Questions asked with varying frequencies: added 2025-11-13

Which letters in queue are silent?

[asked on Tumblr by jan Misali]

I think it's ambiguous, but at least the q and the second u are pronounced. The q is, of course, what makes the /k/ sound at the beginning. The vowel is a sound that u can make, but u after a q is usually not a vowel (it's generally either /w/, like in queen, or silent, like in queso or unique), so the second u being the vowel that's pronounced makes the most sense.

The ambiguity has to do with whether the word contains any digraphs. The combination qu could easily be interpreted as a digraph, in which case the first u isn't silent but rather part of the digraph that makes the /k/ sound. And either eu or ue could be interpreted as digraphs that make the vowel sound; of those, eu making the vowel sound probably makes more sense, since that would make the last e silent, which is common.

I don't know French (which is where the word comes from), but looking at Wikipedia's French orthography page and the French pronunciation of queue, it looks like in French, digraph qu, digraph eu, silent e would give the right pronunciation, which is consistent with my with-digraphs interpretation (although the English interpretation of a spelling doesn't necessarily have to match up with how it's interpreted in the language of origin).

What is math (like, philosophically)? Was it invented or discovered?

There are two things that make sense to me as ways to look at math:

Mathematical statements are generalizations of claims about the real world. That is, a statement like "2 + 3 = 5" is shorthand for saying that a bunch of questions along the lines of "If you have two apples, and you get three more apples, how many apples do you end up with?" have the answer "Five". (This is probably how math started out, and is what math is to most non-mathematicians.)
Mathematics is a bunch of arbitrary rules that people made up, and we can discover a lot of non-obvious consequences from those arbitrary rules, including things that the people who made up the rules didn't know. This is similar to, say, chess, where the rules are completely made up and arbitrary, but we can discover strategies that follow from the rules, including strategies that weren't known when the rules were invented. (This is what pure math is.)

I think there is some sense in which mathematical theorems are universally true. It is not universally true, say, that the Pythagorean Theorem holds (it doesn't hold on the surface of a sphere), but it is universally true that the axioms of Euclidean geometry imply the Pythagorean Theorem (or, put another way, that the axioms of Euclidean geometry are not compatible with the Pythagorean Theorem being false). It is so universally true that it applies not just in the real world, but also when we can make up whatever rules we want, so we can study these sorts of universal truths if we make up rules close to the boundary of what's possible.

How many types of infinity are there?

Infinitely many, for multiple reasons.

There are multiple systems of numbers: natural numbers (not negative, not fractions, may or may not include zero), integers (which extend the natural numbers to include negatives and zero), real numbers (which extend the integers to include non-whole numbers), complex numbers (which extend the real numbers to include imaginary numbers), among others. None of the ones that I listed include infinity, so to have infinity, we need to define a new system of numbers, possibly one that extends one of the other systems I just listed, that includes infinity. There are infinitely many ways to do so (e.g. you could have a number system with exactly 47 infinities, though it probably wouldn't be particularly interesting or useful or have particularly nice properties), so in that sense, there are infinitely many infinities.

One of the systems of numbers that mathematicians tend to care about a lot is the cardinal numbers, which measure the size of sets. If you define sets and "same size" the way mathematicians usually do, then you end up with the cardinal numbers including all the natural numbers (and/including zero, but not negative numbers or fractions) and then infinitely many infinities—so many infinities, in fact, that the number of cardinal numbers is bigger than any cardinal number (and the cardinal numbers are too big to be a set). In the cardinal numbers, adding or multiplying two infinities doesn't give a bigger infinity, but taking anything to an infinite power does. If you hear people talking about "diagonal arguments", this is probably what they're talking about.

I'd guess, though, that the extended real line is probably closer to what a non-mathematicians think of as infinity; that system has exactly two infinities (+∞ and -∞). That or maybe something like the hyperreal numbers, which have infinitely many infinities and also infinitesimals. Both of those are more calculus-y, although my understanding is that in standard calculus, infinity is treated more as just a notation than a number (so there aren't really any infinities there).

