# Aliens use base 12, humans use base 10, what to do?



## caters (Dec 12, 2016)

My aliens have 6 fingers on each hand, 2 of which are thumbs and on opposite sides of the hand. This helps them climb better than we can but this also means in my case that they count in base 12.

I can make a subscript 12 beside each of the base 12 numbers but using just base 12 isn't going to work if I want to publish it(which I don't plan on doing since I write to write). It might not even work for just writing it since I would have to constantly be doing this process:

x mod 12

write digit and subtract its place value

x-y mod 12

write digit and subtract place value

etc.

which means I would have to constantly be using my calculator for anything larger than 144 since 144 is the highest power of 12 I know off the top of my head(12[SUP]2[/SUP]).

But using just base 10, while easier on me and the humans on the generation ship, is not easy for the aliens because since ancient times they have used base 12. 

So what should I do? Use base 12 like the aliens? Use base 10 like the humans? Or use a different base?

No matter what though I am not going as far as binary or ternary or in fact any power of 2 base.

I mean in base 10, 1/5 is .2 right? That is easy, a terminating decimal.

In binary, (1/101)[SUB]2[/SUB] is (.00110011...)[SUB]2[/SUB] A repeating decimal.

In fact, any prime base or power of prime base will have every possible decimal repeat except fractions that have a denominator of a power of the base. So primes are no go as are powers of primes.

So if I use a different base but 1 that is close to either the human's base or the alien's base, that limits me to base 6 and base 14. Base 6 might be understandable by the aliens but probably not by most if not all of the humans and base 14 might not be understandable by either the humans or the aliens.


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## Annoying kid (Dec 12, 2016)

caters said:


> My aliens have 6 fingers on each hand, 2 of which are thumbs and on opposite sides of the hand. This helps them climb better than we can but this also means in my case that they count in base 12.
> 
> I can make a subscript 12 beside each of the base 12 numbers but using just base 12 isn't going to work if I want to publish it(which I don't plan on doing since I write to write). It might not even work for just writing it since I would have to constantly be doing this process:
> 
> ...



[video=youtube;3KtYwWsVKU4]https://www.youtube.com/watch?v=3KtYwWsVKU4[/video]


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## Ptolemy (Dec 12, 2016)

You would use base ten. 

The reasoning why is that both the Humans and the Aliens have at least five fingers on each hand, so they can both theoretically calculate in base ten. Humans cannot (physically speaking, mentally people have) work in base 12, so you would use the base that more combined creatures could use, which would be base ten, not base twelve.


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## caters (Dec 12, 2016)

Let me put this into context.

Say that 5000 people are going on board the generation ship.

If I use base 10, that is easy, just 5000

Base 12 on the other hand is much harder.

12^3 = 1728

so 12^3 goes in there twice

That leaves me with 1544

144 goes in there 10 times which leaves me with 104

12 goes in there 8 times leaving me with 8

So 5000 in base 12 is 2A88[SUB]12 

[/SUB]The subscript 12 tells you it is in base 12.

If I were to use base 6 though, there would be 5 digits.

Doing the division by powers gives me 35412[SUB]6
[/SUB]
The aliens might understand this base 6 and be able to convert this to base 12 without going through a base 10 step first but I doubt the humans will understand base 6. I mean it is hard enough trying to use base 12 but base 6? Powers of 6 are very slow and you might get lost thinking "which power of 6 is next?" if you were trying to convert a much bigger number like a million into base 6.

Base 14, the closest composite base that isn't a power of a prime number to base 12 that isn't base 10 is even harder. I mean, most people don't even know or care about what 14[SUP]2 [/SUP]is.

Doing the division by powers of 14 gives me 1B72[SUB]14[/SUB]

A is for 10 and B is for 11 but you see how while using base 10 is very easy for us, the aliens might have a hard time grasping that our 1000 is different than their 1728(both the base of their respective number system, cubed). And you see how base 12 is harder for humans to understand and how base 6 is relatively easy for the aliens but hard for us and how base 14 is hard for both?

I just don't want to use something like base 11 because then every fraction that isn't 1/(power of 11) like 1/2 or 1/3 will repeat and I can't imagine an alien society that would not want 1/2 to be a terminating decimal.


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## ppsage (Dec 12, 2016)

I think it's only an issue for you, because I frankly don't see how this is ever going to be made interesting for general readers. And I understand the principles. Maybe you'll get good at typing subscripts?


