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Not sure where to put this thread. It's not really cool enough for tech, cars and cool stuff. The similar sounding Dewey decimal system, now that's cool.

So, Zorro noticed the current location in my profile, Dozenal Society of America, and we got to talking about base 12. I said that I thought it was wonderfully impractical, trying to get people to express "fifty" as "42". It seems a heck of a lot harder than getting people to adopt liters and meters, I said. I didn't even think about what to do about the decimal point, but I imagine we'd use fractions. Base 12 is good for fractions.

I also noted that we would need a new word for "fifty" which is a product of the decimal lifestyle. When I was playing with ternary (base 3), I did start to make up words for the numbers so that I could more easily think in base 3. Yeah, for me, different number systems are just a way to kill time before sleep, like playing solitaire. But it turns out Zorro is a dozenist!

Reprinted, with permission:



My main question is, *why* is dozenal better? Take it away, Zorro!

I like dogs.

ok... and do you like dozenal?

Is that like nyquil?

Anyone besides reisender?

I think it's an enormously difficult system to institute. I agree with Zorro that the decimal is based on our fingers. It's the same as the way the 360 degrees of a circle are based on a calendar year. If you were to teach a child from birth using a base 12 system, it would be no problem, but for everyone else it'd be hell. The multiplication tables are learned by rote as a kid, and for an adult to get past that would be extremely difficult. Possibly, just possibly, if there was an advantage to it, you could get it instituted in some branch of science, and if it caught on there, it could spread.

In web design, a base 16 hexadecimal system is used. Wouldn't that be even better? 4x4 equals 10 50 would be 32.

I think the 10s are easier, and lets slow people use their fingers in a pinch.

Rather than bore you with jargon, I will put it simply. Dozenal is easier to work with. Decimal "seems" easier, but its just because you are used to it.

Lets say there is you and two guests at your house. You bought a dime bag and you want the other two to pay their share. How much do they each owe? $3.3333333.....cents. Maybe you got that quickly. Maybe you would not after smoking the dime bag. Anyway, somebody is going to have foot a penny. Some people argue over that stuff.

In a dozenal world, you would have bought a dozen bag because dozens would be standard. You would have paid more, but you would have gotten more spliff to match. Each of your guests would have paid an even four bucks. Easy. If Steve shows up (and he always does when there is weed!) Now its an even three bucks. What to do? Steve pays you three, and you give back a dollar each to your other guests. Simple.

Back to decimal. Steve shows up. How much does each owe? $2.50 cents. So Steve pays up (Maybe he actually has the change, but unlikely cause if he had it, he bought a Mountain Dew with it!). How much do you return to your guests? Do YOU have the change? Uhhhh....

Dozenal is good if you have 2, 3, 4 or 6 people. And if there are changes of plan, its easy to resolve in those numbers. Its tricky if you have 5, 7, 9 or 11.

Decimal is good if you have 2 or 5 people, but tricky if you have 3, 5, 7 or 11. You are more likely to have a group of 3 or 4 than just 5 obviously. Dozenal has more strong points, but the same number of weaknesses. Dozenal is better.

Twelve rocks. That is why your clock goes to twelve. That is why we have twelve packs, and six packs which are half of twelve. (Can you imagine a five pack?) Twelve months on the calendar. Twelve inches in a foot.

Ten sucks. And realization of that fact is why America still refuses to go metric.

If only man had this guy's hands, everything would be different.

Don't forget about the kids!

All you have to do is use the lines on the inside of your knuckles, excluding the thumb. Look at you your fingers with your palm facing you. Three knuckle lines on each finger X four fingers = twelve. Use your thumb to mark where you have counted, or even the index finger of your other hand.

That is useful for keeping scores with two opposing players or teams. I use it when I have to keep score. One score on each hand, marked by the thumb.

I realized this independently. I thought it was my own original idea until I learned its fairly common in India, and ancient.

Don't know about why there's twelve in a foot, but there used to be ten months in the calendar, the other two were for Julius and Augustus Caesar.

I suppose you despise the seven day week then

I agree 12 is rounder than 10, but it's a hell of a lot of work to institutionalize. Gotta buy a new calculator, cell phone, keyboard, ruler, print new money... sounds great for the economy.

