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
).

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 👩🎤

## Comments

I forgot to add the

Moonlight Theorem🤦♀️It’s like some sort of black hole!