Ryan Moulton's Articles

When my kids were in 1st and 2nd grade, I realized that cutting snowflakes for Christmas decorations was a perfect way to learn about prime factorization. I took the opportunity to teach them, and this has paid dividends for their understanding of math for years. It made it easier for them to learn their multiplication tables, to learn to simplify fractions, and my daughter reports that when doing mental math she often factorizes the numbers first to make it easier. I wrote up my explanation as a lesson in case other parents or teachers want to try it with their own kids or class. It is intended for kids who have gotten comfortable with single digit multiplication with very small numbers, perfect for preparing for winter break in 2nd or 3rd grade. If you try it out, please let me know how it goes!

Let’s make a snowflake. I’m going to fold this paper in half 3 times, then cut it at an angle.

Can you guess how many points it will have when I unfold it? Before we unfold it, let’s think a little bit about it and make a prediction. To do that, I want you to think about how many layers of paper we are making as we fold it. What happens to the number of layers of paper when we fold it in half?

First we go from 1 to 2, then 2 to 4. When we fold a stack of paper, every layer of the paper gets folded, so every layer before the fold turns into two layers after the fold. That means every fold multiplies the number of layers by 2.

This diagram might help visualize it. Instead of the folds we’re actually making to cut the snowflake, suppose we just keep folding a piece of paper in half in the same direction each time, and then look at it from the end. From the end you can see the layers of paper wrap around, and you can see why it gets harder and harder to fold. It gets really thick! That’s a lot of layers.

That means when we fold it in half 3 times, we’ve made 2 × 2 × 2 = 8 layers. After we cut it, what do you expect to see? Make a guess, and then unfold it.

That’s surprising! 4 points instead of 8. How could we have predicted this before we unfolded? Notice that every point is made out of two layers of paper, one on each side of the point. That means that however many points we want, we should make double the number of layers before we cut. If we want 4 points, we should make 8 layers. If you go around the snowflake and count the number of sections that the folds split it up into, you can see there are 8 of them, just like we expected, it’s just that 8 layers of paper only make 4 points.

What if we want 6 points? All real snowflakes have 6 points, so if we want to make a snowflake look real, we better learn how to make a 6 pointed one.

(Why do they have 6 points? Because water molecules are shaped like a mickey mouse, and the ears of the mickey mouses stick to the chins of the mickey mouses, which makes hexagons when you get big groups of them. Make your hands into the “aloha” sign. Your fingers sticking out are like the ears of the mickey mouse, and the bottom of your palm is like its chin. Now stick each of your fingers to the bottom of somebody else’s hand. That’s how water molecules stick together when they freeze. If three of us get together with all 6 of our hands, you can make a full ring and see how the water molecules make hexagons.)

If we want a 6 pointed snowflake, that means we need 6 × 2 = 12 layers. 12 is more than 8, so maybe we fold it one more time? Let’s check. If you want, make a prediction for how many points it will have, or you can fold it, cut it, and see.

That didn’t work! That gave us 8 points, more than we wanted. If 3 folds gave us 4 points, and 4 folds gave us 8 points, how can we make 6 points? We kept folding, but the number of points skipped 6. Does that mean it’s impossible to make a 6 pointed star?

It isn’t impossible, but it’s impossible the way we’ve been doing it, and the reason it’s impossible is related to some of the deepest and most important ideas in all of math.

Because we want to end up with 6 points, we want to fold it to have twice that many layers, which is 12 layers. How can we break down the steps you need to make 12 layers? Do you know any numbers that multiply to 12?

We just found one, 6 × 2 = 12.

Do we know any numbers that multiply to 6? Yes, 2 × 3 = 6.

So putting that all together, 2 × 3 × 2 = 12. 

Now think about what this means for the folds we have to do to make 12 layers. We start by making a fold that doubles the number of layers. That’s just the simple fold we’ve been doing. But then the next step is tricky. We have to make a fold that triples the number of layers. If we figure that out, we just have to fold it normally one more time, and we’ll have a 6 pointed star.

The fold to triple the number of layers is tricky, so let me show you how to do it. This is the hardest step, so you can get an adult to help you if you need it. You can’t do it by matching up sides exactly the way we normally fold things, you have to eyeball it and estimate. First you find the middle of the folded side by matching up the corners, and pinch at the fold, but don’t fully crease it. Instead take the side you’re folding over, and turn it so that it’s pointing up and to the right. You want the paper you can see on the layer below to be the same size near the point as the part you’ve folded over.

That’s really difficult to do. It would be nice if we could find some way of making a 6 pointed star that didn’t use that weird 3 layer fold. Is there any other way we can fold it? Let’s go back to our goal. We need to make something with 12 layers. Do you know anything else that multiplies to 12?

How about 4 × 3 = 12? We know how to make something with 4 layers, just fold it in half twice. So the folds we’d need to do are 2 × 2 × 3, but then we’re still left with that annoying triple fold at the end. Are we really stuck? Let’s write down every single option we have to make sure we haven’t missed anything.

2 × 6 = 12

4 × 3 = 12

3 × 4 = 12

6 × 2 = 12

4 and 6 are still too big to fold in one step, so let’s break them down further. 4 = 2 × 2, and 6 = 2 × 3, so we can replace those numbers.

2 × 6 = 2 × 2 × 3 = 12

4 × 3 = 2 × 2 × 3 = 12

3 × 4 = 3 × 2 × 2 = 12

6 × 2 = 2 × 3 × 2 = 12

Now look at that. Do you notice the pattern? Whenever we break down the folds we’d need to make to make 12 layers, we always end up with two folds where we fold it in half, and one fold where we fold it in thirds. It doesn’t matter the order in which we fold them, you always have to have two 2s, and one 3.

This pattern is called the “prime factorization” of 12. Don’t worry about what “factorization” means yet, but think about this word “prime.” You might have learned about the primary colors in art class. All the colors that people can see can be made out of mixtures of those primary colors, red, yellow, and blue for paint, or red, green, and blue for light. “Prime” numbers are the same way. All numbers are either prime, or can be made by multiplying prime numbers together. Every number is a mixture of prime numbers in the same way that every color is a mixture of primary colors.

Even crazier, there is only one way to make any number by multiplying primes, if you ignore what order they’re in. And because there’s only one way to make a given number, that makes it really really easy to find. Just start by breaking down the number any way you can remember. Then check each of the numbers you get, and see if they can be broken down any further.

12 is 6 times 2. 2 can’t be broken down any more. 6 can. 6 is 2 times 3. 2 and 3 can’t be broken down, so we’re done. 12 = 2 × 2 × 3.

It doesn’t matter what order you break down the number, and it doesn’t matter what order you fold the paper. You’ll always end up with the same result.

Suppose we want to make a 5 pointed snowflake, like an ordinary star. Can we use what we’ve learned to figure out how? Let’s figure out the prime factorization of 10.

10 is 5 times 2. 2 can’t be broken down anymore. Can 5? Nope. 5 is also a prime number, just like 2 and 3. 

So that’s it. If we want to cut a 5 pointed snowflake, we have to figure out how to fold something 5 ways. Ich. That sounds even harder than folding something 3 ways.

What about 16? Let’s try to break it down.

Again, no matter what order we break it down, we get the same result. 2 × 2 × 2 × 2. If we want to make a star with 8 points, or 16 layers, we always have to fold it in half 4 times.

So that raises the question, how hard can making a snowflake with a certain number of points get? Is 5 the hardest fold we’d ever have to do?

No, in fact. There are an infinite number of prime numbers, and they just keep getting bigger. I’ll write out the first few below.

2, 3, 5, 7, 11, 13, 17, 19, 23, …

So if you want to make a 7 pointed star, now we know it’s going to be really hard. First fold the paper in half, then somehow figure out how to fold it into equal sections of 7. I’ll stick to 6 points! That’s hard enough.

The fact that every number can be broken down into prime numbers multiplied together, and you always get the same result no matter how you break it down, is so important to math that it is called the Fundamental Theorem of Arithmetic. It is so important because it shows up everywhere, even in cutting snowflakes.

Happy cutting, and if you need some ideas for patterns, Veritasium has a wonderful video about where the shapes of snowflakes come from.

If all that was easy, here’s one more thing. When we write out the prime factorization of something like 16, writing out 2 × 2 × 2 × 2 is a lot of work, so instead we just write that as 2⁴, where the 4 counts how many 2s are multiplied together. Using this way of writing it, we can write out the prime factorizations of the first 20 numbers in a really short way. This is a great thing to practice, either to memorize them, or to come up with them quickly. That little number ⁴ is pronounced “to the fourth” when you say it out loud.

