4/Historical Note
Historical Note on $4$
The number $4$, as was $8$, was associated by the Pythagoreans with the concept of justice, being evenly balanced: $4 = 2 + 2$, where $2$ is the principle of diversity.
Throughout history, the number $4$ has been regarded with particular significance.
There were originally believed to be $4$ elements out of which everything was formed:
- Earth, Air, Fire and Water.
There are $4$ humours:
- Sanguine, Melacholic, Choleric and Phlegmatic.
There are $4$ cardinal points of the compass:
- North, East, South and West.
There are $4$ seasons of the year:
- Spring, Summer, Autumn and Winter.
In the Old Testament, there were $4$ rivers which watered the Garden of Eden:
- Pishon, Gihon, the Tigris, and the Euphrates.
In Islam, these rivers are:
- Saihan (Syr Darya), Jaihan (Amu Darya), Furat (Euphrates) and Nil (Nile).
In the New Testament, there are $4$ Gospels:
- Matthew, Mark, Luke and John.
To bring it all full circle, there are believed to be $4$ fundamental forces of nature:
- Gravitation, the Weak Force, the Electromagnetic Force, the Strong Force.
The most aesthetically pleasing musical intervals are those whose frequencies are associated with the ratio of $1 : 4$.
- Four strong winds that blow lonely
- Seven seas that run high
- All those things that don't change come what may
- But our good times are all gone
- And I'm bound for moving on
- I'll look for you if I'm ever back this way
Sources
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $\text {580}$ – $\text {500}$ B.C.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Pythagoras