CB Wells

Logic. Global ecological crisis.

[CB Wells @c0b1w2]

@thymine235711 Hi! Thanks for your interest. The thesis is at the bottom of the main page of https://t.co/ucCjPDCGm5.

[CB Wells @c0b1w2]

I'm making a wiki: https://t.co/5kdHbJregl

First, I'm loading my thesis into Metalogic, and so far you can see full detail in Ch.1: Span categories.

Second, I'll be making Logic: the story and language of category theory in three parts: Binary Logic, Matrix Logic, and Active Logic.

Research is for making a plan to systematize category theory in the 3D language of metalogic. (It will take a lot of collaboration to map out such a big project.)

Development is for the next steps toward an education and research program based on Color Logic. (Top priority: a drawing app! If you know someone who could help, let me know.)

[CB Wells @c0b1w2]

@Bocse Thank you! That sounds great. Yes, let's talk sometime. Feel free to email me, or message on here.

[CB Wells @c0b1w2]

COLOR LOGIC
Colors are types, and pointers are processes.
This is a world.

Strings are relations, and beads are inferences.
This is a way of thinking about the world.

Processes compose in the world, while inferences compose in sequence.

Relations compose in thought, while inferences compose in parallel.

A logic is a system of these beads, which we compose to build and connect ideas.

[CB Wells @c0b1w2]

@Bocse @mihaimaruseac @cosmicfibretion The string diagrams are drawn in Notability on an iPad. It's been enough for the thesis, but to scale this project we need a better drawing app.

The colored text is regular LaTeX, {\color{Red}x}.

[CB Wells @c0b1w2]

The current drawing app Notability is decent but not enough. One example: math syntax displays *behind* everything else, so I make the colors with highlighter; but this makes the images render wrong (like dark/negative) on some devices/platforms.

So, a better app is needed.

[CB Wells @c0b1w2]

@tangled_zans I think so, but I'm not yet familiar with the notation + terminology. What's the general idea of the definition? Also why are they called "monoidal morphisms"?

[CB Wells @c0b1w2]

@bgavran3 the left and right strings with downward markers.

[CB Wells @c0b1w2]

@MSpondee Hm okay, well this sounds like some kind of double weighted colimit, and if so then the co/descent calculus has an explicit formula for its construction.

[CB Wells @c0b1w2]

Here is my thesis: Logic in 2D, Metalogic in 3D
https://t.co/il8PY9Jzj9
and here is a recorded presentation:
https://t.co/t8OpCDnZ7E

I think I got lucky and discovered a unified visual language of thinking. To me it is mind-blowing; and if you think so too, then let's meet.

[CB Wells @c0b1w2]

(I chose a low-res image on accident. See new post.)

It's all rough and undeveloped, as I only recently grasped the whole idea - but that's why I just want to share it now and connect with people, because it will be much better together.

[CB Wells @c0b1w2]

@tangled_zans Yes, the key duality is the end of Ch2 - Matrix Categories: Descent. Matrix profunctors are 2-profunctors, whose language is the co/descent calculus. Just like "exists + forall" and "coend + end", composition is dual to transformation. This is what makes metalogic higher-order.

[CB Wells @c0b1w2]

@UlyssesPascal Yes, the language of monoidal categories generalizes to that of double categories. The ZX-calculus is for compact closed mon-cats, so once we generalize this to cc dbl-cats, then zx will be contained in this language - as well as *maps* between "zx-calculi".

[CB Wells @c0b1w2]

@prathyvsh Thank you!

[CB Wells @c0b1w2]

@tangled_zans Awesome! Yeah let's definitely talk soon.

[CB Wells @c0b1w2]

@evanewashington @mattecapu @DavidCorfield8 @codydroux @myers_jaz I'll post an extended introduction on zulip soon, and I'm looking forward to hearing your thoughts. Sorry it was delayed.

[CB Wells @c0b1w2]

@evanewashington @mattecapu @DavidCorfield8 @codydroux @myers_jaz Dbl cats are logics: dim V is process (function) and dim H is relation.

Trp cats are metalogics: dim V is "metaprocess" (V-profunctors containing hetero-processes) and dim H is "metarelation" (H-profunctors), while dim T is transformation of inference (double functors).

[CB Wells @c0b1w2]

Blue Ridge Mountains. Sleeping well at Catherine's family home. Grateful for the love that got me through, and excited for the next few years.

[CB Wells @c0b1w2]

@Joe_DoesMath it's the collage. no need for a long, unclear phrase