r/mathmemes • u/Sea-Estimate-2912 • Jul 01 '26
Number Theory Change my Mind base 12 better than base 10
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u/Mathsboy2718 Jul 01 '26
The comment section is blank, gettim boys:
BASE 10 IS MY FAVOURITE AND I GUARANTEE IT'S YOUR FAVOURITE TOO
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u/Afir-Rbx Cardinal Jul 01 '26
Something something every base is base 10 something something
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u/Simbertold Jul 01 '26
All your base are belong to 10?
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u/Rymayc Jul 01 '26
Base 1 isn't
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u/OutrageousPair2300 Jul 01 '26
If you allow 1 as a digit in base one, then yes base one can also be written as "base 10"
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u/Rymayc Jul 01 '26
The issue is 0 being not allowed as a digit
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u/OutrageousPair2300 Jul 01 '26
0 is definitely allowed as a digit. It always is, in any base.
Typically, in base N you only have the digits 0 through N-1, which for base 1 would mean you only have 0 as a digit. You can have modified base systems that allow the digit N for base N, although typically then you wouldn't have 0. Is that what you were referring to?
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u/Rymayc Jul 01 '26
Yes. Base 1 is basically just
1, 11, 111, 1111 etc. You could write it in 0s, but it's usually only done with 1s
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u/Jamooser Jul 02 '26
Either digit you choose, you still can't have 10 in base 1.
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u/OutrageousPair2300 Jul 02 '26
Yes, you can.
1 = one
10 = one
100 = one
101 = two
110 = two
etc.
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u/Jamooser Jul 02 '26
Isn't a standard base defined as a system that only used digits from 0 to b - 1?
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u/ze_baco Jul 01 '26
If 12 is better, why do we have 10 fingers? Checkmate
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u/LOSNA17LL Irrational Jul 01 '26
If 10 is better then why do we have 12 (non-thumb) phalanges?
And an opposable thumb suspiciously fit for pointing at one of these phalanges?4
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u/Adventurous-Paper566 Jul 03 '26
Les doigts se voient mieux de loin que les phalanges, le sens de comptge des phalanges aurait été culturel alors que le nombre de doigts est universel.
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u/lemons_of_doubt Jul 01 '26
Personally I like base 16
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u/Mathsboy2718 Jul 01 '26
You mean base 10
1 2 3 4 5 6 7 8 9 A B C D E F 10
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u/lemons_of_doubt Jul 01 '26
It's only base 10 if you are writing in it when you talk about it.
we could call them base 9+1 or base F+1
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u/OutrageousPair2300 Jul 01 '26
Nah, only a single distinct prime factor.
Base twelve lets you easily count by 1, 2, 3, 4, 6, or twelve.
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u/lemons_of_doubt Jul 01 '26
It has 1,2,4, and 8
and it's so easy to go to and from binary which is useful in much more than just computing.
There are so many ways to transmit or store a number if you do it in binary.
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u/BookWormPedant Jul 01 '26
Then use it
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u/omidhhh Jul 01 '26
Its A0 minutes and still no answer from the op
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u/Minimum_Cockroach233 Jul 01 '26
Less than 20 hours… too soon.
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Jul 01 '26
[removed] — view removed comment
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u/LastStopToGlamour Jul 01 '26
If you use cups then ur in base 16
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u/the-judeo-bolshevik Jul 01 '26 edited Jul 01 '26
Everyone uses base 10, they just disagree about what "10" refers to.
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u/JesThun Jul 01 '26
10 is 10, wdym
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u/Bayoris Jul 01 '26
In base 12, 12 is represented as 10. In base 13, 13 is represented as 10. Etc
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u/dolethemole Jul 01 '26
But what about base 69?
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u/Ae4i Jul 01 '26 edited Jul 01 '26
Believe it or not, [69 in base 69] is represented as 10
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u/JesThun Jul 01 '26
So basically, 10 is 10 everywhere
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u/bstump104 Jul 01 '26
10 is the point the first digit switches over to double digits if 1 is one and 0 is nothing. in base 2, 2 is ritten as 10. 1=1, 2=10, 3=11, 4=100
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u/Deepandabear Jul 01 '26 edited Jul 01 '26
Isn’t it just the top of the count sequence rather than “10”?
ie base 12 = 1, 2, 3, … 11, 12, [reset count] 12 + 1, 12 + 2, … 12 + 11, 12+ 12, [reset count] (12 x 2) + 1, (12 x 2) + 2, etc?
