Let's start with a Googol. One Googol is equal to 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, or 1e100.
But before we get into a Googol, let's take a look at huge numbers and the universe. So, let's ponder for a moment a number we might be more familiar with - one billion. 1,000,000,000. 1e9. Less than one seventh of the population of the plane; a little over 1% of Bill Gates' wealth; or less than 0.004% of the US national debt. One billion eggrolls weighs 93,570 tons. One billion water bottles would fill two hundred Olympic sized swimming pools to the brim. One billion seconds ago was 31 years ago, and one billion minutes ago was early into the Roman Empire.
But that's just one billion. It's not even remotely close to one Googol, and one Googol is unfathomably smaller than a Googolplex.
Now, the universe contains an estimated 1e80 atoms, but I don't feel like that fully conveys the enormity of that amount. Let's try to understand this number.
So say we have a chessboard, eight squares each way, for sixty-four in total. Now, consider a grain of sand. A grain of sand is a very small thing, and a single handful of sand contains roughly 10,000 grains, which is more grains of sand than there are stars visible from earth. We put a single, miniscule grain of sand on the first square. We then place 2 on the second, 4 on the third, and so on. This may not seem like a rapid increase, but by the sixty fourth square, we have 2^63 grains of sand - which is more than the grains of sand in the entire planet. Now, take that same number, 2^63, but in atoms. It seems like it would be a massive area, right? Wrong. 2^63 atoms is one ten-thousandth of a cubic millimeter! You could fit 92 sextillion atoms in a single cubic millimeter! A cubic millimeter is a thousandth of a cubic meter, and a cubic meter is nothing compared to the size of the planet, which is nothing compared to the solar system, which is nothing compared to the Milky Way, which is nothing compared to the entire universe.
All those tiny, unnoticeable, minuscule atoms are packed so tightly they can make an object seem solid. A single human hair is more than one million atoms - in width! And the entire, vast, seemingly infinite universe is just filled to the brim with these things.
And each and every one of those atoms doesn't even amount to anywhere near a Googol atoms. Let's take a look again at Googol's scientific form - 1e100. 1e2 is one hundred. Every time the number after the 'e' goes up by one, the number is being multiplied by ten, because it represents the number of digits in the number. 1e3 is ten times as much as 1e2. 1e30 seems like it wouldn't be much more than 1e20, but it's ten billion times greater. And the increase between exponents only increases as it goes up. If you were to create a Googol atoms, you would need one hundred quintillion universes!
So clearly, a Googol is enormous. But it's not as much as a Googolplex. After all, there's only 100 zeros in a Googol, and it is an inexplicably large number. Yet, a Googolplex outdoes that, with one Googol zeros. We've established that a Googol is huge, but it can be written out very easily. And in scientific notation, a Googol, this massive, larger-than-the-universe number, is a mere 1e100. A Googolplex is 1e10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 in scientific notation.
So, le's try to fully write out a Googolplex. First, you'll need to become immortal and invincible, because you're really going to be exposed to the elements during this. After that's done, go ahead and take a really big sheet of paper, let's say, oh, the size of North America. Now begin to write down a Googolplex until you've filled up that paper. But normal sized numbers won't do, not at all. You'll have to write your numbers microscopically, let's say each number as tall as the head of a pin. Now cover the entire sheet of paper in numbers.
Then you stack another continent-sized sheet on top of that, and you write down some more. Rinse and repeat until the stack reaches the moon. Now, continue this until you eventually have stretched these papers all the way to the planet Pluto. Then go back to Earth, stacking and writing on papers as you go. Continue to traverse between Earth and Pluto, say, ten thousand times. Now, surely you've got to be finished writing down this number now, right? Nope. Send all the paper you just wrote on to the Andromeda Galaxy to keep it out of our way for now, and let's do that entire process again, and send that new stack to Andromeda once more. Go ahead and do this, oh, ten million times, give or take. Surely, all these numbers have got to be enough to write down a Googolplex. But you're not even close, I'm afraid. Continue at this until you fill up the Andromeda Galaxy with paper. Now, do the same for some more galaxies. Messier 81, Sombrero Galaxy, Whirlpool Galaxy, Triangulum Galaxy, and Centaurus A. Fill all of them completely with stacks upon stacks of paper. You're still not even close, and by now it's safe to assume that you're just about done with writing down numbers constantly.
