We know what S is, and the solution to the problem follows. In retrospect, I understand one method for how I could find the answer. But during the test, I can’t see through the noise fast enough (although I can smell the clue). I could go through each guess one by one, but I’m just too slow. Maybe there’s something else I’m missing that would’ve made the guess simpler, but that’s what I’m basing the slow opinion off of.
I don’t know if being slow at inference in this sense is a barrier, or indicative, of deeper creativity issues (or if I’m just suffering from the availability heuristic.)
Anyways your questions all very good, I don’t care for academia perse, I care about the questions. If I don’t keep doing academic stuff, I would hope I would’ve formed enough connections to find some route towards practical problems that still require some creativity.
Your last question is very interesting. I’m not sure how to answer it. My unhealthy worry, I think, is I really don’t like wasting peoples time. I suppose I don’t care about either being “just OK”, if “just OK” isn’t wasting peoples time, but I still get to be creative.
I guess I don’t want to be a pundit? I mean I’ll teach, but I’d be much happier if I was doing something theoretically. If this is impossible for me, I’d like to know the reasons why, and fail out as soon as possible.
Your questions are very interesting though, I still need to think about them more. Thank you for your thoughts, they give very good context to think about this, and its clear you’ve worried about analogous issues.
So, my point regarding the speed.
In the middle of working out a problem, I had to find the limit of
S = 1/e + 2/e^2 + … + n/e^n + …
I had never seen this sum before, so now cleverness is required. If I assumed guess C was true, that would imply
e/(e − 1) = (e − 1)S
This claim is much easier to check,
(e − 1)S = 1 + 1/e + 1/e^2 + … = 1/(1 − 1/e) = e/(e − 1)
We know what S is, and the solution to the problem follows. In retrospect, I understand one method for how I could find the answer. But during the test, I can’t see through the noise fast enough (although I can smell the clue). I could go through each guess one by one, but I’m just too slow. Maybe there’s something else I’m missing that would’ve made the guess simpler, but that’s what I’m basing the slow opinion off of.
I don’t know if being slow at inference in this sense is a barrier, or indicative, of deeper creativity issues (or if I’m just suffering from the availability heuristic.)
Anyways your questions all very good, I don’t care for academia perse, I care about the questions. If I don’t keep doing academic stuff, I would hope I would’ve formed enough connections to find some route towards practical problems that still require some creativity.
Your last question is very interesting. I’m not sure how to answer it. My unhealthy worry, I think, is I really don’t like wasting peoples time. I suppose I don’t care about either being “just OK”, if “just OK” isn’t wasting peoples time, but I still get to be creative.
I guess I don’t want to be a pundit? I mean I’ll teach, but I’d be much happier if I was doing something theoretically. If this is impossible for me, I’d like to know the reasons why, and fail out as soon as possible.
Your questions are very interesting though, I still need to think about them more. Thank you for your thoughts, they give very good context to think about this, and its clear you’ve worried about analogous issues.