Know what a factorial is? It’s a mathematical function often used in statistical representations, denoted by a ‘!’. That’s right, an exclamation mark. You writers out there, next time you end a statement or sentence with an exclamation mark, well, think on its other meaning.
The way it works is that you take a number and calculate its factorial by multiplying it by every integer that preceded it. Here’s an example for 4!:
4! = 4 X 3 X 2 X 1 = 24
Simple concept. You can find this function on your calculator, actually.
I did a bunch of statistics in University. I found it interesting, and I think I did well in class. But the true significance of a factorial eluded me, particularly as it came to describing reality. For example, when used in statistics, a factorial can describe the distribution of outcomes for a set of parameters where the variables are independent ie. they don’t depend on each other at all.
Let’s do an example with a deck of cards. For the first card you select from a deck, there are 52 possibilities. For the next card, there are 51 (because you’ve already removed one card), but the selection of the previous card doesn’t really affect the subsequent one. It’s independent. For the next card, there are 50 possibilities… and so on. The way you mathematically describe the number of combinations that you could draw from a deck of cards is thus 52! That’s 52 X 51 X 50 X 49… all the way down to 1.
Try punching in 52! Into your calculator. It comes out to 8.0658 X 10^67. That’s an 8 followed by 67 zeroes. I don’t know what this number is called. There seems to be no specific nomination, but the number ten times less than this would be called a ‘unvigintillion’ (https://www.basic-mathematics.com/names-of-large-numbers.html). Has a ring to it, doesn’t it?
So a deck of cards would produce 8.0658 X 10^67 different combinations. That means that you could effectively shuffle a deck of cards and you would never, in your lifetime, deal the same combination of 52 cards. Your odds are 1 in 8.0658 X 10^67. It’ll never happen. Try it. It’s functionally impossible.
The magnitude of combinations in a deck of cards is daunting. Here are some examples for comparison.
The odds that you will be struck by lightning in the US is about 1 in 15,300 (https://www.britannica.com/question/What-are-the-chances-of-being-struck-by-lightning). That’s basically 1 in a number that’s 1 followed by 4 zeroes. Four measly zeroes! You’re so much more likely to be hit by lightning than to deal the same combination in a deck of cards that it’s not worth even thinking about.
We’re Going to Need a Bigger Boat
Eaten by a shark? You have a 1 in 3.7 million chance of being consumed by a shark (https://www.peta.org/features/shark-attack-vs-other-causes-of-death/), even if you are positive that it’s going to happen every time you get in the ocean (thanks a lot, Stephen Spielberg!). But that’s still a trillion trillion trillion (and more) times more likely to happen than dealing the same combination of 52 cards twice in a row.
You Can’t Win if You Don’t Play
Winning the lottery? That’s such a remote occurrence that you can’t possibly expect it to happen, right? Someone from Maine just won the $1.2Bn Powerball, so it happens, but the odds are really remote, something like 1 in 292 million (https://www.powerball.ca/odds-prizes/). So you’re more likely to be eaten by a shark than you are to win the Powerball, but you’re still much more likely to win that whopping Powerball than you are to deal those 52 cards in the same order.
A Minivan Won’t be Enough
I have children, but no twins. Or triplets. Or quadruplets (although I know a set of quadruplets). Or quintuplets. I certainly don’t know any sextuplets, six births at the same time. It’s an unlikely event, and far less likely than the odds of you winning the Powerball. The odds of having sextuplets is about 1 in 4.7 billion (https://www.cbc.ca/news/science/multiple-births-1.850647). If you’re a betting person, bet on having sextuplets long before you’ll ever deal the same 52 cards twice in a row. You’ll win that bet every single time.
Dust in the Wind
I love it when people try to count the grains of sand in the world. You can estimate this by looking at the size of a grain, and figuring out how much area (and at what depth) of the world is covered by sand. It’s an imprecise estimate, but it’s possible. Scientists estimate that there are about 7.5 sextillion grains of sand on the planet, or 7.5 followed by 18 zeroes (https://www.oklahoman.com/story/lifestyle/2019/02/05/more-stars-than-grains-of-sand-on-earth-you-bet/60474645007/). Now we’re getting into big numbers: 18 zeroes! But that means there’s still an immeasurably greater number of combinations of 52 cards than there are grains of sand on the planet. We’re not even close to 67 zeroes yet!
Yes, They’re Full of Protein
Insects on the planet? It’s a little known fact that the weight of all the insects on Earth is greater than the weight of all humans, simply because there’s so many of them (https://www.theglobeandmail.com/opinion/the-weight-of-all-those-creepy-crawlies/article4461850/). The same source says there’s about 10 quintillion insects on Earth, or 1 followed by 19 zeroes. At the very least, that means we can take the number of grains of sand on the Earth, multiply by ten (let’s say that’s 10 Earth’s worth of sand grains), and it would still be less than the number of insects on our humble planet. Even so, there’s way more combinations in 52 cards in a deck than there are insects. If you took all the insects on Earth and multiplied their number by 10 a whopping 48 times straight, you’d finally start to get close.
The Unending Night So Full of Bright
Finally, how about stars in the universe? Surely that’s a huge number, an insurmountable one. We think there are about 10^12 galaxies (https://www.esa.int/Science_Exploration/Space_Science/Herschel/How_many_stars_are_there_in_the_Universe). The same references says that you have about 10^11 or 10^12 stars in each galaxy. That’s a lot. Calculate that out, and you have 10^24 stars in the known universe. So yes, there are way more stars in the universe than there are insects on Earth, or grains of sand. Way way more. But you would need trillions and trillions and trillions and trillions and trillions of universes to put all their stars together before you would equal the number of combinations in a deck of 52 cards.
That one little deck of cards is, in fact, bigger than our universe.
I love math, but what I love more is thinking about what we can do. What we have done. We, mere human beings, invented a game that has more combinations than there are stars in the night sky. We did that. We created something inordinately complex, a simple game that has been entertaining us for so long. In that one deck that sits in the palm of your hand, you have more complexity and intricacy than it is possible to imagine – all those zeros work at a universal scale.
If we can create that, what else we can create? How about immense, epic novels with arrangements of letters creating stories that can only be formulated once, by one person? Think of that the next time you sit down to write creatively. Think about where you can go, how far your mind may travel. And when you’re feeling low or uninspired, lift up your head. Lift it up, and just think about the power that is in your hands.