A Googol is a $1$ followed by $100$ zeros. That's
Doesn't look so bad!
A Googol is $10^{100}$.
Seems more compact yet, somehow bigger!
A Googolplex is a $1$ followed by a googol zeros!
A Googolplex is $10^{10^{100}}$.
That's a lot bigger!
One way to think about a Googol is as the number of zeros in a Googolplex. Then it make sense to ask questions like the following:
We might also compare that to a famous large document collection of knowledge, like the bible or the Library of Congress.
According to Wolfram Alpha, the KJV has
If we account for punctuation and a space every fourth character or so, that's still fewer that $4.2$ million characters.
How many letters are there in all the books in the Library of Congress? This was a bit harder.
Suppose we could type one character every 4 microseconds. That's
I wonder what that looks like?
If we could type one character every 4 microseconds, I wonder how long it would take to type out the KJV? That's
A pleasant afternoon
If we could type one character every 4 microseconds, I wonder how long it would take to type out the LoC? That's
We can write this a little more compactly
$$ 12.5\times10^{12} \text{ch} \cdot \frac{1\text{sec}}{250\text{ch}}\cdot \frac{1\text{min}}{60 \text{sec}}\frac{1\text{hour}}{60 \text{min}} \cdot \frac{1\text{day}}{24\text{hours}}\frac{1\text{year}}{365\text{days}} $$ $$ =1585.5 \text{years} $$
If we could type one character every 4 microseconds, I wonder how long it would take to type out a Googolplex? That's
$$ 10^{10^{100}} \text{ch} \cdot \frac{1\text{sec}}{250\text{ch}}\cdot \frac{1\text{min}}{60 \text{sec}}\frac{1\text{hour}}{60 \text{min}} \cdot \frac{1\text{day}}{24\text{hours}}\frac{1\text{year}}{365\text{days}} $$ $$ =\frac{10^{10^{100}}}{250\cdot60^2\cdot24\cdot365} =\frac{10^{10^{100}}}{7884000000} <\frac{10^{10^{100}}}{10^{10}} \approx 10^{99} \text{years}. $$
This is still so unbelievably huge it's silly.
The number of particles in the universe is estimated to be $10^{80}$.