The Instigator
Pro (for)
4 Points
The Contender
Con (against)
0 Points

Thinking In Base 12 Is Easier Than Thinking In Base 10, Disregarding Establishment

Do you like this debate?NoYes+0
Add this debate to Google Add this debate to Delicious Add this debate to FaceBook Add this debate to Digg  
Post Voting Period
The voting period for this debate has ended.
after 1 vote the winner is...
Voting Style: Open Point System: 7 Point
Started: 5/26/2014 Category: Society
Updated: 7 years ago Status: Post Voting Period
Viewed: 1,251 times Debate No: 55463
Debate Rounds (5)
Comments (8)
Votes (1)




In decimal, as you all know, the digits are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9

In duodecimal, the digits are (add a "dek" and "el"):
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ,


While it may sound foreign to you, here is one way to count in that system, vocally:

zen one
zen two
zen three
zen dek
zen el
twozen one
twozen three
twozen three
twozen dek
twozen el
threezen one
threezen two
threezen three
dekzen el
dekzen dek
elzen one
elzen el
gross one
gross two
gross el
gross zen
gross zen one
gross zen el
gross twozen
gross threezen
gross elzen el
twogross one
twogross el
twogross zen
twogross zen one
twogross elzen el
elgross elzen el
zau one
elzau elgross elzen el

and so on, you get the idea. The takeaway is that

12^1 = zen
12^2 = gross
12^3 = zau
12^4 = zyriad
7 = sep

I will be using these pronounciations for my debate.


By "disregarding establishment", I mean disregarding the conventions of society. Obviously we are all accustomed to thinking in decimal, and that's going to be easier BECAUSE it's what we are used to. But suppose we live in a theoretical world, where our previous conventions are irrelevant and we can learn to think in any way we want. I argue, that in that ideal world, we should think in twelves, not tens.


First round is for acceptance and stating whether you are a dozenalist or a decimalist, 2-4 are for arguments, and 5 is for summary. I myself am a dozenalist but use the decimal system because all you other chumps use it too.


I accept the challenge, and I am a decimalist.
Debate Round No. 1


My first argument will be that dozenal's prime factorization is better than decimals. 12=2*2*3, but 10=2*5. So the only numbers than 10 is divisible by are 2 and 5, while 12 is divisible by 2, 3, 4 and 6. That makes floating point representation of numbers easier in dozenal than in decimal. Case in point for the most common fractions:


1/2 = 0.5

1/3 = 0.333...

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1666...

1/8 = 0.125

1/9 = 0.111...


1/2 = 0.6

1/3 = 0.4

1/4 = 0.3

1/5 = 0.2497....

1/6 = 0.2

1/8 = 0.16

1/9 = 0.14

It's easier to think in a system that's more compact. Compression is what makes things easier to think about. That's why we invent so many acronyms for example. Rather than say "too much information", we condense it down into "TMI". And the reason is obvious, we are trimming off redundancy. Huffman coding is used to do this systematically, to find for example the shortest unique binary representation for each of 10 items on a list. Compression speeds up data processing.


My second argument is that the dozenal system can be designed to have a quicker pronunciation. That's why I went through the trouble in round 1 of spelling out each number up to one zyriad. If you have the number 127 in decimal, you have to say "one hundred twenty seven", which is seven syllables. In dozenal, you would only have to say "gross twozen sep", which is 4 syllables. In general, "gross" is one syllable and "hundred" is two syllables, so that speeds up the speaking time. "Zau" is less syllables than "thousand". The most common numbers that are spoken are typically 4 digits. Note that there is no standard way to pronounce numbers in dozenal, but since it's still in the drawing board stage of conception, we can assign pronunciations that are calculated to be more efficient than decimal pronunciations.

Why do we care about how long it takes to pronounce something? For the same reason as above: compression. The less time your brain has to spend telling your voice how to create the syllables, the more time your brain has to do actual computation with the numbers represented by the syllables.


My third argument is that grouping things in twelves is more symmetrical than grouping things in tens. The way we represent time is in based on twelves, because of how much easier it is to divide up the day. The French tried to create a decimal based clock, but it didn't catch on because it was worse than the clock that was already in use that was based on twelves. The 10-hour (or 20-hour) day failed because the 12(2)-hour day was just more convenient and easier to work with.

You also commonly see eggs sold by the dozen, and pizzas sliced by the dozen. You buy doughnuts in groups of 6 or 12 because a box 5 by 2 units long is not as sturdy or convenient as a box 3 by 4 units long. When dealing with radians, many common angles are integer multiples of 2pi/12 radians, but ugly multiples of 2pi/10 radians:

30 degrees = (2Pi)*[1]/12 rads = (2Pi)*[5/6]/10 rads

60 degrees = (2Pi)*[2]/12 rads = (2Pi)*[5/3]/10 rads

90 degrees = (2Pi)*[3]/12 rads = (2Pi)*[5/2]/10 rads

45 degrees = (2Pi)*[3/2]/12 rads = (2Pi)*[5/4]/10 rads

But all of the common angles have better radian values when 12 is the denominator, than when 10 is the denominator.


