Over the ☽

Welp.. I think I’ve officially gone loony! 😅

I can’t stop thinking about the moon.. I learned about (sunny) & (loony) at the same time:

The interesting thing to me is that since we have . It may not be that interesting, but I think it’s a beautiful equation.

Additionally, we have , which leads to another beautiful equation:

A part of what has me in lunatic mode are 2 papers I recently found:

• Impartial games with entailing moves
• A complete solution for a nontrivial ruleset with entailing moves

In the first paper the authors introduce affine impartial / normal play games.

While most of the paper is above my head, it did inspire an idea!

Can in affine impartial () & normal play () be replaced w/ to form & ?

Affine games do not include transfinite nimbers (but they can produce infinitely many finite nimbers). I think replacing w/ would result in a class of games that does include transfinite nimbers. I’m just not sure what, if anything, would break..

My basic line of thinking of why this might work is:

• (right has no moves & left can pass) (1.1)
• (left has no moves & right can pass) (1.2)
• (1.3)
• (1.4)
• (1.5)

I’m not sure how to evaluate or . I might however naively call these & .

I playfully would call these projective games.

Oh right.. the big kicker in all of this? is equal to the set of no nimbers. That is:

#NES to the max 💯

What I keep wondering is.. is “the” master idempotent?? 🤔 That which has the maximal absorbing nature (compared to let’s say the adsorbent nature of the traditional empty set ).

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In other news, after placing a bounty on a question about a multiplication nimonic (nimber mnemonic), I got an amazing answer! I initially randomly stumbled upon a simple multiplication nimonic after seeing 1 for addition. This led me to create a larger nimonic, which then led to trying to find the optimum configuration.

Enter PG(3,2). There is a nice 3d graph that I have been considering updating with labels for the given solution. I started playing around with three.js as well (peep the new hypersurreal homepage).

Need. Coffee. TTFN

~StarGirl 👩‍🎤