11223342²5562×37782³93²102×51111122²×31313142×7153×5162⁴1717182×3²1919202²×5

    

Cumberland Gap, West Virginia — There’s a foot of snow as we climb to the ridge. The rhododendrons around the trail are still green. It feels like a snow jungle. Our group gets separated, so my best friend and I wait for them on the ridge before the turnoff that descends down the mountain. A stony outcrop juts out over a cliff with the whole flat of the land falling away. Distant buzzards circle. We sit on the rock in the warm winter sun and watch.

Clifton Gorge, Ohio — Fresh snow. Descending into the gorge is like entering Narnia. The gray walls of the gorge envelope us. The river at the bottom is half frozen over. Ice at the edges meanders around the current. Limestone boulders the size of houses hem in the river and the trail. Other spontaneous trails spiral up through them and over them. The boulders are all white capped, but the moss on their sides is still bright and green. In the narrows by the old mill the layers of churning falls carve both ice and stone. A quick round of hot cider, then back out into the cold. As we climb out of the gorge it starts to snow. The flakes muffle the sound of the river and everything else. We look back and watch in silence as the dark pines slowly disappear into gray. Every time I imagine beauty I start here.

Philmont, New Mexico — Ponderosa pine shadows cross the trail and their smell fills the air. The dry wind takes the sweat off of me as soon as it appears. Trail dust sticks to the blood on my shin and hardens into cement. They tell us that pioneers would mix cattle blood into this dirt to harden their cabin floors. Ground squirrels lick the salt from our tent stakes. We reach the summit inside a cloud. The wind is too cold to wait to see if it will clear. My dad’s ashes are somewhere in my pack. They don’t weigh much. I don’t really know what to do with them. He was supposed to be on this trip. My crew is a brotherhood. The day we’re off the trail the first thing we eat is pizza served from a double wide trailer, and it’s the best thing I’ve ever tasted.

Wind River Range, Wyoming — Hiked a few days through passes and past whistling marmots into a wide glacial valley where we’re camping for the evening. A meadow fills the bottom of the basin with thin green grass. A clear mirror lake laps at it. It looks like rain across the valley, so we set up in a hurry. The valley slowly disappears in the curtain of it. When it reaches us, it isn’t rain, it’s ash.

White Mountains, New Hampshire — 13 mile day planned. It’s too much. On the first big climb I decide for no reason at all that I won’t stop until I get to the top of it. My body is new, and strong, and I want to see what it can do. Half way up the slope I can see my heartbeat moving my ribs. The hike along the ridge is as hard as the climb, up and down and up and down, half scrambling, one trail marker at the bottom of a cliff and next one half way up, eating peanut butter from the jar with my fingers to keep going. I make it to camp just before dusk. That day I felt ambition for the first time, and loved it. Chasing that feeling carries me through years.

Waimanu Valley, Hawaii — Hard sweaty hike in. Spider webs all across the trail every few feet. No one has been there in a week. We enter the valley just before dusk and camp near the beach. Big centipedes. At dawn the sun creeps down the valley cliffs, uniform tropical green broken only by waterfalls like veins of silver. We hike to the closest one. When you’re swimming in the middle of waterfall spray the rainbow makes a full circle.

Muir woods, California — I make up all sorts of silly things to tell her, and she believes every one. It’s crowded. We wander around looking for a trail where we’re alone. The woods are gorgeous but I’m not really seeing them. We don’t know where we’re going, and we don’t know where we’re going. I take a picture of her, nervous and smiling. She loses the pendant from her necklace somewhere on the trail. The next day I’m at a jewelry store buying a pendant. A month later I’m drawing her portrait from that picture. It’s now on our wall.

Big Basin, California — First hike with kids. The older kid wants to be carried, but the younger is tromping along chomping an apple the same size as his head. Ancient trees tower over them, but they’re more interested in the drainage pipe that lets a little creek flow under the trail. The first tree they really notice has burl several times their size that they can use for a playground.

Big Basin, California — Our first visit after covid and after the fires. It’s too sunny, and too hot. The tree trunks are all black, and their limbs are gone. They’re resprouting with little fuzzy green branches all over. Tall bright grasses wave between them where there used to be ferns and huckleberries. We find the same burl they used to climb on. The kids are big now, taller than the burl. Time goes on.

Portola Redwoods, California — First backpacking trip with the kids. Nervous about how it’s going to go. I’m not sure if they’ll enjoy it, and they aren’t either. A mile in, the huckleberry bushes start, and they don’t stop. They’re all ripe. We eat handfuls along the trail the rest of the day. At camp we head down to the creek for water. The carpet of sorrel around it glows where the afternoon sun cuts through it. After the trip they beg to go back. If someday they make their list of transformational walks in the woods, this will be the first.

When my son was in first grade, he came home from school in tears saying that he hated math. My wife and I are both engineers, so this was the sort of all-hands-on-deck shock that demanded our immediate attention. Before this my son had loved math. He would demand that we challenge him with math problems to do in his head in the car and over dinner. He loved doing flashcards. He played math games on his tablet unsupervised for hours. Even now, years later in 4th grade, he has decided he wants to learn calculus, so he insisted I start explaining it to him as best I could in the car, and started working through pre-algebra in Khan Academy on his own. How is it possible that a kid like this had decided he hated math?

His misery was all due to i-Ready, the software product our district had purchased for math work and testing. During that period my kids’ happiness at the end of the school day was entirely determined by how much time their school had made them spend on i-Ready. If they hadn’t touched i-Ready, they were happy. If they were forced to do it, they were sad. If they had to spend an unusual amount of time on it, they were in tears. I started asking around to the other kids’ parents, and I heard similar stories from all of them. Their kids described it as torture. Some of them would hide in the bathroom to avoid it. None of the parents felt that their kids were learning anything at all from it.

I write software for a living. I have hoped for educational software to revolutionize learning my whole life, and am extremely optimistic about its possibilities. We’ve given our kids lots of educational apps whenever we could find ones that seemed worthwhile. They’ve had tablets from a young age. They love Khan Academy and have gotten a lot out of it. I was happy the kids got chromebooks in school, started learning Scratch, and were using them regularly. I am not objecting to the concept of (or primacy of) educational software. I think it has the potential to do an immense amount of good.

I have no disagreement with i-Ready’s goals. The problem is that the software simply doesn’t work.

i-Ready assumes that the student cannot read, that they must be read to very slowly, that they must listen to the same instructions hundreds of times, and that they cannot ever be allowed to have any control over this. As a consequence it is not physically possible for a student using i-Ready to get a reasonable amount of math practice during the time they have for schooling. The software spends nearly all of its time forcing them to listen to narration instead of doing math.

When a problem starts, the computer slowly reads aloud the text written on the screen. An animation slowly demonstrates the concept. The student is not allowed to do anything at all until it finishes. It repeats this for every single problem, even when the problem is identical to the previous problem. For every minute the student spends actually thinking about math, i-Ready spends 10 minutes narrating the same instructions over and over again. If the student is trying to complete their work quickly, you will see them sit glassy eyed for thirty seconds, then frantically click click click click for 3, then sit glassy eyed for another thirty seconds in a loop. They spend nearly all their time waiting. A talented student could complete 10 equivalent problems on paper in the time it takes a single i-Ready problem to finish talking at them. Most students give up on trying to complete their work quickly, because they realize they are forbidden from doing so. They instead just stare at the screen and try to run out the clock for whatever time they’re required to sit there.

Beyond the unskippable repetition, it’s full of simple UI bugs and oversights that in adult software would quickly cause RSI. When the narration of the question is complete, the input box is not focused. The kid has to manually click it, every single time. The input box doesn’t allow keyboard input, so rather than typing their answer, they have to move the mouse pointer around and click buttons on the on-screen number pad. When the problem requires the student to mark how addition works on a number line they have to drag on those number lines with a tiny track pad, over and over and over again. When their answer is accepted, they aren’t done. They still have to scrunch up their little hands on that little trackpad, and move the pointer to click the “next” button to advance to the next question, every single time.

The software claims to be adaptive to the student’s abilities. I saw no adaptation the entire time both kids were using it. At home prior to the school year our kids had mastered 3 digit addition and were practicing their multiplication tables. In i-Ready they were stuck tracing out single digit addition on number lines and practicing the make ten strategy. We asked their teachers to try to reconfigure it to put more challenging material in, but nothing helped. A few simple multiplication problems would enter the queue for a day, and then they would run out. They’d be back to listening to the computer narrate how to use a number line. The problems they were doing at the end of the year were not materially different from the problems they were doing at the beginning. The problems they were doing in the next year were not materially different from the problems they were doing in the previous year. As far as i-Ready was concerned, they remained in the beginning of first grade for several years.

