I don’t get what role the “gaps” are playing in this.
Where is it important for what a tool is, that it is for a gap and not just any subproblem? Isn’t a subproblem for which we have a tool never a gap?
Or maybe the other way around: Aren’t subproblem classes that we are not willing to leave as gaps those we create tools for?
If I didn’t know about screwdrivers I probably wouldn’t say “well, I’ll just figure out how to remove this very securely fastened metal thing from the other metal thing when I come to it”.
I don’t get what role the “gaps” are playing in this.
Where is it important for what a tool is, that it is for a gap and not just any subproblem? Isn’t a subproblem for which we have a tool never a gap?
Or maybe the other way around: Aren’t subproblem classes that we are not willing to leave as gaps those we create tools for?
If I didn’t know about screwdrivers I probably wouldn’t say “well, I’ll just figure out how to remove this very securely fastened metal thing from the other metal thing when I come to it”.