Plato’s One

The starting point of the modern science is the statement of Descartes: “Cogito ergo sum” (1). The premise of his statement is that the self has properties of the natural number one, which is defined by Plato (2). Plato described in The Republic as follows.

O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you demand, and each unit is equal, invariable, indivisible, –what would they answer?

They would answer, as I should conceive, that they were speaking of those numbers which can only be realized in thought.

This idealized one is Plato’s one, which is the base of all logical thinking. The importance of Plato’s one is increasing in the present age. Now, the digital revolution is in progress. Digital data consists of Plato’s one. It should be noted that “0” of digital data isn’t “0” as a number.

As shown above, 0 of the number is divisible, but 0 of digital data is indivisible. Furthermore, “1” of digital data isn’t a common number. We don’t regard the natural number one as indivisible unlike the ancient Greeks.

That is, our common number one is divisible. Rather, “1” and “0” of digital data are similar to alphabets. For example, “A” of alphabets is equal, invariable, indivisible. Indeed, the computer can handle not only the number but also the text.

Next, the very important difference between Plato’s one and an alphabet is the sensible property. Because the major role of the alphabet is the communication, it must have sensible properties. In contrast,  Plato,s one has no sensible property.

In conclusion, the electrical signal of the computer is very close to Plato’s one. It has no sensible property. Furthermore, it must be indivisible, invariable and equal to each other. Companies all over the world actually compete toward the ideal signal. The base of the digital revolution is Plato’s one.

References

1. The Starting Point of All Science

2. What Is the Natural Number One?