Falsifiable, Physics, Quick Fix

Pokémon Are Made of Styrofoam

One of the best things about taking physics classes is that the equations you learn are directly applicable to the real world. Every so often, while reading a book or watching a movie, I’m seized by the sudden urge to check it for plausibility. A few scratches on a piece of paper later and I will generally know one way or the other.

One of the most amusing things I’ve found doing this is that the people who come up with the statistics for Pokémon definitely don’t have any sort of education in physics.

Takes Onix. Onix is a rock/ground Pokémon renowned for its large size and sturdiness. Its physical statistics reflect this. It’s 8.8 metres (28′) long and 210kg (463lbs).

Onix, being tough. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

Surely such a large and tough Pokémon should be very, very dense, right? Density is such an important tactile cue for us. Don’t believe me? Pick up a large piece of solid medal. Its surprising weight will make you take it seriously.

Let’s check if Onix would be taken seriously, shall we? Density is equal to mass divided by volume. We use the symbol ρ to represent density, which gives us the following equation:

We already know Onix’s mass. Now we just need to calculate its volume. Luckily Onix is pretty cylindrical, so we can approximate it with a cylinder. The equation for the volume of a cylinder is pretty simple:

Where π is the ratio between the diameter of a circle and its circumference (approximately 3.1415…, no matter what Indiana says), r is the radius of a circle (always one half the diameter), and h is the height of the cylinder.

Given that we know Onix’s height, we just need its diameter. Luckily the Pokémon TV show gives us a sense of scale.

Here’s a picture of Onix. Note the kid next to it for scale. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

Judging by the image, Onix probably has an average diameter somewhere around a metre (3 feet for the Americans). This means Onix has a radius of 0.5 metres and a height of 8.8 metres. When we put these into our equation, we get:

For a volume of approximately 6.9m3. To get a comparison I turned to Wolfram Alpha which told me that this is about 40% of the volume of a gray whale or a freight container (which incidentally implies that gray whales are about the size of standard freight containers).

Armed with a volume, we can calculate a density.

Okay, so we know that Onix is 30.4 kg/m3, but what does that mean?

Well it’s currently hard to compare. I’m much more used to seeing densities of sturdy materials expressed in tonnes per cubic metre or grams per cubic centimetre than I am seeing them expressed in kilograms per cubic metre. Luckily, it’s easy to convert between these.

There are 1000 kilograms in a ton. If we divide our density by a thousand we can calculate a new density for Onix of 0.0304t/m3.

How does this fit in with common materials, like wood, Styrofoam, water, stone, and metal?


Density (t/m3)







Oak [1]








From this chart, you can see that Onix’s density is eerily close to Styrofoam. Even the notoriously light balsa wood is five times denser than him. Actual rock is about 85 times denser. If Onix was made of granite, it would weigh 18 tonnes, much heavier than even Snorlax (the heaviest of the original Pokémon at 460kg).

While most people wouldn’t be able to pick Onix up (it may not be dense, but it is big), it wouldn’t be impossible to drag it. Picking up part of it would feel disconcertingly light, like picking up an aluminum ladder or carbon fibre bike, only more so.

This picture is unrealistic. Because of its density, no more than 3% of Onix can be below the water. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

How did the creators of Pokémon accidently bestow one of the most famous of their creations with a hilariously unrealistic density?

I have a pet theory.

I went to school for nanotechnology engineering. One of the most important things we looked into was how equations scaled with size.

Humans are really good at intuiting linear scaling. When something scales linearly, every twofold change in one quantity brings about a twofold change in another. Time and speed scale linearly (albeit inversely). Double your speed and the trip takes half the time. This is so simple that it rarely requires explanation.

Unfortunately for our intuitions, many physical quantities don’t scale linearly. These were the cases that were important for me and my classmates to learn, because until we internalized them, our intuitions were useless on the nanoscale. Many forces, for example, scale such that they become incredibly strong incredibly quickly at small distances. This leads to nanoscale systems exhibiting a stickiness that is hard on our intuitions.

It isn’t just forces that have weird scaling though. Geometry often trips people up too.

In geometry, perimeter is the only quantity I can think of that scales linearly with size. Double the length of the sides of a square and the perimeter doubles. The area, however does not. Area is quadratically related to side length. Double the length of a square and you’ll find the area quadruples. Triple the length and the area increases nine times. Area varies with the square of the length, a property that isn’t just true of squares. The area of a circle is just as tied to the square of its radius as a square is to the square of its length.