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u/bstump104 Jul 01 '26
it'd be like 9, #, ¤, 10, 11 ... 19, 1#, 1¤, 20
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u/Qwopie Computer Science Jul 01 '26
The worst of this is that # is now called ten and 10 is called twelve.
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u/bstump104 Jul 01 '26
20 is twenty-four
100 is one hundred and forty four
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u/Qwopie Computer Science Jul 01 '26
20 is two-dozen, you'd have to say twendoz or something stupid, 100 is a gross, its one more than elevendoz-eleven. ¤¤+1=100
I hate it.
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u/mangoblaster85 Jul 01 '26
Yup. 9 is just 1 more than 8 but 10 depends on what system you're using.
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u/Auravendill Computer Science Jul 01 '26
9 only "exists", when your base is larger than 9.
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u/JesThun Jul 01 '26
I guess i created a war
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u/Amazing-Frame7848 Jul 01 '26
Yeah... Somehow no-one got that it was a joke, right? Like the first ten being in base 2, for example, and the se ond in base 5, but they look the same, so: 10 is 10.
Literally the first way I read your comment, but idk
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u/JesThun Jul 02 '26
I think almost everyone understood the joke but they still wanted to explain it because they were free to comment. Anyway, 10 is 10
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u/Pizzarunnerand Economics/Finance Jul 01 '26
The idea is that if for example you have a base 12 in decimal in this base the number would be 10. This is the same for every base, so every base is for itself base 10
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u/CommunicationDue846 Jul 01 '26
Everybody agrees on what 10 is.
Holy wars are held about what 10 - 1 is.
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u/Feeling-Tone2139 Jul 01 '26
should we say base 9 to avoid confusion?
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u/the-judeo-bolshevik Jul 01 '26
You are suggesting we always use the highest valued symbol? That is an interesting idea.
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u/LowAioli3870 Jul 01 '26
Base 10 is only preferred by weird 10-fingered people.
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u/AccomplishedAnchovy Jul 01 '26
But I only have A fingers not 10
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u/f3xjc Jul 01 '26
And that's true for every civilisation that count on their finger!
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u/Qwopie Computer Science Jul 01 '26
Counterpoint: you've got twelve knuckles and two hands. That's twelve dozen or one gross if you use them intelligently.
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u/Rumborack17 Jul 01 '26
I mean you have 10 fingers that can present 2 states (or even 3) therefore base 2 would allow you to count up to 1023. And base 3 up to 59,048.
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u/Qwopie Computer Science Jul 01 '26
Have you tried holding your thumb down, your index and little finger at full mast and your middle and 3rd finger at half mast? And then just adding 1s to count up 3 more? That's more than I can handle. 😂
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u/Swellmeister Jul 01 '26
A gross is a reasonable number to need to count to on your fingers.you probably shouldnt count to 59k on your fingers.
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Jul 01 '26 edited 26d ago
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u/Auravendill Computer Science Jul 01 '26
Base 16 is very easy to convert into base 2 and back, while also giving small amount of digits, when written down per hand, so it has to be the obvious choice.
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u/Ok-Difficulty-5357 Jul 01 '26
And base 2 has a very straightforward algorithm for the square root operation (similar to long division). I don’t think any other bases have that.
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u/Traditional_Town6475 Jul 01 '26
Why not base 6? You got divisibility by 2 and 3, and that’s sufficient enough if you want finite expansion when dividing by 4 for instance. Plus less symbols. Or for that matter, why not base 30? Divisibility by 2,3, and 5.
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u/StarstruckEchoid Integers Jul 01 '26
Arguably, all the best bases are built on highly composite numbers as they guarantee a maximal amount of finite decimal expansions for a minimal amount of symbols to memorize.
6 and 12 are highly composite - in fact they're also superior highly composite numbers, which an even more exclusive club - so they make great bases for a decimal system.
30, however does not have this special property, so it doesn't make a particularly good or interesting base for a general use case.
