You should be aware that in many cases, the sensible way to proceed is to be aware of the limits of your knowledge. Since the website preaches rationality, it’s worth not assigning probabilities of 0% or 100% to things which you really don’t know to be true or false. (btw, I didn’t say 1) is the right answer, I think it’s reasonable, but I think it’s 3) )
And sometimes you do have to wait for an answer. For a lesson from math, consider that Fermat had flat out no hope of proving his “last theorem”, and it required a couple hundred years of apparently unrelated developments to get there....one could easily give a few hundred examples of that sort of thing in any hard science which has a long enough history.
Uh I believe you will find that Fermat in fact had a truly marvelous proof of his last theorem? The only thing he was waiting on was the invention of a wider margin.
Little-known non-fact: there were wider margins available at the time, but it was not considered socially acceptable to use them for accurate proofs, or more generally for true statements at all; they were merely wide margins for error.
I wonder how much the fame of Fermat’s Last Theorem is due to the fact that, (a) he claimed to have found a proof, and (b) nobody was able to prove it. Had he merely stated it as a conjecture without claiming that he had proven it, would anywhere near the same effort have been put into proving it?
Had he merely stated it as a conjecture without claiming that he had proven it, would anywhere near the same effort have been put into proving it?
Almost certainly not. A lot of the historical interest came precisely because he claimed to have a proof. In fact, there were a fair number of occasions where he claimed to have a proof and a decent chunk of number theory in the 1700s and early 1800s was finding proofs for the statements that Fermat had said he had a proof for. It was called “Fermat’s Last Theorem” because it was the last one standing of all his claims.
You should be aware that in many cases, the sensible way to proceed is to be aware of the limits of your knowledge. Since the website preaches rationality, it’s worth not assigning probabilities of 0% or 100% to things which you really don’t know to be true or false. (btw, I didn’t say 1) is the right answer, I think it’s reasonable, but I think it’s 3) )
And sometimes you do have to wait for an answer. For a lesson from math, consider that Fermat had flat out no hope of proving his “last theorem”, and it required a couple hundred years of apparently unrelated developments to get there....one could easily give a few hundred examples of that sort of thing in any hard science which has a long enough history.
Uh I believe you will find that Fermat in fact had a truly marvelous proof of his last theorem? The only thing he was waiting on was the invention of a wider margin.
Little-known non-fact: there were wider margins available at the time, but it was not considered socially acceptable to use them for accurate proofs, or more generally for true statements at all; they were merely wide margins for error.
I wonder how much the fame of Fermat’s Last Theorem is due to the fact that, (a) he claimed to have found a proof, and (b) nobody was able to prove it. Had he merely stated it as a conjecture without claiming that he had proven it, would anywhere near the same effort have been put into proving it?
Almost certainly not. A lot of the historical interest came precisely because he claimed to have a proof. In fact, there were a fair number of occasions where he claimed to have a proof and a decent chunk of number theory in the 1700s and early 1800s was finding proofs for the statements that Fermat had said he had a proof for. It was called “Fermat’s Last Theorem” because it was the last one standing of all his claims.