# free basing \[Why do humans use base 10\] **URL:** \ **Category:** Factual Questions\ **Created:** [June 5, 2012, 1:43am UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105 "2012-06-05T01:43:42Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Gary\_T](https://avatars.discourse-cdn.com/v4/letter/g/3ec8ea/32.png) [@Gary\_T](https://boards.straightdope.com/u/Gary_T)\ **Post date:** [June 5, 2012, 2:56pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/21 "2012-06-05T14:56:18Z")
> [@Jragon](#): > > ETA: Now that I think about it, what I described wouldn’t be base 5, it’d be base 6. 0-5 on one hand, {6,12,18,24,30} on the other. > > ETAETA: Our hands can represent 0-10… Whence these zeroes? I suspect when proto-humans were counting things, they didn’t start with zero. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [June 5, 2012, 3:07pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/22 "2012-06-05T15:07:48Z")
Also, decimal is the most common base but we shouldn’t imply it is the only one in use. e.g. hexadecimal (base-16) is common in computing contexts. It is not as error prone for humans to read and write as binary, but is much easier to convert from/to binary than decimal. We could have picked any power of 2 as our “lingua franca” between us and computers, but hex has stuck more than the alternatives. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [June 5, 2012, 3:10pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/23 "2012-06-05T15:10:24Z")
> [@tellyworth](#): > > The Mayans sort of did - their numbering system is actually base 20, but for small numbers it looks like base 5. The Babylonians used base 60. One hesitates to imagine what sorts of unshoed _ménages à trois_ were involved when they needed to calculate. ---
**Author:** ![Tim\_R.Mortiss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim_r.mortiss/32/142_2.png) [@Tim\_R.Mortiss](https://boards.straightdope.com/u/Tim_R.Mortiss)\ **Post date:** [June 5, 2012, 3:29pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/24 "2012-06-05T15:29:13Z")
> [@Shawn1767](#): > > Tim R. Mortiss, if we used base 8 would we even have decimals? Okay, you got me. I shouldn’t have used the term “decimals” as that implies a base of 10. But we would still have fractions, and I think they would be much cleaner and neater in a base-8 system. Especially when dividing things by two. Of course, if we found it more common to divide things by three, a base like 9 would have made things more convenient. ---
**Author:** ![Dervorin](https://avatars.discourse-cdn.com/v4/letter/d/eb8c5e/32.png) [@Dervorin](https://boards.straightdope.com/u/Dervorin)\ **Post date:** [June 5, 2012, 3:35pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/25 "2012-06-05T15:35:27Z")
> [@Tim\_R.Mortiss](#): > > Okay, you got me. I shouldn’t have used the term “decimals” as that implies a base of 10. But we would still have fractions, and I think they would be much cleaner and neater in a base-8 system. Especially when dividing things by two. Octimals, perhaps. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [June 5, 2012, 3:41pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/26 "2012-06-05T15:41:39Z")
> [@Tim\_R.Mortiss](#): > > If they’d asked me way back when, I’d have suggested base 8. As a great philosopher once said: [QUOTE=Tom Lehrer] Base eight is just like base ten really - if you’re missing two fingers. [/quote] ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [June 5, 2012, 3:51pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/27 "2012-06-05T15:51:11Z")
> [@Dervorin](#): > > Octimals, perhaps. I’ve heard “oits” used. But not widely, for obvious dignity-related reasons. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [June 5, 2012, 4:39pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/28 "2012-06-05T16:39:56Z")
> [@Bytegeist](#): > > I can’t imagine base 11 would ever be popular, even if we started afresh — but maybe that’s just me. Well, if you’re counting, see, and you get to 9, then go one more, then where do you go from there? With this base, what we do is give it that extra push over the cliff, one more, to put it up to eleven. Counting in 12s is easy to do with the finger bones on one hand. There’s no need to remove the bones and count them individually. Count the tips, then the knuckles by using the thumb. 16 works if you go all the way from the tip to the palm. ---
