math, science

Life in Hyperbolic Space 1: Primer

It’s rare that weird, brain-bending ideas and video games meet, but in my experience, when they do, it’s pretty glorious. Portal, Prey, Antichamber, The Stanley Parable, and SUPERHOT are examples I’ve played personally. Also Miegakure (if it ever comes out, grumble grumble) will probably land instantly in that category, being a 4D puzzle game. But my most recent weird-game obsession has been HyperRogue. HyperRogue is awesome. Like Dwarf Fortress, it’s got a bit of a retro look with clean, minimalist graphics. And like Dwarf Fortress, it’s pretty obvious that a lot of love has gone into it. Here’s what the game looks like:


Like many roguelikes (modeled after the ancient ASCII game Rogue), it’s played on a sort of chessboard. It looks at first glance like one of those board wargame or D&D-type hexagonal chessboards, but instead of being just hexagons, it’s got heptagons (7-sided polygons) too. You know what? That reminds me of the description of another geometric object:

Truncated Icosahedron

(Screenshot from the awesome polyhedron program polyHédronisme)

That is a truncated icosahedron, but I’d wager that most people know it better as either A) a soccer ball/football, or B) a molecule of C60: a fullerene, a buckyball.

Don’t worry. It’ll be clear in a moment what the hell I’m going on about. You see, HyperRogue takes place in the hyperbolic plane. A flat piece of paper is a Euclidean plane. The surface of a globe (or the Earth, or a buckyball) is a sphere. The hyperbolic plane is the third brother in the trio, so to speak, and it’s the weird brother. Their relationship makes more sense to me if I think in terms of polygons. Here’s another picture:


(From the Wikimedia commons.)

The Euclidean plane (the hexagonal tiling above) consists of hexagons, each of which is bordered by six hexagons. The buckyball (football/soccer ball) farther above, representing spherical geometry, consists of pentagons, each of which is bordered by five hexagons. And at the very top of the page, the world of HyperRogue, representing the hyperbolic plane, consists of heptagons (7-sided polygons), each of which is bordered by seven hexagons. The hyperbolic plane is what would happen if you tried to sew up a soccer ball using heptagonal and hexagonal pieces of leather, rather than the usual pentagonal and hexagonal ones. Here’s what that looks like:


(From the page of Frank Sotille, who has awesome templates so you can make your own hyperbolic football. I would’ve done it myself, but all of my Scotch tape has vanished.)

The only buckyball-type tiling that lays flat is the one with hexagons surrounded by hexagons. Pentagons surrounded by hexagons curves into a sphere, and heptagons surrounded by hexagons curls up into what HyperRogue’s creator calls a hypersian rug.

But here’s a more intuitive (though less precise) way to understand the hyperbolic plane. Consider the flat Euclidean plane. Pick a point. Draw a circle centered on that point. Measure the circumference of that circle. Draw another circle with the same center, but twice the radius. Measure the circumference of that circle. The farther you get from your starting point, the larger the circumference, but the increase is very predictable and linear. As a matter of fact, the circumference (the “amount of space”) you cover as you increase the radius of your circle increases exactly like this:

save (1)(1)

(Graphed with

Now do the same thing on a sphere: centered on the north pole, draw a very small circle with a given radius (with the radius measured across the curved surface of the sphere, not straight from point to point). Draw another circle with twice the radius. Up until you hit the equator, the circumference will increase, but eventually it maxes out and goes back down:

save (3)

(Circumference in the Euclidean plane in black, circumference on the sphere in red)

There’s another important effect to consider here: the sphere’s radius matters. That plot assumed a sphere of radius 1. Here’s what it would look like with a sphere of radius 2:

save (2)

It doesn’t make much sense to ask for the “scale” or “radius” of the Euclidean plane, because the answer is “infinity.” Any Euclidean plane is indistinguishable from any other, no matter how you swell or shrink it. Spheres, though, are distinguished by their radii: each has an inherent positive curvature.

Of course, on a sphere, the largest circle you can draw has a radius (measured across the surface of the sphere) of ½πR. the circumference of that circle lies right on the sphere’s equator. After that, the circumference decreases as the radius increases, because your circle’s shrinking as it approaches the opposite pole. It reaches zero when the radius is πR, and your radius-line stretches from one pole to the other.

The Euclidean plane has zero curvature. The sphere has positive curvature. The hyperbolic plane has negative curvature. The “radius” of a hyperbolic plane is defined as 1 / sqrt(-K), where K is a measurement called “Gaussian curvature.” (For comparison, the Gaussian curvature of a sphere is 1/(R²) ). K is the thing that’s zero for the plane, positive for the sphere, and negative for the hyperbolic plane. For a hyperbolic plane of K = -1, with a “radius” of 1, the circumference increases like this:

save (1)

(Hyperbolic circumference is the green line. The red line for a sphere with R = 1 (K=1) is included for comparison.)

That’s the weird thing about hyperbolic geometry: a sphere of infinite radius behaves exactly like the Euclidean plane (it is the Euclidean plane). But as the radius shrinks, the sphere contains less and less space (so to speak). To put it another way: if you were knitting a Euclidean plane (which people do, because mathematical knitting is a thing, which is awesome), then you’d need to knit in twice as much thread at radius 2 than you’d needed at radius 1. To knit a sphere, you’d need to knit less than twice as much thread in at twice the radius. And to knit a hyperbolic plane, you’d need to knit in more than twice as much yarn at twice the radius (according to the formula 2 * pi * R * sinh(r/R), where R = 1/sqrt(-K), and r is the radius measured through the plane; the equivalent relation for the sphere is 2 * pi * R * sin(r/R)). Where the Euclidean knit would give you a flat circular rug, and the spherical knit would give you a hacky-sack ball, the hyperbolic knit would give you something like this:


(Knitted by Daina Taimina, exhibited on the website of the Institute for Figuring.)

