Base 12 advocacy

Miscellaneous and Personal Stuff I Must Share
1

The discussion on pi vs. tau got me thinking about Base 12 (duodecimal) advocacy (Dozenalism) which seems reasonable to me. Base 10 has only two (non trivial) divisors: 2, 5, while base 12 has four: 2, 3, 4, 6, which is the reason we already use base 12 in so many places:
12 inches in a foot
12 ounces in a pound (troy)
12 pence in a shilling
12 items in a dozen
12 dozen in a gross
12 hours in a ‘day’

From the wiki entry:

The renowned mathematician and mental calculator Alexander Craig Aitken was an outspoken advocate of the advantages and superiority of duodecimal over decimal: The duodecimal tables are easy to master, easier than the decimal ones; and in elementary teaching they would be so much more interesting, since young children would find more fascinating things to do with twelve rods or blocks than with ten. Anyone having these tables at command will do these calculations more than one-and-a-half times as fast in the duodecimal scale as in the decimal. This is my experience; I am certain that even more so it would be the experience of others.

Aitken wrote a paper back in 1962 titled The Case against Decimalisation that’s worth reading. Yeah, it’s probably as likely as adopting tau for 2*pi, which is not very. We can’t even get this country on the metric system though a duodecimal metric system would rock, IMO.

2

The British shpuld have created a base-12 metric system. Would have tromped the French…

3

And the question is…?

4

Even the brits don’t use shillings anymore.

5

Base 12 money in a base 12 world would be cool.

6

Standingwave, ignore the skeptics. I’m ready to support you. Lavishly and without hesitation.

7

Thank you, comrade!

8

[moderating]
There isn’t one that I can see.

Moving thread to MPSIMS…
[/moderating]

9

If 12 is good, isn’t 60 better?

It gets you one more factor–and one more prime. And that 5 is an important one–it not only makes it much easier to deal with all those people still using that obsolete decimal system, it also gives you an even fifth, which is critically important for alcoholics.

It worked for the Babylonians. If you don’t try to measure things more accurately than them, it still divides the 360-day year just as well as 12 does, and it makes it much easier to deal with those 30-day months than base 12.

If you don’t want that 5 in there, why do you need the 4? You’ve already got 2, who needs another one. Base 6 should work just as well as base 12. Plus, unlike base 12 and base 60, you don’t need to go to your toes to count it, or invent new numerals to write it.

On the other hand, who says more factors are better? If you use a pure power of a prime (2, 3, 5, 9, 16, whatever) a lot of things get easier. Powers of 2 are especially nice, because doubling and halving things becomes ridiculously easy, and that’s something we do all the time. Plus, we’ll be ready for our future computer overlords that way.

10

And I’ll be the pedant who points out that what you’re talking about isn’t base 12, but base dozen. The terms “12” and “twelve” are themselves decicentric.

11

The “12” I’ll grant–it would be “base 10” in the new base, of course.

But do you really think people would even consider changing the word “twelve” just because we went to that base?

Sure, it’s got hints of its now-numeropolitically-incorrect etymology in there, but so what? That hasn’t stopped us from calling “W” “double-u”, or calling Christmas “X-mas” even though we no longer use “X” for the “ch” sound that the word used to start with, or…

And what kind of new names would make sense to anyone for “eleven” and “twelve”? Not many modern leaders have the testicular fortitude to declare that they be named “july” and “august” after his father and himself. OK, maybe I can imagine the last President doing that, but I suspect that the majority Americans, and almost everyone else in the rest of the world (except maybe Poland–I didn’t forget about them), would refuse to count “… nine, ten, herbert, walker.” Maybe Caroline Kennedy could get away with naming them after her farther and uncle, though.

12

‘12’ certainly is, but I deny that ‘twelve’ is. It really doesn’t matter what the etymology is at this point.

Feel it in your bones, do ya?

13

“dozen” is just as etymologically 10 + 2 as “twelve”.

14

Good point.

Besides, we have far more problems than just naming the numbers formerly known as eleven and twelve.

