[This is a note, which is the seed of an idea and something I’ve written quickly, as opposed to articles that I’ve optimized for readability and transmission of ideas.]

Who’s blog is this?

My name is Dan Abolafia. I am a coder, researcher, and autodidact. For now I work in artificial intelligence and machine learning, but I am more broadly interested in math, philosophy, and physics. I will dedicate my life to that which stirs me most.

I wish to climb to the top of many mountains. Each field of study is a mountain. The well carved paths are the solidified pedagogies. Some fields have smoother paths with shallow slopes, and some fields barely have any paths at all. The tops of these mountains are obscured in thick fog. You don’t know how high they really go. You are always faced with a choice - climb onto unknown rocks, or follow paths.

Why am I writing this blog?

A few reasons… To build a brand. To practice writing. To create useful, interesting explanations. To motivate myself to learn.

I think most of all, because I desire to have a voice. The things I think and the perspective I take needs time and effort to become evident. My day to day interactions with people do not reveal what I really think. Today’s natural philosophers call themselves scientists, mathematicians, and engineers. We interact with our fields and digest it all, but when do we get to say what it all amounts to? When do we synthesize a sweeping perspective as the philosophers do? Research is an art and a philosophical inquiry, and artists and philosophers alike endeavour to express themselves. I am alive, and I must speak.

Who is my audience?

My past self and my future self. I write what I wish existed when I was learning, and what I will be glad to have to refresh my memory.

Anyone similar to my past self in level of knowledge, and perhaps pedagogical aesthetic, can hopefully benefit from my writings. More concretely, I assume my reader has an undergraduate level of math maturity, and is familiar with multivariable calculus, linear algebra and probability theory, as well as some exposure to proofs. I intend my posts to build on each other, and so later posts will assume knowledge of topics outlined in former posts.

You say this is a pedagogical blog, but your posts are incomprehensible

Pedagogy and learning are dual purposes. I can either invest more time into learning new things, or more time into writing well and making what I write more accessible. I try to strike some kind of middle-ground, though I lean towards prioritizing learning. The articles categorized with the tag notes are intended to be raw and a quick recap of something I’ve recently learned, and they are intended to be a more up-to-date log of my studying. The ones categorized as post are intended to be a more comprehensive exposition around a topic, focusing on core insights I’ve gained. However, even posts are going to be rough around the edges, as I give myself a practical time cut-off on writing and I don’t normally get feedback, though it would be most welcome and appreciated.

What’s with the bare look-and-feel?

I deconstructed the beautiful Tufte theme because I want to keep things simple to make my blog suitable for rapid prototyping. This site is more like a workshop for experimenting with pedagogical tools, such as margin-notes. I’ll expand on the functionality and theme on this site as I go.

What is $\hat{z}$?

In machine learning, the convention is that $x$ is the observed input, $y$ is ground truth (target) output, and $z$ is an unobserved representation or generator of $x$ (or $y$).

$\hat{x}$ is a reconstruction of $x$, and $\hat{y}$ is a prediction of $y$, etc. …