But the weird thing is that you can still do almost exactly the same geometry on the hyperbolic plane that you can do in the Euclidean plane. In fact, that’s why hyperbolic geometry is interesting: apart from a couple of weird quirks, it behaves just like a plane. That means you can make rigorous, valid, geometric proofs in the hyperbolic plane.

The Euclidean plane gets its name from Euclid of Alexandria, who is responsible for the infinite misery of people (like me) who just couldn’t get along with high-school geometry. But he condensed many centuries of Greek (and other) geometry into a set of postulates (axioms) from which you can prove pretty much anything that’s true in geometry. Here they are:

  1. You can draw a straight line between any two points.
  2. You can extend an existing straight line as far as you like.
  3. Using a compass, you can draw a circle with any center and any radius you want.
  4. All right angles are the same.
  5. If you’ve got two lines running alongside each other and another line running through both of those, and the angles on the insides of the intersections add up to less than a right angle, then the lines will intersect if you extend them far enough, and they’ll intersect on the side where the angle-sum is less than two right angles.

That last one, called the parallel postulate was a thorn in geometry’s side for a long time, because it seems a lot less elegant than the others, and it seems like the kind of thing you might be able to prove from the other axioms, which would mean it’s not an axiom, since axioms are your starting rules and theorems are what you prove using them. A less messy way to write the parallel postulate is:

5. Given any straight line, and given a point which doesn’t lie on that line, there is exactly one straight line through that point which never intersects the first line (the second line being the parallel).

Spherical geometry and hyperbolic geometry are both based on changing the parallel postulate. In spherical geometry, it becomes:

5. Given any straight line, and given a point which doesn’t lie on that line, there are zero straight lines through that point which never intersect the first line.

Or, to put it in simpler terms: because you’re on a sphere, lines that should be parallel (that is, lines which form a total of two right angles when intersected by a third line), inevitably intersect. Think of the north and south poles as two points. Draw the prime meridian from North to South. Now draw another line passing through the equator at 1° East longitude, 0 ° North latitude. At that point, the two lines are as parallel as lines get: they form ninety-degree intersections with the equator, and therefore, the interior angles on either side form exactly two right angles. But keep drawing those lines, and they’re going to intersect at the south pole, even though they should, according to Euclidean intuition, have stayed parallel.

In hyperbolic geometry, the parallel postulate is modified to the other extreme:

5. Given any straight line L, and given a point P which doesn’t lie on that line, there are an infinite number of straight lines through P which do not intersect L.

Poincare Parallels

That’s the Poincaré disk model, which fits the infinite hyperbolic plane into a finite circle. It’s elegant and simple, and it’s the model HyperRogue uses, so I’m going to stick with it. The red lines are the boundaries of the infinite set of lines which pass through P but never intersect L. It looks like the red lines intersect L at one end each, but the Poincaré disk model distorts distances more and more the closer you get to the edge. A picture’s worth a thousand words, so here’s a series of circles of equal radius starting from the center of the disk and moving outward:


(Both images rendered with the awesome (and free) geometry software GeoGebra)

I know they don’t look like circles of equal radius, but that’s just an artifact of the projection. The same way a Mercator map distorts Greenland so that it looks like it’s bigger than North America (when in reality it’s not much bigger than Quebec or Mexico), the Poincaré disk model distorts distances the closer you get to the edge of the circle. As a matter of fact, that bounding circle, as measured within the hyperbolic plane, is infinitely far from the center. You can’t ever reach it: it’s infinitely far from everywhere. So those intersections that seem to exist in the picture with the red and blue lines, they don’t actually exist, because you’d have to go infinitely far to get there. And keep in mind that, from any given point, it feels like you’re at the center of a Poincaré disk, so those lines don’t actually get closer to the line L the way the projection makes it seem. The projection is a necessary evil. You can do spherical geometry on an ordinary globe and remove all distortion, but you saw how messy and rumpled the hyperbolic version of a globe became: just look at the red crochet thing above. That’s not gonna happen. You have to live with the distortion.

The cool thing about the Poincaré disk model, though, is that it preserves angles, which makes it easy to do the kind of straightedge-and-compass geometry that’s so handy for geometric proofs.

And guess what? Just like we experience the world an almost-flat Euclidean space (relativity says it’s not perfectly flat, but it’s very close in our neighborhood, which I have to say to stop the nitpickers from yelling at me), there are three-dimensional spaces with spherical curvature, and there are three-dimensional spaces with hyperbolic curvature. In the next part, I’m going to talk about life in a highly-curved hyperbolic space. But before I go, let me leave you with a picture of something. In the Euclidean plane, you can only pack six equilateral triangles (all angles and edge-lengths the same) around a single point. The result looks like this:



In the hyperbolic plane, though, you can fit seven equilateral triangles around a vertex, and it looks like this (and don’t forget, those triangle are just as perfect and equilateral as the ones above; it just doesn’t look like it, because of the projection):



You can actually fit eight triangles around a vertex too, although the triangles have to be larger (largeness being a slightly complicated concept in hyperbolic geometry, but we’ll get to that next time):



And actually, it’s perfectly allowable to fit an infinite number of equilateral triangles around every vertex. That looks like this:



And remember, those triangles are still perfect and equilateral and regular. Hyperbolic space is weird. Remember that thing Christopher Lloyd said in Back to the Future? Get ready: we’re gonna see some serious shit.

biology, Weird Food

Weird Food 9: Mam Ca Loc (Mud Fish)

I’ve got good news! For all you curious buggers out there who want to try surströmming, but either can’t afford to have it shipped to your part of the world or simply can’t get it at all, I’ve found a substitute, which you can buy at many Asian or international markets! It’s called mam ca loc: preserved mud fish!

Mud Fish Jar.png

…I might have been lying about the good news.

This is yet another weird dish I tried mainly because I saw the violent reactions of the people who tried it on YouTube. I’m starting to question my judgment.

