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Dozenal Can Be Phased Into Society

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Voting Style: Open Point System: Select Winner
Started: 5/14/2014 Category: Miscellaneous
Updated: 7 years ago Status: Post Voting Period
Viewed: 3,522 times Debate No: 53776
Debate Rounds (5)
Comments (13)
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Dozenal is a numeric system based on ten, not twelve

In decimal, as you all know, the digits are:

In dozenal, there are two more digits added in (dek and el)

The dozenal system behaves exactly like any positional number system. Except it is much better than decimal. I'm arguing that it can be phased into society because there is room for it on the ascii table, dek and el can be represented on a 7-segment display, and in general it's a more efficient system. Decimal representations are more compact than in decimal; for example 1/4 = 0.3, 1/3 = 0.4, 1/6 = 0.2, and these are much more common than 1/5. Also, it is a shame that we should have to be stuck with an uglier mathematical system such as one based on tens, when such a factor-dense number is only two away.

5 rounds, 118 characters.



This is my first debate, and I am excited to begin. First off, I assume that you are saying that all of society can transition from the base ten system into the dozenal system. I'll say first off that BILLIONS of people use the base ten system. Trying to convince that many people to use a system they have never heard of will take hundreds of years. Our current number system took thousands of years to spread. People are obviously creatures of habit. They will choose passwords that are the same for every account, and go to McDonalds for coffee in the morning everyday. Trying to break the habits of billions just seems plain unlikely.
Now, let me take an example from nature - us. We have ten fingers. The earliest human beings often used fingers to count, and children do too. It's an essential part of learning numbers, so if we were to phase to the dozenal system, would we all need to grow more fingers?
Does it really matter if it can be put into the ascii table or a 7-segment display? As humans, we modify things to suit our needs. Even if we did happen to transition into another number system, we would just modify things to suit that system. However, just because the dozenal number system works using things for the base ten system, it doesn't mean it's well suited for society.
You argue that the dozenal system has better decimal representations, and that our current system is "ugly." Ugly has many different meanings, and is based on opinion. What is ugly to you? You can't just go around saying "this is an ugly number system." That's absurd. Your arguments say that the dozenal system might be better in math, but this does not mean that it's likely to phase this whole system into billions of minds.

A bubble is round because it is most efficient. If a base-12 system is the most efficient, why haven't we transitioned to it yet? Some civilizations have tried it, but it hasn't worked out, has it? Or why would be debating this?
Debate Round No. 1


Thank you for accepting 7887082. I hope you enjoy your first debate.


First I will address the number of fingers the average human has. We would not need to grow more fingers, because the way that the hand is built is actually better better for dozenal, not decimal. The dozenal counting technique makes use of the twelve phalanges we have on each hand; here's the technique:

Hold your hands with you palm facing you. Use your thumb to count each phalange which you assign a value. You can use just your left hand, or you can additionally use your right hand to count up to (dec) 144 easily. Count on your left hand until you reach (doz) 10. Then move your right thum to "10". Then count from 1 on your left hand, this time you are counting 11, 12, 13, 14, 15, 16, 17, 18, 19, 1, 1. Continue until you reach (doz) 100 = dec (144). We don't need more fingers, ten fingers work fine for conting in dozenal.

The ascii table and 7 segment display are standards. We could make new ones, but then all our current technology would be incompatible with the dozenal ascii table and dozenal 7seg display. The fact that we can integrate dozenal with current technology means it's a viable transition. Also, computers do math in binary so they would not need to be redesigned either.

When I say dozenal is uglier, I can support it. Look at the representation of fractions in both systems:


1/2 = 0.5

1/3 = 0.333...

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1666...

1/7 = 0.142857...

1/8 = 0.125

1/9 = 0.1...

1/10 = 0.1

1/11 = 0.09....

1/12 = 0.083...


1/2 = 0.6

1/3 = 0.4

1/4 = 0.3

1/5 = 0.2497...

1/6 = 0.2

1/7 = 0.18335...

1/8 = 0.16

1/9 = 0.14

1/ = 0.12497....

1/ = 0.1...

1/10 = 0.1

Decimal has more repeating fractions, and longer decimal representations of fractions. Dozenal also does very well with the common 1/2, 1/3, 1/4, and 1/6. 1/5 simply isn't as common.

