Days of the week. Names and numbers couple and uncouple like KY-jellied orgiasts in a darkened room.
Number theory? Arithmetic? Logic–surely the double count mixup can be symbolized for instant clarity of what went wrong. Does this pitfall lurk in other areas? Has this been expressed, gussied up with more tricks, as a “paradox” for some logical point.
It’s a very amusing thread, but it’s a serious question.
And I think everyone screws this up now and then.*
I read somewhere Bertrand Russell spent eight pages proving 1+1=2. FWIW, my Mother, may she rest in peace, studied symbolic logic (as well as physics) for graduate work at Columbia, and since I was a little kid I was into it.
*I saw a photo of a check Einstein wrote in the first week of January, and he dated it with the wrong year which had ended in December. Made me feel good all day.
I don’t know that it’s particularly useful to try to classify every possible mistake of reasoning with a particular name, but if you like, you might think of this as a variant of a fencepost error (in counting two weeks, both an initial Sunday and a terminal Sunday were counted).
It reminds me of the problem with tertian fever, literally a ‘fever every third day’ which you might think would mean a fever e.g. on Sunday, then Wednesday, and then Saturday. But the Romans counted differently; for them counting started on the day of the fever, not the day after. So a tertian fever is actually a fever every 48 hours: Sunday, Tuesday, Thursday, Saturday. Sunday (fever) is day 1, then Monday is day 2, then Tuesday (fever again) is day 3; the cycle resets and Tuesday (fever) is day 1 again, Wednesday is day 2, and Thursday (fever) is day 3.
The Roman calendar counted down the days to particular reference days like the first of the month or the Ides or Nones, but the reference day counted as day 1, not day 0. So if the Ides were on Wednesday, then the preceding Sunday was ‘four days before the Ides’ and Monday was ‘three days before the Ides’. So there’s a precedent for different day-counting styles.
It also applies to the ‘died and arose on the 3rd day’ bit from the Bible: died Friday, rose Sunday. Friday is day 1, Saturday day 2, Sunday day 3 even though Friday PM to Sun AM is less than 48 hours.
I love the guy who can’t divide 31 by seven, and tries to argue that because he can fit 16 workouts into a month, and also 4 weeks into a month, he must be able to work out every other day. That reminds me of that “where did the dollar go?” puzzle.
Actually, most of the respondents get it right, yet do a terribly obtuse job of explaining what they are trying to explain. And a lot of them never learnt to deal with fractions or averages. And a whole bunch of them can’t spell “moran”.