But before I describe the foul stuff that was in that jar, I should say that I fucking love Vietnamese food. Actually, Vietnamese food might be my favorite. There’s a chance I like it more than pizza, which is really saying something. My favorite soup at the Vietnamese place down the road is pho dac biet (sorry if I spelled it wrong, and sorry that I can’t figure out how to make WordPress do Vietnamese diacritics), which a lot of people shy away from because it’s got tripe and tendon in it. I love that stuff. I want you to keep everything I’ve said in mind as I describe what it was like to taste this substance:

Mud Fish Open.png

The first thing that struck me was the horrible smell. Much like surströmming, mam ca loc (or at least this version of it) emits a sulfurous stench like the world’s ripest fart. Once the initial stench has dissipated, it leaves behind a much worse smell. Pardon me if I get a little gross here, but the smell is as though a grizzly pooped ten pounds of undigested fish into a Port-a-John and it was left to sit in the sun all day. It was absolutely rank.

And, like surströmming, the flavor actually wasn’t too bad. Tasted mostly like anchovies. The texture wasn’t horrible: the texture was annoying: mud fish is very tough, and the meat felt like it was stuck to some sort of silicone-rubber backing. Not that I spent much time trying to get the meat free, because there was no way in hell I was going to swallow something that smelled like that.

Unfortunately, mam ca loc is not the last fermented seafood I’ll be trying. The next fermented seafood I’ll be trying is made by Lee Kum Kee, who spend 95% of their time making tasty soy and hoisin sauces, and 5% of their time making horrible salty fermented shrimp paste.

The Final Verdict: I wouldn’t eat mam ca loc unless the alternative was starvation or other physical harm. If I had to eat it, I’d rinse it off thoroughly and put it in a soup or something. But I wouldn’t be happy about it. I don’t recommend it, unless you want the surströmming experience, but can’t get surströmming. Even then, I don’t really recommend it.

To my Vietnamese readers: I know I didn’t prepare this properly, because I didn’t prepare it at all. How is it meant to be eaten? I’m genuinely curious. I’m guessing soup, but I don’t honestly know.

Weird Food

Weird Food 8: Jackfruit

For me, the jackfruit has always been the holy grail of weird food at the international market. Big, spiky, and mysterious. Like a dragon. But jackfruits are sold by the pound, and they’re big bastards, so I could never justify the expense of buying one, since I didn’t know if it was going to be any good. But lucky for me, my cousin is a bad influence, and because she and I were having a weird food marathon, we bought one.

Jackfruit Whole.png

The picture doesn’t do justice to its size. It was gigantic. It weighed in at 15 pounds (6.8 kg), and it was one of the smaller ones in the pile. I carried it out of the market like a very fat (and very prickly) baby. Admittedly, though, it’s not nearly as spiky as its foul-smelling cousin, the durian. Durians have, on more than one occasion, drawn blood and left little splinters in my hands.

Trying to get into a fruit this size comes with lots of unexpected logistical problems. How do you put it on the table without the spines digging horrible gouges into the wood? What kind of knife do you use? And what the hell part are you even supposed to eat? Cutting the fruit open didn’t make that last part much clearer:

Jackfruit Wedge.png

Lucky for me, I’d tried dried jackfruit before, so I guessed that the yellow bit was the meat. Extracting it was a bit difficult, made more so by the fact that the white pith has latex or something in, which turns your hands sticky as all hell. But eventually, I got it partly disassembled:

Jackfruit Meat.png

You can tell how sticky that pith is by the fact that a strip of it glued itself to the husk.

The good news: jackfruit is delicious. It’s got a peculiar texture that makes you think it’s going to be rubbery, but then it isn’t. There’s not much juice in it. It smells faintly sweet, like pears or pear blossoms. It tastes like a mixture of pear, apple, pineapple, and lychee, but all very subdued and subtle. The only bad thing about jackfruit is that it’s so damned big, which meant, by the time I finished eating that one slice, I was stuffed to the gills. And, because I planned poorly, there wasn’t room in the fridge to save the rest of it, which is a shame, because I totally would’ve eaten it.

Here’s how tasty jackfruit is: I’m actually going to buy another one, because I wanna make jam out of it. I think it’d make amazing jam.

The Final Judgment: It’s expensive, and it’s bulky, but it’s totally worth trying if you can get it. It’s got a subtle, sweet flavor and it’s nice and filling. A good meal all ’round.


Weird Engines

You’ve probably noticed I’ve been on an automotive kick lately. Don’t worry, I don’t think I’m in any danger of becoming a babbling gear-head. Firstly, I don’t have the patience or mechanical skill to actually put an engine together without blowing myself up and setting the neighborhood on fire. Secondly, where I live, working on cars isn’t a cheap hobby, and the fact that I’m considering going to grad school means all my pennies are spoken for.

I’m interested in engines the same way a little boy would be. They’re big, loud, powerful, complicated, and mechanical. I could probably come up with fancy reasons for being curious about engines, but the fact is, I just like them. But I like them in kind of a shallow way. The more intricate details of engines still confuse me. There’s a reason I call myself Hobo Sullivan: in pretty much all the areas I talk about, I’m like a hobo being dragged into an art gallery. I can say “That painting looks like shit” or “That’s a really pretty painting,” but if you start trying to teach me about composition or Postmodernism, my eyes’ll glaze over and I’ll start asking when I get my bowl of soup.

