I was formalizing some linear programming in Lean and came across one of the most surprisingly difficult to prove theorems. ::: {#thm-closed-convex-cones} Let $A : \mathbb{R}^m \to \mathbb{R}^n$ be a linear transformation. Then the set $$ { A x : : : x \ge 0 } $$ is closed in . . . Read more

Netflix has created a masterpiece with Blue Eye Samurai. There are some standard tropes - lonely samurai, mad skilled, dark past, revenge/mercenary for hire, amateur and naive apprentice, etc. A female protagonist with non-japanese ancestry adds a bit of novelty but not sufficient enough a . . . Read more

I have a theory about what meditation practice aims to achieve by urging us to “let go”. I believe consciousness or awareness is the bare minimum state of mind required to function. It’s like the OS kernel (or is the BIOS) that loads when your computer starts, before any other p . . . Read more

I came across a very interesting idea on a Happiness Lab adjacent podcast Thanks to Disney fairy tales, or perhaps even before Disney, the phrase “happily ever after” has . . . Read more

I saw Severance a while back when it was released but was reminded of it by a brilliant episode of Very Bad Wizards. I enjoy reading and watching sci-fi dystopian world . . . Read more

One of the best “hacks” for being mindful and present is to set intentions before starting any task. This includes tasks like planning and concentrated thinking. You just “let your brain know” that this is what it needs to be doing now and it can return to other tasks afte . . . Read more

“Be Here Now,” the classic book by Ram Dass, is supposed to encapsulate the project of meditation. The more I struggle with meditation, the more I realize how central this principle is to the practice. My brain is constantly future-looking, sometimes in small ways - I might be . . . Read more

In a podcast episode on waking up, Oliver Burkeman talks about the necessity to say no to certain things in life because you only have a finite amount of time. This becomes clear when you do the calculation involving the time available and the time required to get things done. This is further emp . . . Read more

I came across this fun theorem in a talk about tree colorings: Combinatorial Nullstellensatz. Let $f \in F[x_1, x_2, \ldots, x_n]$ be a polynomial of degree $t_1 + \cdots + t_n$. If $S_1, S_2, \ldots, S_n$ are nonempty subsets of $F$ such that $\left| S_i \right| \geq t_i . . . Read more

Watch for the impressive acting and the gripping story. . . . Read more