I feel especially guilty about this because I believed the marketing. When they were frustrated at how far below their capabilities all the problems were, I encouraged them to persevere. I assured them that if they were careful and diligent, and put in the time, eventually the software would respond by rewarding them with the kind of math they wanted to learn. It never did. 

Their teachers would assign 20 minutes of i-Ready math per day as homework, not a fixed amount of content, a fixed amount of time, and eventually I just could not bring myself to force them to do it, watching how much of their time it was wasting, and how much of their youth it was spending on something they were getting nothing out of. I expected as a parent to enforce the letter of the law on homework as much as I could because I didn’t want to plant the seed of even more conflict about it later, but after days and days of seeing my kids listless on the couch waiting for the computer to stop talking, I gave up, and gave in. We didn’t make them do it anymore. I still feel guilty that I made them spend any time on it at all, and regret the loss of everything else we could have done with that time. They unfortunately had to continue to use it in class.

It is easy as an adult to feel that this is histrionic, that kids will always be bored or unhappy about school, and that maybe this is all just good for them even if they hate it. If you feel this way, I challenge you to try to recreate this experience for yourself. Go find a video on youtube that slightly annoys you, then watch 30 seconds of it. When 30 seconds are up, using your trackpad, click the pause button, drag the video slider back to the beginning of the video, and then press play. (Using any keyboard controls or a mouse to do this is cheating. It has to be a trackpad, preferably a low quality one. You’ll know you’re doing it right if your hands start cramping.) Do that 30 times in a row. Repeat this every weekday. Repeat this for every week in a year. Make sure you use the same video the entire time. This is what using i-Ready is like.

When we sent our kids to public school, I anticipated them being bored, at least a little. I was also bored in school. It was basically fine. I hoped that the benefits, exposure to kids from a variety of backgrounds, and having social connections to the community, would be worth it, and those aspects have paid off well. When I was in grade school, and bored, for me this practically meant that I could finish my work quickly, then daydream, doodle, or read a book. When school was undemanding, it didn’t demand my attention, and so I was free with my own thoughts.

“Being bored” in school is now an entirely different experience than it was when I was a kid. Software enables the enforcement of arbitrary rules that no human being would have the heart or foolishness to enforce. A teacher, faced with a bored student, would not force them to pay rapt attention to an identical lesson 30 times in a row, 5 days a week, for the entirety of the school year. Software can do that easily. A teacher would not demand that all students take an identical amount of time to finish an assignment regardless of how well they’ve mastered the material. Software can do that easily. A teacher paying attention to a class will adapt to what is working, what is holding their attention, and what is serving their needs. Software is by default thoughtless, and that allows it to be thoughtlessly cruel.

The most galling bit about this is how simple most of these problems could be to fix. Skipping a repetitive animation is not a complex technology. Someone within the company empowered to change the code could implement it in the time it takes you to read this sentence. The kind of UX issues that make entering your answer difficult and fiddly haven’t been tolerated in the industry of web based software for decades, because those issues make you lose customers and money. Even ADA compliance would make it legally compulsory to fix them. I do not know why it fails entirely at its goal of being adaptive. One possibility is that the software is so poor at receiving user input that students can’t reliably enter the answers they know.

When you choose a school or a school district for your kids, you expect to be picking their peers, their teachers, their campus, the park they’ll go to after school. You probably did not consider that you are choosing their software. The software contracts that the district is bound by will likely have as big an effect on your child as all of the other factors you were paying more attention to. The software will be doing much of the instruction. The software will be enforcing the rules. The software may even be occupying most of their school time. Even if the teachers hate it, they may not have a choice. Despite the fact that software is the most malleable invention humans have ever created, no one in an entire school district has any ability to change the slightest bit of behavior in the software they purchase. You would have an easier time convincing your school district to fire a teacher or even to build an entirely new campus than to change a single line of JavaScript in the software they have contracted to use. If the software is bad, your child’s education will be bad, and there is no possible escape within the district.

During the year where their only math education was primarily i-Ready, our kids made no progress at all. As far as we could tell they had regressed. Problems they were happy to do in their heads at the beginning of the year, they could no longer do. During that year, i-Ready became the antagonist of my son’s whole imaginary world. Whenever he drew spaceships or heroes in his elaborate drawings, the villain they were attacking was always i-Ready. Seeing that our kids were likely to learn nothing at all from their in-school math, we enrolled them in Beast Academy after school, which they’ve loved. Beast Academy also delivers homework via software, but the software works. They’re happy to do it, at least as happy as you can expect a kid to be about math homework, and it never wastes their time.

I can’t speak to whether i-Ready is any better at its job after you pass third grade. I also can’t speak to whether any of these issues have improved in the last two years. We left the district. We had several reasons to leave, but i-Ready made it an easy choice. Whenever our kids worried about missing their old friends after we moved, we consoled them by reminding them that they would never have to touch i-Ready again, and that helped.

It started with a flash of insight like a thunderbolt in a snow storm, the sort of insight that can only be induced by high altitude hypoxia and making breakfast. 

“Breakfast is a vector space. You can place pancakes, crepes, and scrambled eggs on a simplex where the variables are the ratios between milk, eggs, and flour. We have explored too little of this manifold. More breakfasts can exist than we have known.”

Like all such hypoxia-addled-brain thoughts, it was a successful tweet.

I stood in the kitchen paralyzed by indecision. The mixing bowl was in front of me, the milk, eggs, and flour next to it, all of them individually as familiar as they had been a moment before, but now the possibilities for their combination were just too great. Breakfast was now an alien fractal intruding on our world like the lighthouse at the end of Annihilation. The thoughts came unbidden.

“In the manifold of breakfast, are there empty subspaces? Might there be breakfasts that no one has ever had? With a theoretical model of breakfast, can we derive the existence of ‘dark breakfasts,’ breakfasts that we know must exist, but have never observed?”

The curtain of reality had pulled back for me, and I could no longer pretend to be ignorant of these eldritch possibilities. I furiously began to map the known breakfasts. If the dark breakfast exists, I must be able to find it in the interstices of the normal familiar world.

First I mapped all that I could recall from memory, pancakes, crepes, waffles, scrambled eggs, popovers, omelettes, and on and on, scouring my brain for every fast I had ever broken. The beginnings of the contours of breakfast began to reveal themselves. A gaping hole stared back at me, but I couldn’t yet be sure. I had to search the dark corners of the world to see if somewhere in far off lands that abyss had yet been filled. I called upon friendly ghosts. I paged through ancient tomes. I added kaiserschmarrn, swedish pancakes, dan bing, madeleines, crumpets, clafoutis, blinis, pannu kakku, parathas, nalesniki. The map filled in bit by bit, but it was no use. The gap in the fabric of breakfast remained.

I searched for benign explanations. Could it be that milk is simply too heavy, and that by including the weight of the water content that boils off I am tilting the simplex too far in its direction? Could it be that by excluding slices of bread as ingredients since they aren’t raw flour and do not go in a mixing bowl, I have excluded breakfasts like french toast, eggs in a basket, breakfast burritos, and breakfast sandwiches that might yet have saved us? Could I have overlooked some arcane culture that breaks their fast with dumplings or egg noodles? None of these satisfied me. The Abyss stared back.

The breakfasts I was able to identify cluster into three major regions:

1. The Pancake Local Group: Here are found most of the conventional breakfasts, pancakes, crepes, waffles, and all of their international variants. Space here is chaotic, fractal. Any slight deviation from your recipe in this region is likely to produce something else entirely. Breakfast here is metastable at best. (prior research on the pancake cluster)
2. The Baked Good Quadrant: The items here are only breakfasts by convention. Any of them could be served at other meals, and often are.
3. The Egg Singularity and Custard Accretion Disk: While only omelettes are labelled for brevity, there are dozens of named dishes that could be stacked on top of the pure egg point, over easy, sunny side up, hard boiled, soft boiled, etc. From these a small tail of egg based dishes sneaks down the right side, each with some amount of milk added, often a variable or optional amount.

I was days into my research before I finally found a clue. In an obscure document on the website of the International House of Pancakes Corporation there was a hint that the dark breakfast had been made. IHOP omelettes include pancake batter. While I cannot place IHOP omelettes exactly on the map, by interpolating between pancakes and omelettes, we can bound where they must occur, and confirm that the manifold possibilities do indeed pass through the Dark Breakfast Abyss.

