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The Contender
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The duodecimal system should be used in society rather than decimal.

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Voting Style: Open Point System: Select Winner
Started: 3/13/2017 Category: Education
Updated: 10 months ago Status: Post Voting Period
Viewed: 467 times Debate No: 100876
Debate Rounds (2)
Comments (15)
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The duodecimal (or dozenal) system, or base twelve, is superior to decimal, or base ten, for a number of reasons. Ten has only 2 and 5 as non-trivial factors. Twelve has 2, 6, 3, and 4. Thus, elementary fractions such as 1/2, 1/3, 2/3. 1/4, and 3/4 all have convenient duodecimal represenations, being 0.6, 0.4, 0.8, 0.3 and 0.9, respectively. This gets rid of problems of repeating numbers that would be encountered particularly with 1/3 and 2/3 in decimal. This means common fractions will be easier to understand in day-to-day use.

For these reasons, I can confidently say that dozenal notation is an objectively superior numerical system than base ten. I have included YouTube videos with explanations of the Base 12 numberng systems for more information and for those curious.


So, the duodecimal system superior to the decimal system? I will have to admit, I'd never heard of it before, but a large number of my criticisms are also of the use of hexadecimal (base-16) system per standard, and therefore can be applied to here as well.

While I do think the concept of not having to write 1/3 as.33333333333333333333333 so on and so forth is appealing, there are numerous issues mathematically and economically to consider. Contrary to popular belief, adding more values to a base point doesn't mean "10" is still written as ten - rather, new characters that take one slot are necessary, so "10" in decimal would be "A" in duodecimal, hexadecimal, or any other "over-decimal" system. Complete integration would require "A" be replaced with a proper, unique character requiring updating of international (or even simply national) keyboards immediately to fit the ruling. With non-decimals in their current seldom-used form, the letter replacements work simply because we don't see them often enough to make them a problem.

Furthermore, you claim 3&4 denominators would have even decimals, but this point is moot because of denominator 5, which would have repeating or irrational decimals due to 12 not evenly dividing by 5 (2.4 in decimal form). The numeral benefit, then, is void because the idea of repeating decimals never disappears. (Oh, and by the way, 1/4 is .25 in decimal and I don't know why that is hard to grasp.)

Now for a massive kicker - economics is hard enough across borders, what with currency exchanges and what have you. Adding in a change in base on top of that would make Value calculations exceedingly more difficult than they already are. Furthermore, the likelihood the entire world would agree to this new base is slim-to-none. People are notoriously difficult to convince that a new form is somehow better than an old form of the same thing, even if benefits could be staring them dead in the face. Coins (like the nickel and the quarter) would have values rehashed compared to a whole "1" dollar, with quarters now requiring 5 to make a dollar and nickels requiring 125. (Let's just not talk about pennies, that's a debate of a whole different contention.) Converting these back into any currency of the base-10 form would leave us with those trailing threes again, in the proper proportions.

Also, all equations and formulas in the major sciences would have to be reworked and rebuilt for this new base, rewritten, and reissued. A Value of "12" in decimal would have to be written as "10" base-12, and a Value like Avagadro's number "6.02 e24" would have to be recalculated and found in terms of base-12 - which isn't a simple process, as calculations based on the number would have to be checked to ensure they still work.

Simply put, I think you posted this debate without fully thinking through the implications that the swap could entail.
Debate Round No. 1


I'd like to welcome my opponent to the debate and commend them for defending the decimal system- in my opinion, a tough job. I've read some very intelligent arguments on their part, and I'm glad to debate. I'd like to start by addressing some of their arguments.

Argument 1:
Right off the bat, I'd like to mention something my opponent says,
"Contrary to popular belief, adding more values to a base point doesn't mean "10" is still written as ten - rather, new characters that take one slot are necessary[...]"
This is partially correct. This would require both ten and eleven to have their own digits, but this is not "contrary to popular belief" at all! How on earth would base twelve function if this weren't true? This isn't even much of a problem. My opponent says unique characters would be necessary with updates to keyboards. Absolutely. Unicode Points 218A (U86;) and 218B (U87;) are proposed dozenal notations for ten and eleven, respectively. Since these are already Unicode characters, the only thing necessary would be updates to keyboards. Admittedly, adding two buttons and replacing keyboards would not be ideal, but the software is already in place.

