Having done so, from both the asking and being asked, yes I was offended. And glad I was asked after actually doing it. And learned to be insistent in asking. We all have hesitation but we should realize that “expertise” is a relative illusion and peer review is the only standard of progress we have ever demonstrated to be (eventually) fool proof. There are no people I trust in any field to be right for the sake of their name or accomplishments. Society needs that feeling to be stymied and eventually eliminated.

https://www.nlp-kyle.com/post/number_computability/

The smallest known Diophantine equation that cannot be solved by any Turing machine last I checked had ~8000 states as a Turing machine. This Turing machine cannot be decided to halt, and if it does halt in finite time then an (outer) Turing machine could execute it to predict that, so this lives beyond decidability:

https://scottaaronson.blog/?p=2725

I find it annoying that the response to this from the Chaitain perspective is to throw your hands in the air and say not all of math is predictable and let “equivalent to halting decidability” be the death of effort. There’s a richer field of ‘hypercomputation’ sitting beyond the pale, and I believe it will be topological applications that untwist this knot [pun intended]. I’m excited for the post Turing world but i dare say I won’t live to see it.

https://science.nasa.gov/mission/mars-2020-perseverance/soun...

https://www.proquest.com/openview/2a5f2e00e8df7ea3f1fd3e8619...

A few of my own experiments in this time with unification over the binders as variables themselves shows there’s almost always a post HM inference sitting there but likely not one that works in total generality.

To me that spot of trying to binding unification in higher order logic constraint equations is the most challenging and interesting problem since it’s almost always decidable or decidably undecidable in specific instances, but provably undecidable in general.

So what gives? Where is this boundary and does it give a clue to bigger gains in higher order unification? Is a more topological approach sitting just behind the veil for a much wider class of higher order inference?

And what of optimal sharing in the presence of backtracking? Lampings algorithm when the unification variables is in the binder has to have purely binding attached path contexts like closures. How does that get shared?

Fun to poke at, maybe just enough modern interest in logic programming to get there too…

If it's not been already there's immediate application, e.g. problem 41.

[1]:https://link.springer.com/article/10.1007/s00453-015-0079-6

My home hobbies resemble work within my area, but not my current job function, but I'm keenly aware my employer may try to take advantage of my other talents and do I guess the only thing that saves having an alternative hobby is that I'm so diversified that whatever my work task is I can work on an orthogonal hobby at home. It's kinda nice, I've got both really.

In my mind if I "sell out" (in terms of trading in for that sense of purpose in my work), and just work for the paycheck, then I would go for max. Work an HFT quant firm as a senior or principal engineer or research analyst. $$$. Or some other juicy gig. But I would hate myself if that became a slog and I had no time for my interests at home.