Great write-up. Inspired me to try how much further ICL could go beyond “simpler” mappings (OP shows pretty nice results for two linear and two quadratic functions). As such, I tried a damped sinusoid:
with the prompt:
x=3.984, y=6.68
x=2.197, y-2.497
x=0.26, y=-7.561
x=6.025, y=-1.98
x=7.126, y=-4.879
x=8.584, y=-0.894
x=9.97, y=3.403
x=11.1, y=2.45
x=12.09, y=-0.452
x=13.72, y=-2.48
x=14.81, y=-0.606
x=10, y=
but didn’t get any luck. Maybe I need more points, especially around the troughs and valleys.
>This type of paper reading, where I gather tools to engineer with, initially seems less relevant for fundamental concepts research like alignment. However, your general relativity example suggests that Einstein also had a tool gathering phase leading up to relativity, so shrugs.
As an advisor used to remark that working on applications can lead to directions related to more fundamental research. How it can happen is something like this: 1. Try to apply method to domain; 2. Realize shortcomings of method; 3. Find & attempt solutions to address shortcoming; 4. If shortcoming isn’t well-addressed or has room for improvement despite step 3 then you _might_ have a fundamental problem on hand. Note that while this provides direction, it doesn’t guarantee that the direction is a one that is solve-able in the next t months.