So the age of human space exploration may be over for the US, but a new form of space travel could be invented – and it could be done in bed.
Check out a mathematical exploration of how a bed sheet could get us to Mars through the power of doubling.
How long would it take us to get to Mars with one folded bed sheet? Between forty-three and forty-six folds. Forty-three folds of a 0.8 millimeter bed sheet will get you to Mars at its nearest, at 56 million kilometers away.
Forty-six will get you to Mars at its farthest, over 400 million kilometers away. Keep folding into the mid-fifties and the sheets will stretch light years.
Okay, obviously not. A fully extended sheet won’t completely reach over my toes through a cold night. It obviously can’t make it to Alpha Centauri. And by now some wisenheimer has decided to fold their bed sheets up like a fan and noticed that they aren’t being blasted into space.
What’s actually happening is the power of doubling. The most famous story about this was the grains of rice on a chess board story. It has iterations in most countries — although the story was said to originate in India — but there is always a might, imperious king, a chess board, and a mysterious stranger.
The king asks the stranger to play chess. Stranger says no. King insists, and sweetens the deal by saying he’ll pay any sum, if the stranger wins. The stranger says he only wants the king to place one grain of rice on the first square, and then double the amount with each successive square. The king scoffs, accepts, and loses.
The first line of the chess board is easy. There are eight squares, so the sequence goes; 1, 2, 4, 8, 16, 32, 64, and 128. That’s not even a serving. The second line doubles the total eight times again; 256, 512, 1024, 2048, 4096, 8192, 16348, and 32868.
Fine, that’s a big meal, but the king is hardly sweating yet. Then things really take off. Two more doublings take the number to six figures. Two more doublings increase it to seven figures.
By the end of the third line in the chess board, the king has to pay over 8 million grains of rice. The next line takes it to billions, where it stalls for another line, and then goes into trillions. By the end, the king would have to pay 210 billion tons of rice.
There’s no ‘trick’ to this doubling, except that many people (Go ahead, mathematicians. Scoff at the normals.) aren’t used to seeing how doubling works. The grains of rice are doubled intentionally.
The sheets, when they’re folded in half, double the number of ‘leaves’ each time. Even tiny amounts, doubled over time, sprout up to incredible numbers. This is one of the reasons why an ordinary sheet of paper can only be folded in half twelve times — and for quite some time, the number was thought to be only eight — before it simply can’t take another bend.
Now if we had a piece of paper that could stretch infinitely around corners while keeping its thickness when straight . . . we’d probably still have better uses for it than folding it to go to Mars. That would still be the coolest use, though.