• 1h Reading sequences in the morning. Was supposed to do memory stuff, but I didn't have a clear goal, so I ended up reading. (later I wrote down a list of things to memorize, which I'll yeet tomorrow)

• 2h Functional analysis

  Read section 2.1 and did exercises, very cool! Especially 2.2, here's an image in case you want to try I briefly tried to apply the same technique to other integrals. It mainly works well with "periodic" functions like $e^t$ and $\cos(t)$. If I ever encounter another finite subspace of $C[a,b]$ I'll try this (polynomials are one such subspace, but they're trivial)

  Read some of 2.2, proving $S(\mathbf{x}) = \int_0^1 x(t)^2dt$ is continuous was interesting, you use difference of squares to eventually get $\delta(\delta + 2\|\mathbf{x_0}\|_\infty)$ then you set $\delta = \min\{1,\frac{\epsilon}{1+\|\mathbf{x_0}\|_\infty}\}$ so $\delta(\delta + 2\|x_0\|_\infty)\le \delta(1 + 2\|x_0\|_\infty) \le \epsilon$ This is a neat example of how to deal with polynomial / "self referential " inequalities, i.e. you use min/max to get rid of inner terms

  Tried to prove 1.36 (that $C^1[a,b]$ is a Banach space), eventually read the solution. They used integrals! Cheaters! I was trying to do it hardcore mode without. (I really need to get better with the mean value theorem...)

• 2h 30 min Systems Biology. Read the first chapter (1h), Reviewed it and wrote notes (~30min) and did some exercises (1h)

  Biology is amazing! Transcription networks are so similar to artificial neural networks its freaky (and apparently human neural networks too!) Math that deals with networks seems very high-leverage, stuff like random graph theory (quantify how "random" a graph is) etc.

• 1h Read about Trajectory optimization. Direct collocation is pretty straight forward, then you just punt it off to a nonlinear program solver.

• 1h 20 min Thinking about an AI Design that may be much more efficient than existing methods given a perfect simulator (i.e. given backtracking, the ability to do otherwise). Didn't work on Brachristochrone, it seems so little and specialized now...

  I did look at my old gym AI code, it's actually not that bad! Might do more stuff like it

• 1h 40 min YouTube, should avoid in the future. Watched an elon musk interview and some chess videos. Found a book called "A billion wicked thoughts"

• 1h Playing ping-pong with brothers

Had an interesting idea while talking on discord: Use statistical analysis to make "issheintoyou.com", a site which predicts if someone is into you. I think the problem is isomorphic to medical diagnosis which is dominated by Bayesian methods, hence the same should be possible here. This is also the kind of project that would be useful, people would like, and isn't needlessly hard to engineer.

What I did good:

• Didn't eat by my computer
• Worked outside (until weird smoke happened, then I came inside)
• Went running

How I'll do better:

• Immediately start reading after dinner instead of YouTube, journal after having read for a bit (at ~7:30).