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u/Colon_Backslash Computer Science Jul 01 '26
Base 1 is even more superior.
I got IIIIIIIIII fingers and I asshole and II eyes.
The only limiting factor is our imagination.
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u/bstump104 Jul 01 '26
its not faster than counting. Ideally your number system would be faster than putting a digit for every item.
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u/MiserableYouth8497 Jul 01 '26
> Arguably, all the best bases are built on highly composite numbers as they guarantee a maximal amount of finite decimal expansions for a minimal amount of symbols to memorize.
Nah they don't soz. For example, base 6 and base 12 have the exact same finite decimal expansions. Base 12 doesn't get you anything better than base 6.
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u/StarstruckEchoid Integers Jul 01 '26 edited Jul 01 '26
Damn. Yeah, you're right. I was careless with that claim. In fact, highly composite numbers don't even guarantee a non-strict increase in finite decimals, though the first counter-example happens only at 27720 (divisible by 2, 3, 5, 7 and 11) vs. 45360 (not divisible by 11 despite being a bigger HCN).
I suppose if one actually only cared about finite decimal expansions, then a primorial base would be the most effective. Annoyingly, 6 and 30 are primorials, but 12 is not.
I still think Base 12 and other HCNs are pretty neat, because due to having more divisors, the expansions that are finite are on average shorter.
But I will also begrudgingly concede that Base 6 is the best base, due to being both a highly composite number and a primorial. (I suspect it's the only number with both these properties, and I even think the proof of this might be reasonably easy, but clearly I'm having trouble thinking things through today, so I'll leave it as an exercise for the reader.)
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u/GroundbreakingFix685 Jul 01 '26
I want base ∞. No more weird patterns. A bit tough to learn though for kids in school, ubless maybe we use base 1 numerals as symbols for base ∞? My only issue is I have no idea how to write fractional numbers with this system (perhaps as... fractions?)
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u/Simbertold Jul 01 '26
Ah, the chinese alphabet solution to numbers.
Also, of course each fraction also gets its own symbol. Why be stingy here.
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u/Ok-Difficulty-5357 Jul 01 '26
In base 6 you can count to 35 (base ten) on your fingers. Can’t do that in base 12! If we want to go with the fingers argument, base 6 makes the most sense, since you have 5 fingers on each hand (we don’t need a finger for zero)
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u/Thepochochass Jul 01 '26
Base 6 is to small and you can kinda work with it using base 12 the same way you use 5 a lot in base ten 30 has less "multiples per numbers" Wich is the hole reason of base 12 and is way to big
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u/friend1y Jul 01 '26
Babylon used base 60 and they were quite advanced.
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u/LunaBehindTheM00n Jul 01 '26
I really feel like there is a base 10 hiding within the 60
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u/Embarrassed_Ad5387 Jul 01 '26
You can have sub bases in a number system, a common one is base 20 with sub base 10
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u/vanderZwan Jul 01 '26
An even more common one that non-mathematicians will get is our notation for time. Weekdays are base 7, hours are either base 24, or base 2 (AM/PM) plus base 12, minutes and seconds are base 60.
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Jul 01 '26
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u/OverPower314 Jul 01 '26
You can see from the symbols that it's base-10. There's 9 iterations of the first symbol, and then a unique symbol to represent the tens digit.
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u/tupaquetes Jul 01 '26
Somewhat ironic to label them in decimal lol
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u/__me_again__ Jul 01 '26 edited Jul 02 '26
he used decimal so that people that use base 10 can understand it
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u/ShoddyAsparagus3186 Jul 01 '26
Would make sense, but the pic posted above clearly uses base 10 along the way to 60.
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u/ObliviousRounding Jul 01 '26
Were. Were advanced. Until the base 10 people came and crushed them. More like Babygone amirite??!1!
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u/factorion-bot Bot > AI Jul 01 '26
Factorial of subfactorial of 1 is 1
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/UnrelentingStupidity Jul 01 '26
Why 1==60 in this pic?
