Thinking In Base 12 Is Easier Than Thinking In Base 10, Disregarding Establishment
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after 1 vote the winner is...
BradK
Voting Style:  Open  Point System:  7 Point  
Started:  5/26/2014  Category:  Society  
Updated:  3 years ago  Status:  Post Voting Period  
Viewed:  811 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: one two three ... sep eight nine dek el zen zen one zen two zen three ... zen dek zen el twozen twozen one twozen three twozen three ... twozen dek twozen el threezen threezen one threezen two threezen three ... ... dekzen el dekzen dek elzen elzen one ... elzen el gross gross one gross two ... gross el gross zen gross zen one ... gross zen el gross twozen ... gross threezen ... gross elzen el twogross twogross one ... twogross el twogross zen twogross zen one ... twogross elzen el threegross ... elgross elzen el zau zau one ... twozau ... elzau elgross elzen el zyriad ... 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, 24 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. 

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: Decimal: 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... Dozenal: 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 10hour (or 20hour) 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. 

What is it with people forfeiting debates? Don't accept if you don't want to debate it. AROD180 forfeited this round. 

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. 

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. 
1 votes has been placed for this debate.
Vote Placed by Enji 3 years ago
BradK  AROD180  Tied  

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Total points awarded:  4  0 
Reasons for voting decision: Forfeit.
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.
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.
10^1 = ten
10^2 = hundred
10^3 = thousand
10^4 = ten thousand.
Same thing, different numbers and words.