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?

Material

Density (t/m3)

Styrofoam

0.028

Onix

0.03

Balsa

0.16

Oak [1]

0.65

Water

1

Granite

2.6

Steel

7.9

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.

Footnotes

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

Quick Fix

May The Fourth Be With You

(The following is the text of the prepared puns I delivered at the 30th Bay Area pun off. If you’re ever in the Bay for one, I really recommend it. They have the nicest crowd in the world.)

First: May the Fourth be with you (“and also with you” is how you respond if like me, you grew up Catholic). As you might be able to tell from this shirt, I am religiously devoted to Star Wars. I know a lot about Star Wars, but I’m more of an orthodox fan- I was all about the Expanded Universe, not this reverend-ing stream of Disney sequels.

Pictured: the outfit I wore

They might be popepular, but it seems like all Disney wants is to turn a prophet – just get big fatwas of cash. They don’t care about Allah the history that happened in the books. Just mo-hamme(r)ed out scripts with flashy set piece battles full of Mecca and characters we med-in-a earlier film.

The EU was mostly books and I loved them despite their ridiculousness. Like, in terms of plots, it’s not clear the writers always card’in-all the books; they often passover normal options and have someone kidnap Han and Leia’s kids.

There were so many convert-sations between the two of them, like “do you noahf ark ‘ids are fine” immediately interrupted by formulaic videos from the kids: “Don’t worry about mi-mam it’s alright, this dude who kidnapped us is a total Luther who just wants to Hindu-s you to vote another way in the Senate”. Eventually they figured out a wafer Leia to communion-cate that the kids needed a bodygod. This led them to Sikh out Winter, who came with the recommendation: “no kidnapper will ever get pastor“.

What else? Luke trains under a clone of Emperor Pulpit-een. Leia is like, “bish, open your eyes, dude’s dark” but Luke justifies it with “well, there’s some things vatican teach me”.
Eventually after Leia asks “how could you Judas to us”, Luke snaps out of it and decides he’s having nun of Palpatine’s evil deeds. He con-vent his anger somewhere else. He comes back to the light side and everyone’s pretty willing to ex-schism for everything he did.
Anyway, I’m really sad that the books aren’t canon anymore. I know there are a lot of ram, a danting number, but I hope I have Eided you in appreciating them.

Philosophy

Cutting the Gordian Knot: Bad Solutions to Good Paradoxes

Russel’s Paradox

Image Credit: Donald on Flickr

In a village, the barber shaves everyone who does not shave himself, but no one else. Who shaves the barber.

Imagine The Barber as similar to The Pope. When he is in his shop, cutting hair, he is The Barber and has all of the powers that entails, just as The Pope only possesses the full power of papacy when speaking “from the chair”. When The Barber isn’t manifesting this mantle, he’s just Glen, the nice fellow down the lane. Glen shaves his own beard. The Barber therefore doesn’t have to.

Alternatively, the barber is a woman.

Omnipotence Paradox

Image Credit: Tim Green on Flickr

Can God create a rock so large that he himself cannot lift it?

It depends.

In Christian theology, God is often considered all-knowing, all-powerful, and all-loving. Some theologians dispute each of these, but most agree he has at least some mix of those three attributes. It turns out the answer to this paradox depends on which theologians are right.

This question is only interesting if god is all-powerful. If God isn’t all powerful, then this question will be determined by which is greater: his power of creation, or his power to manipulate creation. That’s a boring answer, so let’s focus on the cases where God is all powerful.

If God is all-knowing, then we’ll probably be left unsatisfied. God will know if he can or cannot create the boulder, so he’ll probably feel no need to test if he can.

If God is not all-knowing but is all-loving, then the question will only be answered if God cannot lift the first boulder he creates. If he can lift the first one, he will quickly realize that he could end up spending all of eternity trying to make a big enough boulder on the off chance that this is the one he finally cannot lift. An all-loving God would not abandon his flock for such a meaningless task, so we’ll never see the answer.

If God is neither all-knowing nor all-loving and has at least a bit of curiosity, then we should be able to eventually observe him trying to create a boulder large enough that he cannot lift it. This God won’t know the answer and wouldn’t necessarily care that finding out requires abandoning all of his other duties.