Correction. Extra months were added for convenience because 12 is better. The months were only named after those two, not added because of them.



Yes. A six day week with a four day work week and a two day weekend would result in more rest time. About 18 more days a year. BaddaBing!



Exactly. Think of the economy!

This may also be incorrect. According to Wiki, the Roman calendar already had twelve months before the Julian reform. The months were renamed by the Romans to honor the men after the Julian calendar reform. It is unclear whether the men themselves played any direct part in the renaming.

I don't know why I thought they were added. Sorry for the thread jack

What do you think of the hexadecimal system though?

I think hexadecimal is used a lot by engineers. Computer engineers and other kinds as well. All those letters next to numbers look funky, and I'm old enough that "funky" has a positive connotation.

I was just eating a burger at a bar. (Bars are good for estranged husbands). For tipping, I'm a 20% guy unless something goes spectacularly wrong. But, if we make the switch to dozenal, I think I'd rather do (base 10) 18% than 24%. I'm simply not ready to pay 24%.

I think they were added, but at a previous time perhaps? What I can tell you is that that information was there in Wiki somewhere. I am not seeing it now. Not sure what it means but it could be 1) on another page or 2) unceremoniously removed

And you are not threadjacking with that. Either way it demonstrates the usefulness of 12. Either the Romans used a ten month year and gave it up, or the usefulness of the 12 month year was immediately realized and note that they never went to a 10 month year (or back). Ten sucks.



If all you care about is powers of 2 it is freaking awesome. But since humans care about a lot more than that, 12 is more generally practical.

But if you wanted to pay 16 percent (duodecimal) the calculation won't be difficult. It would have the same degree of difficulty as paying 15 percent (base ten), and that is very common.

It would also be equivalent to paying 18 percent (base ten) (as you said), very close to the 20 percent you pay now.

Sagredo, I'm kind of hoping you'll chime in after your trip. I think the French have a weird way of saying, for example "99" -- only an American would say "neuf neuf" -- because of vestiges of an older number system. Vigesimal? Even though you're not French, maybe you can provide some of the historical European angle.

Well, I'm going to drink a pint now.

One more thing you have to notice about twelve. In English and German and I am sure other European languages too, We count in single words (no compounds) right up to twelve, as if it is the base already. It is not until thirteen that we start counting as if we passed the base, using "teen" as part of the compound. The numerals we use do not reflect that, but the words do. Its an interesting mystery as to why that is.

Or was. Another vestige is coins. British shillings. Metrification hasn't been around that long.

12 pence used to be a shilling. 20 shillings in a pound. 240 pence in a pound.

My time system has 12 hours in a day, so 1 of my hours is equal to 2 regular hours. A movie would be about one hour long.

The cool thing about that? The big hand of the clock always points to the sun. At twelve both the hand and the sun are at their highest. At six both are at their lowest. The sun is directly below you at that time. How is that for a sun dial?

There are 144 minutes to an hour and 144 seconds in a minute. This means seconds are fast. About 3 of my seconds in one second, like a fast heartbeat. But one of my minutes is about 50 seconds, so almost the same.

The coolest thing is that time can accurately be written as one solid number. 20903 or 2.06.03 would be the 2 o'clock 6 minutes and 3 seconds. If you start watching a movie at this time, and its 1 hour 2 minutes and 6 seconds long, it will be finished at 3.08.09. Just add them up.

Also, the clock directly corresponds to angles. 90 degrees would be come 30 degrees and minutes would have more importance. However, you could write them like decimal places, so easy to use.

Problems with the system are too many marks on the clock face. But this can be solved by just cutting out minute/second marks. Maybe only every third minute/second is needed. If you want only one minute, just watch the second hand. Otherwise count in three minute intervals, our current 2 min 30 seconds.

Interesting.
Zorro, you should annotate your numbers w/ base 10 and base 12 in your posts, but I think I get it.

This morning, I read some of the pdf from the dozenal society of the uk. They mentioned division and times tables. From what I've played with so far, it is easier both to multiply and to divide in dozenal.

Of course, this is all just a diversion for me. There's no way dozenal will overtake decimal any sooner than Esperanto will overtake English. But it's kind of fun to look at privately.