And lastly, our society already uses dozenal. Our clocks are based on twelves. Our computers are in hexadecimal. If we broke the habit before we can do it again.



First off, you cannot say that something is better because it is "less ugly." That is the same as saying "a cat is better than a dog because a cat looks better." It's based solely on opinion, and debates are won with facts and logic, not what a debater thinks. How are you to judge what is ugly and what is not?
You say that our hand is better built for a base-12 system rather than a base ten system. Let me make a simple comparison in the picture below.
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Your argument is that dozenal can be phased into society. How are children going to learn dozenal if its so complicated to count with something such as fingers? Children are not well adapted to have complex counting. Also, you can count in base 16 if you want on your fingers, pretty much any other base too. Ten is just the best suited. Is counting segments or fingers easier?

So you say that a 7-segment display could support dek and el, but you failed to acknowledge all the other devices, signs, books, etc. in the world that still use base ten. This would mean rewriting thousands of books, signs, and programs just to switch to a number system that supposedly has "better counting."

As for ugliness, you just contradicted yourself by saying in your first post "uglier mathematical system such as one based on tens," then saying that dozenal was ugly.
But I'll take it that you meant decimal. However, there will always be ugly fractions. Even in dozenal.
Here is an example. Don't say that they're rarely used, because they are still used. After all, the point of school is to learn everything (not literally, but a large amount) in a topic. It's no different then learning long base-ten fractions.

15 = 0.24972497... recurring (easily rounded to 0.25)

17 = 0.1868528523518685285235... recurring (easily rounded to 0.187)
1/ = 0.124972497... recurring (rounded to 0.125)
1/ = 0.11111... recurring (rounded to 0.11)
111 = 0.000000... recurring (rounded to 0.00)

Debate Round No. 2


"A cat is better than a dog because a cat looks better" used to imply "A is better than B", is a bare assertion fallacy. Dozenal is better than decimal because of quantifiable differences.
  • Of the reciprocal of the single-digit numbers in dozenal, there are 3 numbers with repeating decimals. Of the reciprocal of the single digit numbers in decimal, there are 4 numbers with repeating decimals. (points for dozenal)
  • Of the reciprocal of the single digit numbers in dozenal, there are 4 numbers with only a single decimal. Of the reciprocal of the single digit numbers in decimal, there are only 2 numbers with a single decimal. (points for dozenal)

This isn't a subjective comparison, it's an objective one. Repeating decimals are irritating because you can't represent them exactly after terminating. Since dozenal has less of them, dozenal is more practical. Cats and dogs don't invalidate this observation.

I cannot access your picture. But in response, I do not see what makes the dozenal counting system from my round 2 more complicated than counting on fingers. If you used just the left hand to count from 1 to twelve, for all intents and purposes the method is the same as counting from 1 to ten on your ten fingers as long as children have motor movements in their thumbs. Most, if not all of them do from about the age of 3. There's no difference but I invite you to try and pick out a difference.

Thanks for making the GOOD point, about how all our books, road signs and other printed goods are in decimal. The change can't happen overnight, but it can happen gradually. Start teaching it as an elective in schools, and have specially identified math books in dozenal. Then make an isolated town that has everything in dozenal, including road signs and grocery markets, for the dozenalists like me. Eventually, dozenal can spread like a virus to other communities based purely on it's superiority to decimal.

"There will always be ugly decimals in both systems" - then its a moot point.



In your whole argument, you have said that dozenal is better than a base-ten system, but you have given no proof to support it, except saying "ugly." I might add that there is a way to exactly represent repeating decimals, by putting a vinculum ontop of the repeating numbers.

\frac{1}{11} = 0.0909\dots = 0.\overline{09}.

You say that repeating decimals are irritating. That's still a subjective comparison as far as I know. Some like repeating decimals, some don't. Saying that dozenal is better because of one less repeating decimal and that it has two more numbers with a single decimal is completely ridiculous. I have to ask you to give actual examples of how dozenal can be useful in society, instead of giving biased opinions. So far, you have only given examples of how dozenal could be integrated with decimal technology, rather than giving examples of dozenal's supposed superiority.

As for counting... you can basically make your hand a way to count in any positional number system, including base twelve. Just notice however, that fingers are much more noticeable than phalanges, making base-ten counting obviously superior then counting little segments.