What color is science?

[from a couple YouTube shorts]

I don't know, but math is blue. Green makes sense I guess for science? I don't think other subjects generally have a color in my mind.

I don't even know why I have this association for math specifically. At school, I didn't use different notebooks for different subjects, but rather put everything in one big binder with dividers. The dividers did have colors, but they also had an order, and I used the order rather than the color to decide what subject got what section. And the order I used was based on my schedule for that term (top divider is whatever class I had first on the first day of the term), so it wasn't even a consistent order.

That said, there is an order that I think of subjects as being in, which is math, science, language arts, social studies, and then everything else (arts, foreign language, etc.), because that was my schedule in both seventh and eighth grade (which were the first years we had different classes for different subjects).

What's your earliest mathematical memory?

[from Math with Bad Drawings, originally on Twitter]

I remember learning to count: "one, two, three, […] eighteen, nineteen, tenteen, eleventeen, twelveteen, thirteenteen, fourteenteen […]". This continued into many "teenteenteen"s. I think I knew how it was supposed to go and just kept forgetting to switch to "twenty", though it's been so long that I'm not sure. (There are a few other counting-related memories, so I'm not sure that's actually the first.)

I also remember typing a number into the calculator where the number was something like "one hundred and twenty-three" and I entered it as "100203", and then probably my mom explained to me that that's not how that works.

My earliest memories with actually learning arithmetic are less interesting (there was something about dividing 7 pennies into two groups in all the ways that were possible, and something involving flashcards with addition problems).

When programming, do you write `margin * 2` or `2 * margin`?

[asked on Twitter by @chordbug]

I think I prefer margin * 2, since that's consistent with what I'd do when adding (x + 2 rather than 2 + x). I'm taking the margin (or whatever it is), then multiplying it by 2. If I say it in words (with the "times", and a full word variable), "margin times two" sounds better.

The exception is if I'm translating from a math formula, either because there's some well-known formula I'm using, or because I did nontrivial algebra to arrive at the expression.

I learned to program before I learned algebra, so it's likely that I was writing things like x * 2 before I was even aware of the algebra convention (or at least before I was used to it), so that's probably a factor.

What was the first programming language you learned?

[asked on Tumblr by apolladay]

The first programming language I learned was a version of BASIC that came with a program called "Learn to Program BASIC". It was a version that didn't have line numbers, had structured control flow, and could do graphics, and it had a really yellow non-standard user interface. Next were C++, Logo (MicroWorlds), Java, and JavaScript, and after that I stopped keeping track of how many programming languages I knew and in which order I learned them. (…although the order I learned them in might be slightly wrong, since I think I used a different version of Logo with some Lego robotics thing a week before learning C++ for the first time, but this is the order I would have listed them back then.)

If you have higher standards that "can write a simple program", then I don't really remember. I feel like I didn't learn quite as much about that version of BASIC as I would have about languages I learned later (I usually like to know how exactly the syntax and type system work well enough to understand various edge cases and such, and I didn't do that there). For the others, I used to go to a lot of week-long computer camps/classes during the summer, and that's where I learned C++, Logo, and Java (C++ and Logo were a couple weeks apart), but I continued all of those at home, so better understanding would have come later, possibly in a different order. (Also when I first learned C++, I didn't know about pointers at all, so full understanding of C++ might be later than others.)

I didn't include HTML on that list; that would be somewhere between BASIC and Java, probably between BASIC and C++. CSS would be between Logo and Java (later than HTML, because the first version of HTML I learned used the now-long-deprecated presentational tags/attributes, like <font> and <center> and bgcolor=). (Does knowing how to get neat shapes from a Graphing Calculator program count? Because I also knew how to do that back then. Also at some point I made an interpreter for a simple programming language that I'd made, and I don't remember if that was before or after Java and/or JavaScript.)