Googol

No, my title is not a spelling error of Google. Googol is a number, a big number, a number that was so large and intriguing it inspired two nerdy University Student to create an easily available to everyone search engine to bring all of the internet to anyone. But talking about Google being awesome is a different article for a different time.

In this article I'm going to discuss the number a googol and a googolplex. Firstly what are they? Well a googol is 10¹⁰⁰, that is a one followed by one hundred zeros, or the less catchy title, ten duotrigintillion. Just how big is that then? Well, there is estimated to be about 1.33×10⁵⁰ atoms in the entire Earth. A googol is almost 10⁵⁰ as much as this number. Nothing like maths to make you feel tiny and insignificant.

If you think that's large, your head may just explode when you're introduce to a googolplex. A googolplex is 10^googol, that is enormous. A one followed by a googol zeros. That is so large it is almost impossible to comprehend. I'll try my best to explain just how mammothly big this number is.

Astronomer Carl Sagan estimated that writing a googolplex would be impossible, why? It would require more space than the known universe can provide. Seriously. There is only about 2.5×10⁸⁹ elementary particles in the known universe, so even if every particle was a digit, it would still need the observable universe to be about one hundred billion times larger.

But, if you could fit the number into the known universe it would take an unbelievable amount of time to write. If you could write 120 digits a minute, it would take around 1.51×10⁹² years to finish (almost a googolplex years!). This amount of time is 10⁸² times the age of the universe. So, I wouldn't really start trying to write it out. There's a high chance, that even if it was possible to write for that period of time, that the entire universe will have inevitably died.

A more nerdy way to try and explain the size of a googolplex is to look at Planck time. Planck time (which I won't go into too much detail now), is the time it takes for light to travel one Planck length in a vaccuum, which is roughly 5.4×10^-44, this is unbelievably quick. A googol is larger than the estimated amount of Planck times that have past since the start of the universe (8×10⁶⁰), so a googolplex is much, much larger than even the smallest measurement of time that has past since the dawn of everything.


There is however a larger number that still has a use, it is known as Graham's number. But that's a different article for a different time. I hope this post has given you a small idea into the enormity Maths can hold.