## Dozenal FTW!

I’m happy to present the world’s *first* online dozenal conversion calculator.^{[1]}

For a number of years, I’ve entertained myself in conversations with friends and family by taking the preposterous position that we’d have been better off, maths-wise, if we’d all been born with 12 fingers instead of 10.

Since that clearly didn’t happen, I’ve maintained hope by vowing that if I ever get my hands on a time machine, one of my first acts-of-historical-correction would be to fly back to early caveman days, find the first people who started counting with their hands, and teach them to eschew fingers in favor of finger segments (of which there are conveniently 12), using the thumb of the same hand to touch the current count on the appropriate finger segment.^{[2]}

With this method and using the second hand as a 12′s placeholder for counts greater than 12, you can actually achieve the incredible sum of 144 (which is “100″ in dozenal) using nothing more than two hands!

But, alas, I have no time machine. So I will instead have to settle for the world’s FIRST *online* dozenal/decimal calculator.

For me, the most alluring argument in favor of the dozenal system revolves around factorization. A base-10 measuring system can only be factored into integer halves and fifths. A base-12 number system, on the other hand, is easily divisible into halves, thirds, fourths, and sixths. And when it comes to measurement, there really aren’t any more important divisors than thirds and fourths. What did you do to the Rule of Thirds, base-10? Seriously, metric-system, show me where to make the mark for 3.3333333… on the wall.

In fact, when one considers number-of-factors as the basic measure of a base-N system, it quickly becomes apparent that base-12 gets you the most bang-for-the-buck. You have to jump all the way up to base-60 to get your next most important factorizations, but base-60 is a bit unwieldy.^{[3]} Base-2, Base-3, Base-8, Base-10, Base-15, Base-16, Base-24, Base-30, etc — all have their unique features and settings where they are the right choice, but none are as naturally ready for human consumption as Base-12.

Still not convinced that Base-12 is Teh Rawk? Imagine replacing timekeeping with a Base-10 system. I know, I know, there are those who have tried it (French Revolutionaries, crazy internet dudes), but really, let’s think about this for just a minute. With a base-10 timekeeping system (for example, 100-minute hours), you can’t say anything equivalent to “see you at 20 after 5″ — at least not without sounding like a moron: “see you at 5:33-and-a-third?” You’d be left with units of half-base10-hours and fifth-base10-hours. Trust me, that’d suck.

If you still aren’t sure that I’m right (even though I am), take a minute or two to watch a bit of Schoolhouse Rock for some real edumacation.

See also the Dozenal Society of America.

(Note: this post has little, if anything, to do with flŭd decentralized backup – except perhaps that both rely on the art of non-base10 mathematics).

^{[1]} At least, it is the first online dozenal-decimal calculator that I am aware of, and, apparently, the first that google is aware of too. Searches for “dozenal|duodecimal|base12|base-12 [online] calculator” don’t yield anything meaningful for me, although the Dozenal Society of Great Britain does have a downloadable calculator for MSWindows available. Also, this online calculator is really more of a converter than anything. There are generic radix integer converters out there that can convert between many different bases, such as this or this, but none can even handle the simplest non-integer values. If you are aware of another online dozenal/decimal conversion calculator, please let me know so that I can retract my outrageous claims and give due credit. ** UPDATE 2009-03-14:** Ray Greaves points to his very fine base-2, 3, 8, 10, and 16 converter in the comments below, which had many other bases (including 12) added sometime in 2008 (not sure if it beats the Jan 12 2008 date of this posting, but either way, check it out, it’s a very nice piece of work).

^{[2]} I haven’t worked out the details of how I’d actually go about reasoning with cavemen. If anyone knows of studies on the comparative efficacy of different teaching techniques on primitive man (perhaps performed in secret government cloning labs), forward plzkthx.

^{[3]} Just ask the Babylonians. Actually, base-60 remains very useful today in some settings, such as timekeeping. And its large cousin, base-360, is a very close friend of navigators and geometers.

January 20th, 2008 at 3:47 am

I enjoyed the calculator greatly as I have been working on this prob. Thank you!

March 20th, 2008 at 6:40 am

You beat me to it! Nice work. I still plan on making mine though…

April 28th, 2008 at 5:54 am

But does it actually calculate? It doesn’t seem to. I’m looking for a base-12 calculator, with at least the basic add/subtract/multiply/divide functions. So far I haven’t found one online yet. Mind you, I only started looking a few minutes ago…. Lots of converters from one base number system to another, but none offering calculations in different base systems.

I’ve long been a duodecimal proponent, since childhood, but thought I was the only such genius on earth. I’m glad to see I’m not alone.

December 28th, 2008 at 11:43 pm

PS By fractions, I mean non-integer values in combination with or separately from integers. As for a true dozenal calculater, you will now find one available on the DSGB website at

http://www.dozenalsociety.org.uk/apps/calculator.html

donated by a user.

I would certainly like to get his source code.

January 18th, 2009 at 9:13 pm

I am sorry to disappoint you but my converter/calculator has been available on my site since 1995, first as The Cornucopia at http://www.omnis.demon.co.uk and since 2000 at

http://www.footrule.com/1/conversn/convjvsc.htm?sr=search&jt=1.2.3.2

The original version provided conversion between base 2, 3, 8, 10 and 16 and basic arithmetic in the decimal entry only. This converter was expanded to include all bases from 2 to 36 in 2008. Thus this qualifies as a converter and a basic calculator.

February 20th, 2009 at 8:34 am

You can find a dozenal calculator and other applications at:

http://www.dozenalsociety.org.uk/apps/appslist.html

The free calculator download is at:

http://www.dozenalsociety.org.uk/devices/Zcalculator.zip

April 13th, 2009 at 7:40 pm

I’ve just been trying to find dozenal calculators for some serialist composition I am doing – base 12 fits perfectly with the 12 semi-tones.

Do you know where I can find a really really powerful dozenal converter/calculator – I need to work out some square roots to 200-300 dozenal (I persume this word can replace decimal in this context) places…

March 12th, 2010 at 8:53 pm

Can you convert pi into base-12 for 2000 dozenal places, for instance, and then check for any unusual things?

There are hints something could come out of it.

August 11th, 2010 at 11:40 am

Source code? Please?

August 11th, 2010 at 12:18 pm

Is it licensed in any way? Open source?

January 22nd, 2013 at 1:23 pm

You can just use this if you want.

Replace “decimal” with an int.

parseInt(decimal,10).toString(12).replace(/a/g,”X”).replace(/b/g,”E”);