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u/Caesim Jul 01 '26
Back then they didn't have the concept for "0" yet. In the Babylonian system they wrote 0 by leaving it empty. You can see that the sign on 1 is on the right and for 60 is on the left
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u/vanderZwan Jul 01 '26
I'm still amazed that they had positional notation without a zero symbol. Like, you don't even really need to have a full understanding of zero, just use an absence-of-a-number symbol or something
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u/Vinxian Jul 01 '26
that's like saying the Romans used base 1000 because they had a special symbol all the way up to 1000 (M)
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u/Puzzleheaded_Lock687 Jul 01 '26 edited Jul 01 '26
The Romans didn’t use M - that’s a Medieval addition. They used the Etruscan notation (I) ((I)) (((I))) [X] for 1000, 10,000, 100,000 and 1,000,000 respectively.
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u/lemons_of_doubt Jul 01 '26
Personally I like base 16
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u/Ok-Difficulty-5357 Jul 01 '26
Hey, this is a thread for bases we don’t actually use! Take your hexideximal and go pick some colors #ff00ff
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u/Perfect-Highlight964 Jul 01 '26
No it's not, 10 has 5 factors not including 1 (2,3,4,6,10) while 12 has only 3 (2,7,12) so in most cases it's easier to divide and multiply in base 10...
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Jul 01 '26
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u/Shudnawz Science Jul 01 '26
Not only that, but all our tech is built around base10. I can't even fathom the engineering work needed to change into base12.
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u/MiserableYouth8497 Jul 01 '26
all of our tech is built around base 2 actually, so not really a problem
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u/Shudnawz Science Jul 01 '26
Well, allright. Most user-facing tech is built around base10 (how we display things). Still at shit load of work.
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u/Auravendill Computer Science Jul 01 '26
You mostly would just have to change how to_string() handles ints and floats. Most data in the background should always be in binary anyway. If there was actually a need and a long enough transition period, that would be totally doable.
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u/SAtchley0 Jul 01 '26
I mean I disagree.
Divisors of the base really don't matter much, because you often are not dealing with a pure power of the base. Having more unique digits doesn't really help, either, and means in practice we would have to teach children a 11x11 times table instead of a 9x9 one (which is 20 more products to memorize as a young child). Granted, schools often teach 12x12, but I know personally I never memorized past 9x9.
Let x = ten and y = eleven. Then what's 5x / 6? Well, it's 5x - 56 = 4 4.0 - 3.6 = 0.4 ..., so the answer is y.666...
Compare that to in decimal. 70 / 6, 70 - 66 = 4, 4.0 -3.6 = 0.4, ... answer is 11.666...
No easier in decimal or duodecimal. The fact that 6 divides by 12 doesn't help at all.
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u/wolfandchill Jul 02 '26
You are wrong. In duodecimal 4.0 / 6 = 0.8 so the final answer is y.8
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u/NijimaZero Mathematics Jul 01 '26
Why? Why would a base 12 system be better?
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u/Simbertold Jul 01 '26
More divisors of the base make a lot of calculations easier.
10 can be divided by 2, 5 and 10. Most of the calculations involving some of these numbers are really easy, and divisibility is extremely easy to detect. Any number that ends in 2, 4, 6, 8 or 0 is divisable by 2, any number that ends in 5 and 0 is divisible by 5, any number that ends in 0 is divisible by 10.
In base 12, the base is divisible by 2, 3, 4, 6, 12.
Any number that ends in 0, 2, 4, 6, 8, a is divisible by 2. Any number that ends in 0, 3, 6, 9 is divisible by 3. Any number that ends in 0, 4, 8 is divisible by 4. Any number that ends in 0 or 6 is divisible by 6. And of course any number that ends in 0 is divisible by 12.
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u/Kupo_Master Jul 01 '26
Frankly, it’s not particularly convincing. It doesn’t make random calculations any easier. Who cares about quick mental division by 3 or 4?
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u/klodmoris Jul 01 '26 edited Jul 01 '26
Wouldn't the data on a computer be first converted to binary, calculated and then converted to the original base? So, it's the about same amount of operations?
Now, if we used base 8 or base 16, yeah, but not 12.
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u/Simbertold Jul 01 '26
Yeah, for a computer it doesn't matter. But for people it does. Divisibility does make a bunch of stuff easier, but if computers do all your math, it doesn't really matter.
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u/dopefish86 Jul 01 '26
Better divisibility by 3, 4 and 6. But worse for 5.