Which is a really long-winded way of saying that this post isn’t intended for engine experts. If you’re into engines, you probably know every single thing on this list. This is a post for people who are casually interested like me. This is me emerging from the Google Caves with a handful of funny-shaped crystals and saying “Look at this cool stuff I found!” This list has nothing to do with with deciding on the best engine or anything fancy like that. This is a list of the engines I’ve found in my bizarre curiosity that made me say “That’s kinda cool…”

The Boxer-6


(Image from

The boxer-6 isn’t all that weird, since it’s still in common use. That’s partly because you’ll find it in sports cars like the Porsche 911, and in some of Subaru’s current cars and SUVs. When I first started learning about weird engines, I thought the boxer-6 was just a V6 where the V got all flattened out. Engines like that do exist, but they’re not called boxer-6s. The difference is, in a boxer-6, pairs of pistons opposite each other move in and out simultaneously. Unlike in a lot of V-engines, each piston’s connecting rod has its own bearing on the crankshaft. What does any of this matter? Well, it’s unusual, for one. For two, the peculiarities of engine dynamics (which I don’t pretend to understand) make the boxer-6 a very smooth-running, well-balanced, low-vibration engine. Also, the fact that its cylinders aren’t crammed cheek-to-cheek in a V means that even fairly high-power boxer-6s can be air-cooled (though some are still water-cooled).

But you guys know me by now. You know I always go to extremes if given the chance. I’m not going to be satisfied with a six-cylinder engine, no matter how nice.

The H-16


(From Wikipedia.)

We’ve made quite a leap. While you could go out right now and buy a car with a boxer-6 in it, the only way you could have an H-16 engine is time travel, or by being an insane millionaire and having one built for you.

The engine above is British Racing Motors’ H16 engine. There are plenty of weird, esoteric terms used in automotive circles, but the weird letters that show up in engine names are perfectly sensible (mostly). My car is powered by an I4 engine, which means it’s an inline-four: four cylinders in a straight line. A V6 has six cylinders in two banks of three, with the pistons angled so that their connecting rods form a V-shape, with the crankshaft at the tip of the V. You’d refer to the boxer-6 above as an F6, for flat-6.

What, then, is an H16 engine? Well, it’s horrifying, is what it is:


(Again, from Wikipedia.)

An H-16 is two flat-8s stacked on top of each other, each with its own crankshaft. The crankshafts are connected at the end by gears. Like I said, I don’t know engines, but that seems like a bad idea.

For some applications, it’s actually not. H-engines are mechanically pretty well-balanced, for one. For two, they’re a bit more compact than, say, a V-engine with the same number of cylinders, which made them popular for high-power airplanes.

But car enthusiasts will know that the H16 I showed at the top of the section didn’t come from an airplane. It came from British Racing Motors’ ill-fated P83 Formula 1 car, which has a peculiar, and if you ask me, slightly unpleasant sound.

BRM’s H16 was plagued with problems. For one thing, having two sets of cylinder heads on opposite sides meant it needed two radiators and a split fuel system. It also needed dual camshafts (which are the mechanical clockwork-type devices that tell a cylinder’s valves when to open the intake valves and let in fuel, and when to open the exhaust valves to let out burned fuel). It needed dual camshafts for each cylinder head. That’s bad enough in a V-engine, where you have two cylinder heads, but the H16 had four. For another, it was more complicated and fuel-hungry than even its competitor, the mighty V16. Unsurprisingly, the engine wasn’t a success, partly because a lot of them just blew up during races. Apparently, British Racing Motors’ troubles at the time, and their obsession with complicated engines, earned them the nickname “British Racing Misery.”

Still, it’s a weird, interesting engine, and somebody had some serious gonads to say “You know what? A V16 is just too damn simple.”

The Napier Deltic


(From Wikipedia, again.)

You remember that scene in the first Back to the Future where Dr. Brown is talking about inventing the Flux Capacitor? “I slipped, hit my head on the edge of the sink, and when I woke up, I drew this.” I’ve gotta figure a bonk on the head inspired the Napier Deltic. For those who don’t know much about engines, let me explain why the picture above shows one of the weirder engines ever invented.

  1. Opposed pistons. In a common piston engine, the air-fuel mixture burns, and the pressure from the hot gas pushes a piston down, which applies torque to the crankshaft, which drives whatever machine the engine is running. There’s just a cylinder head holding the hot gas in. In an opposed-piston engine, though, there isn’t a cylinder head, but rather, two pistons in a headbutt configuration in every cylinder. The fuel-air mixture enters the space between the two heads and burns there, pushing the two pistons apart, driving two crankshafts.
  2. The delta design. As you can see, the Deltic isn’t even as simple as a regular opposed-piston engine. That picture shows three cylinders, containing six pistons, driving three crankshafts. It’s weird, but it’s got a certain geometric appeal to it. It was also, apparently, a lot more compact and powerful than similar engines of the time, which made it attractive for British torpedo boats and locomotives.
  3. It was a two-stroke. If you don’t know, two-stroke engines are usually what you find powering small power tools like weed-whackers and chainsaws.The engines of most modern cars are four-stroke. The differences are subtle. In a four-stroke engine (which most gasoline engines are), the piston has to go up or down a total of four times to complete a full cycle: It moves down to suck in in air and fuel, moves up to compress the air and fuel before ignition, is pushed down by the burning air and fuel, and finally rises up to push out the exhaust. In a two-stroke engine, the intake and exhaust steps happen at the same time: often, the piston pushes down on a fuel-air mixture in the crankcase, and the pressure pushes the mixture into the engine, which pushes the exhaust out. The major advantage of a two-stroke engine is that it doesn’t need mechanically-operated intake and exhaust valves, since the piston controls intake and exhaust. This saves weight and complexity, which is vital when your engine is powering, say, an airplane, or a boat, or a chainsaw that needs to be light enough to hold up for long periods, without getting tired and dropping it on their foot.

The Deltic was fairly successful, since it packaged eighteen or more cylinders (two pistons each) into a smaller package than was possible with other designs of the same cylinder number. It was a lot lighter than comparable engines, too.