Argument 2:
My opponent points out that denominator 5, in dozenal division, results in repeating decimals. Admittedly, this is true. Repeating decimals are not eliminated by dozenal. However, I have a question for my readers and my opponent: do you encounter thirds and quarters, or fifths and sevenths more often in your daily life? In financial calculations? Factors of three (which include six and twelve) are more commonly encountered than factors of five.

Argument 3:
My opponent makes a valid point- if we assume base twelve is suddenly imposed upon everyone, yes, this would be nigh impossible. However, this is not how new ideas spread. In this case, the spread of duodecimal might look something like this:
The dozenal movement becomes popular in isolated places around the world. At the local level, it begins to be taught alongside decimal in schools. People growing up learning both systems mostly adapt to decimal, but usually prefer duodecimal casually. Some begin to enter into local and regional politics. Worldwide acceptance of duodecimal grows. Eventually, more and more parts of life are in duodecimal, and governments naturally change. Some would perhaps stick to decimal the way the United States doesn't adapt to metric, but most realize the potential.

I would also like to commend my opponent for this brilliant quote: "People are notoriously difficult to convince that a new form is somehow better than an old form of the same thing, even if benefits could be staring them dead in the face."

I very much agree.

Argument 4:
I think my opponent overestimates the complexity of the task of formula conversion. There is actually a general conversion algorithm, and computers can do these conversions rather quickly.

Now, let's consider the benefits of base twelve. As previously mentioned, twelve has more factors than ten, making division easier. The dozenal multiplication table has more easily memorable repeating patterns than the tens, including multiplication by 3, 4, 6, 8, 9, and 12 (twelve). Mathematics becomes easier on a day-to-day basis, learning math becomes more interesting for children, and mathematicians can discover new interesting patterns that come with working in dozens. Simply put, duodecimal is more efficient, more interesting (although that is subjective, 12 is a supreme highly composite number and has been commonly used for measurements and money throughout history), and easier than decimal.

Once again, I thank my opponent for debating and look forward to their final response.


Thank you for welcoming me to the debate, and for the complements on my previous statements. I'll cut straight to the chase however.

Argument 1: My opponent poses the question, in regards to base twelve functioning without unique digits, "How on earth would base twelve function if this weren't true?" The problem here, as I mention in my previous argument, is that duodecimal/hexadecimal use temporary monikers: "A" (Decimal "10") and "B" (Decimal "11") to represent what Unicode 281A/B [1] are intended for. As I stated in the original argument, "With non-decimals in their current seldom-used form, the letter replacements work simply because we don't see them often enough to make them a problem." While I still stand by that argument, I will say, in my opening sentence, I may have overestimated how few people knew about non-decimal form, thinking it a "secret" between computer gurus and math nerds mostly. I will thus redact "Contrary to popular belief," on account that I don't have an actual source to back myself up in that regard, just a logic path apparently false. However, I do want to comment on the current shape of 281A/B - in my opinion, they look close enough to "2" and "3" to be easily confused for one another, especially in handwriting. This opinion also holds true in comparing them to "5" and "E". Whether this can be considered a true "argument", I will leave up to discretion.

Argument 2: In answering your questions - I encounter mostly fourths and fifths in my day-to-day. However, the true answer to this is circumstantial and therefore potentially irrelevant to the conversation at hand. In financial calculations, however, given current values of American currency coins: .01 (penny), .05 (nickel), .10 (dime), .25 (quarter), .50 (half-dollar) and 1.00 (silver dollar/dollar bill), it stands to reason that fifths are again fairly common at .20, .40, .60, and .80. How true this really becomes in the actual mix, again, varies rather significantly depending on what coins are used in what proportions. However, in any proportion, halves, fourths, and fifths are all common, with rare chances at rough thirds (.33, .66). Decimal is the only "simple" system that caters to all three of these to the second decimal place, which is commonly used as the end-point of monetary values (of course, hundreds, and anything ending in a "0" would technically fill the requirements, but they aren't truly "simple", as there are multiple stages to breaking these forms back into prime, while "10" immediately breaks into "5" and "2", both of which are prime). I also would like to point to the concept of "places" or the numeric value each proceeding number would have in a complex integer, in which decimal has ones, tens, hundreds, so on and so forth in exponents of ten, while duodecimal would have ones, twelfths, hundred-fourty-fourths, so on and so forth in exponents of twelve. Ten is an easier number to multiply exponentially than twelve, as such is easier to do by hand.