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## Annoying kid (Dec 12, 2016)

Exactly. Do you seriously think any reader is going to keep track of this?


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## EmmaSohan (Dec 12, 2016)

I assume you translate their language into English. Why can't you do the same for base?


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## Bloggsworth (Dec 12, 2016)

I use base 12 - One dozen
Base 14 - 14lbs in a stone
Base 240 - 240 old pennies in a £


I'm sure aliens would be adaptable, after all, if they can cross light years, then I think they'll manage...


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## Jay Greenstein (Dec 12, 2016)

Ptolemy said:


> You would use base ten.
> 
> The reasoning why is that both the Humans and the Aliens have at least five fingers on each hand, so they can both theoretically calculate in base ten. Humans cannot (physically speaking, mentally people have) work in base 12, so you would use the base that more combined creatures could use, which would be base ten, not base twelve.



But they wouldn't use base ten. Perhaps this will clarify: 

You can't write the number ten on the page because there are only ten digits, zero through nine. When you write what you call the quantity ten, you're really writing, "one bunch, and none left over." It helps to think of the early civilization scout returning to base. When the leader asks how many of the enemy there are, he replies, "I saw seven hands of soldiers (70 because he started counting across his fingers and started over seven times)". Eleven is one bunch and one left over. That continues till you reach two bunches, then three bunches, and on till "One bunch of bunches and none left over—or 100.

But when you have twelve fingers the number written as 10 still means a single bunch (the point at which you start over) but there are two more items in his bunch. But it works because numbers _represent _a quantity. And as long as it means the same thing to me as you, it's okay. Both have addition and multiplication tables to memorize, and as long as everyone is using the same tables thy work.

Let's say you want a number of things: * of one thing , ** of another. , *** & **** of two others

A race with two fingers counts, 1, 10, 11, 100 to represent them: Or: One. A bunch. A bunch and one. A bunch of bunches.
(as a side note, because binary requires only ones and zeros, I represent each digit position with one finger, extended for a one and folded for a zero. So...All fingers folder, = zero. First finger up is one. Second up is 10, First and second up is 11, or what we call three. Third finger alone of four, and so on. Given that I have five digits on one hand, I can represent a numbry written as 11111, which is the quantity we decimals call 31. So one one hand I can count from zero to thirty-one. A handy skill to have)

A race with four fingers  would count, 1, 2, 3, 10. And all that matters is that the one shopping gets the intended quantity.

You and I almost never think of the base of our numbering system in daily life, and neither would a race with twelve fingers. That's why that twelve fingered race would never use base ten, and their average citizen wouldn't know it exists, any more then most people know about octal (base 8:  1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 6, 17, 20).

I've probably confused more than clarified, I'm afraid, but because it is confusing, I'd agree that the numbers mentioned in the story should be in a numbering system the _reader _knows. They would have no clue that people count according to the number of fingers they have, and assume that counting is counting. Of those who will realize that the race would use a duodecimal counting system, most would assume you translated. Most of the rest would figure it doesn't matter.

And of course, another way around it is to avoid exact quantities over nine. That would be my choice.


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## Ptolemy (Dec 12, 2016)

Jay Greenstein said:


> But they wouldn't use base ten. Perhaps this will clarify:
> 
> You can't write the number ten on the page because there are only ten digits, zero through nine. When you write what you call the quantity ten, you're really writing, "one bunch, and none left over." It helps to think of the early civilization scout returning to base. When the leader asks how many of the enemy there are, he replies, "I saw seven hands of soldiers (70 because he started counting across his fingers and started over seven times)". Eleven is one bunch and one left over. That continues till you reach two bunches, then three bunches, and on till "One bunch of bunches and none left over—or 100.
> 
> ...



I realize that people with 12 fingers would not count in base 10 regularly. 

But what I'm saying is that it would be easier for the humans to teach the aliens to count in base ten, and "drop" two of their fingers to count like that. 

While I agree that this is a confusing description, it also proves my point here too. The fact that the aliens would need to teach humans to count 1, 2, 3, 10... would be so foreign and more difficult than a base 10 numbering system, which would be easier to teach than a base 12 numbering system. (why do you think we use base ten too? It's one of the easiest way to calculate, that's why I, an american, prefer the SI form of units rather than Americanized units.) 

