I must have been the last developer still confused by the AWS interface. I knew how to access DynamoDB, that was the only tool I needed for my daily work. But everything else was a mystery. How do I access web hosting? If I needed a small server to host a static website, what service would I use? Searching for "web hosting" inside the AWS console yielded nothing.

After digging through the web, I found the answer: an Elastic Cloud Compute instance, better known as EC2. I learned that I could use it under the "Free Tier." Amazon offers free tiers for many services, but figuring out the actual cost beyond that introductory period requires elaborate calculation tools. In fact, I’ve often seen independent developers build tools specifically to help people decipher AWS pricing

If you want to use AWS effectively, it seems the only path is to get certified. Companies send employees to conferences and courses to learn the platform. I took some of those courses and they taught me how to navigate the interface and build very specific things. But that skill isn't transferrable. In the course, I wasn't exactly learning a new engineering skill. Instead, I was learning Amazon.

Amazon has created a complex suite of tools that has become the industry standard. Hidden within its moat of confusion, we are trained to believe it is the only option. Its complexity justifies the high cost, and the Free Tier lures in new users who settle into the idea that this is just "the way" to do web development.

When you are presented with a simple interface like DigitalOcean or Linode and a much cheaper price tag, you tend to think that something is missing. Surely, a cheaper, simpler service must lack half the features, right? The reality is, you don't need half the stuff AWS offers. Where other companies create tutorials to help you build, Amazon offers certificates. It is a powerful signal for enterprise legitimacy, but for most developers, it is overkill.

This isn't to say AWS is "bad," but it obscures the reality of running a web service. It is much easier than it seems. There are hundreds of alternatives for hosting. You can run your services reliably on a VPS without ever breaking the bank.

Most web programming is free, or at the very least, affordable.

 

Returning from a trip to New Mexico to explore some Puebloan ruins, I picked up this beautiful chunk of labradorite in the town of Quartzsite. This mineral creates an eerie blue shimmer in the sunlight: a phenomenon called ‘labradorescence’. Reading up on it, I discovered it’s a form of feldspar.

60% of the Earth’s crust is feldspar, and I know so little about this stuff! It turns out there are 3 fundamental kinds:

• orthoclase is potassium aluminosilicate
• albite is sodium aluminosilicate
• anorthite is calcium aluminosilicate

Then there are lots of feldspars that contain different amounts of potassium, sodium and calcium. We get a triangle of feldspars with orthoclase, albite and anorthite at the corners. You can find labradorite on this triangle:

But not all points in this triangle are possible kinds of feldspar! There’s a big region called the ‘miscibility gap’, where as you cool the molten mix it separates out. Apparently this is because the radius of calcium is too much bigger than that of potassium for them to get along. Sodium has an intermediate radius so it gets along with either calcium or potassium.

And there are also subtler issues. When you cool down the feldspar called labradorite, it separates out a little, forming tiny layers of two different kinds of stuff. When the thickness of these layers is the wavelength of visible light, you get a weird optical effect: labradorescence! You really need a movie to see the strange shimmer as you turn a piece of labradorite in the sunlight.

In fact there are 3 kinds of feldspar that separate out slightly as they cool and harden, forming thin alternating layers of two substances:

• The ‘peristerite gap’ produces layers in feldspars with 2-16% anorthite and the rest albite: these layers create the beauty of moonstone!

• The ‘Bøggild gap’ produces layers in feldspars with 47-58% anorthite and the rest albite: these are labradorites!

• The ‘Huttenlocher gap’ produces layers in feldspars with 67-90% anorthite and the rest albite: these are called ‘bytownites’. For some reason these layers do not seem to produce an interesting visual effect. Maybe their thickness is too far from the wavelength of visible light.

All these gaps are ‘miscibility gaps’: that is, feldspars with these concentrations of anorthite and albite are unstable: they want to separate out. That’s why they form layers.

The physics and math of all this stuff is fascinating. Crystals try to do whatever it takes to minimize free energy, which is energy minus entropy times temperature. That’s why many feldspars have different high- and low-temperature forms. But sometimes when molten rock cools quickly, it doesn’t have time to reach its free energy minimizing state.

For feldspar all of these issues are complex, because feldspar crystals are complicated structures:

Aluminum and silicon have to be distributed among the corners of the tetrahedra here, and there are various ways to do this. The distribution is determined by the relative amounts of potassium, sodium and calcium, which are the white balls. The distribution of aluminum and silicon in turn controls the symmetry of the crystal, which can be either ‘monoclinic’ or the less symmetrical ‘triclinic’.

