Graham’s Number

» Posted by on Nov 26, 2018 in Business, Science And Technology | Comments Off on Graham’s Number

Let’s make a thought experiment. Imagine the biggest number we can possibly think. 100 septillion?100,000 septillion? Now raise it to the power of septillion. Would that be the biggest number we could every possibly arrive at? Not even close. How about infinity? Surely there’s no bigger number than infinity. The very definition of it tells us that it is unending, that it goes on and on forever. But there is an amount so very huge our human brains can barely comprehend its vastness. I can’t even wrap my mind around the concept of a number this large. But this article will try to shed some light about Graham’s number and how truly enormous it is.

Graham’s Number

History

Graham’s number is a solution that arises out of a problem presented by the mathematical field of Ramsey Theory. It was named after Ronald Graham who provided the number as a simple way of explaining the upper bounds of the problem he worked on with Martin Gardner, a Popular Science writer. It was later published by Gardner in the publication Scientific America in 1977 which made it known to the general public. At the time of its publication, it was the largest positive integer ever to have been presented in a mathematical proof.

Context 

Graham’s number came about as a solution to a mathematical problem. In math, there is such a thing as combinatorics which concerns itself with counting. Its application is vast but primarily combinatorics looks at a network of numbers and their relationship to one another. Mathematicians who deal with this branch for mathematics look at ways to “color in” graphs and links to higher dimensional cubes. They try to count the number of possible relationships each number to each other and basically Graham’s number is the solution for that. The possible relationship is almost unending and hugely, hugely vast.

Analogy

To be honest with you, there is no single mathematician out there wise enough to explain Graham’s number in such a way that normal people would be able to digest it. The best analogy Graham used was in the context of hypercube but I won’t even begin to pretend I know what that is all about. The best analogy that I can come up with is by using groups of people. Take note, this is a very watered down version of the real answer, only used to explain the concept to those, not in the field of mathematics. There are four groups of people and we connect them through lines that we color either blue or red. We try to satisfy the question of what is the smallest value of members for each group to satisfy a given parameter. The lowest possible is 6 and the highest possible answer is Graham’s number.

Mind-Bogglingly Big

Graham’s number is huge, so very huge the entire universe does not have enough information to represent its entirety. People use it interchangeably with infinity but they’re wrong because Graham’s number is finite. It has an ending although it will take close to forever to reach.