Math and I have a curious relationship. On one hand, I am delighted by it as a language written in numbers, fascinated by it as tool in interpreting large amounts of data, and humbled by it as converges on correctness when properly applied. On the other hand, I’m sometimes terrible with it—making simple and highly embarrassing errors. 3 + 2 = 6 is one of my most common. 3 x 4 = 7 comes in third.
Ratios though—I love ratios. They make perfect sense. They’re a part of geometry, so they’re a part of shapes, so they’re a part of art. And in keeping with the idea of the language of math, ratios are like similes, constructions to help relate the unknown to the known.
But as often is the case with things I love, ratios can be interpreted—intentionally or not—incorrectly. Inaccurate understandings of the unknown can result. Oh—and being inaccurate versus being incorrect are different things in the language of math, just so you know. Much like they are in the language of English…
In the movie Apollo 13, a ratio is used to relate one of many mounting challenges facing the returning crew and their spacecraft: reentering the Earth’s atmosphere. Even when everything else on a mission is going well, the return into the atmosphere is arguably one of the most dangerous tasks facing any crew and spacecraft, second only to the rocket launch that took them all out of the atmosphere in the first place.
You know those beautiful and fleeting streaks of light seen during meteor showers? Those streaks of light are caused by the immense heat generated as space rocks fall into and through the Earth’s atmosphere. Smaller rocks are vaporized into the atmosphere itself under the pressure generated by the steadily thickening air. Go outside tomorrow and you’ll be lightly sprinkled with the atomic remains of one of the many space rocks vaporized every day by Earth’s atmosphere.
Larger rocks make it though the atmosphere and either splash into the ocean or leave variously sized impact creators on the Earth’s surface. The largest of the larger rocks sometimes suddenly break apart before impact with such force that the shock wave through the atmosphere levels anything below. This is what was suspected and later confirmed to have caused the Tunguska event in 1908. A remote forested area of Russia was found completely destroyed by an apparent explosion so powerful it flatted over two thousand square kilometers of trees.
Remember, the stuff we’re talking about either vaporizing entirely, cratering into the Earth’s surface, or violently exploding was mostly made of solid rock. The returning Apollo command module was mostly made of a manufactured aluminum honeycomb structure with a protective stainless steal base filled with a magical new compound known then as phenolic epoxy. The derivative of this compound is known now as plastic.
In simplified terms, the only thing preventing the destruction of the spacecraft—essentially at reentry a falling ball of aluminum foil and Bakelite with three people inside it—was the angle it was coming in at. Meteors entering the Earth’s atmosphere come in at whatever angle they do and take their chances. If it’s a steep angle the small ones burn up and the bigger ones break apart. If it’s a shallow angle then there’s a chance the meteor won’t even make it past the thicker parts of the atmosphere. It will deflect back into space. Mass and velocity play into all of this as well, but for the sake of keeping things simple, let’s just consider the angle. The angle allowing the Apollo command module to survive the entry back into atmosphere is referred to as the reentry corridor.
In the movie, a newsreel clip needs to highlight how this reentry corridor isn’t very wide, so they come up with an example to illustrate the situation. This is where the amazing power of the ratio can help relate through an exercise in distorted reality:
In order to enter the atmosphere safely, the crew must aim for a corridor just two and a half degrees wide … The re-entry corridor is in fact so narrow, that if this basketball were the earth, and this softball were the moon, and the two were placed fourteen feet apart, the crew would have to hit a target no thicker than this piece of paper.
No thicker than a piece of paper? How did they or indeed anyone else returning from space ever survive such a narrow chance for success?
Because it’s not as narrow as the example might initially suggest. Sure, the image of a piece of piece held up thin‐wise was fantastic drama and added wonderful suspense to the movie. But that piece of paper isn’t real, not real as it relates to the size of the actual Earth. It’s just a ratio, part of an example that only works if the Earth is the size of a basketball—which it isn’t. Remember: the perspective of the observer and participant is tied to the ratio as well. Everyone goes along for the ride, and on an Earth the size of basketball you’re much, much smaller than even the smallest piece of dust on the surface of the ball. In fact, however small you think you are on that basketball surface, you are much smaller than that.
But with an Earth the size of the Earth, this terrifyingly narrow piece of paper’s worth of corridor is actually a terrifyingly narrow half a kilometer wide target once it gets scaled back to what the full‐sized crew of Apollo 13 needed to hit. No one would have ever made it back if they had to hit a corridor the size of the thickness of a piece of paper as compared to the entire Earth. But it’s also no small thing to have successfully hit something that’s half a kilometer wide compared to the entire Earth either. The trouble is something that’s half a kilometer wide sounds pretty wide, and the diameter of the Earth may not be known to most people off the top of their head. To express the scenario as‐is renders it unrelatable. It might even end up sounding easier than it is.
By the way, to be fair to most people, I had to look up the diameter of the Earth when I was working out the numbers for all this. It’s 12,742 km. But anyone watching the movie would understand the size of a basketball. They’d understand the thickness of a piece of paper and could understand the relationship of width and scale between the two…
…Which brings me to truck balls.
You’ve seen these, right? Trucks with balls on them? …No?
…Enjoy!
Aside from every other question I have regarding these delightfully silly fashion accessories for the man who clearly has everything, the main question I have is about scale. The truck to balls ratio isn’t correct, not correct in terms of the message I’m assuming is trying to be sent. From everything I understand about base biological mathematics as applied to testicles, the formula is simple: bigger = better.
So why are the owners of these little things hanging them daintily off their large vehicles? They’re effectively announcing their truck is packing what would equate to a pair of shelled peas lost somewhere in a teabag.
If I was telling the world—for whatever well‐rationed reason I’m sure I have—that my truck had balls I’d bronze an empty bean bag chair after stuffing it with two oversized Rand McNally globes. I’d want those fuckers to drag down the road and shower onlookers with sparks. That’s the intended communique, right boys? Ratios!
And since I’m feeling highly analytical on the issue, wouldn’t the correct place for a truck’s balls to hang be off the differential, between the rear wheels? As pictured above, that truck is wearing its under what I could only assume would be some sort of hilarious “Kick Me” sign just a below the tailbone…
I understand everyone is going to have their own way of announcing to the world that they exist. For some that way might be a little set of fake nuts hanging off the same truck that’s got a decal of Calvin peeing on Bernie Sanders. For others that way might be successfully piloting a returning spacecraft through a target less than 4% the width of the Earth while falling to it at 11 kilometres per second. And for everyone else that way might be some mix of the previous two ways.
But I have a feeling there were and still are no trucks parked outside any NASA facility with anything dangling off of them. There certainty wasn’t anything extra hanging off the Apollo command module. And even if there was—it would have burned up on reentry.




