The open version of four was taught in public schools during the 1960s in California. The closed version was taught in England (where I also schooled). Neither party accepted the other, in fact, a number of years later I was asked by a bank teller in California to write my fours “correctly”. She claimed she had never seen the closed version.
The “purpose” as such, was explained to me as a need to draw a distinction between 4 and the other characters. That seems like nonsense. The closed version only requires one stroke, while the open requires two, so I always preferred the closed.
Hmm. Interesting, because I deal with a lot of old German/ Dutch stuff (16th c) that uses the open 4 (and is often very easy to confuse with a 5 in the way that it is sometimes printed (sort of tilted counter clockwise and sharpened like a sideways backwards “Z”)), and in a book I see Italian handwriting of the same period using a closed 4 (I assume the print did too, although I can’t find an immediate example). So unlike the letter O and zero situation this goes way back. I wonder if perhaps the present situation with 2 4’s is just the end result of the different latin/ fraktur typefaces that have been concurrently in use since then ( and certain regions’ preference for one or another at points in time relates to a vague sort of nationalism/ identity, with a group trying to emphasize either Roman/ classical roots or a vernacular past at any given point in time?).
Europeans tend to make their numberal "1"s with big swooping topheavy flags on them, and they look a lot like American "7"s. The crossbar is used so they can tell their "7"s from their "1"s.
I don’t have a compelling argument for the genesis of the two forms, but I CAN explain the “open four”.
People who use Arabic numerals usually don’t realize this, but when the numbering characters were created, they were meant to reflect the numeric value as well as signifying it in a rational form. Thus, the numeral one had one angle-like an half-arrow, the numeral two had two, so on and so forth.
The numeral for four was left open, and contained four angles. Probably drift set in and people forgot about the original intention, and now Arabic numerals look nothing like what they were intended to result. The letter “A” did come from the Phoenician glyph for “ox”, after all. (Cause it looked like a cow’s head, sorta).
Then, one can only assume, penmanship set in, and now you can tell where someone’s from by checking their numbers. Eurotrash like myself cross their sevens and put a flag on their ones. Geeks and money people slash their zeros. French people and most Europeans make their sixes and nines with comparatively small loops and long curvy stems.
Make that an angular version of the cursive “z” (so the downstroke changes direction, sort of like a mirror-image “3”) and you get… something that lools a lot like the Arabic script character for the numeral 4 (open).
(BTW in modern Arabic script, the numerals most similar to their roman script are 1 and 9; 2 and 7 can be figured out if you turn the page sideways; 3 and 6 you have kind of squint and move the page sideways; 5 and 0 are quite different from what we’d expect and 8 isn’t even close.)
[hijack]
And similarities between numerals and letters would seem to cause the po-lice problems, especially in states where the numbers and letters can appear in any position (OTOH, if its always LLL ###, no confusion)