(that I still remember a decade later)

Evolution on Earth

Fact 1: When foxes are bred to be more docile, their ears become floppy like dogs’ ears instead of pointy like wild foxes’.

Fact 2: Crows can learn to use a short stick to fetch a longer stick to fetch food.

The basic setup of the experiment is: There’s a box with some food at the bottom. The crow can’t reach the food. The crow has a short stick, but the stick isn’t long enough to reach the food, either.

There’s also a second box containing a long stick. The short stick is long enough to reach the long stick. Most crows figure out that they can use the short stick to fetch the long stick and then use the long stick to fetch the food.

If you add a third layer of indirection, where they have to use a short stick to fetch a medium stick and the medium stick to fetch a long stick and the long stick to fetch food, most crows don’t figure it out but a few of them do.

I wrote a rap song about this experiment, it used to be on YouTube but I think it’s gone now.

Physics in the 21st Century

Even before taking this class, I knew that there are four fundamental forces of the universe:

1. Gravity: Things go down. (Or, more accurately, all objects with mass pull toward each other.)
2. Electromagnetism: Many fundamental particles have a positive or negative charge. Oppositely-charged particles attract, and like charges repel; moving electrons creates electricity, and clusters of charged particles create magnetism (or something like that).
3. Strong force: Atomic nuclei are strongly held together even though the protons electromagnetically repel each other.
4. Weak force: ??? something about radioactive decay?

After having previously been confused about what the weak force was and trying to figure it out, this class finally got me to understand it. But since then I have forgotten the explanation and I’m confused again. I wish I could remember how the weak force works.

Intro Computer Science

In first semester computer science, I had been programming for longer than almost any of my classmates (~6 years), and I was the guy my classmates came to for help with CS assignments. By second semester, everyone had caught up to me and my 6-year lead didn’t matter.

Linear and Nonlinear Optimization

Duality: for every convex optimization problem, there is a dual problem that has the same solution.

The dual problem that sticks in my mind: given a set of possible investments, maximizing expected return subject to a given standard deviation is equivalent to minimizing standard deviation subject to a given expected return.

Philosophy of Mind

Philosophy papers routinely make arguments with glaringly obvious logical flaws, but they still get published somehow, and are considered important works worthy of teaching in a class.

I’m a bit conflicted on philosophy as an institution. On the one hand, it’s really hard, and people come up with lots of brilliant stuff that I never would have thought of. On the other hand, many “seminal” papers contain obvious fundamental flaws. I don’t mean I disagree with their conclusions, I mean they make logical arguments that are clearly not logically valid. Like, they have the general structure of “A implies B, A, therefore C” and I’m like…how did you not notice that this makes no sense? and how did the reviewers not notice either? and how did the professor not notice when deciding to assign this paper as reading?

At least that’s what I thought at the time. I don’t remember which papers we read, so I can’t go back and verify that they were indeed as flawed as I thought.

I learned basically nothing on the object level about theory of mind or theory of identity. I still believe all the same things I believed before taking this class. I guess I learned various insane things that some philosophers believe, but I don’t remember what most of those things are.

(“What Is It Like to Be a Bat?” is the best theory of mind paper I’ve ever read—it made me think about things in a new way—but I read it in high school, not college.)

Computer Networking

Fact 1: The web has four layers of transmission:

1. physical
2. IP (send/receive raw packets of data)
3. TCP (manage the transmission of packets)
4. HTTP (tell what types of packets to send/receive)

Fact 2: The Internet is not the same thing as The Web. Internet = IP, Web = HTTP. google.com and facebook.com are on the Web. Email is Internet, but not Web (unless you’re checking your email in a web browser). Multiplayer video games are on the Internet, but not the Web. The Internet dates back to the 1970s, but the Web didn’t start until 1993.

Intro Psychology

Psych textbooks and your psych professor will uncritically repeat claims that were found in a single study that didn’t replicate.

Machine Learning

Four facts:

1. You can solve a lot of problems by throwing a logistic regression at them.
2. I can vaguely explain what a support vector machine is.
3. I can vaguely explain what a convolutional neural network is.
4. I am not good at machine learning.

Sadly this is pretty much all I learned, even though I took four classes on machine learning. I remember various buzzwords like “softmax” and “one-hot” but I don’t remember what they mean.

(I managed to get an A- in one of those classes but I still didn’t really learn anything.)

Linguistics

Fact 1: Gricean maxims explain how statements can convey more information than they appear to.

The four Gricean maxims of cooperative conversation are:

1. Maxim of Quality: statements are true.
2. Maxim of Quantity: statements are as general as possible.
3. Maxim of Relevance: statements are relevant.
4. Maxim of Manner: statements are clear and orderly.

If I say “I have three carrots”, that implies that I don’t have four carrots. If I had four carrots, the Maxim of Quantity would require that I say I have four carrots.

If you ask “Can I eat that carrot?” and I respond by saying, “It’s not mine”, that implies that you cannot eat the carrot. By the Maxim of Relevance, my answer must be relevant to your question, so it can be taken to imply that, as the non-owner of the carrot, I do not have the authority to permit you to eat it.

Fact 2: A Speech Act is when you perform an act merely by stating that you are performing it. For example, “I apologize.” A statement that includes “hereby” is probably a speech act.

(“I declare bankruptcy!” is not a speech act.)

Statistics

I learned almost nothing from the two college statistics classes I took. Everything that I remember about statistics, I either learned on my own or learned from AP Statistics in high school—which was actually quite a useful class, maybe even the best class I took in high school!¹

My college statistics classes were mostly about the mechanics of how to hand-compute integrals of probability density functions, which I will never do in real life. Maybe I would’ve been better off taking a statistics-for-scientists class, but my major required me to take statistics-with-calculus, which is more about calculus than it is about statistics.

I do remember one fun fact: Var[X] = E[X^2] - E[X]^2. I’ve used that one a few times.

Algorithms

How to implement breadth-first search.

I had written graph algorithms in high school a few times, and I always used depth-first search because it was intuitive to me. I never knew how to implement breadth-first search (I’m not sure I even knew it existed) until I learned the algorithm in my algorithms class.

Improv

Fact 1: Peak age for improv skill is older than peak age for most skills. Improv actors don’t peak until their 40s or 50s.

Fact 2: Reincorporation—end your story by bringing back a story element from earlier that the audience probably forgot about.

Reincorporation is the secret to giving a comedic story a satisfying ending.

Now that I know about this concept, I see it show up a lot in comedy. Curb Your Enthusiasm is an excellent illustration of reincorporation, where most episodes weave three or four unrelated plot threads that all somehow come together at the end. Arguably the greatest reincorporation of all time is the Seinfeld episode “The Marine Biologist”.

Science has yet to discover whether crows can understand reincorporation.

Posted on Nov 07, 2025

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