The Cult of Dozenality

Among my super-aspirations is the adoption of base twelve, or “dozenal” for my arithmetic. Here I utilize the prefix “super” to imply I expect to never actually pursue this aspiration, or at least not to the point of actually calculating in dozenal routinely. Adopting various computational bases is of course routine in computer science, which runs on base two (binary), with bases eight (octal) and sixteen (hexadecimal) frequently used as easy shorthand for the fundamental base. Base twelve, however (formally “duodecimal” although as implied I prefer “dozenal”), doesn’t buy you anything in computer science; the supposed advantage is that 12 is evenly divided by 2, 3, 4, and 6, forcing fewer infinitely repeating decimal representations of fractions than the usual base ten (decimal). I’m not sure fewer infinite representations is that much of an advantage: fewer is not zero. Nevertheless, unless I am the victim of some variant of Poe’s law, some folks seriously advocate adoption of this boutique number base, citing further purported advantages you can read about on your own.

No, my super-aspiration has more to do with self-improvement. In my teens, I played with various techniques from The Memory Book by Lorayne and Lucas. These techniques do work, I enjoyed using them, and I still make limited use of some of them. For example, I use the so-called “Major” system to memorize a PIN or phone number. However, beyond simple daily uses I’m not convinced they are much more than mere stunts. If you really get into a topic, the mere repetition of recalling or re-looking-up needed information while studying does similar work. However, I do fancy that when one needs to quickly acquire a relatively high facility in a topic with lots of material to memorize, some of these techniques would be useful for getting up to speed.

In the Major system, you associate the digits 0-9 with consonants, then add vowels at whim to create mnemonic words that then help you memorize long numbers. For example, my German phone number is “boil doobie lich car”. I imagine myself boiling a doobie in my kitchen while looking out the window at what would normally (!) be a bunch of clowns piling into a car, except it is a bunch of lich monsters from Dungeons and Dragons. The so-called “person-action-object” (PAO) system (not described in Lorayne and Lucas) riffs on this groove by associating every two-digit number with a memorable person (whose name is derived from the numbers by the Major system) performing a stereotypical action, say “Santa handing out gifts”. With these pre-memorized mnemonics, you can then even more quickly memorize long numbers, or create multidimensional arrays of memorized items. Again, follow the links if you are interested.

My conceit is that I would derive a dozenal Major/PAO system from twelve, rather than ten, digits. Not to memorize long dozenal numbers (how often does one need to do that?), but to create 12 x 12 x … 12 arrays, so I could memorize arrays of 144, rather than 100, or 1,728, rather than 1,000 items, etc. As I say, this is super-aspirational, and I doubt I’ll ever pursue it seriously. I have gotten so far as to often do 6 or 12, rather than 5 or 10, tedious things at a time. A mundane, but satisfying aspiration.

2 thoughts on “The Cult of Dozenality”

  1. I owe the discovery of the following to the conjunction of a mirror and and encyclopedia.

    I was reading “Tlön, Uqbar, Orbis Tertius” a number of years ago, which, in one paragraph, dwells on the “duodecimal system of numbering (in which twelve is written as 10).”

    The next paragraph mentions a book which was “written in English and contained 1001 pages.”

    This led me to wonder what 1001 represented in base 12, and was amazed to find it was 1729 (The Hardy-Ramanujan number).

    It isn’t clear to me that Borges would or could have been aware of that “rather dull number” at the time of writing.

  2. I almost always have trouble separating Borges and Eco in my mind. I never misattribute Foucault’s Pendulum with Borges, but I often have to pause to recall whether, say, The Library of Babel is one or the other.

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