3/3: Mathematical notation

13 June 2016

Modified: 12 October 2016

1876 words

[Part 3 is about communicating mathematical ideas. Part 1, Part 2. I took care to contain the tedious math bits in single paragraphs, so the point is still clear if you choose to only read the fun parts.¹]

summary. There is no such thing as “wrong” notation. All that counts is that you get the math right and communicate your ideas clearly.

Last time I explained how it’s not accurate to say that an electron “is” a wave function, because an electron is a thing in the universe and a wave function is a mathematical object, and mathematical objects don’t live in the real universe. When people talk about wave functions, they often use the letter $\psi$ . Obviously, even though it looks all nice and wavy, the $\psi$ itself isn’t the wave function either – it’s just its name. The concept of names is one we know and love from the real world: When I point at a chair and say, “This is Bob,” it’ll be clear what I mean when I explain that Bob has three legs. While it’s a terrible idea to call a chair Bob, giving things and their relationships with each other funny names is basically what mathematics is all about.

2/3: Models

30 January 2016

Modified: 13 June 2016

1671 words

[Part 2 is the best part. Part 1, part 3.]

In science, we try to understand the world by building models and theories that describe it. You see an apple falling on your head, think, “oh, maybe that’s how the planets move, too”, and you write down rules that allow for the motion of planets and don’t allow for some phenomena you do not see, like things falling upward. You call the collection of those rules your model, or theory. When you have your model, you perform more experiments to test it, and every time your model’s prediction roughly matches your observations, you get more confident that your model is correct.

Victory!

25 January 2016

Modified: 20 September 2026

1394 words

People tell me I should go to a CFAR workshop and they may well be right, so it’s time to figure out how to prevent what is inevitably going to happen there from happening.

1/3: Just The Way Things Are

28 December 2015

Modified: 13 June 2016

514 words

[Part 1 is about a feeling about the world. Epistemic state: Maybe I shouldn’t commit to writing blog posts about every thought that occurs to me while browsing Wikipedia. Part 2, part 3.]

I decided I don’t like the term “laws of physics” to describe the way reality behaves. Calling them laws makes them sound optional¹. Like, it would be really good if you didn’t break them because they are being enforced by the space police, but if you’re really clever, you can outrun the space police and break them anyway. But you can’t.

Waves of confidence

4 October 2015

Modified: 20 September 2026

541 words

There seems to be a distinct and relatively predictable pattern to my confidence/comfort levels when I’m meeting new people and I’m wondering whether this is a common experience.