We do not know why the Dark Breakfast Abyss is empty. But by anthropic reasoning, we should conclude that it is empty for good reason. The International House of Pancakes is playing a dangerous game. If someday a remote IHOP splashes a little too much batter in their omelette, cooks the Forbidden Breakfast, and thereby brings about the end of the world, well, at least we know the Waffle House will be open.

For other breakfast scholars who wish to further my study, I offer my data and code. If you are so foolhardy that you wish to explore the bounds of dark breakfast yourself, the recipe is as follows:

Dark Breakfast

Ingredients:

• ¼ cup Milk
• 4 Eggs
• ½ cup Flour

Instructions: Unknown

The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age.

H.P. Lovecraft – The Call of Cthulhu

We feel time differently over our lives. As a toddler, an afternoon feels like an eternity. In middle age, “no matter how I try, those years just flow by, like a broken down dam.” For a 5 year old, a year was a fifth of their life, and feels like it. For a 40 year old, it is just another year. 

If you take this model literally, that your experience of an interval reflects what fraction of your life the interval is, then we experience time logarithmically through our lives. Instead of middle age coming at 40 as linear time would suggest, in logarithmic time the midpoint of age 5 and age 80 is age 20. Childhood is one half of our life, and adulthood the other half.

This is a depressing thought to consider in (linear) middle age, but it is hard to escape the feeling that it is essentially true. Childhood memories have an intensity and a vibrancy that it is difficult for the rest of life to match.

So how should this change how we live? Most directly, we should not waste children’s time. The motivation for making school more rewarding and less stultifying should not primarily be its effect on outcomes later in life, but rather that childhood is itself part of life, a very important part.

But what about those of us who are well into the flattening part of the curve, what can we do for ourselves? You can seek new experiences perhaps. If time goes faster because your life has fewer firsts and more routine, then it can be extended by adding firsts. You can learn new things, travel, take up hobbies, or new careers.

This works, to a point, but there are only so many firsts for you, and chasing this exclusively seems to lead to resentment. You remember the things you had as a kid. You remember the excitement and warmth of that world, how immediate and raw everything felt, and you want to go back. You start to regret that the world has changed, even though what changed the most is you.

You can’t go back, but you can come close. The easiest way to add firsts to your life is to become invested in those of someone else, have kids. Nostalgia is only futile and self destructive because it is a sublimated desire to give your own children the life you want them to have.

Firsts

The first set of new firsts that children give you are those you don’t remember from your own life, smiles, laughs, food, words, steps, first rain, first creek. Every week becomes so laden with meaning that it is almost oppressive. Instead of worrying that the weeks are all forgettable, as you might have in your former life, you instead worry that you will forget. They won’t remember it, so the burden falls on you. You are recording the events that will become the mythology of their identity when you later tell the stories back to them.

Then start the firsts that you do remember and that you can recreate for them. Let me tell you about one.

My scout troop was camped in an Indiana field on a November night. The grass was dewy just after dusk, but would be frosted by morning. One of the dads had set up a telescope a little ways from our tents. I hadn’t had any particular interest in it, and came over to it as an afterthought as a break in the middle of all our other games. What he showed me blew me away, Saturn and its rings, right there in front of my eyes, exactly the way I had seen it in all of the books. If you’ve seen this before, you know the feeling. If you haven’t, the best way I can describe it is that it makes space, for the first time, tangibly real. It’s all actually out there.

With a picture in a book or on a screen, you’re never entirely sure what’s between you and what you’re looking at. Your eyes can’t see the characteristic spectrum of hydrogen, oxygen, and sulphur the way Hubble would show you. Your eyes can’t collect light for half an hour. Space in books exists in the theoretical world of parabolas and water cycles instead of the physical world of homeruns and rain. But an optical telescope can’t lie to you. The very light that bounced off of Saturn’s rings a few minutes prior was hitting my own eyes, with nothing in between but glass and mirrors, the same Saturn that Galileo saw. It was as real as the dirt under my feet.

I’m the dad now, and now I’m the one setting up telescopes in fields to show kids Saturn. I can’t experience seeing it for the first time, I have already realized that realization, but I can listen to their gasps and see their wide eyes when they do, and so the experience is renewed.

Transformational experiences are only a small part. It can be as simple as seeing bread dough puff up overnight, or seeing a praying mantis on a fenceline, sledding down a hill a little too steep and screaming the whole way, or watching sparks curl up from a campfire. Children make you childlike. Skipping through the park as an adult man raises eyebrows (deservedly or not.) Skipping through the park as an adult man with your son or daughter skipping next to you on your arm is one of life’s greatest joys, both for you and for anyone who sees you. Whatever self-consciousness you would normally have melts away when your kids ask. You’ll play dress up or tag, climb trees or skip, blow dandelions or wear clover crowns, belt out songs or talk in pig latin. How could you refuse? You might do it reluctantly, as adulthood has conditioned you to, but you’ll love every minute of it, and you’ll be a kid again when you do. 

Cycles

Many yearly traditions gradually get stale. You’ve done them many times. You’re not sure if you should put in the effort this year. Your jack-o-lanterns become fewer, and then vanish. You start to watch 4th of July fireworks on TV, then not at all. Your Christmas trees get smaller, your lights less ambitious. Some find all of these fun for their own sake, but if you are not the type of person who finds ritual appealing you will likely find yourself slowly disconnecting from holidays. You will find yourself asking what all the hustle bustle is for.

Kids. That’s who it’s for. Of all the experiences that children renew, traditions are renewed the most. When you put up a Christmas tree, it’s for kids. When you decorate for Halloween, it’s for kids. All of these holidays are in essence a celebration of childhood, and children let you see them all for the first time again. If you remember the excitement of galumphing excitedly downstairs on Christmas morning, you get to be the person creating that excitement. If you remember the terror and hilarity of being jump scared by your neighbors on Halloween, you get to be the person doing the scaring.

Moreover, children generate tradition. They turn your choices into traditions by accident. You do it once, they demand to do it again, and then it’s a tradition. You discover that you are the one creating tradition, that it all rests on you. It feels like an inappropriate amount of power. If I’m too tired to follow through on something, it just disappears forever. But by the same measure, I can now sieve all the traditions I was given to those that I love the most, make sure they continue, and add to them whatever I want to add to the world.

Trying to improvise vegetarian Thanksgiving and Christmas dinner has turned my adjustment of a random sweet potato casserole recipe from the internet into a family heirloom for my kids, just like my grandmother’s recipes that she cribbed from the flour packaging did for me. For my kids Loreena McKennitt’s recordings are the canonical Christmas songs, because that’s what I put on to recreate the feel of winter in a climate that doesn’t cooperate, but I make sure they recognize Andy Williams because that’s what my mom put on whenever we decorated the tree.

You can even add entire holidays. My kids and I celebrate the first rain in the fall that ends California’s fire season with fancy hot chocolate while we watch it come down outside. Others have introduced Yuri’s day and Pi day to name just a few. Any tradition you expose them to will feel to your kids like it is a hundred years old. You are creating the things that will have always been.

Eternity

When I was young my perception of time was that of a ray from high school geometry, a fixed starting point at birth, a second point to fix the direction of the line at the end of childhood, and then the future stretching off into infinity. I was aware of mortality of course, but I thought of the purpose of life as to somehow transcend that. The duration of my life was the time I had to create something that would keep going.

Maybe you find your great work, and your path to a small or big dent in the universe. If that is you, more power to you, and of such labor is the shape of the world made. But for most of us that start with that conception of our life, our ambitions and our conditions for contentment necessarily narrow over time. If you are the hero of a story, it is a smaller story than you thought.

Kids are a backstop that satisfies this in a more fundamental way than any other success can. We joke about every dad being declared the #1 Dad on Father’s Day, (and the fight to the death that must ensue when two #1 Dads meet) but those mass produced declarations of uniqueness are registering something real. For your own kids, you are the #1 Dad they could have. However you might feel you measure up against the world in every other way, there is one narrow but enormous domain in which you are unequivocally better than everyone else.

For my part, I no longer have to worry about my relationship to eternity, heat death, or whether the mighty will someday gaze upon my works and despair. I have sent a bit of myself into the future, and just have to pass the torch to them. That’s enough. In the end, they will undoubtedly be my greatest accomplishment, and raising them is the most worthwhile way I can choose to spend my days.

