By Brenden Bobby
With Sandpoint Library
Oh no, it’s a post about math! Hide your kids, hide your wife, hide your high school textbook!
It’s okay, I promise. You know how we do things in Mad About Science, and you should be stoked that we’re about to make math awesome up in here.
What does math have to do with science? Everything. Math and Science are like two puzzle pieces in a huge multi-trillion piece puzzle, you just can’t complete the Jigsaw of Nyan Cat without it. Math and Science are like equal weights on a cosmic scale. Try to use one without the other, and your scale will be totally out of balance. It’s hard to weigh things when your scale won’t work.
Since we like to do it big, I’d like to cover some big numbers. What’s the biggest number you can think of? If you’re a kid, a million probably pops into your head: 1,000,000. Not too bad, it’s higher than I can count in one, or several sittings. If you’re an adult, you probably have an even bigger number in mind, one the politicians like to throw around to scare people that don’t know how national economies work: The national debt, which, at the writing of this article, was: $19,249,637,400,000, over Nineteen Trillion dollars. Now that’s a lot of cheddar for one person, which is what is always insinuated when it’s brought up, but if you divide that by 319,000,000 (roughly the population of the United States, including children), it comes out to about $6034 each. Still a lot of money, but not nearly as bad as 19 trillion!
Well that was a big and scary number, what else you got?
How about 100 Octillion? What’s that, and why is it important?
100 Octillion, written out, looks like this: 100,000,000,000,000,000,000,000,000,000. 100 followed by 27 zeroes. That’s pretty cool, but what is it? It’s a rough estimate of how many stars exist in the Universe. The entire universe. Each with any number of planets swirling around them at any given time. Some may have none, some may have, as our system has shown us, up to 8 not including dwarf planets, maybe even more.
That’s a big number, but I think we can go bigger. What about a Googol? You’re probably thinking about what you use to look up the taco truck’s number or random trivial facts for your next science article. That’s Google, and the creators named Google after the number Googol, or 1 followed by 100 zeroes. That’s pretty cool, so if I can just put a big number in superscript behind a 10, I can just make big numbers? What if I do 10 to the Googol power?
Then you have a Googolplex, a 1 followed by a Googol zeroes behind it. I’ll let you write that one out in longhand. Spoiler alert, it would take you well over 13.4 billion years, the age of the Universe from start until now.
That’s mind-bendingly huge. Is it even possible to go bigger than that?
Theoretically, you can go on infinitely, but that’s just cheap. Instead, we’re going to go off with a brief glimpse of what was, at one time, a world record holder for the world’s largest number. This number is so mind-bendingly large, so over-the-top massive, so completely colossal that there is no parallel to it that exists in our entire universe.
So how does it work?
Traditional mathematics has towers of power, like we were showing earlier. Let’s say 3 to the 3rd power, which makes 27, which we put to the 3rd power, which makes 19683, which we put to the third power, which makes 7625597484987 (Thank you, calculator!). Mathematician Ron Graham decided to crank it up a few innumerable notches, and instead of going for towers of power, decided to make towers of towers.
To try to explain how that works, the first layer of the tower is 3. The next layer of the tower is that 762… number we found. The tower after that has 7,625,597,484,987 exponents of 3. The layer after that uses that ridiculously large number to tell us how many exponents of 3 we will use in the next level. This goes on 64 times, creating a number big enough to melt your brain into mush. Must be pretty close to Infinity, right? It’s approximately 0% of Infinity.
Now that your head hurts, there are numbers even bigger than that humans have discovered. The current world record holder is Rayo’s Number, a number even I’m scared to try and explain. Past this point, we start reaching numbers referred to as transfinite. In other words, they may be infinite, they may not be. We’re not adequately equipped to truly understand that quite yet. No matter what happened or what we may or may not understand, we really put that $5 cup of coffee into perspective!
While we have you ...
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