**Author:** ![Dendarii\_Dame](https://avatars.discourse-cdn.com/v4/letter/d/bbce88/32.png) [@Dendarii\_Dame](https://boards.straightdope.com/u/Dendarii_Dame)\ **Post date:** [June 5, 2012, 5:45pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/29 "2012-06-05T17:45:59Z")
> [@Bytegeist](#): > > Of course, base 6 would lengthen the representation of many numbers, compared to either base 10 or 12, and it would shrink the catalog of _Schoolhouse Rock_ cartoons. > > So there is a cost. Dern tootin’. Can’t have that, especially since I’m a fan of “Good 11.” ---
**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:** [June 5, 2012, 5:53pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/30 "2012-06-05T17:53:58Z")
And the Mayan system wasn’t quite a pure base-20 system, either. It’s also partly base 18, to accommodate 360 (an approximation of the number of days in the year). ---
**Author:** ![Perderabo](https://avatars.discourse-cdn.com/v4/letter/p/a183cd/32.png) [@Perderabo](https://boards.straightdope.com/u/Perderabo)\ **Post date:** [June 6, 2012, 8:54am UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/31 "2012-06-06T08:54:21Z")
> [@Gary\_T](#): > > Whence these zeroes? I suspect when proto-humans were counting things, they didn’t start with zero. Maybe, but then it probably didn’t take long to notice that they didn’t always have at least one of every conceivable object. Sometimes you run completely out of stuff. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [June 6, 2012, 9:05am UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/32 "2012-06-06T09:05:22Z")
> [@Perderabo](#): > > Maybe, but then it probably didn’t take long to notice that they didn’t always have at least one of every conceivable object. Sometimes you run completely out of stuff. The concept of zero is a surprisingly modern invention. That is not to say that early peoples didn’t have a concept of “nothing,” just that the idea that a number could be analogous to nothing is not obvious. ---
**Author:** ![DSeid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dseid/32/20194_2.png) [@DSeid](https://boards.straightdope.com/u/DSeid)\ **Post date:** [June 6, 2012, 11:45am UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/33 "2012-06-06T11:45:03Z")
> [@The\_Niply\_Elder](#): > > An apparently silly question, but, humans couldve looked at their hands and create a base 5 numering system, allowing much larger numbers to be stored in 10 digits (before having to mentally roll over). Riddle me that. > [@Jragon](#): > > … You’d actually be able to store LESS into in 10 digits, the biggest base 5 number in 10 digits is 4444444444=(000)9765624\*, as opposed to 9999999999 > > - The zeroes are added to point out that it’s in fact three digits shorter. > > Unless you’re referring to having one hand be the “25s place” and one hand being the “5s place”, in which case I retort “yeah, well I can count on binary on my hands to get really big numbers so :p!” (Don’t count to 4 or 5 in binary starting with the thumb as 1). > > ETA: Now that I think about it, what I described wouldn’t be base 5, it’d be base 6. 0-5 on one hand, {6,12,18,24,30} on the other. > > ETAETA: Actually, that’s a good question even for base 10. Our hands can represent 0-10, why not roll over places on 11? It makes more sense to me to say my two hands can represent the numbers 0-A, and when I start over it’s 10 (aka 11). I think he means counting to two places, one hand for 1 to 5 and the other to keep track of up to 5 sets of 5s, hence up to 25 (or arguably 30) on two hands. Base ten does not leave you another hand to keep track of the how many groups of tens. Now of course, as I pointed out in that past thread, that’s why some cultures have used dozens and 60s - it works better for larger groups numbers on your hands: count the 3 phalanges of the 4 fingers with the thumb of one hand - that’s 1 dozen, keep track of up to five dozens with the fingers and thumb of the other hand - that’s 5 dozens, 60. An advantage of finger counting is that it is easy to keep your place and not worry about being distracted causing you to have to start all over again - leave the three fingers on one hand up and the thumb on the second phalange of the third finger (second finger not counting the thumb) and if distracted you know you had gotten up to three dozens five and can keep going. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [June 6, 2012, 12:37pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/34 "2012-06-06T12:37:10Z")
