Reading the Comics, November 27, 2015: 30,000 Edition


By rights, if this installment has any title it should be “confident ignorance”. That state appears in many of the strips I want to talk about. But according to WordPress, my little mathematics blog here reached its 30,000th page view at long last. This is thanks largely to spillover from The Onion AV Club discovering my humor blog and its talk about the late comic strip Apartment 3-G. But a reader is a reader. And I want to celebrate reaching that big, round number. As I write this I’m at 30,162 page views, because there were a lot of AV Club-related readers.

Bob Weber Jr’s Slylock Fox for the 23rd of November maybe shouldn’t really be here. It’s just a puzzle game that depends on the reader remembering that two rectangles put against the other can be a rectangle again. It also requires deciding whether the frame of the artwork counts as one of the rectangles. The commenters at Comics Kingdom seem unsure whether to count squares as rectangles too. I don’t see any shapes that look more clearly like squares to me. But it’s late in the month and I haven’t had anything with visual appeal in these Reading the Comics installments in a while. Later we can wonder if “counting rectangles in a painting” is the most reasonable way a secret agent has to pass on a number. It reminds me of many, many puzzle mysteries Isaac Asimov wrote that were all about complicated ways secret agents could pass one bit of information on.

'The painting (of interlocking rectangles) is really a secret message left by an informant. It reveals the address of a house where stolen artwork is being stashed. The title, Riverside, is the street name, and the total amount of rectangles is the house number. Where will Slylock Fox find the stolen artwork?
Bob Weber Jr’s Slylock Fox for the 23rd of November, 2015. I suppose the artist is lucky they weren’t hiding out at number 38, or she wouldn’t have been able to make such a compellingly symmetric diagram.

Ryan North’s Dinosaur Comics for the 23rd of November is a rerun from goodness knows when it first ran on Quantz.com. It features T Rex thinking about the Turing Test. The test, named for Alan Turing, says that while we may not know what exactly makes up an artificial intelligence, we will know it when we see it. That is the sort of confident ignorance that earned Socrates a living. (I joke. Actually, Socrates was a stonecutter. Who knew, besides the entire philosophy department?) But the idea seems hard to dispute. If we can converse with an entity in such a way that we can’t tell it isn’t human, then, what grounds do we have for saying it isn’t human?

T Rex has an idea that the philosophy department had long ago, of course. That’s to simply “be ready for any possible opening with a reasonable conclusion”. He calls this a matter of brute force. That is, sometimes, a reasonable way to solve problems. It’s got a long and honorable history of use in mathematics. The name suggests some disapproval; it sounds like the way you get a new washing machine through a too-small set of doors. But sometimes the easiest way to find an answer is to just try all the possible outcomes until you find the ones that work, or show that nothing can. If I want to know whether 319 is a prime number, I can try reasoning my way through it. Or I can divide it by all the prime numbers from 2 up to 17. (The square root of 319 is a bit under 18.) Or I could look it up in a table someone already made of the prime numbers less than 400. I know what’s easier, if I have a table already.

The problem with brute force — well, one problem — is that it can be longwinded. We have to break the problem down into each possible different case. Even if each case is easily disposed of, the number of different cases can grow far too fast to be manageable. The amount of working time required, and the amount of storage required, can easily become too much to deal with. Mathematicians, and computer scientists, have a couple approaches for this. One is getting bigger computers with more memory. We might consider this the brute force method to solving the limits of brute force methods.

Or we might try to reduce the number of possible cases, so that less work is needed. Perhaps we can find a line of reasoning that covers many cases. Working out specific cases, as brute force requires, can often give us a hint to what a general proof would look like. Or we can at least get a bunch of cases dealt with, even if we can’t get them all done.

Jim Unger’s Herman rerun for the 23rd of November turns confident ignorance into a running theme for this essay’s comic strips.

