Returning to mathematics
-------------------------

The good news is that I'm finally getting back
some of my sleep deficit and I'm feeling less
overwhelmingly worn down than I was for a bit
there.

The bad news is that my anxiety has been through
the roof to make up for it. The first few hours
of the day I had that "scream in the back of my
throat" kind of terror. Why? I honestly don't
know.

Looking at the state of the world I'm not sure
if you even really need a reason, though. It's
all just utter fucking madness and getting
madder.

I've been back into doing a lot more
mathematics, like actual mathematics, again. It
feels almost self-indulgent in comparison to the
more managerial work I've been saddled with
lately, but it's important to the work I *want*
to be doing.

It's hard for me to put into words yet but for
the past few years my dream has been to take a
lot of the machinery of PL theory and big chunky
enriched and/or higher dimensional category
theory and apply it to the intersection of
computation and the arts: patterns, procgen,
live-coding, generative art, &c.

My gut tells me there's a lot more algebraic
structure that we can exploit, generalizing a
lot of ad hoc approaches and constructions into
a broadly versatile toolbox.

Even though it's not what I was using in my
doctoral work I've had Spivak &al. style applied
category theory on my radar since '09 and now
that it seems to be maturing, even exploding, as
a field I figure this is the time to
strike. I've been watching lectures from the
topos institute on applied category theory while
I ride our exercise bike, reminding myself of a
lot of the concepts I used to use daily and
seeing them put to new uses beyond the
categorical logic that's my comfort zone.

It feels like something in me waking up again, a
kind of sharpness to my thinking coming back
like I'm sating some need I'd gone without so
long that I'd forgotten it was even there.

There's two broad topics of exploration that I
want to understand first and foremost:

The first is the algebraic structure of
patterns, here I mean patterns in the sense of
Tidal to start but hopefully going
further. I truly believe the most brilliant
thing Alex McLean figured out in Tidal is that a
live-coding system should fundamentally be about
patterns in time and how to combine and
transform them, emphasizing patterns as the
center of gravity everything else revolves
around.

Sure the pattern type in Tidal is a monad, which
is a category theoretic structure obviously, but
I think there's something deeper there. I've got
scribbled notes from last year about what a more
general idea of the laws and operations of
patterns apart from their actual implementation
in Tidal is. I don't know yet if it'll amount to
anything but once there is a really general
notion of pattern we can start talking about
transformations of patterns in new, interesting,
ways by knowing how to preserve those laws.

Again, if this sounds hand-wavy it is a little
bit. It's all guesses and hunches that I haven't
really put the time into figuring out before
now.

The second is that I want to introduce
computation to youth diagrammatically. Like the
ways you can describe kinds of composition with
wire-diagrams that represent calculations in
monoidal categories so that fairly complex
calculations just end up looking like
flow-charts that obey certain rules of
construction, I wonder if we can introduce more
and more complicated notions of computation and
have increasingly rich diagram chasing ways of
explaining and composing them. We could
potentially then make teaching youth programming
something that's no longer dependent on a
particular language but on a set of algebraic
ideas that you can *then* relate to the
particulars of implementation.

Again, I don't know if any of this is actually
realistic or if I'm even good enough to pull it
off. But I think I'm tired of not trying.