[Chinjut]

Why would you need to presuppose some inexplicably shifting number base to get the result of "four times [n]" always equaling n + 7? What does that get you over just more simply observing "For Alice, four times [n] has come to be n + 7"? Shifting number bases are a pointless supposition here. They don't explain anything better than what is already happening without them.

[raldi]

I agree. She’ll never get to 20 because kids only do the times table up to 12.

[eesmith]

The book "The Annotated Alice", mention by a couple of people here, says that is one valid interpretation, at https://archive.org/details/agt-annotated-alice-5807b6/page/... :

> The simplest explanation of why Alice will never get to 20 is this: the multiplication table traditionally stops with the twelves, so if you continue this nonsense progression—4 times 5 is 12, 4 times 6 is 13, 4 times 7 is 14, and so on—you end with 4 times 12 (the highest she can go) is 19—just one short of 20.

Gardner then writes "A. L. Taylor, in his book The White Knight, advances an interesting but more complicated theory" which is the changing base theory.

He ends with "For another interpretation of Alice's arithmetic, see "Multiplication in Changing Bases: A Note on Lewis Carroll," by Francine Abeles, in Historia Mathematica, Vol. 3 (1976), pages 183-84."

Available at https://www.academia.edu/download/122551204/82113901.pdf .

[Xirdus]

Up to 12? Is that a British/Anglosphere/Victorian thing? In Poland they teach up to 10, which is suffinient for arbitrarily large numbers because they also teach long division and how to combine it with times table. Technically up to 9 would be sufficient but 10 is such a nice round number.

[raldi]

Yeah, every US sixth-grader can instantly tell you 12x12=144 but will have to puzzle out 2x13 the long way.

[gerdesj]

Gross!

[AnotherGoodName]

It is yes. The anglosphere has historically been somewhat base 12 in currency, time and units of measurement.

Currency is now metric but there’s still a few base 12 things in common usage (feet and inches) in the us at least. Nobody’s gone to metric time yet and base 12 transfers smoothly to base 60 too.

[Xirdus]

Of course it's because of imperial units. TIL, thanks. But on a sidenote, I question the utility of knowing x11 and x12 when working with time. x15 could be useful, unfortunate they don't teach that (but I think most people with higher education learn it on their own).

[acheron]

Feet and inches long predate imperial units, and the US has never used the imperial system, btw. “Imperial” has a specific meaning and isn’t just “anything not metric”.

Anyway, base 12 is also built into most Germanic languages which have unique names for 11 and 12 (rather than something along the lines of “one-teen” and “two-teen”, which is more common in Romance languages IIRC.

[debugnik]

Out of the most spoken romance languages, Spanish and Portuguese have distinct names up to 15, French and Italian up to 16, while Romanian does stop at 10. This suggests hexadecimal influence to me.

[zabzonk]

It's definitely a UK thing. And 12 is a nicer round number than 10 - ask the Babylonians!

[sltkr]

What's so nice about twelve-and-two (12)? Twelve (10) is a much nicer round number.

Though programmers may prefer base two (10) or base twelve-and-four (10).

[Xirdus]

If you say it in German, it doesn't even sound out of place. Zweiundzwölf, vierundzwölf.