(I’m going to use the full vocabulary to answer this question.)
can we still call that doing a mistake to consider a wrong thoughts if it’s necessary to end up being close to the truth ?
So, there are a few things going on here.
First, the idea of sunk costs. There’s nothing to be gained from regretting the past; the only thing that the past is good for is learning from for the future. So if you did make mistakes, those mistakes cannot be unmade, only not made a second time.
Second, the idea that it is necessary to pass through the wrong thoughts in order to get to the right thoughts. It’s not clear to me that this is always true. Sometimes, you can start off with the right thoughts, do a consistency proof, and then do a uniqueness proof, and now everything else is either equivalent or wrong. But sometimes you do need to show how specific alternatives don’t work. And most of the time, you’re not dealing with mathematical concepts, but ‘muscle memory’ concepts—and it seems very unlikely that one would start with the optimal algorithm at the beginning. Oftentimes, one must crawl before one can walk, and walk before one can run. In such situations, what is there to regret about crawling?
(I’m going to use the full vocabulary to answer this question.)
So, there are a few things going on here.
First, the idea of sunk costs. There’s nothing to be gained from regretting the past; the only thing that the past is good for is learning from for the future. So if you did make mistakes, those mistakes cannot be unmade, only not made a second time.
Second, the idea that it is necessary to pass through the wrong thoughts in order to get to the right thoughts. It’s not clear to me that this is always true. Sometimes, you can start off with the right thoughts, do a consistency proof, and then do a uniqueness proof, and now everything else is either equivalent or wrong. But sometimes you do need to show how specific alternatives don’t work. And most of the time, you’re not dealing with mathematical concepts, but ‘muscle memory’ concepts—and it seems very unlikely that one would start with the optimal algorithm at the beginning. Oftentimes, one must crawl before one can walk, and walk before one can run. In such situations, what is there to regret about crawling?