I have always been fascinated by large numbers and one of the largest numbers ever to be used in a mathematical proof was Graham’s Number. Named after Ron Graham, an American mathematician this number is so big that it is near impossible for the average person to come to grips with its size. To give the number justice and give credit to this great mathematician I have attached a couple of videos from Youtube that help explain it.
While the videos explain what Graham’s Number is and how big it is the main point behind a large number is that it has to represent something real or have some kind of unique process to how it was derived. In other words you cannot just take a very big number and add 1 to it and say that is a bigger number.
To get some perspective on just how big Grahams Number is, even if we took a Google (10 to the power of 100) or a Googleplex (10 to the power of a Google), these numbers would not even come close. In fact even if we filled every available quantum sized piece of space in the universe so that a sub atomic particle was packed next to another sub atomic particle and these were jam packed to fill the entire observable universe then the total number of particles would pale into insignificance in comparison to the size of Graham’s Number.
Now I struggle in explaining things from here but basically Graham’s Number has something to do with finding the upper bound in the number of dimensions it would take to ensure that when you draw a line between 4 vertices on a single plane that you are forced to have all lines drawn in the same color. It is best to watch the below videos which explain things a lot better.
What is Graham’s Number? This video explains the purpose of the number
How big is the number and how do we calculate it? This video explains how we get to it.
Graham’s Number really puts us in perspective and lets us know just how finite we are in this Universe. It has been a point of inspiration for me and the motivation behind the naming of this Stakepool.
R.I.P Ron Graham (1935 – 2020)