June 2021 newsletter

Introduction

So I've been studying math and shit all month again, so I don't really have any updates about what's been going on with timtimestim.com.

Instead I'm going to use this time to talk about some things that I've been thinking about. Think of this like the previous newsletter, where I just wrote about random things that have been on my mind.

Math VS. Programming

Like I said, I decided to study mathematics starting this April. I'm doing this because I want to make progress in the field of AI alignment. Yada yada origin story.

I've been programming far longer than I've been doing mathematics. I learned my multiplication tables before I learned what a for loop was, but I've been solving novel problems with programming since I was like 10 years old while math has always been one of those "guess the teacher's password" things.

I've got a strong intuition about what programming is about. I usually call it programming's "aesthetic". The feeling you get trying to imagine what a processor will do, thinking about memory layouts and cache lines, and so on. There's a very narrow gestalt "form" to programming and computer science.

One of my methods of attack in learning math (quickly) is trying to find math's "aesthetic", the same way I understand programming. And I think I've got a piece of the puzzle:

Programming is about communicating algorithms to computers, while math is about communicating algorithms to other people.

Before you object and say something stupid like, "But other programmers read your code!" yeah I know. But when you're writing you code you must always take your target audience in mind, and the most important VIP audience member is the actual computer.

Think about the limitations that you face when doing math. With math you're trying to communicate with a person, who is able to easily understand context, language, history, and all that other crap that's hard. This person is fallible; they may miss something, or do a computation wrong, or be to lazy to check their work, or any other number of mundane human failings. This person's brain is unusually good at compressing and abstracting information and algorithms; try telling a computer to make an infinite set of natural numbers. This person is also slow; just try multiplying two 3 digit numbers in your head and tell me how it goes.

Contrast the mathematician's mind with the cold, absurdly precise, scary fast, hardware of a computer. There's a reason why you do most of your "hard" computations with calculators these days. But computers can't (yet!) keep the context of the entire field of mathematics in their heads all at once. Computer's power of abstraction and compression are really awesome, but it's harder (right now!) to practically apply those powers the way the human mind can. Just imagine how insane of a problem it would be for a computer to be able to read an arbitrary mathematics paper and convert it into a valid C program, which is something that a smart human can feasibly do with (admittedly fair bit of) training.

This is why mathematical notation is so terse, I think. A human can look at the surrounding context, can find patterns much easier, and accept absurd premises without flinching. It's made for humans to understand, and even the techniques of mathematics (infinity taken as a given, various methods of visualization, how insane the compression ratio of information is, the very idea of sets) are, in some sense, made to help a human mind execute/understand some algorithm. Why not use shorthand everywhere, when it's the equivalent of using slang in a language?

I think a lot of programmers find mathematics alien and weird. I know I did (and still do, a lot of the time). And why wouldn't it be weird, when you've spent so much of your life resisting your human tendency to antrhopomorphize your computer? Suddenly you're expected to take advantage of that particular power instead of resisting it? Math communicates algorithms, but to the programmer the way that they're communicated is, in a sense, total fucking madness at first.

Math is something like 3,000 years old. Computer science as we know it is something like 100. For most of human history the only way to communicate an algorithm was from one human mind to another. What other computational device was Pythagoras supposed to use besides his brain and other's brains?

Coming to this realization, that math is about communicating algorithms to and from humans, has given me a much stronger appreciation of math and programming. It's allowed me to make great strides in some of my confusion about why someone would choose to do things this way. I think I can see where some of this mysterious mathematical beauty is, now.

A few words on productivity techniques

Oh no I used the P Word. I'm sorry to everyone who gets anxious when people say "productivity". It's all going to be okay.

Productivity gets a bad wrap. Here's something that a huge amount of people want, and yet everything "productivity" thing you try just... peters out (Richard). Like some horrific hedonic treadmill of time effectiveness.

Sure sure your new "system" is working great right now, but how's it going to be in a month? Two months? Do you actually expect it to be useful a year from now?

(To be clear, I'm talking about actual productivity here, not fiddling around with "productivity tools/systems" until the sun sets and not getting any actual work done. I should probably stop using the word "actual" so much.)

This problem is everywhere! You get all excited about a new productivity thing, it works out well for like a month, and then you're back where you started. And trust me, I've read so many fucking self improvement books you have no god damn idea.

There's a rare person who will find the tool/system they need to become X times more effective, but those people are crazy and we should all be afraid of them. The rest of us morals must deal with tools that seem to diminish in their usefulness as time goes on, like a rotting marriage after the honeymoon...

...Or do we? Imagine the set of all possible productivity tools, effective or not. Is every single one of these things part of the "diminishing" subset? Can there be tools out there that grow with power over time?

One technique that comes to mind is habits. If you can figure out how to pay the (sometimes extreme) up-front cost of building a useful habit, it will eventually become easier to do the habit than it would to not do it. The hard parts are having the habit interrupted, starting it up in the first place, and picking the right habits to build when you have imperfect information (since stopping a strong habit is hard).

There's a certain elegance to the idea I'm trying to communicate here. That a good productivity technique should become easier to use while it becomes more useful. That the maintenance of such a technique should be low. It shouldn't buckle under normal strain.

I've given this problem years of thought and experimentation. You would think I'm crazy if you heard some of the mental flips I've tried to do over the years. With that said, I have come up with quite a few ideas, many of them have actually been useful in the long term beyond the honeymoon period.

...But the problem is that I have way way way to much to say about this topic. So much in fact that I know I'm not going to finish this newsletter in time if I indulge right now. Instead I'll probably just write a blog post or something.

Yay! Useless section.

(I wanted to sneak the phrase "Are you trying to build software or an effigy to The Flying Spaghetti Monster?" in this section somewhere, but couldn't come up with a relevant spot. So instead it goes here. You will never know the internal experience of ceaseless madness that is my brain.)

That's it

Really, what do you want from me? The math stuff I'm looking at isn't interesting to anyone except myself, and I'm not well versed enough in it to make anything actually entertaining. Beyond that I've been quietly obsessed with some typography things again, but that's a recurring thing that's been mentioned before countless times in the newsletter. I could put in links, but I don't really want to talk about any links today.

So here we are, at the end. Hardly any beginning in this thing, let alone an end. I'd apologize, if there was actually anything to apologize for.