There is a webcam in my office that I use to take photos of the whiteboard. This setup was inspired by Dror Bar Natan’s Blackboard Shots. You can read more about the setup here. If you know of anyone else with a similar setup, please let me know.

A happy welcome back after a long break.

My colleague Nick Cheng asked about the curve $f(p) = x^p - x$ for $x \in (0,1)$ and $p \in (0,1)$.

Here is a wonderful interactive essay about the spacing effect: How to Remember Anything Forever~ish. I also really like this paper about how we’ve failed to apply this result to education:

This is $ \LaTeX $.

This is my friend Alex Teeter, manifold explorer.

Raw photo

This is my friend, Paco Estrada.

The designer graph on the first term test for MAT A29 Winter 2022.

This is the current layout of my Backup System. It shows how: archive-servers.sh, offline-backup.sh, and offsite-backup.sh work. The Syncthing and Tailscale connections are not shown for the sake of clarity.

We find the height of water in a conical tank such that: $$ V = \frac{1}{3} \pi x^3 $$ given that water is flowing in at a rate $dV/dt = 1 m^3 / min$.

We find a linear system with solution set $\operatorname{Span}({ (1,0,2,3), (0,1,4,5)})$.

WolframAlpha Calculation

My daughter Mira came in to the office this afternoon and coloured.

The canonical start of a linear sequence is a point in nearest LFn string. In this simple example, there are three possible linear sequences (with the correct orientation) but only $L2, L5, R1$ has the correct start point.

I’m working with Eric Vandendriessche and Alfredo Braunstein to understand a bit about how the string figure calculus acts of canonical linear sequences.

For positive integers $m$ and $n$, let $f(m, n)$ denote the number of $n$-tuples $(x_1, x_2, \dots , x_n)$ of integers such that $|x_1|+|x_2|+ \cdots +|x_n| \leq m$.

For another discussion of this, see: From a Markov Sequence to a Heart Sequence.

This photo has a sketch of an embedding $\heartsuit_n \leq B_{2n}$.

We check a simple lemma leading up to Bessel’s Inequality. Suppose that ${e_n}$ is an orthonormal system of vectors, with a Hermititan inner product $\left\langle x,y \right\rangle$ inner product.

Three loop manipulations are shown. What should we call them?

A quick peek at the braid group $B_3$

Labelled generators of $H_{n} \subseteq B_{2n}$.

There is a webcam in my office that I use to take photos of the whiteboard. This setup was inspired by Dror Bar Natan’s Blackboard Shots.

Dave has an amazing summation: $\displaystyle \sum_{n=1}^\infty \frac{n^{13}}{e^{2\pi n} - 1} = \frac{1}{24}$ Moreover, this is exactly equal to the integral!

Thanks for reading! If you have any comments or questions about the content, please let me know. Anyone can contact me by email.