0

In our daily lives, we generally use $10$ digits to define the numbers, i.e., $0$ to $9$. Based on these ten digits, we define all the natural, rational, and irrational numbers, etc. This representation is known as the decimal representation.

I know that one could also define the number system in other ways. For example:

  • Unary: 1 11 111 1111 ...
  • Binary: 0 1 10 11 100 ...
  • Hexadecimal: 0 1 2 3 4 5 6 7 8 9 A B C D E F ...

Similarly, I can define my own number system, for example say: $\alpha \,$ $\beta\,$ $\gamma\,$ $9\,$ $\alpha \alpha \,$ $\beta^{2} \alpha\,$...

But I am wondering, why do we use the decimal system to learn mathematics or say in our everyday lives. I know that a computer uses a binary number system since the most basic unit of storage is $0$ or $1$. However, I want to know, why humans use the decimal number system. Is there any logical advantage of using decimal representation over say Unary, Binary, or anything other? Thanks.

IY3
  • 92
  • 10
    This would probably be a better fit for the history of math stackexchange. – Noah Schweber Jan 29 '21 at 16:48
  • 2
    The logical advantage is that it's the system everyone else uses. – Misha Lavrov Jan 29 '21 at 16:49
  • 6
    This is generally attributed to the fact that we have ten fingers. And now that everyone uses base-10, the cost of switching to a more logical base system is just too great. – Joe Jan 29 '21 at 16:51
  • But also it's interesting to note that, the way human hands are designed, it seems like base six might have been a better choice for counting on fingers. – littleO Jan 29 '21 at 16:56
  • One reason that binary is impractical for humans is that the number of bits needed to represent numbers of moderate size is larger than what many humans seem to be able to remember. 2021 is easy for most humans to remember in a way that 11111100101 is not, even though they convey the same information. In the same way that I can remember my zip code but not my credit card number, there are tradeoffs between the amount of symbols to potentially get wrong, the size of the set of symbols, and human memory. TW Korner has a good discussion of alternate bases in "The Pleasures of Counting" Ch. 10. – leslie townes Jan 29 '21 at 17:00
  • 1
    "Based on these ten digits, we define all the natural, rational, and irrational numbers" Not sure if this is just bad wording, but I would like to strongly note that none of the definitions for any of these sets of numbers relies on the decimal system. (It sounds as if you're thinking that in binary or hex, some numbers would be (ir)rational which are not in base $10$. That's not the case.) – Torsten Schoeneberg Jan 29 '21 at 20:42

1 Answers1

0

We use the base $10$ because we have $10$ fingers, and we learn how to count with them.

Note that there were some people (https://en.wikipedia.org/wiki/Numeral_system) who used base $8$ to count, and it was due to the fact that they would count between knucles instead of counting on fingers

NHL
  • 1,045
  • 1
    Well I'm not convinced by this fingers (only) explanation, many old numerations systems where constructed on base $12$ because we can count on our $12$ phalanxes with the thumb. So the decimal system must have had other advantages to impose itself over the duodecimal one. – zwim Jan 29 '21 at 18:40