn't true. Skepticism is a wonderful, wonderful, important thing, but recognizing that someone might be right even if they lack the ability to prove themselves right now is, in fact, more correct--and slightly more kind.
Posted by Saheli
A speciality of this same question is being discussed (not very actively) in QubitNews: "What do you believe is true about Quantum Computing (and/or Quantum Information) but cannot prove?" ( http://quantum.fis.ucm.es/article.pl?sid=05/01/08/1233206&mode=thread ). You are welcomed to join the discussion, maybe you can shine some light on complexity, P vs NP vs BQP...
ReplyDeletePosted by Alejandro Gaita-Ariño