- Most everyone is familiar with the “real” numbers, but far more types of numbers exist. Among them, the best known are the complex numbers, which include a square root of –1.
- We can build higher-dimensional number systems as well. But we can define all the four basic operations—addition, subtraction, multiplication and division—in only a few special cases.
- One such case is the octonions, an eight-dimensional number system. Mathematicians invented it in the 1840s but, finding few applications, paid little attention for the next 150-plus years.
- Mathematicians now suspect that the octonions may help us understand advanced research in particle physics in fields such as supersymmetry and string theory.
As children, we all learn about numbers. We start with counting, followed by addition, subtraction, multiplication and division. But mathematicians know that the number system we study in school is but one of many possibilities. Other kinds of numbers are important for understanding geometry and physics. Among the strangest alternatives is the octonions. Largely neglected since their discovery in 1843, in the past few decades they have assumed a curious importance in string theory. And indeed, if string theory is a correct representation of the universe, they may explain why the universe has the number of dimensions it does.
The Imaginary Made Real
This article was originally published with the title The Strangest Numbers in String Theory.