I also agree that, that this cannot be in the book, it's super confusing to any reader that would even try to comprehend it.


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## Phil Istine (Dec 12, 2016)

Bloggsworth touched on something.  Like him, I was brought up with various number bases in a non-metric Britain.  Base 16 (16 ounces to the pound weight), 14 pounds weight to the stone, 12 pennies to the shilling, twenty shillings to the pound money, eight pints to the gallon etc.  Somehow, we seemed to manage, even though it looks ludicrous now.
If your alien race is technologically advanced, maybe base 16 would work - our hexadecimal.  As it's just a convenient way of managing binary notation (1 or 0 being on or off respectively) it's reasonable to think that when they became more dependent upon machinery, hexadecimal eventually took over (A to F becoming 10 to 15).  Octal could be another way but to avoid wasted computer bits, maybe the aliens had just six bits in a byte.  This would save having to use letters for numbers.


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## senecaone (Dec 12, 2016)

The most advanced aliens will start with base 16, and therefore intuitively understand hexadecimal math. To them, subtracting A2B6 from FF3D would be as easy as 87435-29643 for us mathematically challenged decimal heads

It's hard to imaging eight fingers though. Maybe eight tentacles from each side of a central mass? That might work. I see a story there!


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## Kyle R (Dec 13, 2016)

caters said:
			
		

> The aliens might understand this base 6 and be able to convert this to base 12 without going through a base 10 step first but I doubt the humans will understand base 6.



Who says aliens and humans need to share the same numbering system? Why not give them each their own systems?

It'd be a great excuse to have coexisting species who don't fully understand each other's ways.

Trevor eyed the scrawl of text running up the wall. The markings were haphazard at best. Chicken-scratch, really. As if whoever made them had done so without even paying attention to what they were doing. "What _is_ that?" he finally said.

The phrevlorian followed his gaze to the wall and smiled her upper set of lips. "That?" she said. Her voice warbled in two distinct notes—even her English sounded alien. "That's my record of each circadian rhythm I've spent in orbit so far. I believe you would call this a _tally_."

Trevor raised his eyebrows. "Those are _numbers?_"

Her upper lips widened even more. "Of course. What kind of numbers are you used to?"

"One, two, three," he said, lifting his fingers, one at a time. "You know—standard stuff."

She shook her tentacled head. "I swear, you humans are so bizarre."
​


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## The Fantastical (Dec 13, 2016)

This is all to complicated...  just keep it simple, knock of the extra fingers from the aliens and use the base ten. You readers (if there ever are) will thank you. As it is now, I can see a huge chunk of text being devoted to explaining the base 12 to the readers which is never fun to read unless you are really really into lots of math...


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## Bishop (Dec 13, 2016)

When world building goes too far...

In a novel taking place in any form of computer age, this is window dressing that will only serve to obscure the reader's understanding. Communicate cultural differences in concepts your readers can easily understand and would be entertaining to them. Base numerology doesn't appeal to readers. 

Humorous, accidental social faux-pas where a human accidentally shakes what he thinks is a hand and is in fact a sexual appendage... those appeal to readers--the least of which reasoning being that the reader has likely committed a social faux-pas, and can relate to that embarrassment while finding humor in it. When's the last time you went to a party and had to deal with the host's annoying use of base 8 for the drink measurements?


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## Terry D (Dec 13, 2016)

Bloggsworth said:


> I'm sure aliens would be adaptable, after all, if they can cross light years, then I think they'll manage...



This. Completely.


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## Jay Greenstein (Dec 13, 2016)

> But what I'm saying is that it would be easier for the humans to teach  the aliens to count in base ten, and "drop" two of their fingers to  count like that.



No, it wouldn't. They would have to memorize different multiplication and addition tables, and practice them till they were proficient. And no one is going to do that.  2x7 = 14 in base ten, for example, but 12 in base twelve.

This is a tech-savvy civilization, so they'd say the equivalent of, "Siri, what it 143 in base twelve?" Problem solved.

But in the end, if the numbers mean so damn much and it's critical that they have better gripping power, toss the extra fingers and give them sandpaper hands.