This also seems to be a good spot to insert an argument I had not considered upon building my original set of statements, that being SI, or metric, units. These are based off the concept of moving up and down measurement accuracy by moving a decimal up or down the number. With numbers having different place-values, measurements in metric would have to be reworked somewhat to correspond - for example, there would have to be twelve decimeter marks on each meterstick rather than ten. Therefore, each individual decimeter would have a slightly different physical value (distance the measure actually covers, in this case) from decimal. This would require a slight hump in learning metric, but nothing drastic.

Argument 3: While I noted this as the "big kicker", this could very readily be determined to actually be my shakiest argument. The first segment we covered above - that being the actual economics. I still stand that duodecimal would have a hard time establishing in currencies, especially through the "slow ascension" method my opponent describes. In fact, through this method, some miracle of timing would have to occur to even give it a chance, as a single country applying this would be scorned on the global scale - made a laughing stock of, and duodecimal would recede into obscurity once more. At least two would be simultaneously necessary to get duodecimal's "foot in the door", so to speak.

Argument 4: I touched on the counter here up in Argument 2, which, admittedly, my response to is rather long. I think I have covered the argument well enough up there.

As a final note, I want to cover the "sexagesimal" system mentioned in the comments, in regards to clocks. Sure, taking "min." and "sec." as individual places themselves breeds base-60, however, it feeds into either base-12 or base-24 depending on the clock. From there, base-7, base-4, and base-12 before resetting. Clocks don't have a "metric base".

Thanks again.

Debate Round No. 2
15 comments have been posted on this debate. Showing 1 through 10 records.
Posted by whiteflame 10 months ago
>Reported vote: FuzzyCatPotato// Mod action: Removed<

7 points to Con. Reasons for voting decision: Con's arguments about transitioning from current decimal systems (keyboards, SI) and about the relative prevalence of certain decimal-favorable fractions show both that the transition would be hard -- perhaps impossible -- and that the benefits would be negligible or negative.

[*Reason for removal*] The voter is required to specifically assess arguments made by both debaters. Assessing only Con"s arguments is not sufficient.
Posted by Sensorfire 10 months ago
That's only because of learned bias towards the decimal system. That would be irrelevant to someone growing up using duodecimal.
Posted by SteveHeist 10 months ago
I was accounting for finding the immediate value of the next place over. In one's head, ten is easier to multiply than twelve, so it's easier to find a set of values. 1, 12, 144, 1728, so on and so forth is harder to do in one's head.
Posted by Sensorfire 10 months ago
Right. One gross. 1-0-0. The one represents one gross, the first zero represents no additional dozens, and the second zero represents no additional units. In dozenal, 10 (one dozen) * 10 (one dozen) = 100 (one gross). 10 (one dozen) * 8 (eight units) = 80 (eight dozen). Exactly as easy as multiplying tens in decimal.
Posted by SteveHeist 10 months ago
Not quite, Sensor - the numeral itself would be 100, yes, but the value the "1" represents is not 100 of something, but rather 144 of something, so it sits in the "hundred-fourty-fourths" place, or 12^2.
Posted by Sensorfire 10 months ago
The debate is over, so this doesn't count for anything, And I don't expect voters to take this into account. But con said, "Ten is an easier number to multiply exponentially than twelve, as such is easier to do by hand." Not in base twelve, in which 12 would be 10 and 24 would be 20 and 144 would be 100.
Posted by SteveHeist 10 months ago
Yes, I am aware of a few linguistic fubars in my statements:

Firstly, in Argument 2, I list ".66" as a rough third, when proper rounding would be ".67".

Secondly, ignore "In fact," on Argument 3, or replace with "In theory,", if need be. Bad wording on my part.
Posted by SteveHeist 10 months ago
Oh, sorry - I guess I hijacked it without looking at comments :P. Just figured it was something I could debate without drowning from the get-go, and no one else had taken the mantle.
Posted by Capitalistslave 10 months ago
Damn, I got back to this debate way too late. I wish there was a notification on the site for when someone else comments on a debate you've commented on. Email just doesn't do it well enough for me. I'm more likely to check notifications on here than notifications from my email.

Oh well, you got to debate the original intent of this debate, which was for someone to defend the decimal system. Maybe that's for the best.
Posted by Fourth_Right 10 months ago
I would have accepted that debate, but I would have been arguing in bad faith since I'm on your side.

Cheers though, I'm looking forward to wherever this goes.
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