Kids have the urgency that forces you not to waste an hour, or a day, or a week. They want things from you now. They can’t wait, and they’re right. Time is not to be wasted, and they feel the waste more. 

You recreate your memories in them. They recreate childishness in you. Life folds back on itself, but not quite the same. It loops, but continues. A helix.

Life, then, is the creation of childhoods. You have yours, and then you get to create childhoods for others. The time is yours, and theirs. Don’t waste it.

It is undeniably the best time to be alone in human history. If you are sitting immobile on your couch with a phone under your thumb you have infinite information, infinite conversation partners, infinite movies, infinite games, infinite music, infinite video, infinite takes, infinite porn, infinite ragebait propaganda (whatever floats your boat) available for free or for at most a nominal subscription.

And yet despite this abundance, people consistently report being unhappy. We have fewer friends, participate less in public life, care less about our neighbors or our countrymen, feel that life outside of our phones is slowly but surely evaporating, and that our phones are a poor substitute that is slowly killing us all. 

So if everyone is unhappy with the current situation, why don’t we just stop? Why don’t we all just go outside?

You guessed it. Equilibria! If nobody outside is doing the thing you want to do, you can’t do it. If nobody gets off their couch, then nobody is doing the thing you want to do. As everyone’s couch gets more entertaining, it can make everyone worse off!

Here’s the graph. We’ll get into the model details for you to nitpick in a sec, but first let me describe the basic behavior. The X-axis here is “How fun it is to be on my phone on my couch.” Don’t worry about the units yet. What we see is that as it becomes more fun to stay in, everyone gets less happy, until you reach a threshold where almost everyone has abandoned the outside world (the gooner singularity) and then everything gradually gets better again as couch living continues to improve and the Children of Men apocalypse outside no longer bothers you.

Ok now for the details for you to nitpick. I assume:

• There is a range of extroversion/introversion in the population. I model this as a coefficient that balances your utility between being with people and being alone. For the graph above I assume the population values of extroversion are distributed as a Beta(3,3) because it’s a nice normalish curve, and makes a nice sigmoid, but any distribution gives you the same conclusion.
• The value of doing things with other people is linear in the number of people doing it. You might object that you only need a small minimum number of people doing a thing to be happy, e.g. once you have enough people for a pickup game of soccer, you don’t really benefit from more. We’ll get to that later. For now assume that this is a niche interest or a small community where the number of people doing it still has incremental returns, things like “Are there kids playing in the local park” or “Does your block have a block party” or “Do my friends of friends host house parties that I’m invited to.” This also models things that require a very large amount of effort to organize that few people are willing to do, so you need a large amount of people choosing to invest in your community to get just a few willing to put in the hours, things like “Does your grade school have an active cub scout troop” or “Are there community choirs nearby.” At minimum, the density of people willing to do the thing determines how far you have to drive to do the thing, and how much of a pain it is to do.

This makes each agent’s payoff α*n for going outside, where α is their extroversion and n the number of people outside, and (1- α)β for staying in, where β is how fun their phone is, and they choose whichever they like better. One more thing:

• I’m starting the simulation at full participation. This is appropriate to model the gradual decline of community over time, but you get even more depressing results if you start with low participation like we saw after covid. Even ignoring the fact that 0 is an absorbing state, the gradual growth of the group often fails to attract the next most extroverted member, and stalls out well below the best case equilibrium. In an infinite continuous model this wouldn’t be a problem,  but the real world has finite integer people who sometimes doom a group by dropping out or never joining.

These assumptions produce that graph, which you can view as an evolution of society over time. As the couch experience improves, marginally introverted people drop out of the community, which reduces the value of the community to everyone else, which causes even more people to drop out. In this fashion the level of community activity drops below what most people want, and everyone ends up less happy. Most people would prefer to be social until the x-axis reaches 100, if the level of social activity at the start of the graph could be sustained, but social activity falls off to near zero at half of that level because of this compounding process of marginal participants dropping out.

What happens if we cap the benefit of other people instead of making it fully linear? Maybe you live in NYC, and there are so many people around that the fraction of them that go outside is immaterial to you because there will always be enough. Maybe you’re interested mainly in football, and it’s so popular that the stadium will still fill up even if 80% of the population are hikikomori.

Here’s another graph where the benefit of other people caps out at 50% of them going outside. The situation is much better! Your couch can be pretty great before the activity starts seriously dying off. But again, just like before, once it reaches that critical threshold, average happiness gets worse for a bit before it gets better again in the world of only shut-ins.

So the moral of the story is, to avoid isolation and depression, move to a big city, pick popular hobbies, and if someone asks you to go caroling this Christmas, go even if you don’t want to, because it will make the experience better for everyone else.

The only way out of this trap is if everyone does more things than they want to. It’s now a good deed to just show up.

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Here’s the colab if you want to play with the model assumptions yourself. Let me know if you find anything interesting! Thanks to gemini for reducing the activation energy of writing this to 0.

The house that is perfect in every way but one has much to recommend it.

First, a bedroom, with a room for parents across the hall. It has a little orange nightlight and glow-in-the-dark stars on the ceiling, and as you drift off to sleep they become the real sunset and the real sky.

Next, a room full of bunnies. Hundreds of bunnies? Thousands of bunnies! Bunnies to cuddle everywhere you look. And what do you do about their food? A greenhouse full of carrots of course. And what do you do about their poop? This is the house that is perfect in every way but one. There is no need to worry about bunny poop.

Then the pasta room, yes, a whole room dedicated to pasta, pasta of every shape and size, and you can eat as much as you want. (This pasta is a whole meal with all the vitamins.) Behind the pasta room, there is another, secret room, dedicated to ice cream, vanilla and chocolate and mint chocolate chip, with colored sprinkles and chocolate sauce. The ice cream room is so well hidden that you only notice it because everyone walks out smiling.

Now a perfect house must have a treehouse, and so the house that is perfect in every way but one does too. (Lacking a treehouse is not the way in which it is not perfect.) There’s a rope ladder to go up, and a zip line to go down. A rope hammock spreads out between the branches with leaves overhead and the ground far below. Little drips of sunlight make it through to warm your skin in patches if you lie there. It’s scary, but not too scary. It is just right scary.

There is a cozy room with blankets and couches and pillows on the floor. Books line every single wall, all the books you could ever want to read. There is a fireplace with a fire anytime you want it, and a hot chocolate making machine. A big comfy chair sits by the fire or by the window depending on your mood and the season. This is the cat’s favorite place to sit. This is also all of the stuffies’ favorite place to sit. Sometimes they sit together.

The basement of the house that is perfect in every way but one has guitars on the wall and a drum kit in the corner. It has a pool table that can be a D&D table in a pinch. There are video games and board games and beanbag chairs, and if it weren’t for just the tiniest windows at the top of the wall no one would even know you are there. You can make as much noise as you want here without anyone hearing you. On the stairs there is even an extra door to the backyard that you can slip out of without anyone seeing.

The loft in the house is bare and drafty. It is a little small. It is too cold with the radiator off, and too hot with it on. But all of that, the hard edges and little annoyances, just make it better. They make it more real. It has a dishwasher, a washing machine, and a dryer. Its floor is original parquet that was covered by carpet for 50 years so still in great shape. You can get a cross breeze going from the windows, and the fire alarm never goes off when it isn’t supposed to. Most importantly, this room is all yours. There is a rail stop down the block. It comes every few minutes and can take you anywhere you want to be.

The house is rat proof, flood proof, foundation strapped, rewired and replumbed. The school is close enough for walking, and people walk. There are so many trick-or-treaters that you run out of candy no matter how much more you think you bought than last year. The backyard is big enough to run around with a kids and a dog, big enough for a water fight or kicking around a soccer ball, but not too big to mow or too big to weed. There are trees, big enough for shade, but far enough from the foundation and the sewer line that you don’t have to worry about roots, at least not for another 20 years. Their branches might even be strong enough for a treehouse. The kitchen has more tools than you really strictly need, and the workshop has more tools than you really strictly need, but not too many, not so many that you can’t find things when you look.

Believe it or not, it is not too big to manage, or too big to clean without getting tired. A ground floor bedroom overlooks the garden bed where chickadees sing in the afternoon and monarchs visit in the summer. There is a ground floor bathroom with beautiful blue tiles that remind you of the ocean, and a handrail in the shower. A perfect house has to be perfect for you as you are, not for someone else with a stronger heart and stronger legs. The living room has a comfortable chair where you can watch the light change in the evening and hear the sound of kids playing drifting through the window, but the chair is not so soft that you have any trouble getting up from it when it’s time. If the walk up to the porch ever gets icy, the house has lots of nice neighbors who will shovel and salt it for you, sometimes before you even wake up.

