So way back about fifty years ago, when pop science started to seriously explain how computers worked, and when the New Math fad underscored how much mathematics is an arbitrary cultural choice, the existence of number bases other than ten got some publicity. This offered the chance for a couple of jokes, or at least things which read to pop-science-fans as jokes. For example, playing on a typographical coincidence between how some numbers are represented in octal (base eight) and decimal (base ten), we could put forth this: for computer programmers Halloween is basically another Christmas. After all, 31 OCT = 25 DEC. It’s not much of a joke, but how much of a joke could you possibly make from “writing numbers in different bases”? Anyway, Isaac Asimov was able to make a short mystery out of it.
Tony Cochrane’s Agnes for the 21st is part of a sequence with Agnes having found some manner of tablet computer. Automatic calculation has always been a problem in teaching arithmetic. A computer’s always able to do more calculations, more accurately, than a person is; so, whey do people need to learn anything about how to calculate? The excuse that we might not always have a calculator was at least a little tenable up to about fifteen years ago. Now it’d take a massive breakdown in society for computing devices not to be pretty well available. This would probably take long enough for us to brush up on long division.
![Teacher: 'Agnes, take out your math book.' Agnes: 'No need. I now own a semi-educational, quasi-computer electronic pad or something. If I boop enough buttons in the correct sequence, all world info will be there to behold! Including all the indecipherable doggerel *you're* pushing.' [ At the Principal's Office ] Agnes: 'Math teachers are fans of big numbers ... not so much big words.'](https://nebusresearch.files.wordpress.com/2020/02/agnes_tony-cochran_21-february-2020.gif)
It’s more defensible to say that people need to be able to say whether an answer is plausible. If we don’t have any expectations for the answer, we don’t know whether we’ve gone off and calculated a wrong thing. This is a bit more convincing. We should have some idea whether 25, 2500, or 25 million is the more likely answer. That won’t help us spot whether we made a mistake and got 27 instead of 25, though. It does seem reasonable to say that we can’t appreciate mathematics, so much of which is studying patterns and structures, without practicing. And arithmetic offers great patterns and structures, while still being about things that we find familiar and useful. So that’s likely to stay around.
John Rose’s Barney Google and Snuffy Smith for the 21st is a student-subverting-the-blackboard-problem joke. Jughaid’s put the arithmetic problems into terms of what he finds most interesting. To me, it seems like if this is helping him get comfortable with the calculations, let him. If he does this kind of problem often enough, he’ll get good at it and let the false work of going through sports problems fade away.
Stephan Pastis’s Pearls Before Swine for the 21st sees Pig working through a simple Retirement Calculator. He appreciates the mathematics being easy. A realistic model would have wrinkles to it. For example, the retirement savings would presumably be returning interest, from investments or from simple deposit accounts. Working out how much one gets from that, combined with possibly spending down the principal, can be involved. But a rough model doesn’t need this sort of detailed complication. It can be pretty simple, and still give you some guidance to what a real answer should look like.
John Zakour and Scott Roberts’s Working Daze for the 21st is a joke about how guys assuming that stuff they like is inherently interesting to other people. In this case, it’s hexadecimal arithmetic. That’s at least got the slight appeal that we’ve settled on using a couple of letters as numerals for it, so that wordplay and word-like play is easier than it is in base ten.
And this wraps up a string of comic strips all with some mathematical theme that all posted on the same day. I grant none of these get very deep into mathematical topics; that’s all right. There’ll be some more next week in a post at this link. Thank you.
Pearls Before Swine: When you divide by zero, are your retirement savings undefined or infinite?
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It’s an interesting case really. We look at 0 divided by 0 and it’s easy to see the reasoning why it can’t be defined. But when it’s put as zero retirement savings over even zero years it’s hard to avoid seeing zero as the result. I’m not sure what it is that makes it different; possibly the attachment of units. Possibly that nobody really believes they’re going to live zero years in retirement. Even if they don’t think it’ll be long, they think it’ll be long enough to finish the thought of “how long will I live” … and zero dollars divided by a hundredth of a second is meaningful enough.
But then it seems like the relevant measure isn’t
how long someone lives'' buthow many chances to spend money” someone will have. If you’re washed up on a deserted island, there’s no chance to spend any money. Whether you had a million dollars, ten dollars, or a penny you’d live just as well and just as long. So wouldn’t having zero dollars be exactly as good?There’s something incomplete in our intuition here.
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