Why aren’t there more Deltic-type engines around? Well, a little research suggests that’s mostly because Napier was bought out after World War 2, and switched to making things like turbine engines and turbochargers, the former of which were rapidly filling a lot of the niches the Deltic once occupied. I suspect the peculiarity of the delta design also played a part, since my first reaction to it was “there’s no way that was a success.” I was wrong about that, but I bet the Deltic scared off more than a few mechanics.

The W12


(Still Wikipedia.)

We’re not done with Napier yet. Above, you see the Napier Lion.

Although it’s not entirely accurate, you wouldn’t be far off if you described a V8 engine as two I4 engines driving the same crankshaft. The Napier Lion is a broad-arrow W12, which is what you’d get if you took a V8 and jammed another I4 down the V (sounds like a weird fetish fantasy…)

You’ve probably heard of W engines before, even if you’re not into cars. A W16 is the powerplant behind the Bugatti Veyron, which is famous for two things: holding the Guinness record for fastest street-legal car, and being a rare example of a supercar that isn’t absolutely horrible to look at. (I mean, it’s still not great, if you ask me. It looks like ergonomic furniture. But look at a Lamborghini Aventador and tell me the Veyron isn’t better-looking, if only because it’s not as…pointy.) But the W16 in the Veyron is a different type: it has two banks with eight cylinders each, and those cylinders are jammed just about as close as you can get them. Each of the banks is essentially a VR8: a V8 with a very narrow V. Since it only has one crankshaft, W isn’t exactly a good letter to use, but as a double-vee, I guess I get it. (I’m tempted to call the Napier Lion a Ш12, but Sh-12 isn’t exactly catchy.)

What the hell are you getting at, I hear you ask.  I get that question a lot. The reason I bring up the Napier Lion is that it demonstrates, better than the Veyron’s W16, that you can take a pretty ordinary set of cylinders (banks of I4s) and turn them into bizarre, high-power variants. It was weird aircraft engines like the Lion that got me interested in weird engines to begin with. Unsurprisingly, someone took a pair of W12 Lions and put them in a car, breaking a land-speed record and becoming the first to break the 350 mph barrier. And trust me, it’s not the last time we’re going to see weird engines dropped in cars.

The Radial



For some reason, I think that looking at that animation while you had a really bad fever (or after eating funny mushrooms) would be really scary. But there’s not that much scary about it. It’s just a radial-5 engine, which proves that, there are more interesting ways to arrange pistons than lines and Vs.

I really like radial engines. There’s something pleasing about that five-fold symmetry. It’s like a starfish made of explosions. It also offers some serious advantages if you’re looking for an engine to stick in a propeller-driven airplane: compact and powerful, but with pistons still far enough apart that you can air-cool them, which eliminates the radiator, which is a notoriously brittle piece of hardware. And you don’t want brittle stuff on, say, a fighter plane.

For symmetry and smoothness, nearly all four-stroke radial engines have odd numbers of cylinders. A two-cylinder radial is just a two-cylinder boxer. I’ve seen videos of three-cylinder radials, but I like pentagons better than triangles, so I won’t bother with those. Plus, talking about five-cylinder radials gives me an excuse to show you a video of a Toyota being powered by an airplane engine. And this whole section has pretty much been an elaborate segue to talk about two bad-ass vehicles. The first is the Plymouth Air Radial Truck:


(From Motor Trend.)

Because, sometimes, you wake up in the morning and think “You don’t see enough nine-cylinder hot rods out there.” That is a 300 horsepower Jacobs 9-cylinder radial airplane motor from the 50s. There are plenty of things about hot rods that I don’t like (they’re always alarmingly low to the ground, for one, which bothers me for some reason), I will never deny that hot rodders are insanely creative in all the right ways. My proof? Look at that picture again.

Naturally, the radial engine lost a lot of its popularity when turboprop and turbojet engines became reliable and affordable for airplanes. It didn’t help that, eventually, engines like the I4 and F4 became refined enough and powerful enough to do the same job as a radial without needing the specialized radial construction.

But there was a period when the radial was king of the air. Within that period was a really wild period when planes needed more power than an ordinary radial could give them. Trouble is, if you want to make a radial engine with more than 11 cylinders, you have to make it really wide so that those cylinders can stick out to be air-cooled. And if you do that, then you’ve just stuck what amounts to a dinner plate on the front of your airplane, which is no good for aerodynamics. Engine manufacturers solved this with multi-bank radial engines.

The Wasp Major


(Bet you can’t guess the source.)

That is a cutaway of the Pratt and Whitney Wasp Major, which is a beast of a machine. It has 28 cylinders (four banks of seven cylinders) and a built-in supercharger. It has a displacement of 71 liters (compare that to the Bugatti Veyron or Dodge Viper, two high-power cars, both of which displace all of 8 liters.) It produced up to 3,500 horsepower in its original form, and over 4,000 once they added turbochargers. It also sounds pretty fucking awesome. If I was a millionaire and wanted to build a hot rod, I think this is the engine I’d put in it. Either this, or our next weird engine…

The Zvezda M503


(From Flickr, this time.)

I live in North Carolina. We’re one of the home states of NASCAR, which might be the ultimate in redneck racing. I went to a monster truck show last weekend, at which one of the events was lawnmower racing. That’s kinda what we do down here. We like big trucks, noisy cars, and bizarre racing. Tractor pulling is popular down here, too.

If you don’t know, tractor-pulling is an odd sport where you hook a tractor to a weighted sled and try to pull it a specified distance (usually 300 feet or 100 meters). On top of the sled is as sliding weight which is geared to the wheels so that it moves forward in proportion to the distance pulled, making it harder the farther you pull. Unsurprisingly, that takes a lot of power. I’ve seen pictures of tractors with as many as five or six supercharged V8s, tractors with 18-cylinder radial engines, tractors with two diesel V12s, and tractors with helicopter turboshaft engines.