Those are the 3 arguments I'm putting forth to start. To summarize, dozenal gives a more compact form than decimal, and no one wants large, stupid, clunky ways to represent their numbers. This is everything I wish to say for round 1.



AROD180 forfeited this round.
Debate Round No. 2


What is it with people forfeiting debates? Don't accept if you don't want to debate it.


AROD180 forfeited this round.
Debate Round No. 3


There are arguments you can use in THE COMMENTS.

I'm calling it right here. Con chickens out of the next 2 rounds.



AROD180 forfeited this round.
Debate Round No. 4


This was Con's strongest argument:

"I am a decimalist."

He did not support it however, at all. So I think I win.


AROD180 forfeited this round.
Debate Round No. 5
8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by GibbyCanes 7 years ago
And to edibleshrapnel, Mensa is a high IQ society not a math society. Some of its members didn't even finish high school. Also you're*
Posted by GibbyCanes 7 years ago
The problem with just the concept of this argument is that a duodecimal system has the same number names. The symbols change, not the English words. In fact, that is sort of the point:

The number symbol "10" would represent the number word "twelve." Thus 100 = One hundred forty four, 10/3 = 4, 10/4 = 3, etc. The usual "Ten's Place" becomes the "Twelves Place" and the "One Hundred's Place" becomes the "One Hundred Forty Fourth's" place.

Changing the number names would mean you are no longer using elements from the set of all real numbers, it would be it's own set of elements with it's own properties and mathematical operations, and those properties would all have to be proved, and the entire set would be useless because all of the benefits of a duodecimal system are based on prime numbers and factors, which are concepts that are drawn from real numbers.
Posted by BradK 7 years ago
Sorry to hear you were interested in this one.

I actually lean very personally towards my side in the debate, so I was interested to hear if people could come up with any counter arguments.

Some of the ones that I can think of in favour of con would be:

-in base ten, 10 log_10 (2) = 2.98 ~=3. In other words, doubling the signal power is the same as adding rougly 3 decibels. It's only an accident of using base 10, that doubling the power of a signal results in a decibel value VERY close to an integer (or in other words, halving the signal power is the same as subtracting 3 decibels) .... however in base twelve, 10 log_10 (2)=3.42 dB. So when people talk about the 3dB point in base 10, they are talking about the uglier 3.42 dB point in base twelve. That's an argument in favour of con.

-in base ten, the powers of two happen, by accident, to show this pattern:
2^9 = 512
2^10 = 1024 ~= 1000
What that means is that say you have 2^6 which is 64. 2^16 is about a thousand times more than 64 (when you work it out it's 65536, close enough. Often memory is rounded off, say in this case, to 64 kB)
in base twelve, 2^10 is NOT close to any power of 10. It is actually 2454. We can't round that to anything close to a power of the base because it's too far away. People who make memory would not be able to easily say "64 kB" or "64 GB", because no such unit conversion exists. It's for the same reason you can't say "there are about 120 inches in a yard"; it's actually 36. It just doesn't convert that way. So base ten is also better for working with powers of 2.

So those are two arguments that my opponent could have used against me, if he had not forfeited. Seeing as how the debate is still ongoing though, he can use them if he comes back from quivering in the bushes.

I am not sure how he could have countered the 3 arguments I put up initially though. I'm not gonna try to counter them yet haha.
Posted by SeventhProfessor 7 years ago
It's so annoying. A lot of people come to the website for a day, accept a few debates, and never return. I'll be voting in your favor, and was really looking forward to this debate.
Posted by BradK 7 years ago
He'll forfeit the whole thing now watch.
Posted by Logi 7 years ago
I think the strategy here will be to entrap one's opponents in one's nonsensical language lol.
Posted by BradK 7 years ago
..No it's not mensa. It's just using different names for powers of 12, the same that you use for powers of ten

10^1 = ten
10^2 = hundred
10^3 = thousand
10^4 = ten thousand.

Same thing, different numbers and words.
Posted by edibleshrapnel 7 years ago
Dude, your really confusing. Is this like Mensa math stuff? Looks complicated.
1 votes has been placed for this debate.
Vote Placed by Anonymous 7 years ago
Agreed with before the debate:--Vote Checkmark0 points
Agreed with after the debate:--Vote Checkmark0 points
Who had better conduct:Vote Checkmark--1 point
Had better spelling and grammar:--Vote Checkmark1 point
Made more convincing arguments:Vote Checkmark--3 points
Used the most reliable sources:--Vote Checkmark2 points
Total points awarded:40 
Reasons for voting decision: Forfeit.

By using this site, you agree to our Privacy Policy and our Terms of Use.