Good day, got up at 8, did my routine and started work by 9.

Spent 30 minutes practicing italian, and downloaded the michel thomas audiobooks

Spent an hour doing the chapter 2 drills for geometricalgebra, spent 3 hours doing the structural drills and reviewing/practicing (mostly reviewing). Should have time boxed more, I spent too long trying to justify distributivity of the outer product, I did come up with a cool interpretation of area using projections and an imaginary sandstorm though.

Spent 1h rewatching A swift introduction to geometric algebra then I watched and studied the Addendum, I have a good picture of the inner and outer product now! And I understand the names!

The inner product is the parallel part (ie. the inner part), the outer product is the perpendicular part (the outer part).

That video gave me a good visual understanding of the geometric product, barring some details. I'll have to review how it works with rotation and how exactly magnitudes get scaled, but I at least know what the result will roughly be.

Here's another example, a vector times a bivector We decompose the vector into it's inner (in the plane) and outer (perpendicular to the plane) parts, the inner part gets rotated by 90 degrees (I visualize this as the vector moving to the bottom, and the arrow of the bottom vector points to the tip of the new vector). The outer part is obviously a trivector.

Anyway, after that I was procrastinating doing the analysis/abbott writeups I needed to, so I spent 30 minutes reading math wikipedia, read about q-analogs and the Umbral calculus. The umbral calculus is hilarious, take a look at these lines from wikipedia

The method is a notational procedure used for deriving identities involving indexed sequences of numbers by pretending that the indices are exponents. Construed literally, it is absurd, and yet it is successful

And

These similarities allow one to construct umbral proofs, which, on the surface, cannot be correct, but seem to work anyway.

Apparently it took a long time for people to figure out why these techniques worked, which is hilarious since encountering it in the wild it would seem like a notational mistake.

Anyway, I stopped procrastinating and did 30 minutes of analysis, solved a simple problem but had to go before I finished writing it up.

Spent 2h 30m shopping with mom for a suit

Spent 1h eating dinner at home, talked with my younger brother about programming (he's learning). that was good

Spent 15m fixing my computer, the filesystem got corrupted and I had to run fsck from a liveusb. The first time it failed because I forgot to decrypt the drive

Now its 8:00, I forgot about my goal to read lesswrong instead of doing discord or youtube! Agh! Tomorrow I'll be sure to look at my todo list (often when my schedule is slightly derailed I stop looking at it, which is bad)

Spent an hour chatting on discord and helped a guy with some trigonometry. Realized every rational multiple of $\pi$ lies at algebraic coordinates on the unit circle, ie. $\cos(p\pi/q)$ and $\sin(p\pi/q)$ can be written in terms of roots (they aren't transcendental). Also realized you can write

etc, evaluating $(-1)^{1/q}$ or $i^{1/q}$ feels more tractable then finding a point on the circle, but they're equivalent.

Spent 30m watching youtube, I felt tired so I really should have journaled then shut off my computer, tomorrow I'll shut it off at 9.

Spentt 30m journaling, it's 10 now and I'm shutting down.