I always assumed tractor pulling was exclusive to American rednecks. Clearly, I was ignorant, because a lot of the really good tractor-pulling videos are from Germany, the Netherlands, and Australia, where it’s apparently a really popular sport. And my favorite tractor by far is the German “Dragon Fire.” I don’t care if you don’t like big engines or tractor pulls. I insist you watch this video of Dragon Fire in action.

As much as I like big engines and weird engines, I’ll freely admit that tractor pulling seems a bit excessive. I mean, no wonder it’s so expensive to get into engines: how can I hunt down a good V8 when there are bastards out there sticking five of them on one tractor? And, while I’m at it, stop hogging all the damn superchargers!

Dragon Fire, though, has a more elegant solution. Well, kind of. It depends how you define “elegant,” I guess. Dragon Fire isn’t powered by a bunch of V8s. It’s powered by a single 42-cylinder radial engine: the Zvezda M503, built for use in Soviet missile boats. The 503 has 42 cylinders (6 rows of 7). It weighs five times (almost five and a half times) as much as my car. It displaces 143 liters (which is about the volume of a bathtub, according to Wolfram Alpha). In its stock form, it produced nearly 4,000 horsepower. And it’s a diesel, too.

I should mention that the M503 powering Dragon Fire is running on methanol, not diesel fuel. And it, apparently, produces closer to 8,000 horsepower, which is absolutely ridiculous, and which makes me happy.

The Swashplate


(From the website of Douglas Self, who’s compiled a whole bunch of awesomely weird engines.)

I wouldn’t want to be the guy who proposed that design. I’m sure some stuffy executive looked at that, took out his monocle, took his cigar out of his mouth and said “Stop bringing me nonsense and bring me a real engine!” But the swashplate engine is real, and it’s pretty damn cool. It operates just about the same as any other piston engine, but instead of turning a crankshaft, the swashplate engine pushes on an eccentrically-mounted disk. Not only does this squeeze four (or more) pistons into a compact package, but it also eliminates the heavy crankshaft and provides a natural gear reduction. Apparently, it has been used on a few cars, and was considered for use in airplanes, its main use is as the powerplant in torpedoes, where its small frontal area and corresponding tiny drag is vital.

For some reason, I really like the swashplate engine. It’s about as far as you can take a traditional fixed-cylinder design. It’s just delightfully weird, and it’s weird that it actually works. (Make it any weirder, and you’ll get awesome stuff like the Duke engine, which didn’t make the list because its cylinders aren’t fixed, and that was one of the arbitrary qualifications I came up with.)

I also like that the swashplate engine has been built in Lego form, by the awesome YouTuber DrDudeNL.

The Chrysler A57 Multibank


(Found via Jalopnik.)

When the United States entered World War 2 in 1941, apparently, Chrysler was tasked with producing a high-power engine for the M4 Sherman tank as quickly as possible. They delivered a 30-cylinder engine. 30 cylinders isn’t as many as 42, so the A57 shouldn’t be as impressive as the Zvezda M503. But it is, for my money. Because Chrysler did a clever thing to meet the deadline. To allow them to use existing engineering, they didn’t exactly build a 30-cylinder radial. They built a 30-cylinder engine made of five Chrysler I6 engines, attached to the main output shaft by gears. Here’s what that looked like:


(From Old Machine Press.)

Using five existing I6s saved Chrysler design time, and they already had the machinery set up to make I6s, so they didn’t have to retool any factories, presumably. The A57 really is just five straight-6 engines stuck together. That’s the kind of Mad Max/McGyver creativity I like. Sure, the engine only produced 450 horsepower, but it was surprisingly compact, and I love this kind of simple innovation.

Honorable Mentions

I wanted to include the Junkers Jumo 205, but I’m running long as it is, and I already talked about opposed-piston two-stroke engines when talking about the Napier Deltic. I wanted to include the Duke Engine, but it’s got rotating cylinders, which disqualified it. For the same reason, I didn’t talk about the weird rotary radials developed early in piston-engined flight. I didn’t include the Wankel rotary engine, because it has no pistons. I didn’t mention awesomely weird concepts like the nutating engine or the gerotor combustion engine for the same reason. Plus, there’s only so much time in the day, and I’ve taken up enough of yours. But if you’ve got any weird engines you think I should’ve included, leave them in the comments. I might stick then in an addendum later on.


Weird Food

Weird Food 7: Baikal (Байкал)

Okay, I lied. I wanna do one more weird food before I get back to thought experiments for a while, because I wanted to drink another Russian soda, and figured I might as well get a review out of it.

And, I guess if you’re going to name a soda after something, might as well name it after a gigantic, pretty lake. There’s something charming about Baikal soda. The label is all rustic and inviting. See?


I’m cheating a little bit, because I’ve tried Baikal (Байкал) in the past, and I already know that it’s one of the best sodas I’ve had. But I’m gonna crack this one open and have some more.

Байкал smells like cinnamon and rosemary when you first open it. Maybe a little eucalyptus. The flavor is very smooth. It’s mostly cola, but after a second, I taste lemon, and it finishes off with aromatic herbiness, like tea with lemon and rosemary.

Don’t worry. I’m not turning into some sort of horrible wine-snob. I’m not about to start babbling about “lacings” and “nose” and “bouquet.” Mainly because I have a palate like the underside of a sheep. But I really do taste all those things in Байкал, and it leaves behind a pleasant herbal aftertaste.

One of the reasons Байкал is one of my favorite sodas is that the flavor is complicated. Baikal is made with at least five different herbs. There’s Siberian ginseng (no relation to actual ginseng), black tea, cardamom, eucalyptus, and lemon. The Siberian ginseng is actually a berry from Chinese medicine called Eleutherococcus senticosus. At first, I thought it was kinda weird that a Russian soft drink contains Chinese berries. Then I remembered that Russia is gigantic, and that Lake Baikal is on the eastern end, right over by Mongolia and China.

