I understand in places in the United States last week wasn’t the first week of school. It was the second or third or even worse. These places are crazy, in that they do things differently from the way my elementary school did it. So, now, here’s the other half of last week’s comics.
Zach Weinersmith’s Saturday Morning Breakfast Cereal presented the 8th is a little freak-out about existence. Mathematicians rely on the word “exists”. We suppose things to exist. We draw conclusions about other things that do exist or do not exist. And these things that exist are not things that exist. It’s a bit heady to realize nobody can point to, or trap in a box, or even draw a line around “3”. We can at best talk about stuff that expresses some property of three-ness. We talk about things like “triangles” and we even draw and use representations of them. But those drawings we make aren’t Triangles, the thing mathematicians mean by the concept. They’re at best cartoons, little training wheels to help us get the idea down. Here I regret that as an undergraudate I didn’t take philosophy courses that challenged me. It seems certain to me mathematicians are using some notion of the Platonic Ideal when we speak of things “existing”. But what does that mean, to a mathematician, to a philosopher, and to the person who needs an attractive tile pattern on the floor?
Cathy Thorne’s Everyday People Cartoons for the 9th is about another bit of the philosophy of mathematics. What are the chances of something that did happen? What does it mean to talk about the chance of something happening? When introducing probability mathematicians like to set it up as “imagine this experiment, which has a bunch of possible outcomes. One of them will happen and the other possibilities will not” and we go on to define a probability from that. That seems reasonable, perhaps because we’re accepting ignorance. We may know (say) that a coin toss is, in principle, perfectly deterministic. If we knew exactly how the coin is made. If we knew exactly how it is tossed. If we knew exactly how the air currents would move during its fall. If we knew exactly what the surface it might bounce off before coming to rest is like. Instead we pretend all this knowable stuff is not, and call the result unpredictability.
But about events in the past? We can imagine them coming out differently. But the imagination crashes hard when we try to say why they would. If we gave the exact same coin the exact same toss in the exact same circumstances how could it land on anything but the exact same face? In which case how can there have been any outcome other than what did happen? Yes, I know, someone wants to rush in and say “Quantum!” Say back to that person, “waveform collapse” and wait for a clear explanation of what exactly that is. There are things we understand poorly about the transition between the future and the past. The language of probability is a reminder of this.
Hilary Price’s Rhymes With Orange for the 10th uses the classic story-problem setup of a train leaving the station. It does make me wonder how far back this story setup goes, and what they did before trains were common. Horse-drawn carriages leaving stations, I suppose, or maybe ships at sea. I quite like the teaser joke in the first panel more.
Dan Collins’s Looks Good on Paper for the 10th is the first Möbius Strip joke we’ve had in a while. I’m amused and I do like how much incidental stuff there is. The joke would read just fine without the opossum family crossing the road, but it’s a better strip for having it. Somebody in the comments complained that as drawn it isn’t a Möbius Strip proper; there should be (from our perspective) another half-twist in the road. I’m willing to grant it’s there and just obscured by the crossing-over where the car is, because — as Collins points out — it’s really hard to draw a M&oum;bius Strip recognizably. You try it, and then try making it read cleanly while there’s, at minimum, a road and a car on the strip. That said, I can’t see that the road sign in the lower-left, by the opossums, is facing the right direction. Maybe for as narrow as the road is it’s still on a two-lane road.
Tom Toles’s Randolph Itch, 2 am rerun for the 10th is an Einstein The Genius comic. It felt familiar to me, but I don’t seem to have included it in previous Reading The Comics posts. Perhaps I noticed it some week that I figured a mere appearance of Einstein didn’t rate inclusion. Randolph certainly fell asleep while reading about mathematics, though.
It’s popular to tell tales of Einstein not being a very good student, and of not being that good in mathematics. It’s easy to see why. We’d all like to feel a little more like a superlative mind such as that. And Einstein worked hard to develop an image of being accessible and personable. It fits with the charming absent-minded professor image everybody but forgetful professors loves. It feels dramatically right that Einstein should struggle with arithmetic like so many of us do. It’s nonsense, though. When Einstein struggled with mathematics, it was on the edge of known mathematics. He needed advice and consultations for the non-Euclidean geometries core to general relativity? Who doesn’t? I can barely make my way through the basic notation.
Anyway, it’s pleasant to see Toles holding up Einstein for his amazing mathematical prowess. It was a true thing.