The picture here shows the difference between monoclinic and triclinic crystals:

But the picture doesn’t fully capture the symmetry group of an actual crystal—because there’s more to a crystal than just a shape of a parallelipiped! There may be the same atoms at all corners of the parallelipiped, or not, and there may also other atoms not on the corners.

Let’s get into a bit of the math.

The symmetry group G of a crystal, called its ‘space group’, fits into a short exact sequence:

where T ≅ ℤ³ is the group of translational symmetries and P is the group of symmetries that fix a point, called the ‘point group’. This sequence may or may not split! It splits iff G is a semidirect product of P and T.

For a triclinic crystal, there are only two possible space groups G, and both are semidirect products. P is either trivial or ℤ/2, acting by negation.

For a monoclinic crystal, there are 3 choices of the point group P as a subgroup of O(3):

• P = ℤ/2 (a single 2-fold rotation)
• P = ℤ/2 (a single reflection)
• P = ℤ/2 × ℤ/2 (generated by a 2-fold rotation and inversion
(𝑥,𝑦,𝑧) ↦ -(𝑥,𝑦,𝑧): their product is a reflection).

For each choice of P there are 2 fundamentally different choices of lattice T ≅ ℤ³ it can act on. One is made up of copies of the parallelipiped I showed you. The other is twice as dense; then we call the lattice ‘base-centered monoclinic’:

So, we get 3 × 2 = 6 space groups G that are semidirect products.

But there are 7 other non-split extensions! These other 7 give nontrivial elements of the cohomology group H²(P, T). It’s not obvious that there are just 7 options. Thus, the hardest part of the classification of all 13 monoclinic space groups is essentially the computation of H²(P, ℤ³) for all 6 choices of groups P and their actions on ℤ³.

I knew that cohomology rocks. But it turns out cohomology helps classify rocks!

Now, which of these various groups are symmetry groups of feldspars?

Apparently all the feldspars in the triangle have just two different symmetry groups:

• For the monoclinic feldspars (including sanidine, orthoclase, and high-temperature albite), the crystal has a 2-fold rotational symmetry, a mirror plane, and inversion symmetry

The point group is the Klein four-group ℤ/2 × ℤ/2. The lattice is base-centered monoclinic, so there’s an extra translational symmetry shifting by half a cell diagonally across one face of the parallelipiped.

• For the triclinic feldspars (including microcline, low-temperature albite, and anorthite), the only symmetry beyond translation is inversion. So the point group is just ℤ/2. And there are no extra generators of translation symmetry beyond the three edges of the parallelipiped.

Alas, each of these space groups G is the semidirect product of their point group P and their translation symmetry group T ≅ ℤ³. So, no interesting cohomology classes show up!

Nontrivial cohomology classes show up only in crystals where you can’t cleanly separate the translations from the symmetries that fix a point of the crystal. This happens when your crystal has ‘screw axes’ or ‘glide planes’. A screw axis is an axis where you’ve got a symmetry of translating along that axis, but only if you also rotate around it:

A glide plane is a plane where you’ve got a symmetry of translating along that plane, but only if you also reflect across it:

But wait! There’s a rarer kind of feldspar made with barium. It’s called celsian, after Anders Celsius, the guy who invented the temperature scale. Chemically it’s barium aluminosilicate. And its crystal structure has both screw axes and glide planes! So its space group G is not a semidirect product! It’s an extension of ℤ³ by the point group P = ℤ/2 × ℤ/2 that gives a nonzero element of H²(P, ℤ³). See the end of this post for some details.

All this is lots of fun to me: you start with a pretty rock, and before long you’re doing group cohomology. But the classification of symmetry groups is just the start. For mathematical physicists, one fun thing about feldspars is their phase transitions, especially the symmetry-breaking phase transition from the more symmetrical monoclinic feldspars to the less symmetrical triclinic ones! There’s a whole body of work—by Salje, Carpenter, and others—applying Landau’s theory of symmetry-breaking phase transitions to map out the space of different possible feldspar crystals! Here’s one way to get started:

• Ekhard Salje, Application of Landau theory for the analysis of phase transitions in minerals, Physics Reports 215 (1992), 49–99.

Even if you don’t particularly care about feldspars, there are a lot of good general principles of physics to learn here!

Details

Let me sketch out why barium aluminosilicate, or celsian, has a space group G that’s described by a non-split short exact sequence:

Its point group is P = {e, r, m, i} ≅ ℤ/2 × ℤ/2, where we can take r to be a 180° rotation about the y axis and m to be a reflection that negates the y coordinate, so that i = rm is inversion. In coordinates:

r acts as (x, y, z) ↦ (−x, y, −z)
m acts as (x, y, z) ↦ (x, −y, z)
i acts as (x, y, z) ↦ (−x, −y, −z)

We can take the translation lattice T ≅ ℤ³ to be the lattice generated by

f₁ = (1,0,0), f₂ = (0,1,0), f₃ = (½,½,½)

Note that (0,0,½) is not in T.

