The past week started strong for mathematically-themed comics. Then it faded out into strips that just mentioned the existence of mathematics. I have no explanation for this phenomenon. It makes dividing up the week’s discussion material easy enough, though.
John Zakour and Scott Roberts’s Maria’s Day rerun for the 19th is a lottery joke. Maria’s come up with a scheme to certainly win the grand prize in a lottery. There’s no disputing that one could, on buying enough tickets, get an appreciable chance of winning. Even, in principle, get a certain win. There’s no guaranteeing a solo win, though. But sometimes lottery jackpots will grow large enough that even if you had to split the prize two or three ways it’d be worth it.
Tom Horacek’s Foolish Mortals for the 21st plays on the common wisdom that mathematicians’ best work is done when they’re in their 20s. Or at least their most significant work. I don’t like to think that’s so, as someone who went through his 20s finding nothing significant. But my suspicion is that really significant work is done when someone with fresh eyes looks at a new problem. Young mathematicians are in a good place to learn, and are looking at most everything with fresh eyes, and every problem is new. Still, experienced mathematicians, bringing the habits of thought that served well one kind of problem, looking at something new will recreate this effect. We just need to find ideas to think about that we haven’t worn down.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st has a petitioner asking god about whether P = NP. This is shorthand for a famous problem in the study of algorithms. It’s about finding solutions to problems, and how much time it takes to find the solution. This time usually depends on the size of whatever it is you’re studying. The question, interesting to mathematicians and computer scientists, is how fast this time grows. There are many classes of these problems. P stands for problems solvable in polynomial time. Here the number of steps it takes grows at, like, the square or the cube or the tenth power of the size of the thing. NP is non-polynomial problems, growing, like, with the exponential of the size of the thing. (Do not try to pass your computer science thesis defense with this description. I’m leaving out important points here.) We know a bunch of P problems, as well as NP problems.
Like, in this comic, God talks about the problem of planning a long delivery route. Finding the shortest path that gets to a bunch of points is an NP problem. What we don’t know about NP problems is whether the problem is we haven’t found a good solution yet. Maybe next year some bright young 68-year-old mathematician will toss of a joke on a Reddit subthread and then realize, oh, this actually works. Which would be really worth knowing. One thing we know about NP problems is there’s a big class of them that are all, secretly, versions of each other. If we had a good solution for one we’d have a solution for all of them. So that’s why a mathematician or computer scientist would like to hear God’s judgement on how the world is made.
Hector D. Cantú and Carlos Castellanos’s Baldo for the 22nd has Baldo asking his sister to do some arithmetic. I fancy he’s teasing her. I like doing some mental arithmetic. If nothing else it’s worth having an expectation of the answer to judge whether you’ve asked the computer to do the calculation you actually wanted.
Mike Thompson’s Grand Avenue for the 22nd has Gabby demanding to know the point of learning Roman numerals. As numerals, not much that I can see; they serve just historical and decorative purposes these days, mostly as a way to make an index look more fancy. As a way to learn that how we represent numbers is arbitrary, though? And that we can use different schemes if that’s more convenient? That’s worth learning, although it doesn’t have to be Roman numerals. They do have the advantage of using familiar symbols, though, which (say) the Babylonian sexagesimal system would not.
And that’s the comic strips with enough mathematics for me to discuss from the first half of last week. I plan tomorrow to at least mention the strips with just mentions of mathematics. And then Tuesday, The A-to-Z reaches the letter Q. I’m interested to see how that turns out too.
8 thoughts on “Reading the Comics, October 22, 2019: Bifurcated Week Edition”
‘Maria’s Day’ says more in two frames about gambling than many an official study, I’ll be bound!
It does make me wonder when you see a lottery get to some Brobdingnagian jackpot, like when the Mega Millions rolled over a billion dollars a year or two ago, whether any obscenely rich people tried putting together a pool that would buy up every combination. Even if they had to split the jackpot, well, $300 million in, $500 million out, for a half-week’s worth of work? That’s not a crazy plan. Is it just the liquidity problem of getting that much cash together that’s keeping that from happening?
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Haha, perhaps those with lots of mazoola have easier ways of making more?
I don’t know. There’s some obvious hard work involved, particularly in arranging the purchase of all these tickets. But the expected profit is hundreds of millions of dollars, and it doesn’t take long to realize. There must be some subtler limitation to the plan.
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Leaving aside any purely mathematical dimension, if you’ll permit me – tax havens perhaps, leaving the poor to buy lottery tickets?
Yeah, perhaps. Also maybe once the tax bill to lottery winnings is added on there’s few enough prize pools big enough to be worth it, especially given the chance of multiple winning tickets being sold, that it’s not worth the bother. (Which is a dizzying implication and one worth eating the rich for, if a billion-dollar lottery pool isn’t worth the bother of trying to win.)
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Also interesting to observe that a lottery is almost the reverse of financial investment – huge odds against winning with any benefit for most being an addictive yet unrealised dream versus a steady accumulation of profit bringing definite physical rewards!
Yeah; it’s only in rarefied circumstances that playing the lottery can make sense from an expected-value sense. And even then it can’t make logical sense if you’re going to buy one or two (my limit) or even a reasonable office pool’s worth of tickets.
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