# Would an alien species also likely come up with a 10 base number system? **URL:** \ **Category:** Great Debates\ **Created:** [October 6, 2016, 9:59pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802 "2016-10-06T21:59:59Z")\ **Posts on this page:** 16\ **Page:** 2
**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\ **Post date:** [October 8, 2016, 4:06am UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/21 "2016-10-08T04:06:02Z")
> [@Voyager](#): > > A federation of aliens, each with different bodily features, would probably come up with a base 8 or base 16 system, since they would certainly use that for their computers no matter how many digits they have. Base 10 is about the worst non-prime choice in the first 15. (Yes 15, I’m a world authority on base 1 arithmetic.) Around here we call base one arithmetic tally marks. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [October 8, 2016, 6:05am UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/22 "2016-10-08T06:05:59Z")
> [@Robot\_Arm](#): > > 23, same as always. What about in town? ---
**Author:** ![aldiboronti](https://avatars.discourse-cdn.com/v4/letter/a/9fc348/32.png) [@aldiboronti](https://boards.straightdope.com/u/aldiboronti)\ **Post date:** [October 8, 2016, 8:33am UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/23 "2016-10-08T08:33:16Z")
> [@John\_Mace](#): > > Only, as noted above, if you have a zero. Try writing in Roman Numerals, which are a representation of a base 10 system. Not so difficult as might be thought. The Romans had separate symbols for [large numerals](https://en.wikipedia.org/wiki/Roman_numerals#Large_numbers). XX with a line above each X for instance is 2000000, which is considerably more precise than our own notation. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [October 8, 2016, 9:12am UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/24 "2016-10-08T09:12:05Z")
> [@aldiboronti](#): > > Not so difficult as might be thought. The Romans had separate symbols for [large numerals](https://en.wikipedia.org/wiki/Roman_numerals#Large_numbers). XX with a line above each X for instance is 2000000, which is considerably more precise than our own notation. I think you missed something on that page. XX with a line over it is 20,000. Twenty million would be |XX| with a line over it. Or perhaps better described as a three-sided box around the XX. And it’s no more (or less) precise than our current numbering system. Maybe you meant “concise” which it is for that particular number, but is not the case for all numbers. And it does have a problem with significantly larger numbers, such as in the trillions and higher. ---
**Author:** ![MichaelEmouse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/michaelemouse/32/101_2.png) [@MichaelEmouse](https://boards.straightdope.com/u/MichaelEmouse)\ **Post date:** [October 8, 2016, 2:02pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/25 "2016-10-08T14:02:35Z")
> [@Voyager](#): > > A federation of aliens, each with different bodily features, would probably come up with a base 8 or base 16 system, since they would certainly use that for their computers no matter how many digits they have. Why would they use base 8 and 16 for their computers as opposed to 4, 32 or 64? 64 seems like a lot but the Babylonians used a base 60. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [October 8, 2016, 3:02pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/26 "2016-10-08T15:02:37Z")
> [@Robot\_Arm](#): > > It’s worth pointing out that however many digits these aliens use in their number system, they will call it “base 10”. Only if they use a place value system similar to ours, which may itself be an anthropocentric assumption. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [October 8, 2016, 4:24pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/27 "2016-10-08T16:24:45Z")
> [@MichaelEmouse](#): > > Why would they use base 8 and 16 for their computers as opposed to 4, 32 or 64? 64 seems like a lot but the Babylonians used a base 60. In this post I’m using words for numbers to preclude confusion about what base they’re expressed in. Numbers in words are traditional modern human base 10=ten. Agree that we chose base eight and/or base sixteen for computers because it was close to our human base ten. Had we been using a Babylonian system AND used it with sixty different symbols and a powers-of-sixty place value system, then base sixty-four would have been a natural choice. But … A close look at the Babylonian system shows they didn’t exactly have sixty discrete symbols. Instead they had a symbol for one and a symbol for ten. Which they wrote in tight groups (\*a la \*tally marks)to form the larger values. If we use “o” for one and “t” for ten the Babylonian representation of thirty seven is “tttooooooo” Switching to conventional base-ten notation … Their quasi-positional representation for 12x60[sup]1[/sup] + 37x60[sup]0[/sup] is “too tttooooooo”. Their quasi-positional representation for 42x60[sup]2[/sup] + 12x60[sup]1[/sup] + 37x60[sup]0[/sup] is “ttttoo too tttooooooo”. It’s not obvious to me this really extends nicely to large numbers. And having 60 truly discrete arbitrary symbols would be a lot like using “0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx” as a symbol set. At least for mere humans, memorizing the addition and multiplication tables for that would be tough. Quick, what is the sum of T and j? Or the product of g and 7? Ultimately the Babylonians chose a one-ten-sixty system, not a one-sixty system. Much like the now-obsolete but still fairly recent British pence-shillings-pounds system. Aliens with a much larger working memory set might pull off a one-sixty system and would react to our base ten about the same way we feel looking at doing addition or multiplication by hand in base two. i.e.: Waay too many digits but not nearly enough variety \*of \*digits. > [@Great\_Antibob](#): > > Only if they use a place value system similar to ours, which may itself be an anthropocentric assumption. _May._ But it has a lot going for it. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [October 8, 2016, 5:33pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/28 "2016-10-08T17:33:33Z")