To compute the 2-cocycle we need a set-theoretic section s: P → G. We choose

s(e) = identity
s(m) = a glide reflection: (x, y, z) → (x, −y, z + ½)
s(i) = inversion: (x, y, z) → (−x, −y, −z)
s(r) = s(i)·s(m): (x, y, z) → (−x, y, −z + ½)

As usual, the 2-cocycle c: P² → G is defined by

c(g,h) = s(g)·s(h)·s(gh)⁻¹

The interesting value is c(m, m): the glide composed with itself gives (x, y, z) → (x, −y, z+½) → (x, y, z+1), so s(m)² = translation by (0, 0, 1), while s(m²) = s(e) is the identity. Thus c(m, m) = (0, 0, 1). The other values are trivial: c(i, i) = 0, c(r, r) = 0.

Now, is this cocycle nontrivial in H²(P, T)? It would be trivial if we could find a different section that makes the cocycle zero—that is, find a function b: P → T such that replacing s(g) with s'(g) = s(g) + b(g) makes

c'(g,h) = s'(g)·s'(h)·s'(gh)⁻¹

be the identity for all g,h. I will spare you the calculation proving this is impossible. The idea is simply this: the reflection m squares to the identity in the point group, but no matter how we choose b, s'(m) is a glide reflection, so it squares to a nontrivial translation. On the other hand, s'(m²) is trivial since m² is, so

c'(m,m) = s'(m)·s'(m)·s'(m²)⁻¹

is nontrivial.

I keep hearing variants of this complaint lately:

“This (tool / workflow / service / slot machine) is slower than me doing it manually.

Therefore, it's not worth using.”

These people are missing the point. Speed is easy to measure - that’s great. But focusing on speed overlooks the importance of subjective effort and mental load.

Let's talk about grocery stores, naval signaling flags, and the value beyond time saved.

The grocery store self-checkout

In the grocery store, do you choose a human cashier or the self-checkout machine?

People who prefer self-checkout often believe that it's faster. But in my highly-scientific study (loitering in the soup aisle with a stopwatch, n=24), the fastest self-checkout user was only equal in speed to the average cashier in scanning items. Once you add in the time to bag items and pay (not to mention "unexpected item in bagging area"), most people have no chance to outpace a human cashier.

The true value of the self-checkout is to offload social effort, the weight of interaction. Arthur Schopenhauer lived too early to scan his own groceries, but he did write, "A man can be himself only so long as he is alone... for it is only when he is alone that he is really free."

Decoding naval signaling flags (semaphore)

Quick, what is this sailor saying to you?

It's flag semaphore for the letter "U", of course. One weekend, I was tired of staring at the lookup table for flag semaphore (a common cipher used in puzzle hunts), so I made an interactive graphical tool to help me decode it.

It worked great and I felt that it was way faster, just like our self-checkout users above. But after a highly-scientific evaluation (decoding four phrases from my friend Johnny), I was surprised to learn the decoder was only equal in speed to the lookup table.

The true value of the semaphore decoder is to offload cognitive effort. Instead of burning mental energy trying to match a shape in a lookup table, I can mechanically use my tool to grind through the rote decoding process - no faster, but still easier.

That means I'm free to focus my efforts on more interesting, fun, and challenging aspects of the puzzle. I keep more energy for the next puzzles in the hunt.

Lighter burdens make your journey feel faster

Via my third and final highly-scientific study (my personal vibes), I've come to believe we fixate on speed and time measures for two reasons:

1. "Time is money" is a pervasive metaphor in our culture.

2. It's easy to measure and compare.

But even if a new approach is equally slow or even slower, the value of reducing effort is real.

I've previously written a bit on the history of the command bar/palette seen in apps like VS Code, Notion, and Slack. That’s a UI pattern that is actually slower than dedicated keyboard shortcuts, but it provides a better user experience by providing better discoverability and reducing cognitive load.

The self-checkout is slower, but I can relax a little. The semaphore decoder isn't any faster, but I feel less mentally tired. And the command bar is slower, but I can always find what I was looking for.

Sure, if all things are equal, I prefer faster. Who wouldn’t? But if you only prioritize hard numbers and squeezing out every moment of savings, you are going to miss the opportunity to make your effort lighter - and relax for the same result.

I like the tools that make my work lighter, not just faster.

A few years ago, some sort of a bug at my work caused all of the timestamps appear as “54 years ago,” a seemingly arbitrary date. It took me a bit to realize: “Wait, you know what year was 54 years ago? 1970!” “Why is 1970 important?” asked another designer. I explained that by convention, Linux time counts up from Jan 1, 1970 – and so if the time “value” is zero or unavailable, as it was because of the bug, it would be rendered not as an error, but as that specific day long ago.