The house that is perfect in every way but one is small, and quiet, but there are good friends down the hall that are good at scrabble, and it’s still big enough for the whole family to pile in on Christmas and light up everything with hustle bustle. It doesn’t fit all of your furniture, but at least it fits the furniture you always liked the best. The dining hall has food you like, and the kitchenette is enough to make your favorites that the dining hall doesn’t. In the summer the garden plot is weeded and blooming. In the days when it is frozen and fallow, at least the Christmas cactus still blooms in the window.

Oh, the house that is perfect in every way but one is indeed a wondrous place, but of course there is that one way that it is not perfect, that one vexatious and infuriating way, the pea under the mattress, the stone in your shoe, the one flaw that is almost enough to undo everything else. Perhaps by now you’ve guessed what it is.

You can only live through it once.

Your camera has the ability to take three dimensional photos. Your screen has the ability to display three dimensional photos. You’ve probably never used either. This isn’t a hidden feature of some new phone hardware release, it’s a feature of your brain. All your brain needs to see in 3D is two pictures, and you can trick your brain into seeing 3D on a flat screen using just your eye muscles. I will teach you how. I’ll also tell you why you should.

Binocular Vision, and Faking It

Around a third of your brain is devoted to vision, and accordingly, it is amazing at it. From just the two small 2D images that are sent to your brain from the backs of your eyeballs, your brain reconstructs the entire 3D scene that you experience when you look around. Because your eyes are a few inches apart, they see two different views of the same scene, and those two views are all your brain needs. Distance causes objects to shift relative to each other when you see them from different angles. You can see this most clearly by moving your head from side to side and watching how things move. Your brain uses that discrepancy between the two views of your two eyes to reconstruct depth. 

Because your brain has this power, all you need to do to see an image in 3D is to send different images to each eye. It doesn’t matter how you do it. Every 3D display technology works this way, the only difference between them is how they get each image to only one eye.

Red/Blue 3D glasses filter out images that have the same color as the plastic lens. Modern 3D movies use polarizing filters, but the principle is the same. Two images are projected using orthogonal polarizations of light, and are filtered out by lenses in the glasses with the opposite polarization. Holograms show different images at different angles, and your eyes are at different angles. VR goggles put separate images on the screens in front of each eye that correspond to the views of two eye-spaced cameras in the virtual world.

Seeing Cross Views

If you don’t have any fancy technology, that doesn’t matter. You have eyes, a camera, eye muscles, and a brain, and it turns out that’s all you need.

If you have two images that show the views from two different positions, all you have to do to see the objects in 3D is to have one eye look at one image, and the other eye look at the other, and your brain will do the rest. You can do this either by crossing your eyes a little bit, or diverging your eyes a little bit. Most people have only ever deliberately controlled their eye muscles to cross their eyes, so find that to be easier. (It is also easier to focus on an object in front of the image than behind, because you can just put something in front of it and look at it.) Accordingly most stereograms are designed to look correct when you cross your eyes. To use the other method, the images have to be swapped or the 3D effect will be inverted.

Peephole Method

If you are doing this for the first time or aren’t comfortable crossing your eyes, then the easiest way to start is the peephole method. Hold your hand up with your fingers in a circle and look through the circle at the image. Position it so your left eye can see the right image through it, and your right eye can see the left image through it. Check each eye by closing the other until you see only one side in both, then open both eyes. If you focus on your hand, you should see the 3D image pop up inside of it as if you are holding it. It may appear blurry at first. Of all the methods, this one produces the least eye strain, and has proven to be the easiest for beginners. Positioning your hands this way tells your eyes exactly where to focus.

Cross-eyed Method

If you are comfortable crossing your eyes and feel like you have good control of how crossed they are, then this method is faster, and gives you a more complete view of the image. Just cross your eyes slowly, and stop when the images align. Doing it correctly feels like this: First the images split in two, and you’ll see flickering blurry copies of both images slightly offset from each other. Then as you cross your eyes more, eventually the two images in the middle will align. The center image will resolve into a clear 3D image, with two flickering copies of it next to them.

Anchor Method

If neither of those work, then the best way is to focus on something in front of the picture, and hope that the images align on top of each other as a side effect. You can do this by holding your finger substantially in front of the image, and focusing solely on the finger with your eyes, while turning your mind’s attention to the image behind it while keeping your eyes still. To find the right distance to put your finger, make the ratio of the distance to the image to the distance between images the same as the distance to your eye to the distance between your eyes. If the images are the same distance apart as your eyes, put your finger half way in between.

Making Cross Views

All you need is two pictures taken from two different positions shifted horizontally. The easiest way to do this is to take a picture, take a small step to the left or right, and take another picture. If the object is close, you only need to move the camera a few inches. If the object is far away you may need to take a full step to the side. How far you step will determine how strong the depth effect is, which is ultimately a matter of taste. A stronger depth effect makes the result more dramatic, but makes the image harder to resolve when you cross your eyes.

To turn the image into a cross view, you just need to put the images next to each other. Any way you do this is fine, even just looking at the two pictures next to each other in your camera roll. If the 3D effect looks backwards, just swap the images. There is free software that can do a better job by aligning the images automatically, adding borders, and allowing easy adjustments, Stereo Photo Maker for Windows or OSX, Cross Cam for Android.

Why bother? Isn’t 3D just a gimmick?

3D has mostly been a gimmick. 3D movies use the depth effect mainly to throw things at you and make you flinch, not to add to the art. But every sense we have should have art in it, and our depth perception has been shortchanged. Depth is such an immature medium that we haven’t gotten past the kind of whiz bang novelty of The Arrival of the Train. (Notable exceptions to this are Avatar and Half Life: Alyx, which are enormously enhanced by being in 3D.) It is a huge part of how we experience the world, we shouldn’t give up on it.

There are some things that just can’t look the same without depth. To photograph a forest, and convey anything like the experience of being there, you need the world to give you other visual cues to add depth to the image, like fog. The world usually doesn’t do this, and as a result nearly every photograph of a forest looks like a flat disorganized mess. Add depth, and suddenly all the complexity and beauty reappears. You can show people what a forest is for the first time.

To photograph a cave, and convey the layers and scale of the rock, you need clever lighting, and even then it usually fails. The geometry of a cave is too unusual for cues like lighting and shadow to work reliably. The rocks are all the same color. Add depth, and there is no more ambiguity. The shapes take shape.

Depth literally adds another dimension to the composition. You’re no longer just positioning objects to lead the eye around the page, but also to lead the eye through space. What compositions could we create with this? Architecture or stage plays probably have more to tell us about this than visual art does. But it’s mostly still brand new and wide open. Go explore!

Gallery

Places for more images:

• r/CrossView reddit community
• Cross View Flickr group.

Parallel Views

If you are able to diverge your eyes instead of crossing them, then arranging the images the opposite way can give you a more relaxing and more natural stereo effect. This corresponds to focusing past the image instead of in front of it. There is an upper limit to how far you can physically diverge your eyes, they can’t go past infinity, so parallel view images need to be smaller to take up less of your viewing area.

For more images with this orientation, try the r/ParallelView subreddit.

The end of the age where it makes much sense to read to our kids is the most bittersweet childhood transition so far. To memorialize it, this is a list of my favorite of the picture books we read to them, to pass it forward for everyone with kids younger than ours.

These are books that neither I nor the kids ever got tired of reading no matter how many times we read them, and where all the time reading them felt well spent. They are arranged roughly in order of age from toddler to kindergartener.

The Water Hole – Graeme Base

As a toddler this book is about counting animals. As a preschooler this book is about finding hidden animals. As an adult this book is about the apocalypse.

You Choose – Goodhart Pippa

This is like a toddler Rorchach test. Before they turned 4, I probably learned more about what they were thinking about from reading this book to them than I learned from actually talking to them.

Grandmother Fish – Jonathan Tweet

This does about as good of a job teaching evolution to a toddler as I think it would be possible to do. It explains the evolutionary path from vertebrate to human by highlighting the new behaviors of each clade and asking the kid to pantomime them, wiggling and chomping (jawed fish), crawling and breathing (reptiles), squeaking and cuddling (mammals), grabbing and hooting (apes), and finally walking and talking (humans.) The illustrations work for the age it is geared to, though wouldn’t have much interest on their own.