I'll give this example of switching to base twelve again.
Switching to dozenal is like replacing a working printer with another working printer, except the new one is the same, or broken, but it comes with more instructions and costs more. It's obvious to see that there's no point in switching, since dozenal isn't better at all.

Now, here is a question - spend probably more than a trillion, quadrillion perhaps, to go to a number system without proof that it is better, or just stay how it is. People are creatures of habit, only spurred when things are wrong. As far as I'm concerned, nothing is wrong with decimal. Dozenal is simply a novelty.
Debate Round No. 3


For this debate, we are taking it as a give that dozenal is better. Even if you don't think dozenal is better, you have to assume it for this debate. The resolution is "Dozenal Can Be Phased Into Society", not "Dozenal Is Better Than Decimal". Those are 2 separate debates.

Calling the viniculum an "exact" way to represent repeating decimals is an equivocation fallacy. If you tried to type out the decimal point notation of 1/3 = 0.333... to enter it in a computer, eventually you have to stop, say at 0.3333333. That's not exactly equal to 1/3.

"Saying that dozenal is better because of one less repeating decimal and that it has two more numbers with a single decimal is completely ridiculous". This is a ad hominem. You called the argument "ridiculous" rather than counter it.

As I explained before, being able to recycle decimal-based technology with dozenal implementation, supports the resolution. When a new idea can be realized with old technology, it makes the transition easier. Another example would be with stereo FM radio. Stereo FM waves can be received by a mono FM reciever. That meant radio stations could broadcast in stereo and all the old radios would still work. It's the same idea with dozenal 7seg displays. Whether the software is dozenal or decimal, every 7seg display can handle it.

Phalanges have advantages over fingers. Try to extend your ring finger straight out while keeping your pinky completely down. Impossible right? You don't encounter problems with phalanges because your thumb has full range to all twelve of them even, at the tip of your pinky. That's points for me; loss for you.

"It's obvious to see that there's no point in switching since dozenal isn't better at all." Again, in this debate we agreed that dozenal was better. The resolution is about phasing it into society. And the numbers that you pulled out of the air are an "argument from ignorance" fallacy.

Please attack my suggestion about making an isolated dozenal community. I was hoping you would.


I don't think you're seeing any of my pictures, use Chrome next time.

Let me say that if the discussion topic is Dozenal Can Be Phased, then whoever accepts it has lost from the beginning. After all, anything can be (verb). The question is if it's practical enough to actually happen. In your other debate, "God is Fake," you've already lost since there is no proof that he is fake, but none to prove his existence either. So, saying that would pretty much be a trap, therefore I take that the debate means if dozenal is practical enough to be phased.

You have misused vinculum - it can also be the line ontop of the repeating segment in a number, meaning that it repeats indefinitely, making it the same as a fraction.

"Except it is much better than decimal," is what you said. You have never said that dozenal should be presumed better until the fourth round, since you have been arguing that dozenal is superior to decimal the whole time before. It was said out of desperation, since you could not prove that dozenal is better. Also, one less repeating decimal and two more numbers with a single number IS ridiculous, due to the mass cost of changing, and the low payout.

Dozenal is obviously not practical due to the huge cost of changing almost anything that contains numbers, and with billions of electrionics worldwide, it would be foolish to replace them just to change to dozenal, since no country has the money to do so. Dozenal might fit on a display, but will anyone change the programming inside of devices one-by-one? And companies wouldn't mass produce, due to a loss of profits. Therefore your 7-seg display transition to current technology is impossible.

Fingers are also a way of communication. How would anyone demonstrate how many they wanted using phalanges? There are also other ways of counting in base ten too, therefore countering your arguments. (Picture below).

There's more to lose then what's to gain if society switches, making it an inadvisable choice.
Debate Round No. 4


I'm not the type of person to set a trap to win debates. That's a dishonest thing to do, in my opinion. It's hard to make the resolution say everything you want it to say, even if you have round 1 to expand on it. 7887082, you can also say that "Dozenal is practical enough" if you wish. Ideally, if we built society from the ground, dozenal would be the best number system, period. Since we have a Decimal society, I want to debate the viability of making the switch. So I hope that is clear.

With the veniculum, I ask you: how can you represent 1/3 EXACTLY if you have to use the decimal point format. Show me the decimal point representation of a number that is equal to 1/3 that I can enter as a floating point variable in a computer. If you cannot, then you committed an equivocation fallacy, simple.