Computing is filled with all sorts of arbitrary numbers like these. The most famous one was Y2K (99 + 1 = 00 if you only allocate two digits), Pac-Man’s kill screen was number 256, people still bring up the infamous and likely non-existent “640 kilobytes should be enough for everybody” quote, and the Deep Impact space probe died a lonely and undignified death after its timers overflowed the two pairs of bytes given to them.

Here’s a new magic number to remember: macOS Tahoe has, for a while at least, a kill screen of its own – after 49 days, 17 hours, 2 minutes, and 47 seconds (or, 4,294,967,295 milliseconds), one of its time counters overflows and no new network connections can be made, rendering the machine rather useless. The only solution is a reboot. Talk about a deadline!

(Well, new-ish. In perhaps a bit of karmic payback, Windows 95 and 98 once had a similar problem with the exact same threshold of 49.7 days.)

Wikipedia has a nice list of other time storage bugs. The next big one? The problem of the year 2038. The technical fix, as always, is to give the numbers a bit more room to breathe. This is, in a way, kicking the can down the road, but that might be okay since the road is rather long:

Modern systems and software updates address this problem by using signed 64-bit integers, which will take 292 billion years to overflow—approximately 21 times the estimated age of the universe.

However, as always, the technical side won’t be the hard part.

#bugs

There are two articles out this week about my tech-free experiment, one in The Atlantic (gift link) and one in Chalkbeat. I thought the articles did a good job capturing my experiment so I won’t retread everything. Go read the articles, or if you want to see my writing on technology you can check it out here, and here, and here. I do have a few quick reflections on some responses I saw to the articles.

I’ve Moved On

It’s funny these articles came out now because I did the experiment in January. I feel like I’ve moved on. It’s not an experiment anymore. It’s just the way I teach. I radically reduced technology use in my class, I’m happy with that, and I’m thinking about a lot of other aspects of my teaching these days. I emphasize this because there’s a growing movement advocating for less technology in schools. I think that’s a good thing! But classroom technology is just one of many, many things that matter for student learning. Some of the big claims I’ve seen about technology use harming learning don’t seem in line with the evidence. Let’s reduce classroom technology use, sure, but let’s be realistic about the impact that will have on student achievement, and also work on the dozens of other things that can help students learn.

Just a Tool

A few responses said something along the lines of, “Sure, technology can be overused, but computers are a tool just like any other. Why is it such a big deal not to use student-facing technology at all? Why not only use it when it benefits learning?”

Before my experiment, I would have said that I’m someone who doesn’t use technology very much. I’d estimate we used Chromebooks about 20% of class time. Going cold turkey for a month was a helpful way to see that even that 20% was way too much. I’m also not completely zero-tech now. We’ve used Chromebooks twice in the last three months, both for narrow practical purposes.1 I’d recommend teachers give a tech-free experiment a try, just to see how they feel about it.

A related point here is that schools spend a ton of time, energy, and money on student technology. Something like 90% of US schools provide one-to-one devices to students. On Monday, when I asked students to pull out their Chromebooks, one looked like this:

This is the type of stuff teachers and other staff deal with when students carry Chromebooks around all day every day. The practical question here is whether schools should be providing one-to-one devices. Maybe schools should have a computer lab or shared Chromebook cart instead.

Assessment

A final response I saw a few times was surprise that I was giving quizzes and tests on Chromebooks before my tech-free experiment. I get it. That was dumb. In retrospect, it seems obvious students should be assessed on paper. I started giving assessments online during covid for practical reasons, and kindof just never thought twice about it again. They were easy to grade and there was no paper to keep track of for absent students. Students take most high-stakes assessments online now, so there’s a common logic in schools that students should practice taking other assessments online. There’s also a bit of cachet that comes with doing things with technology. I remember one time a few years ago the superintendent was doing a classroom walkthrough and I was giving a quiz. She complimented how nifty one of the interactive online questions was. They can be pretty nifty! That doesn’t mean it was good teaching, but there’s an assumption in education that using technology is innovative or whatever. This is a long-winded way of saying: trying a tech-free experiment can help teachers look at their practices from a new perspective, and maybe realize that they’re using technology for the wrong reasons.

There’s a lot of talk these days about how students are addicted to their phones. I think teachers can just as easily get addicted to classroom technology. The classroom tech I used before definitely made my life a bit easier. I work a bit harder now. That’s fine with me. I think it’s worth the trade. Students work a bit harder too! Those are exactly the types of conversations I hope schools start having about their technology use.

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