When I was a kid, I read a short story about chess. I don’t remember it by heart and I can’t look it up, so I’ll just tell it how I remember it. If there’s a detail I got wrong, I apologize.
A long time ago, a Persian king was a big fan of chess. One day, he decided to invite the man who created it. The king talked about how much he enjoyed his game. He offered to give the creator anything he wanted; nothing was off the table. The man sat in silence and thought about it for a while. He took out a chessboard and said he wanted one sesame seed for the first square. He wanted two seeds for the second one, four seeds for the third one, eight for the fourth one, etc. He wanted double the amount for every square.
The king thought it was a strange request, but he said yes. He gave his advisor a new task; find out how many seeds they need to give to the creator. The next day, the advisor came back with the results. It turned out that they owe the man over 18,446,000,000,000,000,000 sesame seeds. They would need to convert all the land, seas and oceans of the world into sesame fields in order to fulfil that request.
And that’s where the story ends. I don’t know what happened afterwards; maybe the creator of chess said, “It’s just a prank, bro!” The story made me wonder; how big would that pile of seeds be? How many squares would you need to make it bigger than Earth? Or bigger than the sun. Let’s do some math.
According to Google, a sesame seed is 3.5 mm long, 2 mm wide and 1 mm thick. That would make its volume 7 mm^3. If we convert it to cubic meters, we get 7 times 10^-9 m^3. The pile of seeds from the end of the story would be 129,127,208,516 m^3 large; or 1.29 * 10^11 if you want a shorter number. According to the cube root calculator, such a pile would be around 5 kilometers tall, thick and wide. Where was the creator of chess planning to keep it?
What if we kept going? Google says that the volume of the Earth is 1.08 * 10^21 m^3. How many squares would the creator need to get a pile that large? Accoring to my calculations, (7 * 10^9) * 2^97 equals 1.109 * 10^21. He would need only 97 squares; that’s approximately one chessboard and a half.
Let’s take it a step further. What if we wanted a pile that was bigger than the sun? Once again, Google says that the volume of the sun is 1.44 * 10^27 m^3. It doesn’t look too different from Earth when I write it like this, but the sun is still over a million times larger than the Earth. If we go to the calcutor, it turns out that we would need to multiply the volume of a sesame seed by 2^118 to make it bigger than the sun. We would still only need two chessboards.
I think that’s enough math. I could keep going with even larger things, but that would just be repetitive. I guess the message of the original story is that math is more exciting than it appears; we can do some crazy things with it. If I made some kind of mistake in this post, feel free to point it out. I’m not a mathematician; I’m just a guy with Google and a calculator.