Do you think that the point about mathematicians coming consistently to this strategy does not constitute evidence? It certainly isn’t overwhelming evidence, but it seems suspicious that virtually all mathematicians who talk about mathematical process talk about the importance of walking away from problems. I’m personally not aware of a single mathematician who thinks that such a practice is unnecessary.
(My dissertation was on mathematicians’ methods for navigating struggle in their research, and as part of that I did a fair amount of looking both at mathematicians’ accounts and at summaries of such accounts. The closest thing to denying this phenomenon I’ve encountered is the strong insistance of a very tiny minority of mathematicians that “intuition” has nothing to do with mathematics—but those same people still reported needing multiple problems to work on in parallel so that they could turn their attention away from a given problem they were stuck on.)
Mathematicians’ claims may too be explained by selective memory effects mentioned by fubarobfusco in the first comment in this thread. The question is how to discriminate between the case when the mathematicians’ testimonies are reflecting an existing phenomenon and the case when they result from a bias. Even if the insights were less likely to materialise after stepping away, there would be plenty of cases of this happening, so the fact that virtually every mathematician can remember few of them wouldn’t be surprising.
Even if the insights were less likely to materialise after stepping away, there would be plenty of cases of this happening, so the fact that virtually every mathematician can remember few of them wouldn’t be surprising.
Point taken. I guess the likelihood ratio for this strategy being actively helpful is closer to 1 than I had previously thought.
However, it’s not just a few incidences. It’s remarkably frequent. And it’s also still valuable to note that problem-solving can occur in the background without the need for conscious attention. Even if the background process turns out not to be as efficient as conscious reflection, freeing up attention while still working on the problem looks like an obvious win to me.
Do you think that the point about mathematicians coming consistently to this strategy does not constitute evidence? It certainly isn’t overwhelming evidence, but it seems suspicious that virtually all mathematicians who talk about mathematical process talk about the importance of walking away from problems. I’m personally not aware of a single mathematician who thinks that such a practice is unnecessary.
(My dissertation was on mathematicians’ methods for navigating struggle in their research, and as part of that I did a fair amount of looking both at mathematicians’ accounts and at summaries of such accounts. The closest thing to denying this phenomenon I’ve encountered is the strong insistance of a very tiny minority of mathematicians that “intuition” has nothing to do with mathematics—but those same people still reported needing multiple problems to work on in parallel so that they could turn their attention away from a given problem they were stuck on.)
Mathematicians’ claims may too be explained by selective memory effects mentioned by fubarobfusco in the first comment in this thread. The question is how to discriminate between the case when the mathematicians’ testimonies are reflecting an existing phenomenon and the case when they result from a bias. Even if the insights were less likely to materialise after stepping away, there would be plenty of cases of this happening, so the fact that virtually every mathematician can remember few of them wouldn’t be surprising.
Point taken. I guess the likelihood ratio for this strategy being actively helpful is closer to 1 than I had previously thought.
However, it’s not just a few incidences. It’s remarkably frequent. And it’s also still valuable to note that problem-solving can occur in the background without the need for conscious attention. Even if the background process turns out not to be as efficient as conscious reflection, freeing up attention while still working on the problem looks like an obvious win to me.