Up in the Garden, Down in the Dirt –  Kate Messner

This is a beautiful, lyrical introduction to all the things that live around you in the Eastern US. It will make you feel guilty for not raising your kid on a farm. Unlike most of the kids’ books about the natural world, this one actually takes pains to be accurate, and also to be relevant to the environment they’re likely to experience. The art is evocative, but not detailed enough to reward a lot of looking. The text and the mood are what make it shine.

Moonshot – Brian Floca

This puts the Apollo 11 mission into beautiful verse with wonderful drawings. This era needs to be passed on.

If I Built a … Series –  Chris Van Dusen

These books inspired my son to make inventing an imaginary world the main subject of his drawings. You can tell that the author/illustrator was exactly that kind of kid too, and now gets to do it for his job.

The Findus and Pettson Series – Sven Nordqvist

You can think of it as Calvin and Hobbes, but Hobbes is an elderly Swedish man, and Calvin is a cat. It is supremely cosy. If it had originated on the other side of the North Sea, it would be the embodiment of Hygge.

The relationship of Findus and Pettson is much like parent and child, but unlike most parental relationships in kids’ books, the teaching doesn’t just go one way. Anyone who has been sick and sleep deprived while their toddler begs them to play will recognize the interaction in Findus goes Fishing. You will probably also recognize the way that Pettson finally giving in and going out to do something with Findus cheers him up more than he thinks it will.

On top of the main story, the illustrations are full of “mackles,” tiny creatures that only Findus can see that find all sorts of amusing things to do with the objects in the scene. Wimmelbilderbuchs!

Standouts are Findus and the Fox, Pancakes for Findus, Findus goes Fishing, and Findus at Christmas, but they’re all wonderful.

The Bone Series – Jeff Smith

When kids start having the attention span for longer books but before they might be willing to listen to a chapter book without any pictures, the bone series of graphic novels fits perfectly. Be forewarned, if your kid is easily scared, some of the creatures in it might be a little much for them, but if so, you’ll probably know within the first few chapters. If you enjoy making character’s voices when you read aloud, this has an abundance of opportunities, different pitched Gollum voices for the rat creatures, low growls for Kingdok, James Earl Jones voice for Roque Ja, and whispers for the hooded one.

The Dinotopia Series – James Gurney

These are the most exquisitely illustrated books ever made, and they’re about people living with dinosaurs. This is the sort of book Jules Verne would have written if he were primarily a painter.

A Child Through Time –  Philip Wilkinson

This is the only kids’ history book I was able to get my kids interested in. The childrens’ perspective makes it something they can relate to, and the illustrations are beautiful. It’s rare to find books like this that aren’t all CG anymore. My kids particularly enjoyed finding the civilizations that they might have ancestors in.

One of the vertiginous features of modernity is that most manufactured products don’t cost much more than a few meals. The steak in a steak dinner costs much more than the plate it sits on, as does the cocktail cost more than its glass. The constraint on material wealth in manufactured goods slowly shifts to space to keep them, and information to find them. This makes sharing information as important as production.

Each of these products has made a material difference to the overall quality of my life, but rather than just a list of generally good things, these are also all things that took me a long time to figure out. I suffered for some number of years, and then finally relieved that suffering with an insight. The insight was just that one of these products would solve my problem.

Office Vertical Mouse

Since the mouse was invented, people have tried to invent various kinds of pads and protectors to keep your wrist from getting damaged by the pressure of the edge of your desk. None of these work, but that isn’t the only problem. Turning your palm face down is an unnatural position for your arm bones. It keeps your forearm muscles in a constant state of engagement, and narrows the space in your wrist. If you narrow the space in your wrist, your tendons are under pressure, and are more likely to become inflamed.

A vertical mouse solves all these issues. Your arm bones are straight and undisturbed, and the hard edge of your ulna is the only part of your arm that comes in contact with the table, rather than your soft vulnerable tendons. I started getting RSI in my wrist after just a few years of working, and a vertical mouse entirely solved it.

There is a catch, using a vertical mouse has reduced my twitch FPS skill substantially (this is almost certainly just cope.)

Binaural Nature Recordings 

I am unable to do serious coding, or deep work of any kind, while listening to music. Whatever part of my brain processes text also processes melody, so listening to anything with a melody interferes. But noise canceling headphones on their own don’t block out enough noise to work anywhere with conversation in the background, so I needed something to play to mask the surrounding sounds.

Binaural nature recordings are perfect for this. The spectrum of the sounds is broad enough to mask background noise, but unlike a pure noise track, it never feels claustrophobic. The sounds are varied and pleasant, but not distracting. With an exceptional recording the sense of space in the audio can make the soundscape seem even more real than the background noise, and make those conversations seem even more unreal and ignorable.

There are many sources of this but Gordon Hempton’s work is a standout. You can also make your own.

Hanayama Puzzles

Compiling code, training models, running pipelines, executing queries, or being in unnecessary remote meetings often involves a lot of waiting. If I don’t have anything to do with my hands, I compulsively crack my knuckles, and if I do this enough they get inflamed and hurt. Fidget spinners or other fidget toys don’t work for me, mainly because they’re boring. What does work for me are Hanayama puzzles. Each state of the puzzle moves in a different way, so the fidgeting doesn’t get repetitive. The puzzles themselves use physical intuition that operates at a nonverbal, almost subconscious level, so I can play with them without it pulling me away from my primary task. They entirely supplanted the bad habit.

The most beautiful of their puzzles that I’ve tried are the Baroq and the Radix. They’re a delight to hold, and to move. The most fiddly I’ve played with is the Infinity so if your main goal is to level-up from a fidget toy, start there.

Kneeling chair

You may or may not like kneeling chairs, they are certainly an acquired taste. I put this on the list as a recommendation not because I think everyone necessarily will benefit from a kneeling chair at their office all the time, but because they are different from other chairs. If you are the kind of person who sits at a computer at work and then sits at a computer at home, it will help you to have substantially different chairs in those two places so that you are sitting in different ways. Ergonomic injuries are injuries from repetition and duration, and the best thing you can do to prevent them, aside from doing things less, is to do them differently.

Kinesis Freestyle Pro

A split keyboard forces better typing habits if you aren’t a great typist. It also allows you to keep your wrists straight while typing. Just like with the vertical mouse, any position that kinks your wrists narrows the area in which your tendons can move, and makes them more likely to become inflamed.

The fact that the two halves of the freestyle can be positioned arbitrarily helps in several ways. Your hands can be spaced far apart, farther apart than a conjoined keyboard would permit. Your hands can be placed in slightly different places every day which reduces the amount of repetitive stress from having an identical setup. If you game, then the right half of the keyboard can be moved out of the way entirely to make more space for your mousing hand.

Cherry M switches are delightful to type on without being too clicky. There is probably little material ergonomic benefit to them, but they just feel nice.

Bluetooth Foldable Split Keyboard

Economy airplane seats are now too small to fit a laptop on the tray table. Fortunately, everyone is walking around with much smaller devices in their pockets that can partially substitute, but a phone can’t easily be used to create instead of consume because of its small size. A foldable bluetooth keyboard fixes this. Just having a real keyboard is enough to make a phone a capable general computing device. I’ve done a lot of writing on planes this way.

Bedroom  Air filter 

A third of the air you breathe in your life you breathe while you’re sleeping. During most of the day, you don’t have much control over the air you breathe, but at night you do.

Having an air filter on high all night during allergy season made my seasonal allergies almost entirely disappear. They went from being debilitating and needing medication (which, regardless of the class of antihistamine, always made me feel like a zombie) to a minor annoyance. Beyond allergies there’s a growing body of literature that air pollution may be a major cause of dementia as well as a variety of other health effects, like premature birth. Air filters also might make you less likely to get sick from your family.

As side benefits, an air filter serves all the same functions as a fan. It increases air circulation, which reduces CO2 concentration in your bedroom, a common cause of poor sleep and morning grogginess. It also functions as a white noise machine. The best white noise machines are themselves just fans in a box.

I have had enough trouble with the electronics of these conking out over the years that I don’t want to recommend any particular brand or model, but wirecutter has a regularly updated list.

Laser Projection Clock

Most of us are in the habit of checking the time on our phones instead of a dedicated clock. This is fine during the day, but it’s a terrible idea in the middle of the night, where your phone is not only very bright, but also very distracting. The ideal case, if you wake up in the middle of the night, is that you fall back to sleep without ever becoming fully conscious. To do this, you need some way of knowing that it is still the middle of the night with as little conscious action as possible.