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## Ptolemy (Dec 13, 2016)

Jay Greenstein said:


> No, it wouldn't. They would have to memorize different multiplication and addition tables, and practice them till they were proficient. And no one is going to do that.  2x7 = 14 in base ten, for example, but 12 in base twelve.
> 
> This is a tech-savvy civilization, so they'd say the equivalent of, "Siri, what it 143 in base twelve?" Problem solved.
> 
> But in the end, if the numbers mean so damn much and it's critical that they have better gripping power, toss the extra fingers and give them sandpaper hands.



But since they are "advanced" aliens wouldn't it be conceivably correct to assume that they could contain a higher level of intelligence than their human counterparts and could adapt to bar ten quicker. Which would make it easier for the humans, since they wouldn't have to learn base 12.

i can totally agree with Bishop though, it's kind of overworld building, overhwelming, and just wrought with confusion.


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## Annoying kid (Dec 14, 2016)

Ptolemy said:


> But since they are "advanced" aliens wouldn't it be conceivably correct to assume that they could contain a higher level of intelligence than their human counterparts and could adapt to bar ten quicker. Which would make it easier for the humans, since they wouldn't have to learn base 12.
> 
> i can totally agree with Bishop though, it's kind of overworld building, overhwelming, and just wrought with confusion.



"Kind of" as in completely off the deep end. 

To the question of if aliens should use base 10 or 12, my answer is: Go outside.

If I want boring maths theory I'll get pick up a textbook, not a novel.


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## Sam (Dec 14, 2016)

Here are your options:

(a) Have aliens use base ten; (b) have humans evolve to use base twelve; (c) stop worrying about something that holds absolutely zero interest for anyone other than approximately five people on the face of the planet. 

I suggest you pick 'c'.


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## JustRob (Dec 14, 2016)

EmmaSohan said:


> I assume you translate their language into English. Why can't you do the same for base?



Emma has made the key point here. Don't confuse the mathematics with the language we use to express it. Whatever base we use to express a number it is the same number, just as whatever language we use to express a concept it is the same concept. The fact that your aliens use a number base based (!) on the number of digits on their appendages means that they aren't very alien at all. In fact even the ancient Romans with their numbering system were far more alien. Aliens would be just as likely to use a completely different way of expressing numbers, such as by means of their factors rather than by addition of a power sequence, so ten might be expressed as 25 and twelve as 223. In fact that's why human dozenalists prefer twelve, because it has more useful factors than ten, and therefore they consider themselves to be more advanced than decimalists.

In fact even I, who don't consider myself to be_ that _alien, contrived a two-dimensional numbering system which used the four symbols "red", "blue", "green" and "reverse" however you care to depict them. This system is based on the idea that instead of identifying one object and then adding more like it one contemplates what proportion of everything the thing that one is representing constitutes. This is much more appropriate for aliens who may be contemplating taking over say two thirds of the universe, rather than 10000000 planets, whatever base that number happens to be expressed in. I actually used my numbering system in a computer programme which draws virtual planets as it happens, so it does work. Hopefully this demonstrates that "alien" is not a trivial concept at all, even when applied to mathematics.

Let's go even further and consider whether their "language" is even one dimensional, a linear series of symbols or sounds, at all. What does a number base even mean under those circumstances? My numbers were two-dimensional and had no one-dimensional equivalents at all, so it's quite possible that a whole alien language could be as well. For example just think about how dolphins communicate, given that they can do things like seeing inside closed containers with their sonar, which is also their speech mechanism. Can we even tell where the information is in their behaviour? Then again, in _Clan of The Cave Bear _Jean M Auel portrayed Neanderthals as communicating solely by body movements, gestures and expressions so subtle that Cro-Magnons thought that they didn't communicate at all and were just wild animals because they never uttered any sounds.

No, aliens are alien.


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## Kyle R (Dec 14, 2016)

The whole concept of how aliens would count is pretty fun to think about.

But ultimately, fiction isn't reality. Trying to figure out how aliens _could_ or _would_ count is, to me, mostly a waste of time. Fun to discuss on a message board, for sure!—but ultimately, this is time that, for the author, would probably be better spent writing.

It's fiction—you write whatever you want to write. The only logic required is the internal logic of the story itself.

How would twelve-fingered aliens count? However the hell you want them to count. What kind of conversion formula can work for both the humans and the aliens? Whatever formula you want! It's your story, your universe. The laws of reality are at your whim.

As long as you write convincingly and engagingly enough, the reader will go along with pretty much whatever you toss their way. :encouragement:


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