The birth of the forbidden number
The magic of the complex plane
Surpassing i with quaternions
The infinite climb of dimensions
007skaty The Cayley-Dickson construction doubles the dimensions of mathematical number systems.
007skaty The 8D Universe
Forget the i, let's step right through the gate, Where tiny strings vibrate in dimensions eight.
007skaty Combine these 16-dimensional numbers to discover why division fails in higher dimensions.
007skaty John T. Graves and Arthur Cayley designed a procedure doubling number dimensions from 1D to 2D, 4D, and 8D.
What is the name of the algebraic process used to double the dimensions of a number system?
Starting with real numbers, how many dimensions are created in the third step of this construction?
007skaty The eccentric octonions introduce seven distinct imaginary units to modern algebra.
The magic eight: Octonions are so mathematically perfect for 8D space that they are used to solve the 'kissing number problem,' packing spheres in higher dimensions.
What is the name of the sixteen-dimensional number system that follows the Octonions?
What bizarre algebraic property do Sedenions possess that makes division impossible?
An indivisible ultimate unit that is the basic constituent of physical and metaphysical reality. Alexander questions the nature of this ultimate unit, which the text defines as the collective unconscious.
Which cutting-edge theory of physics uses Octonions to model the vibrations of subatomic particles?
In how many dimensions does superstring theory propose our universe actually operates?
007skaty Real numbers, Complex numbers, Quaternions, and Octonions are the only systems where you can add, subtract, multiply, and divide.
Which of these is NOT one of the four division algebras permitted by Hurwitz's Theorem?