> [@MichaelEmouse](#): > > Why would they use base 8 and 16 for their computers as opposed to 4, 32 or 64? 64 seems like a lot but the Babylonians used a base 60. There’s a trade-off. If you have a system with a lot of elements in it, you can compose short sequences with a high density of information. But the downside is you have to memorize a lot of elements. In number systems, compare base-two, base-ten, base-twenty-six, and base-sixty systems. In base-two, you only have to elements to remember: 0 and 1. The first ten numbers are 1, 10, 11, 100, 101, 110, 111, 1000, 1001, and 1010. A million is 11,110,100,001,001,000,000 and a billion is 111,011,100,110,101,100,101,000,000,000. In base-twenty-six, you have to remember twenty-six elements (I’ll use the alphabet as an example). So the first numbers are A, B, C, D, E, F, G, H, I, and J. A million is CEXHO and a billion is DGEHTYM. In base-sixty, you have to remember sixty elements (0-9,A-Z,a-x). A million is 4bke and a billion is 1H9bke. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [October 8, 2016, 5:47pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/29 "2016-10-08T17:47:48Z")
> [@chrisk](#): > > The Romans didn’t really have that. A V pretty much always meant five… maybe you could underline it to multiply it by a thousand or something like that, but there’s a limit to how many times you can underline XVII 😉 If it came to that, they could have developed a simple, thousands-based scientific notation that might look like [sub]III[/sub]DLXVII for 547 billion, then used a separator like we use a comma to mark the lower place groups (with just a blank underline for 000 sets). ---
**Author:** ![aldiboronti](https://avatars.discourse-cdn.com/v4/letter/a/9fc348/32.png) [@aldiboronti](https://boards.straightdope.com/u/aldiboronti)\ **Post date:** [October 8, 2016, 5:59pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/30 "2016-10-08T17:59:16Z")
> [@dtilque](#): > > I think you missed something on that page. XX with a line over it is 20,000. Twenty million would be |XX| with a line over it. Or perhaps better described as a three-sided box around the XX. > > And it’s no more (or less) precise than our current numbering system. Maybe you meant “concise” which it is for that particular number, but is not the case for all numbers. And it does have a problem with significantly larger numbers, such as in the trillions and higher. Sorry, had a brainfart. I did indeed mean concise and you’re right about the erroneous notation. Oh well, can’t win’em all. 🙂 ---
**Author:** ![Randolph](https://avatars.discourse-cdn.com/v4/letter/r/e5b9ba/32.png) [@Randolph](https://boards.straightdope.com/u/Randolph)\ **Post date:** [October 8, 2016, 6:48pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/31 "2016-10-08T18:48:06Z")
> [@GIGObuster](#): > > > [@Broomstick](#): > > > > The Mayans used a base 20 system. > > I remember that it came by the Mayas realizing that they could count also their toes, 20 digits really, so it made sense to have a base 20. And in ultiMayan societies, the men used a base-21 system, whilst the women used base-22. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [October 8, 2016, 8:46pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/32 "2016-10-08T20:46:45Z")
> [@Bryan\_Ekers](#): > > Well, the base doesn’t really matter - the critical element is the concept of zero. It took humans quite a while to get it; I can picture an alien species somehow finding an alternative. It depends on what you mean by the “concept of zero”. Although many ancient counting systems did not explicitly have a number for zero, they used positioning or other indicators for multiples of a base raised to a power. The concept of zero is really only critical when you get into number theory and computation, and the practical applications of a concept of zero, negative, and imaginary numbers only started with physics, hence why these apparently simple concepts took so long to be discovered. Really, the critical elements in our mathematics are 0, 1, e, i, and pi, which are actually base independent, and of course all related through [Euler’s identity](http://mathworld.wolfram.com/EulerFormula.html), which is also gives us the association between exponentiation and logarithms, and from there trigonometry and continuous periodic functions. Although the near-universal system of “counting numbers” that we use in everyday arithmetic today is decimal, there are plenty of other cultures in history that used essentially every base from 2 to 16, and some higher increments. Of course, in computation, we use base-2 as the fundamental unit of logical calculation, and octal and hexadecimal for ease of calculation and compactness in dealing with digital computers. Our adoption of a decimal base system is essentially arbitrary and doesn’t really reflect any particular scaling of natural