My mom doesn’t understand the difference between a Googol and a Googolplex.
It’s not her fault. Years ago, I tried to explain it (poorly) and wouldn’t give up long after she was tired of hearing of it. I think maybe I’m better at it now. Check me:
This is a one:
This is a one followed by one zero:
We know that as a “ten.” Now here’s a one followed by two zeroes. Count them. A one, and then 1 – 2 zeroes.
We call that a “hundred.” What if we put that many zeroes after a one? Count ’em up. A one, and then 1 – 2 – … – 99 – 100 zeroes.
Now let’s follow a one with a googol of zeroes. Count those. 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 … 999 – 1,001 – 1,002 … you’ve probably run out of paper by now, start on another one … 99,999 – 100,000 – 100,001 … … … 999,999,999,999 – 1,000,000,000,000 … still going, you’re probably out of that notebook … 999,999,999,999,999,999,999,999,999 … 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 – 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,001 … uh oh. We’re out of atoms in the universe, and we’ve only written 1×1082 + 1 zeroes.
But if we were able to write a one followed by googol of zeroes – not a hundred zeroes, but 1×10100 zeroes – we will have written what mathematicians call a “googolplex“.
The googolplex is a tough concept, I admit. There are a lot of zeroes there, and trying to reach them is literally impossible. It’s tough enough to wrap our minds around the googol, and then we’re asked to increase that already unbelievable number by another unbelievable number. It makes the mind reel.
In the Bible, a man named Isaiah had a similar mind-reeling moment. Isaiah 6 tells us about the moment he first stepped before the God of the universe. What he saw broke his mind and turned his life around entirely. But one of the most unfathomable moments came when the angels around God began to speak.
You see, the word “holy” was well-known to Isaiah: it means set apart, other. As different from normal as can be. Incomprehensibly incomprehensible. But the angels didn’t say God was holy.
And one called to another and said: “Holy, holy, holy is the Lord of hosts; the whole earth is full of his glory!”
They said He was holy, holy, holy. Set apart. Then set apart again. Then set apart again. More incomprehensibly incomprehensible than the most incomprehensible thing we can’t comprehend.
God is not just infinite. See, infinite is easy to understand. It just goes on forever. God is infinite – but he’s also massive. The biggest things in the universe bow and tremble before him. He created all of time and space and holds it together without a thought.
But let’s go back to the googolplex for a second – where does it start?
With a 1.
The most unfathomable number we humans have come up with starts with a one. It’s the smallest whole number. It’s the most accessible. It’s the most understandable. One thing. One person. One moment.
Just like the googolplex, the infinite and indescribable God of the universe has reached down and touched Earth with a single number – with a one. That one is Jesus Christ. The infinite made intimate. He’s just as important as the uncountable digits of God.
Think of that next time you write a zero. Or a hundred of them.
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Want to learn more about unbelievably huge numbers? Steven Strogatz’s [amazon text=The Joy of x: A Guided Tour of Math, from One to Infinity&asin=B006R8PL7G] is available on Amazon Kindle right now, and buying it through this affiliate link helps support Redeeming Culture at no additional cost to you. Thank you!
I’m happy that you call it “the” googol. That’s just the way I think of it; that darn googol!
You’ve done a good job of explaining it here, we did have some wild conversations about this…typically ending in laughter! (and frustration on my part.) Somewhere along the way I have come to a type of understanding, maybe acceptance is more accurate.
I really appreciate the description of the angels around the Throne. I’ve always read this as ‘a continuous song of praise to He Who Is Worthy of All Praise.’ Which is true, but further, as you explain, He is set apart, and apart, and apart. More different from us than googolplex is from ten. Yet, I can say He is my God and He knows me. That is another idea that I find difficult to comprehend. I accept it as true and I am coming to understand it as He draws me more into a relationship with Him. He causes my spirit to sing!