‘Life would be Simpler If We Counted in Base 12.’ Do you agree with this statement?

The decimal system is the most commonly used counting system in our everyday lives. While it feels logical and intuitive to count in chunks of ten, the decimal system is adopted because of one simple reason: we have ten fingers. Had our ancestors been born with twelve fingers, perhaps we would have used the dozenal system. In fact, a few tribes used number bases other than ten, Mayans counted in twenty and Babylonians counted in sixty.

While we have been used to counting in ten, this shouldn’t discourage us from exploring other number systems. In the vast world of number systems, the dozenal system stands out to be a better one than the decimal system. It is a number system that uses twelve digits instead of ten and each digit represents a power of 12.

As suggested by advocates of the dozenal system, base-12 would fare much better for our day-to-day, human applications. As a matter of fact, there is a myriad of examples of base-12. For timing and dating systems, there are two sets of twelve hours in a day and twelve months in a year. When counting eggs, pastries, and inches, we use dozens. Besides, twelve pitches come up in a chromatic scale and twelve inches make up to afoot! Because of this, the vocabulary for counting in twelve already exists. You just need to count one up to eleven and then a dozen, and so on until two dozen, three dozen, and four dozen. A dozen dozen is a gross and a dozen gross is a great gross. Because we need to have two extra symbols in base-12, we would call ten ‘dek’ (Ⅹ) and eleven ‘el’ (Ɛ). In the dozenal system, a twelve (10) is called ‘doh’ instead of twelve or dozen and a gross (100) is called a ‘gro’ and a great gross (1000) is called ‘mo’.

In my opinion, life would indeed be simpler if we counted in base 12. Let’s delve into why the dozenal system is superior to the decimal system entrenched in our lives.

One reason that base-12 trumps base-10 is that it is a highly composite number. In fact, it has four distinct factors: 2, 3, 4, 6. Meanwhile, the number ten only has 2 and 5 as its divisors. While it seems perplexing at first to count using the dozenal system, the same can be said for a child learning the decimal system for the first time. Once we have got used to counting in twelve, we will realize the tremendous benefits it brings us. Even though high level mathematics would not change if we adopted the dozenal system, base-12 would make our everyday lives much easier. For instance, learning multiplication for the first time as a child is a difficult and demanding task. The easiest multiplication tables to learn in any base are the numbers that divide that base. Looking at base-10, we know that the two and five multiplication tables are the easiest to learn because they are just even numbers and numbers ending in fives and zeroes. On the other hand, base-12 would provide a more convenient tool for us to learn multiplication. Since the number 12 can be divided by 2, 3, 4 and 6. There are distinct, recurrent patterns in the tables, making multiplication much easier to learn and memorize.

However, what mathematicians appreciate about the dozenal system doesn’t lie in multiplication, rather in the inverse of multiplication, division. Consider the fraction 1/3 in base-10, it works out to be 0.3 recurring. In the dozenal system, 1/3 is equivalent to 4/12, and 12 is the same as 10 in base-12, so the fraction becomes a neat decimal, 0.4. Likewise, 1/4 in decimal is 0.25 and in dozenal it becomes a slightly simpler version, a 0.3.

Defenders of the decimal system pointed out that base-12 would not be as efficient as base-10 because we don’t have ten fingers. However, as dozenalists like to point out, humans can utilize the biology of our finger structure to count in twelve with ease. Starting with the index finger, we can identify one, two and three on from the bottom to the top of the finger. And we can do the same for our middle finger, ring finger and our little finger.

Another advantage of the dozenal system is that it is the optimal compromise between symbol size and high divisibility. While larger number bases like base-60 and base-5040 has more factors than base-12, there are so many more symbols than base-12 that one needs to memorize. With base-12 there are more factors than base-10 and we only need to learn two extra symbols. In addition, counting in base-12 allows one to represent bigger numbers with smaller units than in base-10, thus having smaller space complexity.

Finally, a lot of our present ways of measuring weight, capacity, space, distance, time, latitude and longitude are based on geometrical and physical laws that the decimal system cannot meet. The fact that a circle has 360 (12x30) degrees is a good case in point. Besides there are 60 seconds in a minute and 60 minutes in one hour. Clearly, with base-12, we enjoy a lot of advantages with our natural measurement.

Unfortunately, switching to base-12 from base-10 would, by and large, be impractical and time-consuming. The obvious reason is that we are accustomed to a different number system, namely the decimal system. Even if we started counting in twelve, it would always feel more natural and intuitive to count in ten because we are more used to it. People would have to remember two more symbols before counting and calculating. Learning to read numbers correctly would also take a significant period of time. While there are many long term benefits to switching to base-12, it might not be worth the short term hassle. Besides there would be a chain of side effects as a consequence of switching to base 12. Numbers are used in a multitude of applications, and we would have to change all of the numbers to suit the dozenal system. One apparent thing to do is to change the dates in calendars and books, especially mathematics textbooks have to be rewritten under the dozenal system. The keyboard I am using to type this article also has to be redesigned. You see, literally everything in the world would have to transform if we were to switch to the dozenal system. And economically speaking, the opportunity cost of doing so would be too high that we might be better off changing something else.

While the decimal system isn’t as good as the dozenal system, it does serve to be a system that most people don’t have great difficulties understanding. Thanks to the biology of the structure of our hands, it feels natural to count in base-10. Also, we only need to know ten units to start counting and calculating. Quoting from The Universal History of Numbers by Georges Ifrah, ‘To be sure, base 10 has a distinct advantage over larger counting units such as 60, 30, or even 20: its magnitude is easily managed by the human mind, since the number of distinct names or symbols that it requires is quite limited, and as a result addition and multiplication tables using base 10 can be learned by rote without too much difficulty.’ It is an easy task to use the decimal system.

Indeed, there are a couple of advantages and disadvantages in both systems, but ideally, life would indeed be simpler if we counted in base-12. Not only does counting in base-12 allow us to have nicer numbers in division as well as recurring patterns in multiplication, it also paves a smoother path for children to learn basic multiplication. This could potentially improve the general level of numeracy in children and adults, thus making transactions in our everyday lives more convenient. Also, it wouldn’t affect serious mathematics if we switched to the dozenal system. While it is easy to count in ten because we are born with ten fingers, it’s just as easy to count in twelve thanks to the structure of the index finger, the middle finger, the ring finger and the little finger. As mentioned above, there are lots of examples that show how the dozenal system can meet the geometrical and physical laws on which ways of measuring are based. However, the decimal system we are using doesn’t quite meet those laws. Undeniably, switching to the dozenal system would cause tremendous resources and time for society. That said, in a hypothetical situation, life would be so much simpler if we were to use the dozenal system.

Had our primate ancestors been born with six fingers on each hand, we would have easily adopted the dozenal system, thus enjoying the benefits it has over our decimal system.

This is a free newsletter, but if you would like to be one of my early supporters, consider becoming a paid member so that I can continue to bring out quality mathematical treats. 🍩

Happy reading,

Barry 🍩