I really like Байкал, partly because it feels more wholesome to drink than most American sodas, many of which are just over-flavored sugar water. I mean, Байкал is still a soda. It’s still flavored sugar water, and like the Тархун (Tarkun) I tried previously, it’s a little too sweet. But I’d much sooner drink over-sweet Байкал, which tastes like tasty herbs and sugar, than over-sweet Orange Crush, which tastes like fake oranges and sugar syrup. So I guess I am kind of a snob. I wish I had a big bottle of Baikal, because I’d love to make a slush puppy out of it. I bet that’d be amazing.

The Verdict

Baikal (Байкал) is a very tasty soda with a smooth, complicated, herby flavor. It’s similar enough to a standard American cola that I think most Americans would enjoy it. If you can find it, you should try it. I don’t think you’ll regret it. Unless you’re, like, a type-2 diabetic, in which case, why the hell are you drinking soda? Quit it! I’m talking to you, cousin Kerry! And put down that bag of gummy bears!

Weird Food

Weird Food 6: Tarkun (Тархун)

I know I’ve been doing a lot of weird food posts lately. Don’t worry, this isn’t becoming a weird-food-only blog. This’ll be the last one for a while, so I can get back to ridiculous thought experiments. But, frankly, I don’t want to end this string of weird foods on something nasty like surströmming. So, I hit up my local international market and got, among other things, some Chernogolovka (Черноголовки)-brand Russian sodas.

Let me first say that the two Russian sodas I’ve had before came from the same company, so I had high hopes when I decided to try Tarkun (Тархун, yes, I am going to keep doing that, because Cyrillic is awesome). Sure, the color is a little too much like the green flavor of those horrible ice pops, but Chernogolovka haven’t steered me wrong so far.


Then, I read the back of the bottle, and the main ingredient (besides carbonated water and sugar) was tarragon. I started to get concerned, because I’d seen the guys at awesome YouTube channel Cult Moo try a Russian soda that had the same bizarre color, and they weren’t very fond of it. Still, I had high hopes, so I opened it and smelled it. What came out was a shocking smell almost exactly like black licorice. I’ve had absinthe before, but I don’t remember what it tastes like very well (imagine that), but I’m pretty sure this is the soda equivalent.

Smell-wise, at least. When I actually tasted it, it was pretty damn tasty. I like Тархун. Тархун doesn’t taste nearly as strongly of licorice as it smells, and the flavor is made up of multiple subtle flavors. That’s something I’ve noticed about Russian soda: its flavors are a lot more complicated than you get in American sodas (even the good-quality ones). At some point in the future, I’ll be reviewing Baikal soda, which has cola, lemon, and weird Chinese herb flavors, and is also delicious. Another selling point for me: none of that damn over-sweet high-fructose corn syrup. I haven’t done my research to find out whether there’s any truth to the claims that high-fructose corn syrup is especially bad for you, but now that I’ve switched over to drinking sodas made with proper sugar, I don’t wanna go back, just because real sugar tastes better.

I will say, though, that as much as I was pleasantly surprised by Тархун, it was too sweet. Luckily, it comes in small bottles. I’d bet money that it’d make a delicious cocktail with vodka, or rum, or maybe even tequila. You could make a sort of weird tarragon mojito!

The Verdict

Tarkun (Тархун) is a good soda if you don’t mind black licorice, but I wouldn’t drink a lot of it at once, since it’s so sweet. Then again, that’s kind of true of all soda, isn’t it?

Weird Food

Weird Food 5: Surströmming

For the short version, scroll down to the block of bold red text.

My curiosity got the best of me. Usually, I’m of the “Curiosity killed the cat, but satisfaction brought it back,” school: it’s rare that curiosity actually makes your life worse.

In this case, curiosity made my life worse. Before I describe what it was like to open and taste surströmming, let me give you a warning: Don’t try this at home. Seriously. It’s not worth it. I don’t regret having done it, but that’s only because of my rabid curiosity. Watch YouTube videos of people trying it and vomiting, and take my word for it that nothing they say is exaggeration.

Surströmming is bad in a transcendent way. I don’t think it’s actually possible to exaggerate when describing it. To give you an idea how bad I expected it to be (and it turned out to be worse), here are the tools I brought with me to try it:

Surst Prep

My instincts told me to leave the can in the bag and throw it in the woods. You’re really not supposed to eat anything from a can that’s that bulgy. Chuck it out. But I know from a bit of research that surströmming just does that.

My curiosity has limits. I had a glass of seltzer water at the ready so that I could wash my mouth out right after tasting it. With a bulgy can like that, I really didn’t want to risk botulism.

As soon as I opened the can, I started regretting committing to any of this. It emitted a fizzy juice that was all cloudy with bits of herring and scales. I should point out that I actually put the can opener in the bag and opened it by manipulating it through the plastic, like I was dealing with an honest-to-God biohazard.

The stench that came out of the can is hard to describe. Very sulfurous, like durian or natural gas, only sharper. It also has a putrid odor. It’s not quite as putrid-smelling as, say, spoiled roadkill, but it’s bad. I’d compare it to a bag of spoiled chicken and bad hardboiled eggs.

The actual stuff inside looked deceptively like food:


That gives me hope that I won’t actually get botulism. It helps, too, that the inside of the can seemed to be pristine: no rust, no punctures in the sealant, no discoloration. Still, if you’ve got a bulgy can, throw it away. Even if it contains surströmming. Especially if it contains surströmming. I don’t care if it’s supposed to bulge. Throw it out.

I really wish I’d used a utensil to take my sample out of the bag, but I used my fingers. My original plan was to be all brave and eat a whole fillet of fermented herring, but not even I’m that crazy. The herring was actually fairly well-preserved. It had the consistency of raw fish, but its other properties were like that of cooked fish. It and its brine were alarmingly fizzy, but then again, kimchi’s fizzy, too, and it’s safe. (Here’s hoping.) I wrestled free a piece the size of a pea and touched it to my tongue. At no point did I willingly ingest any significant quantity of surströmming, because I don’t want to die and I definitely don’t want my burps to taste anything like this stuff.