Eric Teitelbaum and Bill Teitelbaum’s Bottomliners for the 24th of November has a similar confient ignorance. This time it’s of the orders of magnitude that separate billions from trillions. I wanted to try passing off some line about how there can be contexts where it doesn’t much matter whether a billion or a trillion is at stake. But I can’t think of one that makes sense for the Man At The Business Company Office setting.

Reza Farazmand’s Poorly Drawn Lines for the 25th of November is built on the same confusion about the orders of magnitude that Bottomliners is. In this case it’s ants that aren’t sure about how big millions are, so their confusion seems more natural.

The ants are also engaged in a fun sort of recreational mathematics: can you estimate something from little information? You’ve done that right, typically, if you get the size of the number about right. That it should be millions rather than thousands or hundreds of millions; that there should be something like ten rather than ten thousand. These kinds of problems are often called Fermi Problems, after Enrico Fermi. This is the same person the Fermi Paradox is named after, but that’s a different problem. The Fermi Paradox asks if there are extraterrestrial aliens, why we don’t see evidence of them. A Fermi Problem is simpler. Its the iconic example is, “how many professional piano tuners are there in New York?” It’s easy to look up how big is the population of New York. It’s possible to estimate how many pianos there should be for a population that size. Then you can guess how often a piano needs tuning, and therefore, how many full-time piano tuners would be supported by that much piano-tuning demand. And there’s probably not many more professional piano tuners than there’s demand for. (Wikipedia uses Chicago as the example city for this, and asserts the population of Chicago to be nine million people. I will suppose this to be the Chicago metropolitan region, but that still seems high. Wikipedia says that is the rough population of the Chicago metropolitan area, but it’s got a vested interest in saying so.)

Mark Anderson’s Andertoons finally appears on the 27th. Here we combine the rational division of labor with resisting mathematics problems.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

11 thoughts on “Reading the Comics, November 27, 2015: 30,000 Edition”

  1. I’m feeling pretty pleased with myself after reading this post since I’d actually heard of the Fermi Paradox before. I know it basically just boils down to, “Many scientists estimate that intelligent life should be common in the universe, so where is everyone?” Nevertheless, I’m puffing my chest out and strutting around like a mathematical genius this week.

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    1. Oh, do. It’s always fun to run across something and recognize it. And the Fermi Paradox does after all relate to one of those Fermi Problems: if we make some reasonable guesses about how likely aliens are to exist, we’re forced to look for reasons why they’re much less likely than we imagine. There’s good science to be done figuring out why our estimates are wrong, or why our reasoning is misfiring.

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      1. My own personal theory is that the cosmos is teeming with intelligent life but it’s all hiding from us (while sniggering tee hee hee, probably), or alternatively, there is no other intelligent life in the entire universe. I’m pretty sure it’s either one of those two — or else something in between. (Alright, I admit it. I have no idea.) :)

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        1. It’s hard to say, really. The obvious alternatives are despairing in different ways. There’s nobody else in the universe, or there’s no way of contacting them; or they all have a social order so strict that in billions of years there’s no defying a quarantine rule. There’s no rule that the universe has to be constructed so that it’s pleasant, but there’s something at least my mind rebels against in facing those options.

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          1. My best guess, and of course it is just a guess, is that life is fairly common, intelligent life less common but around, and technologically advanced civilizations pretty rare.

            Of those technologically advanced civilizations that do exist and that avoid annihilating themselves, perhaps the window during which they are using technology primitive enough for easy detection from afar is fairly brief. If they don’t want to be found or if they have no particular interest in communicating with the local insect life, they might simply not be visible to us.

            I’d hate to think that in a universe of such unbelievable size, we’re the only ones here. Just because I’m not fond of the idea doesn’t mean it’s not the right one, though. Whatever they happen to be, the facts are the facts.

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            1. The idea that technological civilizations only spend a short time being able or willing to contact an Earth-type civilization is probably the least lonely of the options. It’s still disheartening, though; the universe seems too big to be that effectively empty. But perhaps it is. Probably we’ll only become confident of that if we try to work out all the ways it wouldn’t be effectively empty and see what follows from trying to prove or disprove those.

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