Given that this question was first posed right before the crusades, I believe that we’re experiencing the third scenario. The mere act of raising this paradox caused God to turn his face away from the world and worry about more interesting problems than those caused by a bunch of jumped up apes.

Zeno’s Paradox

Image Credit: Miranche on Wikimedia Commons

If you want to go somewhere, you first have to get halfway there. But to get to the midpoint, you have to go a quarter of the way. But to get to a quarter… When you subdivide like this, you’ll see that there are an infinite number of steps you must take to go anywhere. You cannot accomplish an infinite number of tasks in a finite time, therefore, movement is impossible.  

It’s a common mistake that space is infinitely sub-dividable. In fact, there is a limit to how finely you can cut space. You cannot cut the universe more finely than 1.61x 10-35m, a length called the Planck Length. The Planck length is to the width of a hair as the width of a hair is to the whole universe. It’s an unimaginably tiny length.

An important property of halving things: you get really small numbers very quickly. If you halve a distance of 1m a mere 116 times, you’ll have cut the distance as finely as it is possible to cut anything. At this point, you can halve the distance no more and you can proceed to your destination, one Planck length at a time.

Sorites Paradox

Image Credit: David Stanley on Flickr

There is a pile of sand in front of you. If you remove a grain of sand from it, it will still be a pile. If you remove another, it will still be a pile. But if you keep removing them, eventually it won’t be. When does it stop being a pile?

I’m emailing ISO and the NIST about this one. I expect to have an answer after ten years and three hundred committee meetings.

The Ship of Theseus

Image Credit: Verity Cridland on Flickr

The Athenian Theseus bequeathed his ship to the city. As the ship aged, the Athenians kept it in perfect condition by replacing any planks and fittings that rotted away. Eventually, the entire ship had been replaced. This caused all of the philosophers in Athens to wonder: was it still Theseus’s Ship.

We could leave this one to ISO as well, but luckily as a Canadian I have another recourse.

The Comprehensive Economic and Trade Agreement between the EU (of which Greece is a member) and Canada considers a car “Made in Canada” or “Made in Europe” if at least 50% of the car came from there and at least 20% of the manufacturing occurred there.

Treating boats with a similar logic, we can see that as long as the Athenians were using local materials and labour (and weren’t outsourcing to the Persians or Phoenicians), the ship would count as “Made in Greece”. Since the paradox specifically states that the Athenians were doing all the restoring, this is probably a safe assumption.

If we take this and assume that Theseus had a solid grounding in trademark law – which would allow us to assume that he made his ship a protected brand like Harris Tweed, Kobe beef, Navaho, and Scotch – then we can see that the ship would still fall under the Theseus’s Ship™ brand. Most protected brands require a certain geographic origin, but we’ve already been over that in this case.

Even when philosophers argue that the boat is no longer Theseus’s Ship, they have to admit it is Theseus’s Ship™.

Unexpected Hanging Paradox

Image Credit: Adam Clarke on Flickr

A prisoner is sentenced to hanging by a judge. The judge stipulates that the sentence will be carried out on one of the days in the next week, that it will be carried out before noon, and that it must be a surprise to the prisoner.

The prisoner smirks, believing he will never be hung. He knows that if it is Thursday at noon and he hasn’t been hung, then the hanging would have to be on Friday. But then it wouldn’t be a surprise. So logically, he has to be hung before Friday. If this is the case though, he can’t be hung on Thursday, because if he hasn’t been hung by noon on Wednesday then a hanging on Thursday won’t be a surprise. Following through this logic, the prisoner could only be hung on the Monday. But then it will be no surprise at all!

This is indeed a problem if the judge is as good at logic as the prisoner. But if the judge remains blissfully unaware of logical induction, there is no paradox here. The judge will assume that by picking a day at random she can surprise the prisoner. The prisoner will no doubt be quite surprised when he is hung.

This becomes more likely if we set the problem in America, where some judges are elected and therefore aren’t governed by anything so limiting as qualifications.