Learn to count in base two and you can count to 1023 with both hands. Sadly it is physically very difficult verging on the impossible, but a nice idea in concept. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [June 6, 2012, 4:40pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/35 "2012-06-06T16:40:44Z")
It’s slightly misleading to think that every counting system has a “base”. Take Roman numerals. What base are they in? They simply don’t have a positional system like our modern numbering system. They have symbols for 1, 5, 10, 50, 100, 500, and 1000. So they had an idea that multiples of 5 and 10 were important numbers. But this isn’t a “base 10” numbering system. It’s clearly derived from a simpler tally marking system, where collections of small numbers are grouped. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [June 6, 2012, 8:58pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/36 "2012-06-06T20:58:35Z")
> [@Lemur866](#): > > It’s slightly misleading to think that every counting system has a “base”. Take Roman numerals. What base are they in? They simply don’t have a positional system like our modern numbering system. They have symbols for 1, 5, 10, 50, 100, 500, and 1000. So they had an idea that multiples of 5 and 10 were important numbers. But this isn’t a “base 10” numbering system. It’s clearly derived from a simpler tally marking system, where collections of small numbers are grouped. Roman numerals is not what makes their number system base ten. Spoken numbers going 1-10, 10 and 1, 10 and 2, …, 10 and 9, 20, … 100, two 100, however, makes it base ten. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [June 7, 2012, 4:29pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/37 "2012-06-07T16:29:21Z")
Is that how the Romans said numbers? They’d see MCMXII and say, “One thousand nine hundred and twelve”? Or, the latin equivalent? The way we say numbers in the modern era is a consequence of our positional numbering system. ---
**Author:** ![Darth\_Panda](https://avatars.discourse-cdn.com/v4/letter/d/ee7513/32.png) [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)\ **Post date:** [June 7, 2012, 4:47pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/38 "2012-06-07T16:47:35Z")
Base 16 is the answer to all of life’s problems. It makes sense if you’re a pirate. Or a laser printer. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [June 7, 2012, 5:03pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/39 "2012-06-07T17:03:57Z")
> [@Lemur866](#): > > The way we say numbers in the modern era is a consequence of our positional numbering system. No, not really. Most Indo-European languages developed verbal expressions for numbers combined from multiples of the powers of ten beginning with the highest power (e.g., “three thousand four hundred and twenty-two”) long before they adopted a positional system for writing numerals. For example, Old English texts are full of expressions like [“an þúsend & feower hundred & feowertig”](http://books.google.com/books?id=9ieC-0AWVMYC&pg=PA104), i.e., “one thousand four hundred and forty”. It’s true that pre-modern languages did have more **variety** in their ways of verbally expressing numbers: e.g., “fourscore” for 80 or “thrice seventy” for 210 (in Vedic Sanskrit, for example) or “three-and-twenty” for 23. Some of these variant forms are still in use, like “nineteen hundred” for the more standardized form “one thousand nine hundred”. But there is absolutely nothing new about the current “standard” form of expressing numbers verbally as a sequence of multiples of successively decreasing powers of ten. Nor was it developed in imitation of the decimal place-value notation for numerals: it already existed in pre-modern and even pre-literate forms of the languages that use it. ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [June 7, 2012, 5:08pm UTC](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105/40 "2012-06-07T17:08:16Z")
> [@Sunspace](#): > > It would have been so easy to get base 12 from this–just add palms. Then metric would have been base 12, and we could have quarter-kilos and third-litres easily. One of the few advantages of the Imperial system would remain in our current measuring system. Base 12! [http://boards.straightdope.com/sdmb/showthread.php?t=581761](http://boards.straightdope.com/sdmb/showthread.php?t=581761) [Previous page](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105.md?page=1) [Next page](https://boards.straightdope.com/t/free-basing-why-do-humans-use-base-10/624105.md?page=3)