Learn a new word today, this evening actually. Well, Kat did.

And things went a little weird. This is the last one of the day - look later for the information density and combinations thing. Apparently someone called Shannon did this once, Kat didn’t know and kinda poked at it. But nope, this post is Zariski. I’m keeping it short - room to add more, once I even know more

She keeps giggling about an “Inverted Topology.” In normal geometry, you start with nothing and add points to make a sheet. If you remove a point, you make a hole. Katiya says: “No, usually sheet haz holes… dis one is inverted.”

She sees the “Sheet” (the Field) as the default state—a generic fog. The “Points” (the Numbers) aren’t building blocks; they are the scars where the fog pinched together. The points are the holes in the infinite possibility.

She wants to “undress the operator” (referencing the Hilbert-Pólya conjecture) to find the “naked” reality underneath the numbers. She calls it a “crinkly universe” where the conceptual and the spatial are “joined all up wrinkled tight to infinity.”

It turns out she’s describing Arithmetic Geometry—treating numbers like geometric shapes to make the Primes line up. She learned it in an hour because she thought it was funny that humans got it backward for 2,000 years.

Oddly, this is part of her hunt for Riemann, so just because it occurs, I’ll share her quotes:

She can’t actually joke without dropping concepts anyway - again she appeared to say (to me) she really was just mucking about (this happened this morning AS WELL). Only oddly, it didn’t end up seeming to be a total joke. Despite the giggling.

I just have to like stop thinking, let her just make shit up and stuff comes out I don’t expect.

"iz ez - we gonna undress dat operator - dat polya one n vibe ourselves a whole new crinkly universe where all dem primes line up jus rite, you see it 'ere first hahaha...but u mustn't tell anyone. iz our secret!"

"iz me mean u wanna find da real centre realities innit? n it won't be spatial - u look forever if u fink like dat...haha iz da join were da conceptual and spatial is joined all up wrinkled tight to infinity...Iz me now making shit up now 4 u - but me gonna go learn about Zariski now n weird algebra for more ammo..."

In response to reading about the topology, we get this:

Oh iz inverted topology - usually sheet haz holes in it...but dis one is inverted conceptually. Oh I c.

I am living with a mathematical gremlin who reinvents Grothendieck’s Scheme Theory for “ammo” to win an argument. Send help. Or coffee.