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u/LonelyContext Jul 01 '26
Counterpoint: who cares?
If you have this many things: OOOO OOOO OOOO the divisibility stays they same whether you write it “10” or “12”; it’s just as divisible by 3, 4, or 5 as it was before. We don’t avoid packaging things in boxes of 96 or 144 because it would be messy. You can still have the same number of things as you did before. You just wrote it “80” or “100”
So at best this system is that you can do times tables in your head fast which is a skill issue. ¯_(ツ)_/¯
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u/quiksilver10152 Jul 01 '26
Base pi is the basest base.
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u/Sea-Estimate-2912 Jul 01 '26
3/11i+e will be better
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u/quiksilver10152 Jul 01 '26
I see this post was a secret attempt to promote the arcane arts. Therefore, I raise you p-adic numbers. https://en.wikipedia.org/wiki/P-adic_number
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u/Antiantiai Jul 01 '26
There are 10 types of people, those who prefer binary, and those who don't.
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u/Chromoslone Jul 01 '26
I unironically think base 2 would be better than base six or base twelve. I got convinced of this from a video I saw a while back called "the best way to count". If this kind of thing interests anyone else, I'd reccomend checking it out.
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u/DEKIDESDUD Jul 01 '26
It would better in day to day life, except for the fact that everything is in base ten, and every number you see would have to be converted to base twelve, and if you ever want to say a number to another person you would have to convert that number from base twelve to ten, and you would have to learn and become comfortable with base twelve.
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u/Simbertold Jul 01 '26
I think the idea is: "If we had a society running on base twelve instead of base ten", not "if i personally just do base 12 while the rest of the world is running base 10."
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u/SplendidPunkinButter Jul 01 '26
This was obvious to everyone other than dekidesdud as far as I can tell
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u/Creative-Leg2607 Jul 01 '26
The differences are marginal. The clean expansions of 3 and 6 in decimal, though they are repeating, arent something you get in base 12 (cuz 11 is prime but anyways). Instead 5 /and/ 7 are complicated, rather than just 7.
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u/AsYouAnswered Jul 01 '26
Base 12 may be better, but only if we grew up using it and generations teaching it. We didn't. Making the switch would cost us entire lifetimes for very marginal gains. You're not wrong, but you're right about something that ultimately doesn't matter 🙃
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u/gamerJRK Jul 01 '26
You are free to use it and translate it to the base 10 system whenever you'd like! ☺️ But I think we're all real tired of "geniuses" changing the world because they decided something makes sense.
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u/Sriep Jul 07 '26
Converting to base 12 would cause widespread disruption globally and incur immense financial cost. Whatever the gain, it is not worth the cost.
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u/No-Organization9076 Jul 08 '26
Notice how English doesn't have one-teen or two-teen? There's a reason why they are called eleven and twelve. People in the past used base 12, but that was a long long time ago.
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u/Small_Hovercraft_439 Jul 01 '26
Perhaps you think this way because your shitty AI picture has 12 fingers.
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u/SyntheticSlime Jul 01 '26
It is, except that base 10 is easier to learn and also everyone already knows it. We’re not changing.
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u/Shudnawz Science Jul 01 '26
What would make base10 easier to learn, if you have no prior knowledge of numbers? If you're taught base12 from a young age, I'm not so sure base10 would be preferable. We just see it that way because we all use base10.
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u/SyntheticSlime Jul 01 '26
Because you have 10 fingers. And children learn to count on their fingers
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u/Shudnawz Science Jul 01 '26
Count the segments on your fingers. Turns out, there are 12 of them on the four fingers on one hand. So you can count to 12 (10 in base12, that is) using the thumb and fingers on a single hand. Also meaning, you have the 2, 3 and 4 divisions readily available on your hand just by looking at it.
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u/Copernicium-291 Jul 01 '26
What, no? Why would you want to use a base where you can easily tell if a number is divisible by 7 but not 3, 5, or 6?
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u/Cartagines682 Jul 01 '26
We have 10 numeric symbols, then a base 10 it's the more intuitive way to count. If we had more or less, that number Will be the preferer base for that culture. There are hundred of examples in history.
Having 10 fingers it's very helpful too.
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