2/Historical Note

From ProofWiki
< 2
Jump to navigation Jump to search

Historical Note on $2$ (two)

The number $2$ (two) is understood to have been treated as a special case of a number from the earliest historical records.

Many early languages have specific forms of nouns for when two of an object are under consideration, as well as different forms for singular and plural.

To the ancient Greeks, in addition to having problems with the idea that $1$ is a number, it was questionable whether or not two ($2$) was actually a number either:

While it has a beginning and an end, it has no middle
Multiplication by $2$ consists merely of adding a number to itself, and multiplication was expected to do more than just add.

Thus $2$ was an exceptional case.

To the Pythagoreans, odd and even numbers were considered to be either male or female, but sources differ on which was which.

Some suggest that $2$ was considered to be the first male number, and said to personify the principle of diversity.

Such sources state that in contrast, the odd numbers were considered to be female.

However, other sources suggest that it was the even numbers which were female, while the odd numbers were male.

The dyad, as such, is never specifically defined in Euclid's The Elements, but introduced without definition in Power of Two is Even-Times Even Only.

In the words of Euclid:

Each of the numbers which are continually doubled beginning from a dyad is even-times even only.

(The Elements: Book $\text{IX}$: Proposition $32$)