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Esteban Trev HNY ET. I studied philosophy in university with everyone saying “whaddya gonna do with that?”. They predicted I’d end up in IT, which is fairly correct, but I also kept doing philosophy as a hobby, and that ended up adding to my net worth.

Anyway, the philo guy I zoomed in on most was Ludwig Wittgenstein, wondering if you’ve grokked him. I live until the 1950s. He came out with essentially two famous philosophies with an interim in between. From a very rich Vienna based family, fought for Austria as an artilleryman, made a prisoner of war.

But he skipped out on being rich, ironically because his family put pressure on the siblings to really succeed, make a name for themselves, and since he was born into a rich family, becoming rich was not an option, as he was rich already. No fame and glory down that road for sure.

So he lived like a hermit so he could pal around with other philo guys, like Bertrand Russell, and investigate the meaning of language to its logical (or illogical as the case may be) core.

When it comes to your example of 5 + 5 = 12, his later talk was of “language games” and he’d give examples of simple games in his posthumous Philosophical Investigations (book) which overlapped his Remarks on the Foundations of Mathematics. Some guy says “slab” and another guy brings him a slab. He sketches these actions, sometimes involving color coding and lookup tables.

It’s branching off the latter philosophy that I’d bring up the game of Quadrays and the Alternative Volumes Table (AVT) that goes with.

Games as a concept come with rules, fouls, but also innovation, and maybe episodes of ambiguity, when people just aren’t in agreement on how the rules should extend in some special case situation.

Speaking of which, this will seem tangential: I’m interested in sports wherein someone does an amazing move that’s not explicitly against the rules, but then it’s banned right away after.

I learned of two such examples recently on YouTube. (1) A figure skater does an actual flip on the ice, heals over head. She lands gracefully but the sport’s judges don’t relish all the neck-breaking and cleanup that’d stem from many imitators failing, on and off camera. Similarly: (2) a long jumper dude set a record by including a flip in mid air. Wow. Banned. Same reasons I imagine.

A lot of people aren’t familiar with what a contrarian Cantor was. I’ve read some of his original stuff and found out he took on our notion that “space is three dimensional” big time. If you ever allow your space to be both finite and discrete for some reason, i.e. let infinity drain away, then Cantor will say: hey, I can visit all your points in sequence, like we do in computer memory, so why do we say your space is “3D” even if XYZ works for ya?

At which point the mathematicians get defensive and say “yadda yadda” and innovation occurs.

A lotta layfolks will answer “space is 3D because I only need 3 coordinates, x, y, and z” (Cantor: you sure you don’t need less?). But then an athlete stunt man comes along and says “space is 4D because 4 coordinates works just as well and the minimum inside-outside made of edges faces four ways when enclosing a center”.

At this point, I could add: 5 + 5 =12 i.e. if you make your base different, a tetrahedron instead of a cube (different base shape), or 12 instead of 10 (arithmetic base), you get new moves, new rules, and therefore new truths. You get new truths for new games. Language games. And sometimes there’s confusion about which game we’re playing.