1) DATA I was thinking about whether all metrizable spaces are “paracompact”, and tried to come up with a definition for paracompact which fit my memories and the claim. I stumbled on the right concept and dismissed it out of hand as being too weak a notion of refinement, based off an analogy to coarse/refined topologies. That was a mistake. 1a) Question How could I have fixed this? 1a1) Note down concepts you come up with and backtrack when you need to. 1a1a) Hypothesis: Perhaps this is why you’re more productive when you’re writing down everything you think. It lets your thoughts catch fire from each other and ignite. 1a1b) Experiment: That suggests a giant old list of notes would be fine. Especially a list of ideas/insights rather than a full thought dump.
1) DATA I was thinking about whether all metrizable spaces are “paracompact”, and tried to come up with a definition for paracompact which fit my memories and the claim. I stumbled on the right concept and dismissed it out of hand as being too weak a notion of refinement, based off an analogy to coarse/refined topologies. That was a mistake.
1a) Question How could I have fixed this?
1a1) Note down concepts you come up with and backtrack when you need to.
1a1a) Hypothesis: Perhaps this is why you’re more productive when you’re writing down everything you think. It lets your thoughts catch fire from each other and ignite.
1a1b) Experiment: That suggests a giant old list of notes would be fine. Especially a list of ideas/insights rather than a full thought dump.