[deong]

There's another issue as well. His mapping of difficulty reaching a key isn't really the whole picture. On a conventional QWERTY layout, neither the E nor the C keys are especially hard to reach, but if you had to frequently type them successively, that would be terrible. What matters is not just where a key is in relation to your hands, but also where two keys are in relation to one other.

In grad school, I did a lot of work on the Quadratic Assignment Problem (https://en.wikipedia.org/wiki/Quadratic_assignment_problem). If you model that "key reachability" metric as two-key sequence difficulty instead, you actually get a QAP instance to solve. I built a little toy project that would look at the source text of my dissertation in LaTeX as well as the accompanying C++ source code for bigram frequencies, and I mapped out a flow matrix manually in a similar way to the author here, but including that successive keypress difficulty, and ran my multiobjective QAP solver to generate a range of keyboards optimized for my specific dissertation work.

I did this as a fun little gimmick as part of a sort of "ignobels" within my department, so the results weren't really a thing you could use. To generate a usable keyboard layout, you need to also include a ton of heuristics for things like "put all the number keys together" and the idea that you can treat "a" and "A" as the same letter, but "2" and "@" may make sense to separate, none of which I really properly handled. But I think with some work one could actually formalize the problem of finding a real layout for normal people to use.