In Winning Ways Volume 2 (pg. 334) they say
In many ways the games and behave like enormously magnified versions of and
& give us an infinitely magnifying operation defined by
As an example they also give:
Which reminds me of the function ..
After reading the affine games paper & then seeing the formula in my notes again, I got to thinking…
They essentially define . No problems there. But they also define . I don’t have a problem with that. I just think is, well.. bigger 🤷♀️
Aside interval arithmetic & fuzzy numbers
It made me wonder if something like
would be valid.
I also wondered about this equation, because I find it rather aesthetic:
I might call this a moon magnifying operation & speculate that
I was also trying to think about game analysis for projective games. I think chess endgames could be a good fit since loopy situations are possible. Also, affine theory defines check games. So it seems a rather natural setting.
Was playing around with some custom cases as well just for fun ( x boards w/ 2 kings).