I was all set to say how complaining about GoComics.com’s pages not loading had gotten them fixed. But they only worked for Monday alone; today they’re broken again. Right. I haven’t tried sending an error report again; we’ll see if that works. Meanwhile, I’m still not through last week’s comic strips and I had just enough for one day to nearly enough justify an installment for the one day. Should finish off the rest of the week next essay, probably in time for next week.

Mark Leiknes’s **Cow and Boy** rerun for the 23rd circles around some of Zeno’s Paradoxes. At the heart of some of them is the question of whether a thing can be divided infinitely many times, or whether there must be some smallest amount of a thing. Zeno wonders about space and time, but you can do as well with substance, with matter. Mathematics majors like to say the problem is easy; Zeno just didn’t realize that a sum of infinitely many things could be a finite and nonzero number. This misses the good question of how the sum of infinitely many things, none of which are zero, can be anything but infinitely large? Or, put another way, what’s different in adding and adding that the one is infinitely large and the other not?

Or how about this. Pick your favorite string of digits. 23. 314. 271828. Whatever. Add together the series — *except* that you omit any terms that have your favorite string there. So, if you picked 23, don’t add , or , or or such. That depleted series *does* converge. The heck is happening there? (Here’s why it’s true for a single digit being thrown out. Showing it’s true for longer strings of digits takes more work but not really different work.)

J C Duffy’s **Lug Nuts** for the 23rd is, I think, the first time I have to give a content warning for one of these. It’s a porn-movie advertisement spoof. But it mentions Einstein and Pi and has the tagline “she didn’t go for eggheads … until he showed her a new equation!”. So, you know, it’s using mathematics skill as a signifier of intelligence and riffing on the idea that nerds like sex too.

John Graziano’s **Ripley’s Believe It or Not** for the 23rd has a trivia that made me initially think “not”. It notes Vince Parker, Senior and Junior, of Alabama were both born on Leap Day, the 29th of February. I’ll accept this without further proof because of the very slight harm that would befall me were I to accept this wrongly. But it also asserted this was a 1-in-2.1-million chance. That sounded wrong. Whether it is depends on what you think the chance is *of*.

Because what’s the remarkable thing here? That a father and son have the same birthday? Surely the chance of *that* is 1 in 365. The father could be born any day of the year; the son, also any day. Trusting there’s no influence of the father’s birthday on the son’s, then, 1 in 365 it is. Or, well, 1 in about 365.25, since there are leap days. There’s approximately one leap day every four years, so, surely that, right?

And not quite. In four years there’ll be 1,461 days. Four of them will be the 29th of January and four the 29th of September and four the 29th of August and so on. So if the father was born any day but leap day (a “non-bissextile day”, if you want to use a word that starts a good fight in a **Scrabble** match), the chance the son’s birth is the same is 4 chances in 1,461. 1 in 365.25. If the father was born on Leap Day, then the chance the son was born the same day is only 1 chance in 1,461. Still way short of 1-in-2.1-million. So, Graziano’s Ripley’s is wrong if that’s the chance we’re looking at.

Ah, but what if we’re looking at a different chance? What if we’re looking for the chance that the father is born the 29th of February *and* the son is also born the 29th of February? There’s a 1-in-1,461 chance the father’s born on Leap Day. And a 1-in-1,461 chance the son’s born on Leap Day. And if those events are independent, the father’s birth date not influencing the son’s, then the chance of both those together is indeed 1 in 2,134,521. So Graziano’s Ripley’s is right if that’s the chance we’re looking at.

Which is a good reminder: if you want to work out the probability of some event, work out *precisely* what the event is. Ordinary language is ambiguous. This is usually a good thing. But it’s fatal to discussing probability questions sensibly.

Zach Weinersmith’s **Saturday Morning Breakfast Cereal** for the 23rd presents his mathematician discovering a new set of numbers. This will happen. Mathematics has had great success, historically, finding new sets of things that look only a bit like numbers were understood. And showing that if they follow rules that are, as much as possible, like the old numbers, we get useful stuff out of them. The mathematician claims to be a formalist, in the punch line. This is a philosophy that considers mathematical results to be the things you get by starting with some symbols and some rules for manipulating them. What this stuff means, and whether it reflects anything of interest in the real world, isn’t of interest. We can know the results are good because they follow the rules.

This sort of approach can be fruitful. It can force you to accept results that are true but intuition-defying. And it can give results impressive confidence. You can even, at least in principle, automate the creating and the checking of logical proofs. The disadvantages are that it takes forever to get anything *done*. And it’s hard to shake the idea that we ought to have some idea what any of this stuff *means*.

Was the pregnancy planned? Was the mother of Vince Parker, Jr. induced? If 2,134,521 fathers (or mothers) who were born on leap day planned the pregnancy and the mothers were induced, I think far more than one of them would succeed in having a baby born on leap day.

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Good questions and I have answers to none of them. I think planning for a leap day delivery is chancy, but not ridiculous; I seem to remember news stories at least of people attempting to have children come due at the start of 2000, or of 2001, or for that matter for August of 1988 (as 8/8/88 would be a particularly auspicious day in some cultural traditions). And that if there were good reasons to induce pregnancy (including simply the parents wanting to set it for a convenient date) then the chance of picking an unusual day like Leap Day is probably higher. I can also imagine that it’s more likely to have sex on one’s birthday, or one’s partner’s birthday, or an anniversary day, which skews what birth dates are most likely.

As ever, there’s fair reasons to doubt whether the birth dates are quite independent events. But it’s so hard to be sure about independence.

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Is there a name for the opposite of leap year? Not to brag but I was born on Feb 1st instead of the 29th. If that means anything?

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There is! Well, there’s several names. The name that won’t get you slugged is “common year”, which is boring but is at least descriptive and understandable to someone who’s not deeply into calendar lore.

If you want to be treated like you were in middle school, there’s

`non-bissextile year''. Leap Years are sometimes in the trade known as`

bissextile years” because the old Catholic cycle for dominical letters and of feast days treated the leap day as a doubling of the sixth day before the start of March (as the Romans figured it, so, February 24th doubled over). They picked that date for reasons you are going to think are my joke, but, that’s where the Romans used to insert an extra little 22-day month known as Mercedonius when their calendar, which was 11 or 12 days short of the true year, got too far out of synch with the actual seasons. Years with an extra (`intercalary'') month like this so they're 13 months long are known as`

embolismic years”. Which we have nothing to do with anymore but which make a comeback in many calendar-reform proposals.So. The leap day, as a bissextile day, gives that adjective to the whole year so you can say that 2020 is a bissextile year and people will think you’re making a joke that you’re not. And so non-bissextile years follow from that. Don’t try to get away with “non-bissextile” while playing Scrabble.

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