Admittedly, though, the flavor wasn’t that bad. Shocking, I know, but it mostly tasted like overly salty fish. I touched it to my tongue three times, then rinsed my mouth with most of a glass of seltzer water and spit repeatedly, because, once again, don’t trust bulging cans. Three tastes of surströmming were enough for one lifetime, so I re-sealed its bag and disposed of it:

Surst Aftermath.png

You might think I’m being melodramatic, but like I said, no reaction to that stench can be called an over-reaction. Plus, I did it in my father’s yard (the only yard big enough to contain the smell), and he specifically instructed me to bury it when I was done. I get the feeling six inches was far too shallow, but I wanted to go inside and wash my hands.

And there’s where surströmming’s real horror strikes. I’ve never had an odor that was so hard to remove. Not cigar smoke. Not really bad farts. Not fish extract.

Actually, fish extract is a good segue. I used to work at an organic fertilizer company, and while organic fertilizer is good stuff, a lot of it stinks horribly. Somehow, even when I got a really good smell of the surströmming, I did not vomit. I think that’s only because I’ve smelled some of the following: fishy-smelling soy protein that had gotten wet and fermented; liquefied fish fertilizer; soil-microbe juice that’s been fermenting in Carolina heat all day; and a jug that contained soil-microbe juice contaminated with fishy-smelling soy protein. That last one very nearly did make me vomit, and I’d say it’s surströmming’s closest competitor for “worst thing I’ve ever smelled.”

It’s probably about thirty minutes later as I’m writing this, and even though I’ve washed my hands three times (soap every time, and a scrub-brush the last time), my fingers still stink of putrid flesh. My father, who is much more sensible than me and refused to even consider trying it, wouldn’t stand near me when I came back inside. I’m writing this post in my underpants, because the smell seeped into the overshirt I wore to protect my good shirt, it seeped into my good shirt, and probably seeped into my pants. I had to take the protective case off my phone, because I used it to take pictures after handling surströmming, and the smell got on the case. The case is now downstairs in the same bag as a cup of bleach, to kill the smell.

Surströmming is an Internet legend, and for a good reason. I’m normally all about open-mindedness, but I swear, if any of my Scandinavian readers try to justify or explain surströmming to me, I will answer with incoherent cursing. If you wanna eat surströmming, that’s your business, but please don’t ever offer me any.

I think I know how surströmming came about: in the long, dark Scandinavian winter, famine struck. The pickled vegetables were gone. The hunters were coming back empty-handed again and again. In desperation, they’d already eaten all the lichen they could find, their horses, and their dogs. They had a barrel of pickled herring in the cellar, but it had developed a foul odor. Still, better to risk dying of food poisoning than a certain death from starvation, so even though the smell that came out of the barrel was worse than corpse farts, they ate it. And they didn’t die. And it became tradition.

And to end the article, let me concisely answer some of the questions I imagine people will have, since surströmming has gotten so well-known on the Internet:

Q: What does it smell like?
A: Sulfur, fish, and rotten meat.

Q: What does it taste like?
A: Overly salty preserved fish, with a faint tang of nastiness.

Q: Did you vomit?
A: No, but I have an inhumanly high threshold for vomiting. I think most people would vomit at the smell.

Q: Did you swallow any?
A: No. I want to be alive this time next year. I also want to be allowed back inside buildings, which I don’t think I would be if I burped surströmming.

Q: Where did you buy it?
A: On the Internet. I’m not telling you where, because I seriously don’t think you should try any. You’ll regret it. Even if you think “I’m morbidly curious like Hobo! I can handle it!” Don’t do it. Even if you’re an exact clone of me, don’t do it.

Q: What did you do with it when you were done?
A: I sealed the fish and its can into a plastic bag and buried the bag in the dirt.

Q: Did you try it with the traditional accompaniments (sour cream, flatbread, etc.)?
A: No. I didn’t have any of those handy, and I didn’t want to risk actually chewing it up, in case it was genuinely toxic. As far as I know, surströmming by itself isn’t actually dangerous, but my surströmming was shipped here from Sweden, and the can was very bulgy and a little dented, so I wasn’t willing to take the risk. I think I got the full experience just from the smell, anyway.

Q: Would you try it again?
A: No. If you send me a can, I’m going to bag it and bury it right away. If you send me a can and pay me a hundred dollars to eat it, I’ll send the can and money back with a note reading “FUCK YOU!” in very large letters. If you pay me a million dollars, well, yeah, I’ll eat it. If you have a million dollars to spend on something that ridiculous, e-mail me. We’ll talk. But I’m still going to swear at you when I’m done.

Q: How would you rate it?
A: I’m not going to give it a numerical rating. I’m going to do something I feel is more informative and rate it by what conditions would have to occur for me to eat surströmming again.

For reference, in order to eat durian again, one of two things would have to happen: I’d have to be overcome by curiosity, or I’d have to be “haven’t eaten in twenty-four hours” hungry. Or there’d have to be at least a $20 bet on the line.

In order to eat tarantula again, I’d probably only need some encouragement from a friend, or, say, a $5 bet, or I’d have to be “haven’t eaten in 12 hours and there’s nothing else in the cabinet” hungry.

In order to eat surströmming again (or, more accurately, in order to eat it, since I didn’t eat any this time), I’d require one of the following: 1) I am currently starving to death, and if I don’t ingest something, I’ll be too weak to keep looking for food. 2) Someone is threatening me or a loved one with a gun unless I eat some surströmming. 3) Someone is willing to pay me $10,000 or more, up front. 4) I’ve contracted a horrible alien parasite that is currently burrowing through my liver and chewing on my pancreas, and the only way to get rid of it is to scare it out of my body is to eat surströmming.

Kids, remember: don’t try this at home.