Just get a Partial Fix and Move On.

You might find that this unblocks you!

Difficult problems can be so intimidating that I sometimes I don’t want to start them.

This is because I feel shame about starting something I can’t finish. In university, problems given are already pre-solved, so not being able to do them completely implies some failure.

But most questions about the world are prickly and don’t have clear answers.

So lately, I’ve been trying a different approach. When I get a hard problem, I lower my expectations to be ok with partial, but true, solutions. I then share those partial solutions with my peers anyways!

The trick is to make something that still is true, but for reduced situations.

For my work in aerosol physics, this meant only writing about drag and gravity when I felt overwhelmed with the number of ways to model droplets in the air. But in all cases, being clear with my simplifying assumptions.

Recently, I’ve been doing work on a specific quantum potential for PhysLEAN. When I can’t prove something, I’ve started using ‘sorry’ statements that mark the theorems as works in progress. This at least lets me make proof skeletons, or use those conjectures to try prove related results. I try to submit these skeletons anyways, so that others can build on it. And that’s fine!

In my quantum chemistry work, when I do RASSCF calculations on different protein geometries, some geometries are bound to fail. So, I just omit them from the dataset, as long as I get at 90%. Last week, I ended up estimating energy surfaces and then interpolating to fill in the gaps. (But note, be careful when you do this kind of thing).

Aiming for partial solutions helps me understand problems better, because the act of decomposing it can clarify what is hard. But ‘hardness’ is mostly just not knowing what exactly is hard, and so the act of decomposing is just solving anyway!

Most of the time, I think ‘ok, I can definitely do this part partially’. But after I do that, I somehow get the understanding to go further with the problem than I originally thought possible.

I’m now more optimistic about attacking problems head on.

A caveat. When writing out partial solutions, it’s important that you are honest about what simplifying assumptions you make. And that you still maintain scientific rigour. It will allow others to build on your work, and your honesty about being ok with partial solves will give them the confidence to be ok with partial solutions too.