Unfortunately, all that work was for nothing, because you had no hope of writing down a Googolplex. There's simply not enough space in the entire universe. So we need to change strategies.
You are now going to be writing down one hundred billion numbers - on every single atom in existence. That includes atoms inside objects, atoms that make up air, even all the atoms inside every planet in the universe. Once you've done that, you're going to go to a parallel universe and do the same for all of their atoms. Go ahead and do this for one million parallel universes. Once you've finished writing down this, you've finally finished. You now have written down...a number that is nowhere near a Googolplex. Congratulations.
So obviously writing down a Googolplex is completely, fundamentally, impossible. And all that atomic writing would take a very long time. In fact, even if the universe stretched on infinitely, and even if you could consistently write down three digits of Googolplex every second, it would take you 6,341,958,396,752,917,300,862,506,341,958,396,752,917,300,862,506,341, 958,396,752,917,300,862,506,341,958,396,752,917,300,862 years to write it down. And unless you're prepared to do this for six octillion years...then you're definitely going to need to write faster.
In all likelihood, you probably even want to be finished with this in time to be home for dinner. If you begin this early in the morning, twelve hours before dinner, then you would need to write 231 nonillion numbers every second. However, the incredible speed in which you are moving in order to write all this down is going to have to be much, much, much greater than even the speed of light. After all, light takes 46 billion years just to go in a straight line across the universe. You're travelling to every single point in one million universes, and you're doing it all in twelve hours. Unfortunately for the universe, any object that has mass and travels at the speed of light will release an infinite amount of energy, instantly vaporizing everything in existence. On the bright side, you'll definitely be home in time for dinner...but that dinner has been erased from existence like the rest of everything.
So obviously writing down one Googolplex isn't possible by any means. So let's represent this number in a different manner, using atoms. We have already established that there aren't even one Googol atoms in the universe, meaning of course that there aren't one Googolplex atoms in the universe, either. So we're going to need some more space. First, we'll start with a smaller number, 1ee8, or 1e100,000,000. Keep in mind that a Googolplex is 1ee100.
So, like we've covered, scientists estimate there are around 1e80 atoms in the entire universe. That's an 80 digit number. We're trying to visualize a ONE HUNDRED MILLION digit number.
So, let's try to create that many atoms. Let's take each and every atom in the entire universe, and turn it into another another universe. Now each and every one of those 1e80 atoms, now contains 1e80 atoms. (We're obviously going to ignore the fact that this would simultaneously create a black hole at every single point in the universe). We now have 1e160 atoms, because we squared 1e80, which means we add the exponents. That entire universe-bending, logic-defying, mind-blowing process hasn't even brought us remotely close to 1e100,000,000 atoms.
Let's do it a second time. We take each and every atom in our universe, including all the ones inside each atom, and once again turn all of those into another universe. We're still not close, but we can use this to see how to make our number. So, we take this process, and we do it over and over, constantly turning uncountable numbers of atoms into entire universes, growing and growing. If we want to create 1e100,000,000 atoms, we will need to do this process 1,250,000 times!
But that's only 1ee8. For 1ee9, we would need to do this process 12,500,000 times. For 1ee10, it would take 125,000,000 times. That's the insane increase in size when you increase the number after two e's, and we're trying to make 1ee100.
To have a Googolplex atoms, we would need to do this process 125 sexdecillion times! That's 125 million million million million million million million million million million million million million million million million times! (1.25e98)
After all this space-time-continuum bending and physics defying work, we have finally created one Googolplex atoms. I mean, the universe is now completely worthless and unstable, because there is so much mass contained inside it, and every living thing died after the first time...but, hey, it worked! Now we have a more deep understanding of the absolute insane extent of this number, and we can begin to visualize just how massive it is.