Recently, I was listening to an episode of “The Rest is Science “, a podcast hosted by Hannah Fry and Michael Stevens (which I absolutely recommend), that made me realize how subtly huge numbers can arise from very small combinations.

Let’s say we are in a room with 3 chairs and 3 people: Marc, Catalina, and Bob. The number of different seating combinations we can have is as simple as 3 factorial.

3! = 1 × 2 × 3 = 6

Hence:

(1) Marc – Bob – Catalina
(2) Marc – Catalina – Bob
(3) Bob – Catalina – Marc
(4) Bob – Marc – Catalina
(5) Catalina – Marc – Bob
(6) Catalina – Bob – Marc

It’s not that big and not surprising at all. But now let’s say there are 20 chairs and 20 people in the room. How many seating combinations are there? One would naturally think of a big number, but how big? The answer again is as simple as 20 factorial.

20! = 1 × 2 × 3 × … × 20 = 2.432.902.008.176.640.000

Right! The number of combinations is 2 trillion (or 2 quintillions). That number is absolutely nuts, it’s certainly out of hand.

Now, how many combinations do you think those 20 people could try in their whole lifetime? A typical human lives around 80 years, which is about 29.200 days, or 700.800 hours, or 42.048.000 minutes, or 2.522.880.000 seconds.

Even if those 20 people ran around the room like crazy (from their literal birth to their literal death) trying one combination per second, that would only give 2.522.880.000 combinations, which is about 0.0000001% of the total. Yes, basically zero. That’s ridiculous.

One more. Take a deck of cards, which has 52 cards. The number of possible ways of arranging them is 52!, which is about 8 × 10⁶⁷, that’s an 8 followed by 67 zeros. So huge that it barely makes sense. One conclusion from this is that if you shuffle a deck a few times (assuming you’re not trying to cheat), the order you end up with is almost certainly one that has never existed before in history. Ever.

Finally, since we are here on Nostr, a Bitcoin-friendly environment, let’s finish with the Bitcoin seed phrase. If you go to any random person and tell them you created your bitcoin password from 2.048 words, it might seem stupid. Like, very few words. But if you go to a calculator and compute 2.048!, you’ll see how immense that number really is.