In mathematics, Cutler's bar notation is a notation system for large numbers, introduced by Mark Cutler in 2004. The idea is based on iterated exponentiation in much the same way that exponentiation is iterated multiplication.
Contents
Introduction
A regular exponential can be expressed as such:
However, these expressions become arbitrarily large when dealing with systems such as Knuth's up-arrow notation. Take the following:
Cutler's bar notation shifts these exponentials counterclockwise, forming
This system becomes effective with multiple exponent, when regular denotation becomes too cumbersome.
At any time, this can be further shortened by rotating the exponential counter-clockwise once more.
The same pattern could be iterated a fourth time, becoming
Advantages and drawbacks
The Cutler Bar Notation can be used to easily express other notation systems in exponent form. It also allows for a flexible summarisation of multiple copies of the same exponents, where any number of stacked exponents can be shifted counter-clockwise and shortened to a single variable. The Bar Notation also allows for fairly rapid composure of very large numbers. For instance, the number
However, the system reaches a problem when dealing with different exponents in a single expression. For instance, the expression