Reading the Comics, March 17, 2020: Random Edition


I thought last week’s comic strips mentioning mathematics in detail were still subjects easy to describe in one or two paragraphs each. I wasn’t quite right. So here’s a half of a week, even if it is a day later than I had wanted to post.

John Zakour and Scott Roberts’s Working Daze for the 15th is a straggler Pi Day joke, built on the nerd couple Roy and Kathy letting the date slip their minds. This is a very slight Pi Day reference but I feel the need to include it for completeness’s sake. It reminds me of the sequence where one year Schroeder forgot Beethoven’s birthday, and was devastated.

Sue: 'So, Roy, what big fun did you and Kathy have for Pi Day this year?' Roy, caught by surprise, freezes, and then turns several colors in succession before he starts to cry. Ed, to Sue: 'Hard to say which is worse for him, that you forgot, or that you remembered.'
John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2020. Essays featuring Working Daze, which often turns up in Pi Day events, are at this link. And generally essays tied to Pi Day are at this link.

Lincoln Peirce’s Big Nate for the 15th is a wordy bit of Nate refusing the story problem. Nate complains about a lack of motivation for the characters in it. But then what we need for a story problem isn’t the characters to do something so much as it is the student to want to solve the problem. That’s hard work. Everyone’s fascinated by some mathematical problems, but it’s hard to think of something that will compel everyone to wonder what the answer could be.

At one point Nate wonders what happens if Todd stops for gas. Here he’s just ignoring the premise of the question: Todd is given as travelling an average 55 mph until he reaches Saint Louis, and that’s that. So this question at least is answered. But he might need advice to see how it’s implied.

Quiz: 'Many lives in Los Angeles. Todd lives in Boston. They plan to meet in St Louis, which is 1,825 miles from Los Angeles and 1,192 miles from Boston. If Mandy takes a train travelling a constant 80 mph and Todd drives a car at a constant 55 mph, which of them will reach St Lous first?' Nate's answer: 'That depends. Who ARE these people? Are they a couple? Is this romance? If it is, wouldn't Todd drive way faster than 55 mph? He'd be all fired up to see Many, right? And wouldn't Mandy take a plane and get to St Louis in like three hours? Especially if she hasn't seen Todd in a while? But we don't know how long since they've been together because you decided not to tell us! Plus anything can happen while they're traveling. What if Todd stops for gas and the cashier is a total smoke show and he's like, Mandy Who? I can't answer until I have some real intel on these people. I can't believe you even asked the question.' Out loud, 'Also, Todd and Mandy are dorky names.' Teacher: 'This isn't what I meant by show your work.'
Lincoln Peirce’s Big Nate for the 15th of March, 2020. Essays with something mentioned by either Big Nate or the 1990s-repeats Big Nate: First Class are gathered at this link.

So this problem is doable by long division: 1825 divided by 80, and 1192 divided by 55, and see what’s larger. Can we avoid dividing by 55 if we’re doing it by hand? I think so. Here’s what I see: 1825 divided by 80 is equal to 1600 divided by 80 plus 225 divided by 80. That first is 20; that second is … eh. It’s a little less than 240 divided by 80, which is 3. So Mandy will need a little under 23 hours.

Is 23 hours enough for Todd to get to Saint Louis? Well, 23 times 55 will be 23 times 50 plus 23 times 5. 23 times 50 is 22 times 50 plus 1 times 50. 22 times 50 is 11 times 100, or 1100. So 23 times 50 is 1150. And 23 times 5 has to be 150. That’s more than 1192. So Todd gets there first. I might want to figure just how much less than 23 hours Mandy needs, to be sure of my calculation, but this is how I do it without putting 55 into an ugly number like 1192.

Cow: 'What're you doing?' Billy: 'I'm devising a system to win the lottery! Plugging in what I know about chaos theory and numerical behavior in nonlinear dynamical systems should give me the winning picks.' (Silent penultimate panel.) Cow: 'You're just writing down a bunch of numbers.' Billy: 'Maybe.'
Mark Leiknes’s Cow and Boy repeat for the 17th of March, 2020. The too-rare appearances of Cow and Boy Reruns in my essays are here.