A bedside clock that projects the time with a red laser on the ceiling accomplishes this. It emits a very small amount of light (and red light, so supposedly doesn’t interfere with your circadian rhythm) but just by cracking your eyes you can immediately see what time it is and can decide to go back to sleep without fully waking up.

This was especially helpful for me to triage nighttime wakeups with a baby and toddler. I could immediately decide whether I was preparing for the morning, putting the baby back to sleep, or ignoring them for a bit in the hopes that they’ll go back to sleep on their own. It is even more helpful if you’re trying to take care of the situation before your spouse wakes up too.

0.3 mg Melatonin

When you’re out camping, going to bed right after the sun goes down feels like the most natural thing in the world. There’s no light. The word disappears. It’s bed time. You feel it instinctively.

At home, all manner of things intrude. Phone, TV, lights, etc. Melatonin reproduces the sleepy feeling you get when you are out in nature. If your sleep schedule is going out of whack, or there’s a night where you absolutely need to sleep, 0.3mg of melatonin a half an hour before bed makes a huge difference. Usually I only need to take it for a few days to get back on schedule. I do find I am groggier in the morning after I have taken it than when I don’t. So I usually only use it as a temporary fix. That grogginess is almost always worth it if I’ve been trying to catch up on sleep.

It is also extremely useful for getting over jet lag. Staying up late to undo jetlag is much easier than going to bed early, but sometimes the time shift requires going to bed early. This is the gap that melatonin can fill.

It is no substitute for good sleep hygiene. Don’t scroll your phone in bed. Read non-fiction instead.

(Note: most melatonin in drug stores has way too large of a dosage, 3mg or even 10mg. Try to find the smallest dosage you can. Even 0.5mg feels like too much.)

Kitchen Get Two of Things

This is not a product, but rather an insight that you should apply to whichever objects you use most. I often found myself waiting around unnecessarily while cooking because the throughput of my tool was too low. If making crepes, I could only make one crepe at a time. If making pancakes, I could only fit three on the skillet. The waffle maker only makes one waffle. If you find yourself in this situation, just get another one. Get another skillet. Get a double sided waffle maker. This took me embarrassingly long to realize. They aren’t that expensive relative to your time, and they don’t take up that much space. Making pancakes became something I wouldn’t hesitate to do on a school day, just because it became so much faster.

Whatever you use most, consider whether you could do things faster with two of them.

Magnetic Double-ended Measuring Spoons

As part of the general principle of “get two of things” the two ends of these measuring spoons, combined with the compactness with which they fit in a drawer makes them a standout among my kitchen tools. There is no need to root around anymore for the right size. They organize nicely, stay organized, take up a tiny amount of space, and function as well as having two sets. They’re just perfect.

Chef’s Turner and Carbon Steel Skillet

I’ve gone through many varieties of non-stick skillet over the years, and many varieties of spatula. At long last, I think I’ve found the set of tools that I don’t think can be improved upon.

Plastic spatulas melt. Rubber spatulas break and tear. Neither can apply much pressure to something stuck on a surface. Metal ones are the only kind that last and function properly, but if you use them on Teflon you’ll destroy it. This alone makes it worth switching to cast iron or carbon steel.

Cast iron or carbon steel skillets are intimidating because caring for them is portrayed as a complicated hobby. They are in fact very easy. They are best thought of as being “self-healing” non-stick. If there’s a teeny bit of oil or grease on it when you heat it up, then everything you cook afterwards remakes the coating. (Just use something else for acidic foods like onion or tomato.)

Because the coating is self-healing you don’t have to worry about scratching it, and so the rigid metal spatulas sold as “chef’s turners”  work best. They’re small enough to fit under anything, wide enough to balance things to lift, and both sharp and rigid enough to scrape with.

Instant Pot

I was a late convert to Instant Pots, but they have dramatically reduced the amount of time I spend cooking. I’ve gradually been retooling all of my recipes to use the instant pot as much as possible.

Before my wife made us buy one, I was skeptical. “A pressure cooker on a timer, how much better could it be? We already have pressure cookers, we already have timers.” I was completely and utterly wrong. The key feature is that you set the timer, and then leave. Much of the time spent cooking is actually spent waiting. With an Instant Pot, you can leave the house. We cook a lot of dry legumes, so pressure cooking is essential, and being able to do that while at work frees up a ton of time. Even if you don’t leave the house, the fact that you don’t have to listen for a timer and be available when it goes off means you can fully commit to using that waiting time for something else.

I’m now convinced these are the most substantial addition to kitchen automation since the microwave.

A Cook Book that you Trust Unconditionally

The internet has an unbounded number of recipes, and they’re free. A book has a fixed number of recipes, and you have to pay for it. The internet aggregates the preferences of the entire world. A book is just one person’s opinion. This ought to make a book strictly worse, and yet it doesn’t.

Cooking a meal is an investment. Sifting through a sea of possibilities that you don’t entirely trust makes you doubt that investment and shy away from it. Having a book that you can browse, where you don’t have to second guess which link to click, where you can be confident that the result will be worth it, makes it worth taking a risk to cook new things. You’ll explore more, and branch out more, by giving yourself less choice.

Our current favorite is The New Vegetarian Cooking for Everyone by Deborah Madison. It hasn’t failed us yet.

A Stash of High Quality Canned Chicken Soup

Chicken soup is widely considered the best food to eat when you are sick. This makes it extremely convenient that it also tastes great from a can. You don’t want to cook. Your loved ones are probably sick too, or will be very soon. This saves you the indignity of paying a lot for doordash for a dish that won’t satisfy you. You can keep an emergency “I have a cold” kit in the pantry. which will also serve you well in the event of a long power outage as long as you have a camp stove to reheat it.

Canned soup has drastically improved since I was a kid, as long as you pay the extra $2.50 for the brands that don’t need to be reconstituted with water, like Campbell’s Chunky. Their chicken tortilla soup is my favorite to eat when I’m sick, because the little bit of spice also helps clear out my nose.

Living Room Foldable Coffee Table

Coffee tables are either too small for board games, or too big to leave enough space for doing anything else with your living room. Foldable coffee tables fix this. You unfold them, they raise to game-playing height, and your most frequent boardgames are stored right underneath. This makes even a small living room adequate for both boardgames and dancing, neither of which I was willing to sacrifice for the other.

Swoop Bags

Building with Lego pieces practically requires spreading them out over the floor. If you keep them in a bin, that bin will be dumped out. This makes cleaning them up a nightmare. Swoop bags elegantly solve this, and have eliminated Lego cleanup as an issue in our house entirely. You spread the bag out on the floor, find the Legos you need, and clean it up instantaneously by pulling on the cord.

Love Letter (card game)

A little out of character for the rest of the list, but I felt I had to include it. This is the one board game I can recommend to any possible disposition. It distills all of the fun of a trick-taking game into as little time as 10 minutes and a package as small as a deck of cards. It’s silly, it’s clever, it’s fast, it’s subtle. You can learn it in minutes. Anyone old enough to read can play it, but experienced jaded board gamers will still enjoy it.

Despite the fact that the theme of the game is about sending a love letter to a princess, the game itself is so good that even 8 year old boys beg to play it. That is the best recommendation I can imagine.

Clothing Tilly Endurables LTM6 Airflo Hat

If you’re light skinned and live in the US you’re probably a lot farther south than your ancestors evolved and your skin would benefit from sun protection all the time. I hate putting sunscreen on my face, and no amount of fear of skin cancer could make me do it every time I go outside. But if a hat looks nice enough and is comfortable enough I’ll wear it, and Tilly hats work. Their main feature is that they look great and have a broad brim, but in addition their neck and head straps keep the hat on your head in high winds while still hanging comfortably from your neck when you aren’t wearing it. They also float if you ever drop them in water, pack flat in a suitcase, and are generally indestructible.

With the history of skin cancer in my family it’s not an exaggeration to say that getting in the habit of grabbing my hat every time I leave the house has materially improved my life expectancy, even if the benefits of avoiding skin aging and sunburn weren’t enough on their own.

Carhartt Utility Jeans

Carrying phones is one of the major functions of a modern pair of pants but few pants are designed for it. As phone sizes have gotten bigger, ordinary front pockets aren’t enough. The phone digs into your hip when you sit down. If you take it out whenever you sit to prevent this, then it’s much harder to avoid checking it in conversation. It’s no longer out of sight, out of mind.

Most styles of Carhartt pants have phone pockets stitched into the side, and they work perfectly. I won’t buy pants without this feature anymore. The difference in comfort and convenience is just too big.