Volume is even trickier than radius. It scales with the third power of the size. Double the size of a cube and its volume increases eight-fold. Triple it, and you’ll see 27 times the volume. Volume increases with the cube (which again works for shapes other than cubes) of the length.

If you look at the weights of Pokémon, you’ll see that the ones that are the size of humans have fairly realistic weights. Sandslash is the size of a child (it stands 1m/3′ high) and weighs a fairly reasonable 29.5kg.

(This only works for Pokémon really close to human size. I’d hoped that Snorlax would be about as dense as marshmallows so I could do a fun comparison, but it turns out that marshmallows are four times as dense as Snorlax – despite marshmallows only having a density of ~0.5t/m3)

Beyond these touchstones, you’ll see that the designers of Pokémon increased their weight linearly with size. Onix is a bit more than eight times as long as Sandslash and weighs seven times as much.

Unfortunately for realism, weight is just density times volume and as I just said, volume increases with the cube of length. Onix shouldn’t weigh seven or even eight times as much as Sandslash. At a minimum, its weight should be eight times eight times eight multiples of Sandslash’s; a full 512 times more.

Scaling properties determine how much of the world is arrayed. We see extremely large animals more often in the ocean than in the land because the strength of bones scales with the square of size, while weight scales with the cube. Become too big and you can’t walk without breaking your bones. Become small and people animate kids’ movies about how strong you are. All of this stems from scaling.

These equations aren’t just important to physicists. They’re important to any science fiction or fantasy writer who wants to tell a realistic story.

Or, at least, to anyone who doesn’t want their work picked apart by physicists.


[1] Not the professor. His density is 0.985t/m3. ^

Model, Politics

Why does surgery have such ineffective safety regulation?

Did you know that half of all surgical complications are preventable? In the US alone, this means that surgeons cause between 50,00 and 200,000 preventable deaths each year.

Surgeons are, almost literally, getting away with murder.

Why do we let them? Engineers who see their designs catastrophically fail often lose their engineering license, even when they’re found not guilty in criminal proceedings. If surgeons were treated like engineers, many of them wouldn’t be operating anymore.

Indeed, the death rate in surgery is almost unique among regulated professions. One person has died in a commercial aviation accident in the US in the last nine years. Structural engineering related accidents killed at most 251 people in the US in 2016 [1] and only approximately 4% of residential structure failures in the US occur due to deficiencies in design [2].

It’s not that interactions with buildings or planes are any less common than surgeries, or that they’re that much inherently safer. In many parts of the world, death due to accidents in aviation or due to structural failure is very, very common.

It isn’t accidental that Canada and America no longer see many plane crashes or structural collapses. Both professions have been rocked by events that made them realize they needed to improve their safety records.

The licensing of professional engineers and the Iron Ring ceremony in Canada for engineering graduates came after two successive bridge collapses killed 88 workers [3]. The aircraft industry was shaken out of its complacency after the Tenerife disaster, where a miscommunication caused two planes to collide on a run-way, killing 583.

As you can see, subsequent safety improvements were both responsive and deliberate.

These aren’t the only events that caused changes. The D. B. Cooper high-jacking led to the first organised airport security in the US. The Therac-25 radiation overdoses led to the first set of guidelines specifically for software that ran on medical devices. The sinking of the Titanic led to a complete overhaul of requirements for lifeboats and radios for oceangoing vessels. The crash of TAA-538 led to the first mandatory cockpit voice recorders.

All of these disasters combine two things that are rarely seen when surgeries go wrong. First, they involved many people. The more people die at once, the more shocking the event and therefore the more likely it is to become widely known. Because most operations involve one or two patients, it is much rarer for problems in them to make the news [4].

Second, they highlight a specific flaw in the participants, procedures, or systems that fail. Retrospectives could clearly point to a factor and say: “this did it” [5]. It is much harder to do this sort of retrospective on a person and get such a clear answer. It may be true that “blood loss” definitely caused a surgical death, but it’s much harder to tell if that’s the fault of any particular surgeon, or just a natural consequence of poking new holes in a human body. Both explanations feel plausible, so in most cases neither can be wholly accepted.

(I also think there is a third driver here, which is something like “cheapness of death”. I would predict that safety regulation is more common in places where people expect long lives, because death feels more avoidable there. This explains why planes and structures are safer in North America and western Europe, but doesn’t distinguish surgery from other fields in these countries.)

Not every form of engineering or transportation fulfills both of these criteria. Regulation and training have made flying on a commercial flight many, many times safer than riding in a car, while private flights lag behind and show little safety advantage over other forms of transport. When a private plane crashes, few people die. If they’re important (and many people who fly privately are), you might hear about it, but it will quickly fade from the news. These stories don’t have staying power and rarely generate outrage, so there’s never much pressure for improvement.

