Did you say google?

Many people have heard of a googol. No, not google, the term googol describes a number which can be written as a 1 followed by 100 zeros. Maybe you have even heard of a googolplex. This number is a 1 followed by a googol zeros. A googolplex is so large that if you numbered every plank length point in space you would run out of room in the visible universe before finishing. But this is just a tiny spec.

Lets get bigger MUCH BIGGER.

3^^^^3

we all know 3^3 is 27
well 3^3^3 is 3^27 or 7,625,597,484,987
Now you probably can't picture what 3^3^3 is but you at least have a concept of what 7.625 trillion is.

When these terms are combined the up-arrow ^^ notation invented by Donald E. Knuth can be used.
3^3^3 can be re-written using up-arrow ^^ notation as 3^^3 lets add one more ^.
3^^^3, the number we are discussing is equal to 3^^(3^^3)
This is a series of 3^3^3^...^3^3^3 with a total of 7,625,597,484,987 terms.

Exponent towers

The series of 3^^^3 can be visualized by picturing an exponent tower of 3s which is composed of 7.6 trillion terms.
What about an exponent tower of 3's that contains 3^^^3 terms.
That only gets us to 3^^^4.
An exponent tower of 3's with 3^^^4 terms.
That is just 3^^^5.
Repeat this process 3^^^3 times.
That inconceivable number is 3^^^^3

But wait it gets worse

Imagine a series of 3^^....^^3 where there are 3^^^^3 arrows in the series.
Then take that number and stack it in another tower of 3^^^^3's up arrows.
Repeat this process 62 more times.

Welcome to Graham's Number

64 levels of magnitude removed from reality we reach Grahams Number. It was created as an upper bound on the solution to a problem in Ramsey theory. Relating to possible degrees of freedom in hypercubes. I can not tell you in words nor mathematical notation what Grahams number is. The last 12 digits are 262,464,195,387. Mathematicians have discovered the last 500 digits.