phenomena; it is largely just a happenstance of convenience and history. However, there is an underlying assumption here that needs to be considered; that an alien species would use any type of discrete counting of equal increments at all, rather than some kind of continuous or variable distributions of quantities. We use incremental counting systems because of how our brains are wired for numerical cognition; we see people and objects as individuals, and the way our brains work actually tries to break up continua into discrete bins for categorization. This is reflected in our mathematics, grammar, sociology, and pretty much every other aspect of human existence to the point that we struggle to understand concepts of continuous variation or probabilistic distribution, even though essentially everything we experience as the scale that we can observe it is some kind of continuum with essentially infinite variability[SUP]\*[/SUP]. It is entirely reasonable that an alien form of intelligence may not make such distinctions and would develop a mathematics that does not use discrete counting, Euclidian geometry, or some of the other fundamental assumptions of our system of mathematics. Stranger [SUP]\*[/SUP]That objects and apparent continua are composed of discrete atoms and molecules, and below that of fundamental particles, is not evident to the point that our description of mechanics has only reflected this in the past couple of centuries, and it was just over a century since we’ve experimentally verified the atomic nature of matter. Most of our practical evaluations of structural and fluid materials still assume that they are a continuum, often using rules and properties that are empirically determined due to the essential difficulty in calculating and observing behavior at the level of individual molecules or atoms. ---
**Author:** ![Wallaby](https://avatars.discourse-cdn.com/v4/letter/w/dc4da7/32.png) [@Wallaby](https://boards.straightdope.com/u/Wallaby)\ **Post date:** [October 8, 2016, 9:40pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/33 "2016-10-08T21:40:15Z")
> [@dtilque](#): > > Well then, how many tentcles on each pod… maybe they have 4 tentacles on the right pod and 6 on the left… or even a variable number on each, then what base would the use? I remember reading a nice puzzle in Scientific American one time. It was a version of the ‘Try and work out what numbers these symbols represent, and what base they are using’ from a mathematical equation some astronauts found scrawled on a wall on a distant planet. The only clue was that they knew the aliens had manual dexerity and formed their base-number system from the digits on their ‘hands’. When the answer was given - “Base-9” - there were protests from many readers asking "How can it be Base-9? How many digits do they have on each arm?’ The answer of course being 3. ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [October 8, 2016, 10:07pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/34 "2016-10-08T22:07:09Z")
> [@eschereal](#): > > If it came to that, they could have developed a simple, thousands-based scientific notation that might look like [sub]III[/sub]DLXVII for 547 billion, then used a separator like we use a comma to mark the lower place groups (with just a blank underline for 000 sets). Did the Romans need number notation to describe numbers past a few millions? Their equivalent of an accountant, quantity surveyor or whatever isn’t going to have needed notation for billions, surely? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 8, 2016, 10:25pm UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/35 "2016-10-08T22:25:11Z")
The number of digits you have need not be the same as the number of distinct symbols. The Mayan system, for instance, had three symbols. Their zero was zero (it looked sort of like a seashell or maybe an Easter egg), but all of their other digits were composed of combinations of horizontal lines and dots. One dot was “1”, two dots was “2”, and so on, until you got to a line was “5”. Then you’d have a line and a dot for “6”, and so on, until three lines and four dots formed the digit for what we’d call “19”. And the number of digits that’s convenient depends not just on physiology, but on psychology. Maybe, for instance, the aliens are better at distinguishing slightly different symbols than we are, and better at learning a large number of symbols, in which case they might not think that a hundred different symbols was a big deal. Or maybe even a thousand: Even among humans, speakers of Asian languages learn more symbols than that (though of course those are mostly more complicated symbols than the Arabic digits). ---
**Author:** ![DrDeth](https://avatars.discourse-cdn.com/v4/letter/d/b487fb/32.png) [@DrDeth](https://boards.straightdope.com/u/DrDeth)\ **Post date:** [October 9, 2016, 1:55am UTC](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802/36 "2016-10-09T01:55:16Z")
> [@Vicsage](#): > > I know the Romans didn’t have a 0, but this confuses me. If you asked a roman child this question “Ceasar has 2 apples, Brutus took two apples from Ceasar, how many apples did Ceasar now have?” what would the roman child say?😕 Its not a zero. Saying that just confuses the matter. It’s the idea of a placeholder number, and you do have to have a zero number for that, of course. So if V=5 In a placeholder system VV=55 but otherwise VV=10 (aka X) [Previous page](https://boards.straightdope.com/t/would-an-alien-species-also-likely-come-up-with-a-10-base-number-system/767802.md?page=1)