Can someone make a progress-indicator based on this idea?
Something that shows you're between 10% and 100% done?
I do this kind of stuff all the time (guesstimate or back-of-the-envelope a value for every number relevant to a hypothetical, then smoosh 'em together to come up with a thumb suck value to sanity-check an idea.) It's great, and the comparison to dimensional analysis is spot on.
There's an amazing calibration training game where you can practice Fermis and see where you are orders of magnitude off:
Fermi estimation is just adding up the number of digits of every factor, what's really hard about answering these questions is having an encyclopedic knowledge of random quantitative trivia.
The trick is to just guess - with enough steps your errors will cancel each other out, unless you're grossly wrong, in which case you can go back and fix it. Back when these were common interview questions, because Microsoft did it, bad interviewers would pick at whether you knew the "right" number for each step.
Gives me flashbacks of high school Mensa meetings.
Gwern is an extremely strange site
I wish there were more sites and people thinking like this.