I agree, with respect to (e.g.) math. People reason that “someone would have noticed” implies that there is no undiscovered low-hanging fruit in math.
My skepticism of this conclusion is based on my perception of how mathematicians work. They are fairly autonomous, working on the things that interest them. What is interesting to mathematicians tends to be the large problems. They swing for the fences, seeking home runs rather than singles.
Plus, there are unfashionable areas of math. A consensus that certain areas of math have been fully explored (nothing new remains) has developed, but not in a systematic way. So, it’s not clear whether this consensus is accurate, because politics (for lack of a better term) were involved in its formation.
It’s only reasonable to be confident that ‘someone would have noticed’ if someone knowledgeable about what they are looking at actually looks in that direction.
The other thing that happens is that those who notice something that goes against the orthodox view are dismissed out of hand. As in Alicorn’s point 2, soothsayers are ignored. They often are outsiders, untrained/unconditioned by the accepted view, so their arguments are frequently inadequate.
Nowhere is this more apparent than with the abusively named “Cantor-cranks”. They have noticed something fishy about Georg Cantor’s 3 proofs that the real numbers are uncountable, but because Cantor did such a good job of diverting attention so completely onto the reals, the cranks tend to fall into the same trap. Yet all along the cause of their dislike of Cantor’s proofs lies with his treatment of the natural numbers as a finite quantity.
Generally, the experts dismiss all objections as boring, or as pseudo-maths, and if the crank can argue against one proof, then the “experts” move on to the other proofs, as did Cantor, further reinforcing the original misdirection.
I agree, with respect to (e.g.) math. People reason that “someone would have noticed” implies that there is no undiscovered low-hanging fruit in math.
My skepticism of this conclusion is based on my perception of how mathematicians work. They are fairly autonomous, working on the things that interest them. What is interesting to mathematicians tends to be the large problems. They swing for the fences, seeking home runs rather than singles.
Plus, there are unfashionable areas of math. A consensus that certain areas of math have been fully explored (nothing new remains) has developed, but not in a systematic way. So, it’s not clear whether this consensus is accurate, because politics (for lack of a better term) were involved in its formation.
It’s only reasonable to be confident that ‘someone would have noticed’ if someone knowledgeable about what they are looking at actually looks in that direction.
The other thing that happens is that those who notice something that goes against the orthodox view are dismissed out of hand. As in Alicorn’s point 2, soothsayers are ignored. They often are outsiders, untrained/unconditioned by the accepted view, so their arguments are frequently inadequate.
Nowhere is this more apparent than with the abusively named “Cantor-cranks”. They have noticed something fishy about Georg Cantor’s 3 proofs that the real numbers are uncountable, but because Cantor did such a good job of diverting attention so completely onto the reals, the cranks tend to fall into the same trap. Yet all along the cause of their dislike of Cantor’s proofs lies with his treatment of the natural numbers as a finite quantity.
Generally, the experts dismiss all objections as boring, or as pseudo-maths, and if the crank can argue against one proof, then the “experts” move on to the other proofs, as did Cantor, further reinforcing the original misdirection.