Is Base 10 the Best Number System for Humans?

When it comes to number systems, base 10 (decimal) is the one to which most people are naturally inclined. However, considering the question of whether it is the optimal number system for humans is a fascinating exercise in numerical flexibility. Let's explore the advantages and disadvantages of base 10 and other systems, and what the implications are for both humans and computers.

Base 10: A Familiar but Not Optimal Choice

While we are all quite familiar with decimal arithmetic, it is important to understand that there is no inherent superiority of base 10. It is simply the system that has evolved with the natural human condition, with most people born with ten fingers.

Base 2: The Optimal System for Computers
For computers, base 2 (binary) is the most efficient. Binary systems use just two symbols, 0 and 1, which makes it easy for machines to process and store data. In electronic circuits, a switch can be in one of two states: "on" or "off," or "open" or "closed," corresponding perfectly to binary notation.

Base 8 and Base 12: For a Natural Bias in Arithmetic
If humans had evolved with more than two hands and feet (i.e., eight fingers on each hand and eight toes on each foot), we might have naturally gravitated towards a base-8 (octal) or base-12 (duodecimal) system. For instance, a base-8 number system would require digits from 0 to 7, while base-12 would necessitate digits 0-9 and two additional symbols, such as 10 and 11.

Base 36 and Beyond: Complexity and Length
Higher bases, such as base-36, would naturally require a larger number of symbols. For example, base-36 uses all the digits 0-9 and all the letters of the Latin alphabet (a-z). On the other hand, base-24, while using fewer symbols, would make numbers longer when written. For example, in base-24, the number 400 is represented as '100', whereas in binary it is '110010000'. These systems offer their own benefits in specialized fields, such as mathematics and computing, but may not be as practical for everyday human use.

The Flexibility of Base-10 in Human Life

Human history is replete with examples of the use of different bases. The Babylonians, for instance, used a base-60 (sexagesimal) system, which is still prevalent today in measurements of time and angles.

While base-10 is not optimal for all purposes, it has several practical benefits for humans. It is relatively easy to use and count with, making it suitable for everyday arithmetic and financial calculations. Additionally, the divisibility of 10 is far from ideal; it can only be divided by 2 and 5. Compare that to the factors of base-12, which can be divided by 2, 3, 4, and 6, and base-60, which can be divided by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. These properties make base-12 and base-60 more versatile in many practical scenarios.

Scientific and Mathematical Independence
It is worth noting that the laws of physics and mathematics are independent of the number system used to describe them. Numbers themselves transcend the system used to represent them. For example, the laws of Newton, such as F ma, and Einstein's E mc2, are valid regardless of the number base.

Conclusion

The choice of number system is a complex issue, balancing the need for unique symbols with the need for short representations. For mathematical purposes, base 'e' (approximately 2.71828) would be the optimal base in terms of minimizing the number of unique symbols required to represent a wide range of numbers. However, this does not work well for humans, as it lacks the simplicity and intuitiveness of base 10.

For everyday use, base 10 remains the most practical choice, despite its limitations. It balances the need for simplicity and divisibility, making it ideal for human computation and communication. The lesson here is that the core truths of mathematics and physics remain unchanged, regardless of the number system used to express them.

Keywords: number system, base 10, base 2, base 8, base 30