The best alternative to this model that I can think of is one that focuses on the “danger differential” in a field and predicts that fields with high danger differentials see more and more regulation until the danger differential is largely gone. The danger differential is the difference between how risky a field currently is vs. how risky it could be with near-optimal safety culture. A high danger differential isn’t necessarily correlated with inherent risk in a field, although riskier fields will by their nature have the possibility of larger ones. Here’s three examples:

  1. Commercial air travel in developed countries currently has a very low danger differential. Before a woman was killed by engine debris earlier this year, commercial aviation in the US had gone 9 years without a single fatality.
  2. BASE jumping is almost suicidally dangerous and probably could be made only incredibly dangerous if it had a better safety culture. Unfortunately, the illegal nature of the sport and the fact that experienced jumpers die so often make this hard to achieve and lead to a fairly large danger differential. That said, even with an optimal safety culture, BASE jumping would still see many fatalities and still probably be illegal.
  3. Surgery is fairly dangerous and according to surgeon Atul Gawande, could be much, much safer. Proper adherence to surgical checklists alone could cut adverse events by almost 50%. This means that surgery has a much higher danger differential than air travel.

I think the danger differential model doesn’t hold much water. First, if it were true, we’d expect to see something being done about surgery. Almost a decade after checklists were found to drive such large improvements, there hasn’t been any concerted government action.

Second, this doesn’t match historical accounts of how airlines were regulated into safety. At the dawn of the aviation age, pilots begged for safety standards (which could have reduced crashes a staggering sixtyfold [6]). Instead of stepping in to regulate things, the government dragged its feet. Some of the lifesaving innovations pioneered in those early days only became standard after later and larger crashes – crashes involving hundreds of members of the public, not just pilots.

While this only deals with external regulation, I strongly suspect that fear for the reputation of a profession (which could be driven by these same two factors) affects internal calls for reform as well. Canadian engineers knew that they had to do something after the Quebec bridge collapse created common knowledge that safety standards weren’t good enough. Pilots were put in a similar position with some of the better publicized mishaps. Perhaps surgeons have faced no successful internal campaign for reform so far because the public is not yet aware of the dangers of surgery to the point where it could put surgeon’s livelihoods at risk or hurt them socially.

I wonder if it’s possible to get a profession running scared about their reputation to the point that they improve their safety, even if there aren’t any of the events that seem to drive regulation. Maybe someone like Atul Gawande, who seems determined to make a very big and very public stink about safety in surgery is the answer here. Perhaps having surgery’s terrible safety record plastered throughout the New Yorker will convince surgeons that they need to start doing better [7].

If not, they’ll continue to get away with murder.


[1] From the CDC’s truly excellent Cause of Death search function, using codes V81.7 & V82.7 (derailment with no collision), W13 (falling out of building), W23 (caught or crushed between objects), and W35 (explosion of boiler) at home, other, or unknown. I read through several hundred causes of deaths, some alarmingly unlikely, and these were the only ones that seemed relevant. This estimate seems higher than the one surgeon Atul Gawande gave in The Checklist Manifesto, so I’m confident it isn’t too low. ^

[2] Furthermore, from 1989 to 2000, none of the observed collapses were due to flaws in the engineers’ designs. Instead, they were largely caused by weather, collisions, poor maintenance, and errors during construction. ^

[3] Claims that the rings are made from the collapsed bridge are false, but difficult to dispel. They’re actually just boring stainless steel, except in Toronto, where they’re still made from iron (but not iron from the bridge). ^

[4] There may also be an inherent privateness to surgical deaths that keeps them out of the news. Someone dying in surgery, absent obvious malpractice, doesn’t feel like public information in the way that car crashes, plane crashes, and structural failures do. ^

[5] It is true that it was never discovered why TAA-538 crashed. But black box technology would have given answers had it been in use. That it wasn’t in use was clearly a systems failure, even though the initial failure is indeterminate. This jives with my model, because regulation addressed the clear failure, not the indeterminate one. ^

[6] This is the ratio between the average miles flown before crash of the (very safe) post office planes and the (very dangerous) privately owned planes. Many in the airline industry wanted the government to mandate the same safety standards on private planes as they mandated on their airmail planes. ^

[7] I should mention that I have been very lucky to have been in the hands of a number of very competent and professional surgeons over the years. That said, I’m probably going to ask any future surgeon I’m assigned if they follow safety checklists – and ask for someone else to perform the procedure if they don’t. ^