There's more to dozenal than just "1/3, 1/4, and 1/6 only have one decimal point digit", and "there are less repeating decimal point representations". I don't have the space to get into it, but I assure you there is much more efficiency in that radix than there is with the radix of ten. The efficiency, in short, comes from the superior factor density. 12=2*2*3. 10=2*5. That doesn't look like much, but 12 has the factors 1, 2, 3, 4, & 6. Ten only has 1,2 & 5. It's easier to count by 3's or 4's or 6's. The times table is easier. The list goes on.

Sorry, on the 7seg display argument you made I'm going to have to point out another argument from ignorance. The way programming a device works, is you write the code once and it goes into thousands of ROM's in an automated factory. They won't mass produce because there's no market, but it's an easy change to make. It's like when Fruit Loops puts out the blueberry cereal every couple of years and they change the image on the back of the box. You like Fruit Loops right?

And even if we were a dozenal society, those hand gestures would still stand for "1,2,3,4,5". The phalange-method does not prevent finger comunication, does it?



It was a pleasure debating you, but our world is buried so deep in decimal, it's unlikely to change.

I'll try to represent it with text, since I can't find the symbol for the vinculum, and it seems you can't see my pictures.
Also, I think that your argument style is dropping things when checkmated, then fabricating things out of thin air, as I have conclusively proven many points wrong, and you have made no effort to combat that. You try to discredit your opponent by saying "argument from ignorance," or by calling things wrong, though it is actually you that is wrong.
.3 = 1/3 which is ~ .333

The line ontop of the 3 signifies that the 3 repeats infinitely, making it the same as 1/3.

This is a dozenal times table, and I'd say it's more complex, due to its larger size, 12x12. Memorizing a times table isn't exactly complex. It's the size, meaning there is more to remember.

Bakers and merchants adopted the dozenal system because of decent fractions and superior factor density, for things such as measuring. Though it might be good for certain crafts, our world revolves around decimal for its simplicity.

Let me note that ROM is difficult to modify, since it is "read-only memory." The software in ROM is usually not meant to be updated, the device is to be replaced, therefore meaning that recycling 7-seg displays is impossible without tedious work. The way you described is how the programming occurs when you make a device. If you change to dozenal, the programming will change as well, meaning that you cannot apply that method to changing the programming in the memory without hard changes. You're misinformed on how ROM works.

Note that there are still hand gestures needed for dek and el, so... unless humans evolve to all be double-jointed, I don't see us bending our phlanages in such positions any time soon.

Good luck.
Debate Round No. 5
13 comments have been posted on this debate. Showing 1 through 10 records.
Posted by sendttmail 6 years ago
I am also a supporter of base 12 for counting and for a new and improved system of weights and measure.
Check out the website,
Posted by BradK 7 years ago
I'm just commenting that I realize that the veniculum notation is mathematically equal to the fraction. So case in point 0.3BAR is equal to 1/3. I'm aware of that I just didn't have the character space to say.
Posted by BradK 7 years ago
I can see some of your pictures. You have to upload them to DDO then copy and paste, you can look up the procedure for it. Web browser doesn't matter as far as I know.
Posted by BradK 7 years ago
Also you are not allowed to place text in an image rather than typing it. The point of the low character limit is that it forces you to be concise. I have not addressed anything in the text picture, because it is not part of the debate.
Posted by BradK 7 years ago
oh god typo.

I meant to say DECIMAL was ugly, and DOZENAL was eloquent and beautiful. I accidentally said

"When I say dozenal is uglier, I can support it. Look at the representation of fractions in both systems:"

but i meant to say

"When I say decimal is uglier, I can support it. Look at the representation of fractions in both systems:"

I did that when I woke up this morning so I wasnt fully awake my apologies
Posted by nerosmoke 7 years ago
wtf the dozenalist sound like something un american
Posted by AlbinoBunny 7 years ago
Yes, dozenalists unite!
Posted by BradK 7 years ago
Sexagesimal would be great but as humans we just don't have the capacity to work with it in our daily lives. The multiplication table would be too big and it would take forever to memorize all the sums of 2 one digit numbers
Posted by tahir.imanov 7 years ago
But the best system is Sexagesimal.
Posted by tahir.imanov 7 years ago
I think, it SHOULD be phased into society.
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