I'm curious about any new words you might have invented to make dozenal feel more comfortable.
And, when you're doing your movie time calc, is it a pain to convert back and forth? Do you use a calculator?
I've had a Binary Calc app on my ipod touch for years. It happens to also have base 3, 4, 5, and most others, all the way up to base 20. So, when I type in decimal digits I can instantly see the dozenal equivalents, even before I do any calculating. Both systems are displayed at once. Without it, I get lost quickly.

I'm off to buy a dozen eggs.

I pretty much used "my" to denote base 12 numbers according to my system. If I did not specify like that, the number was base 10.



Oh yeah. And the quirks are equivalent in number to base 10, so you will get used to them. Stuff like repeating decimals.



I am mostly taking a private interest as well. I also considered setting up a cult like group and to of course, employ my dozenal systems, among other things

But there are ways dozenal could overtake, but it will have to come by force or decree. Metric were not an instant hit among the masses either. I think the best way would be for America to make a new measurement system employing dozenal and institute it just to trump (and skip) metrics. I would sell it to Americans as America leading the world instead of bowing to it and metrics, and also hammer the economy point. Not only Americans, but other country's companies too would have to buy measuring devices using our systems in order to do business with us. And they will, and many of those will be ours, because we will be the experts of our own system. But the sales will have be something other than "dozenal is better", even though it is. You have to think politically, not mathematically.



I already mentioned expressing 14 (base 12) as "one doz(en) four", so you could just say "doz" (duzz) to express dozens. 38 (base 12) would be "three doz eight".

I can't recall if I made any others. I was serious about this years ago and have not dabbled in ages. I think I mostly recycled words. Other than that, my systems all bear my name, and as I choose to remain anonymous here, I cannot tell you that. But if my name were Boston, the systems would be called Bostonian. I also have my own alphabet and all the written letters resemble hand signs so it can all be signed easily, and its extremely phonetic.

If I remember any dozenal words I made, I will post them later. I might even dig into my old web page files. Yeah, I used to have a dozenal web page.



I did no conversions. I just avoided any number above ten.

The other time conversions, such as one second is about the same as 3 of my seconds was from memory. Actually one second is equal to 2.88 of my seconds, but 3 is close enough.

In order to give more complicated examples, we will have to come up with symbols for eleven and twelve. I usually use * for ten and & for eleven. I don't like to use A and B because when you see them you instinctively say "A" or "B". You have to fight to call those ten and eleven. You do not usually verbalize the symbols, so its easier to get your mind to verbalize them as eleven and twelve. It aids understanding of what they really mean if you are verbalizing them correctly in your mind.



Sweet! I am stuck with the windows calculator and pen and paper. I divide the paper into base 10 on one side and base 12 on the other so that I can double check figures. Sometimes I do the completely wrong thing, but if the numbers are side by side, I can sometimes see that one is off.



In Japan they sell eggs in ten packs. Metric fools!

In the works of J.R.R Tolkien, the elves are said to have used base 12. So that raises the question of whether there were a thousand caves at Menegroth or if it should be translated as 1728 (base 10) caves at Menegroth.

Or, was it already translated for us, and there were actually 6&4 (six hundred eleven doz four) caves at Menegroth?

http://en.wikipedia.org/wiki/Menegroth

Of course, I doubt it was ever meant to be a precise figure, but which is closer to the truth?

With that kind of talk, we're never going to get this thing mainstream.

I made a times table the other day w/ pencil on paper, and damned if it isn't a lot easier to learn than decimal.
For example, when you multiply 4 times other numbers, the product always ends in 0, 4 or 8. As def said, Base 12 is rounder.

Division of course is where the decimal-centric-named duodecimal system really shines, as in your example above, sharing among 3 or 4 friends.
Even though the world will never go dozenal, perhaps we can press for things to still be sold in six-packs and dozens. There's a real practical benefit from that.

By the way:
My weight is ~ 1 gross and 2 doz.
My height is 6 doz ( a "half gross" ), less an inch.
My age is 3 doz. & 2 or 32 base12 --- I'm miles away from 4 dozen, yay! Months: I guess 320 base12 (3 gross, 2 doz)