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title: "The superiority of base-12" date: 2011-02-04T10:07:00Z
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It should be evident that, all other factors being equal, base-12 is a superior number base for humans than base-10. I won't go into too many details why this is true; there are[1] many[2] resources[3] that discuss[4] these details in length, but it's main strength is that it has more prime factors than base-10. 12 is divisible by 1,2,3,4 and 6; 10 is divisible only by 1,2, and 5. As to it's suitability over other systems, the next step up occurs at sexagesimal (base-60), which is divisible by 1,2,3,4,5 and 6, and that's an inconveniently large set of base numbers for humans. Dozenal is so useful that it's still commonly used today; a dozen eggs, a gross, our analog clocks, the number of signs in the zodiak, inches in a foot, etc., etc.
1: http://www.youtube.com/watch?v=-nu_pjgTIZ4
3: http://www.dozens.org/articles/db043r2.pdf
4: http://www.dozenalsociety.org.uk/basicstuff/campbell.html
What this post is about, however, is how useful this is even beyond the first 12 numbers. Consider a gross (a dozen dozen, or 144~10~), or 100~12~:
┌────┬──────────────┬──────────────┐ │ │ 100 base 10 │ 100 base 12 │ ╞════╪══════════════╪══════════════╡ │ 2 │ 50 │ 60 │ ├────┼──────────────┼──────────────┤ │ 3 │ 33.33... │ 40 │ ├────┼──────────────┼──────────────┤ │ 4 │ 25 │ 30 │ ├────┼──────────────┼──────────────┤ │ 5 │ 10 │ 24;1 │ ├────┼──────────────┼──────────────┤ │ 6 │ 16.66... │ 20 │ ├────┼──────────────┼──────────────┤ │ 7 │ 14.285714... │ 18;6A3518... │ ├────┼──────────────┼──────────────┤ │ 8 │ 12.5~10~ │ 16 │ ├────┼──────────────┼──────────────┤ │ 9 │ 11.11... │ 14 │ ├────┼──────────────┼──────────────┤ │ A │ 10 │ 12;5 │ ├────┼──────────────┼──────────────┤ │ B │ │ 11;11... │ ├────┼──────────────┼──────────────┤ │ 10 │ │ 10 │ └────┴──────────────┴──────────────┘
There are really only two (base) numbers that produce non-terminating divisors in a gross: B and 7. For 100~10~, you have 3, 6, 7, and 9. Sidenote: I'm not thrilled with the selection of ";" as a floating-point character, but it seems to be what everybody is using, and there's really nothing better (unless we just stick with "."). Thankfully, there's no universal agreement on the character to use, and I reject the Dozenal Society of America's choice of "*" -- it's a really, really poor choice, as anybody who does any programming or, verily, *basic math* can tell you. "A" and "B" aren't very good, either, but at least they're recognizable to anybody who's ever taken a computer programming course.
BTW, the Dozenal Society of America has been busy[5] building a nice new site; check it out.