This article may be confusing to those who are not familiar with different number bases, so I will give a brief explanation. A number base is generally defined by the number of digits used in that base. The most commonly used base is base 10 or decimal, which has the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Notice that there are 10 digits. The base of a number system also defines what the difference places mean. In all bases, the first place is always 1s. The next place is the the base itself. For base ten, the second place is the 10s place. The third place is the base squared (100 in base 10), the fourth is the based cubed (1000, in base 10) and so on. Another common base is base 2 or binary. Base 2 has 2 digits, 0 and 1, and the places are powers of 2. The first place is 1s, the second is 2s, the third is 4s, and so on. Some bases have more than 10 digits. Base 16 or hexadecimal has 16 digits. It uses 0 through 9, like base 10, but it runs out of traditional digits there, so it adds A, B, C, D, E, and F for the 10, 11, 12, 13, 14, and 15 digits. Other systems (like base 12) have been invented that reuse other symbols or have unique symbols for those past 9. Math in different bases works very much like base 10, except that you carry and borrow differently, based on the number of digits available.
There have been numerous discussions about numerical bases. Base 10 is rather inconvenient in many aspects, and bases like 12 have some significant benefits. Base 12 is especially useful, because it makes common fractional math extremely easy. Base 12 makes division by 2, 3, 4, 6, and 12 trivial. In base 10, 1/3 = 0.333... This makes any math involving division by 3 complicated and difficult. Even division by 4 is a bit hairy in base 10, where 1/4 = 0.25. The problem with this is that the most frequent division we do is division by small numbers. We might divide a restaurant bill between 2, 3, or 4 people. If there are more people than that, they are generally in groups, where 2, 3, or 4 people end up paying. A great example of why base 12 works so well is time. Seconds and minutes are counted in base 60, but hours are counted in base 24 (in this case, base 24 is just double base 12, so it works the same way). If we need to break up the time for some task between several people (work shifts, for example), base 24 makes it easy. An 8 hour shift is 1/3rd of a day. If you have 4 people, you have 6 hour shifts. It does not work so well with 5 people, but with 6 people, you have 4 hour shifts. With 8 people, it is 3 hour shifts. The fractions involved here, 1/2, 1/3, 1/4, and 1/6, are not just found in time math though. They are found all over the place. The argument for switching to base 12 is quite strong, but there are some problems with it.
The biggest problem with base 12 is that it is not a natural base for humans. We don't have enough fingers to count in base 12 on our hands. This is actually the only logical argument against using base 12. The other problems all stem from the fact that nearly all historical math uses base 10, and while teaching base 12 to children should not really be any more difficult than teaching base 10, it would not be sufficient. Children would have to learn both base 10 and base 12, because there is so much work done in base 10. They would also have to learn to convert between them. Besides that, a lot of practical stuff would have to be transitioned, at great cost. This would include speed limit signs, prices, a huge number of computer programs, measurement systems (though some, like the Imperial System, are already partway there), and the entire world would have to change at the same time to avoid international confusion. It is just not practical. There are certainly major benefits, but they are not worth the cost.
So, why do we use base 10 in the first place? Supposedly it is because it is the most natural way to count for a species with 10 fingers. If humans had 6 fingers and each hand, we would probably count in base 12 instead of base 10. The problem is that this is not actually true. Base 10 is not the most natural way to count for a species with 10 fingers. We actually use base 10 because of a mistake. That mistake is caused by the fact that humanity learned to count before the number 0 was discovered.
The real natural way to count with 10 fingers is base 11. Because humans had not discovered 0 though, only the 10 positive digits that can be counted on hands were considered. In fact, looking at ancient writing systems, we will find that many don't use base 10. Many also have a single glyph (or digit) for the number 10 (instead of combining 1 and 0). Many civilizations that learned to count from fingers had difficulty counting higher than 10, because the lack of a 0 made the place value system currently used almost impossible to discover. A few civilizations did create a placeholder digit for this, but it had no meaning by itself. At least one just left a blank space for empty places, which often made the numbers difficult to interpret. There was clearly a lot of confusion over this, but ultimately, base 10 came to the forefront. Our current base 10 system seems to come from Arabic, which retained the 10 digits idea, but shifted it down one to include 0 and exclude 10. The fact, however, is that on 10 fingers, you can represent digits from 0 to 10, which is actually 11 digits, not 10. Counting on 10 fingers, if you realize that 0 is a number, naturally leads to a base 11 system, not a base 10 system. (Be glad we did not get stuck with base 11 though. As a prime number, 11 is not divisible by anything but 1 and itself, which puts it in the category of the worst possible bases for practical use. In base 11, even division by 2 is difficult!) If you dig a bit deeper though, you might find something else that is interesting.
Base 10 is not the only common number system used anciently. Aside from some very unusual systems, like Roman Numerals that do not have a clear base, there are some that use smaller bases very effectively. The Mayan system (which did include 0) was written in base 5, presumably originating from the fact that humans have 5 fingers. The Mayans are not the only example of a civilization that used base 5. Base 10 systems seem to be the most common, historically, but base 5 systems are actually quite common as well. Even modern tally marks use base 5. The interesting thing with base 5 with fingers though, is that when you include 0 and get base 6, you get a base that is actually quite useful!
Like base 10, base 5 is not natural, because 5 fingers offer 6 digits, if 0 is not forgotten. Base 6 is the natural base for counting with 5 fingers. Including 0 through 5, you can represent a single base 6 digit on one hand. Unlike 11 or even 10, base 6 is quite flexible. It is not as flexible as base 12, but it is, perhaps, close enough. Base 6 fixes the division by 3 problem just as well as base 12. In base 6, 1/3 = 0.2. Base 6 does not fix division by 4, but it does not make it any worse: 1/4 = 0.15 in base 6. It still manages division by 2 as gracefully as base 10 or 12: 1/2 = 0.3 in base 6. The only thing lost that base 10 provides is division by 5, which is only important because we use base 10 everywhere: 1/5 = 0.12 (though, this is no worse than 1/4 in base 10). The advantage base 6 has over base 12 is that you can count in base 6 on your hands. Base 6 has another significant advantage over base 12 and base 10 in hand counting though: Since you only need 6 digits, and these can be supplied with only one hand, the second hand can be used for a second place, which in base 6 is the 6s place. In other words, you can count to 35 on your hands in base 6! (In base 6, 35 is written 55, which is 5 fingers on each hand.)
It turns out that there are two natural ways for humans to count using their fingers. The most obvious one is base 11, and the less obvious one is base 6. Base 11 is completely unsuitable for practical math, but base 6 is surprisingly good. Not only that, but base 6 allows counting to 35 using two hands.
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