Mark Leiknes’s Cow and Boy repeat for the 17th sees the Boy, Billy, trying to beat the lottery. He throws at it the terms chaos theory and nonlinear dynamical systems. They’re good and probably relevant systems. A “dynamical system” is what you’d guess from the name: a collection of things whose properties keep changing. They change because of other things in the collection. When “nonlinear” crops up in mathematics it means “oh but such a pain to deal with”. It has a more precise definition, but this is its meaning. More precisely: in a linear system, a change in the initial setup makes a proportional change in the outcome. If Todd drove to Saint Louis on a path two percent longer, he’d need two percent more time to get there. A nonlinear system doesn’t guarantee that; a two percent longer drive might take ten percent longer, or one-quarter the time, or some other weirdness. Nonlinear systems are really good for giving numbers that look random. There’ll be so many little factors that make non-negligible results that they can’t be predicted in any useful time. This is good for drawing number balls for a lottery.

Chaos theory turns up a lot in dynamical systems. Dynamical systems, even nonlinear ones, often have regions that behave in predictable patterns. We may not be able to say what tomorrow’s weather will be exactly, but we can say whether it’ll be hot or freezing. But dynamical systems can have regions where no prediction is possible. Not because they don’t follow predictable rules. But because any perturbation, however small, produces changes that overwhelm the forecast. This includes the difference between any possible real-world measurement and the real quantity.

Obvious question: how is there anything to study in chaos theory, then? Is it all just people looking at complicated systems and saying, yup, we’re done here? Usually the questions turn on problems such as how probable it is we’re in a chaotic region. Or what factors influence whether the system is chaotic, and how much of it is chaotic. Even if we can’t say what will happen, we can usually say something about when we can’t say what will happen, and why. Anyway if Billy does believe the lottery is chaotic, there’s not a lot he can be doing with predicting winning numbers from it. Cow’s skepticism is fair.

T-Rex: 'Dromiceiomimus, pick a number between one and a hundred thousand million.' Dromiceiomimus: '17?' T-Rex: 'Gasp! That's the number I was thinking of!' Dromiceiomimus: 'Great! Do I win something?' T-Rex: 'You just came out on a one in a hundred thousand million chance and you want a prize? It's not enough to spit in the face of probability itself?' Utahraptor: 'It's not THAT unlikely she'd chose your number. We're actually pretty bad at random number generation and if you ask folks to pick a number in a range, some choices show up more often than others. It's not that unlikely you'd both land on the same number!' T-Rex: 'But *I* didn't choose 17 randomly! It's ... the number of times I have thought about ice cream today, I'm not even gonna lie.'
Ryan North’s Dinosaur Comics for the 17th of March, 2020. Essays that mention something brought up in Dinosaur Comics are gathered at this link.

Ryan North’s Dinosaur Comics for the 17th is one about people asked to summon random numbers. Utahraptor is absolutely right. People are terrible at calling out random numbers. We’re more likely to summon odd numbers than we should be. We shy away from generating strings of numbers. We’d feel weird offering, say, 1234, though that’s as good a four-digit number as 1753. And to offer 2222 would feel really weird. Part of this is that there’s not really such a thing as “a” random number; it’s sequences of numbers that are random. We just pick a number from a random sequence. And we’re terrible at producing random sequences. Here’s one study, challenging people to produce digits from 1 through 9. Are their sequences predictable? If the numbers were uniformly distributed from 1 through 9, then any prediction of the next digit in a sequence should have a one chance in nine of being right. It turns out human-generated sequences form patterns that could be forecast, on average, 27% of the time. Individual cases could get forecast 45% of the time.

There are some neat side results from that study too, particularly that they were able to pretty reliably tell the difference between two individuals by their “random” sequences. We may be bad at thinking up random numbers but the details of how we’re bad can be unique.


And I’m not done yet. There’s some more comic strips from last week to discuss and I’ll have that post here soon. Thanks for reading.

Author: Joseph Nebus

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

6 thoughts on “Reading the Comics, March 17, 2020: Random Edition”

    1. Randomness is a legitimate way to make guesses! Or to improve guesses you already have. A good strategy in numerical mathematics, if you don’t know where to start, is to try adding a random element and let it help you to an answer.

      Liked by 1 person

        1. It is roughly that, yeah. This kind of randomness works best for problems in which it’s relatively easy to tell whether you’re finding a better or a worse solution, but hard to tell whether you’ve found the best. Also where you can make an experiment and discard the ones that make matters worse. So it’s kind of like, finding the best way to make a commute through a complicated network of streets by trying out alternatives every day for a month, which is great if you’re going to be making that commute for a year. It doesn’t help much if you’re only going to be making the trip four times.

          Liked by 1 person

Please Write Something Good

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.