You can’t call 24 (the number formerly known as twenty-eight) “twenty-eight” anymore. But “twenty-four” is just confusing (even beyond the treasonous counter-revolutionary sentiments betrayed in its etymology). And “two-dozen-and-four” is too many syllables and keystrokes.

I guess we could have “dozen, twozen, throzen, forzen, fifzen, sixzen, sevenzen, eightzen, ninezen, tenzen, perdozenzen” (we still need a name for 11) for the multiples of dozen.

Then “gross” is fine.

But we need a name for the 3rd power. Maybe this is the chance to fix the “billion” problems. It’s silly that 1000^3, ^4, ^5, etc. have names that mean “two”, “three”, “four”, etc. And the fact that the UK sometimes uses them the US way and sometimes differently just makes it more confusing. And wasn’t it the French who came up with this system anyway? We’re Americans, we can’t stand for that! So, how about “mizen, bizen, trizen, quadrizen, …” for dozen^3, ^6, ^9, ^12, …?

Meanwhile, we’ll also need a whole new set of SI-style prefixes. Considering how well Ki, Mi, Gi, etc. have caught on for the 10th, 20th, 30th, etc. powers of 2, I’m guessing Kz, Mz, Gz, etc. will have an even harder time for the 3rd, 6th, 9th, etc. powers of a dozen.

And don’t forget about the fractions. Can you even pronounce “grossth” without spitting?

15

Here’s somebody who seems to be all for it.

16

Your post is made of awesome! I award you one internets!

I don’t know why, but the thought of mizen, bizen and quadrizen made me laugh out loud multiple times.

17

The true secret to comedy is waiting until everyone has not only stopped making “The Artist Formerly Known As Prince” jokes, but has completely forgotten that he was called that for a while, and then making a really bad one. After that, anything else you say just seems funny by comparison. :slight_smile:

18

… or do we need to point out what the name of this month is and how many months into the year we are?

19

Along which lines is the math joke that Christmas and Halloween are exactly equivalent, since 25 (Dec) = 31 (Oct).

20

LOL! A fifth is wonderful but really, wouldn’t a sixth encourage more temperance? After all, a person who drinks a sixth of whiskey per day clearly isn’t as much of an alcoholic as one who is downing a fifth per day. I can see it now: MADD and AA for Dozenal!

Sure, sexagesimal is great and the Babylonians certainly thought so. And its remnants persist today for minutes and seconds. It does have more factors but that rather modest increase in factorization comes at the expense of requiring fifty more characters instead of just the two additional ones for duodecimal. Imagine what a keypad would look like. It would take up most of your keyboard. And memorizing a 60x60 multiplication table would be rather tedious. A 12x12 table is actually easier to memorize than a 10x10 because of all the repeating patterns: Remember how easy it was to learn the Twos and Fives multiples? 2, 4, 6, etc. 5, 10, 15, etc. In a dozenal system, similar patterns would exist for Two, Three, Four and Six.

It’s not that I don’t want the 5. I love the 5. I’m going to name a child 5. (It’s Joe DiMaggio’s number so not only is it an all all-round beautiful name, it is also a living tribute…) It’s just that I think it makes more sense to bring in 1, 2, 3 and 4 first.

If finger counting is that important, then note that each hand has four fingers and a thumb. Each of the four fingers has three (visible) phalanges for a total of twelve. You can even use the thumb of the same hand to count them. Further, if you designate the other hand as the first power (positional notation) of twelve, you could count to 144 just on your hands!

More lol. I for one, welcome our new Skynet overlords. But, as far as binary goes, and so long as we’re still in charge, I’m of the opinion that computers should adapt to us rather than the other way around. I just has a flash of the ED-209 from RoboCop trying to use an ATM and swearing when posed the question, “Dozenal or Binary?”

But, like decimal, dozenal has 2 as a factor, so at it least has that going for it. (No worse than decimal in that respect.) But wouldn’t a prime number, even 2, would be a terrible base for everyday use? Imagine using 11 as a base. Eleven eggs? How would you package them? Would 12 become the new Bakers Dozen? And how would you evenly divide them amongst 2, 3 or 4 people? Imagine 23 hours in a day or 61 minutes in an hour. Madness, I say.