# Paper folding math **URL:** \ **Category:** Factual Questions\ **Created:** [December 14, 2015, 5:50am UTC](https://boards.straightdope.com/t/paper-folding-math/740397 "2015-12-14T05:50:10Z")\ **Posts on this page:** 4\ **Page:** 2
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 15, 2015, 6:53am UTC](https://boards.straightdope.com/t/paper-folding-math/740397/21 "2015-12-15T06:53:33Z")
> [@bob\_2](#): > > It’s the same as the story about a [Chinese] wiseguy who had a chessboard. He wanted one grain of rice on the first square, two on the second, three on… and so on. > > Long before it reached 64 squares, he would own all of the possible grains of rice in the world. I mentioned the book _One, Two, Three . . . Infinity_ by George Gamow recently, in a thread about 4-dimensional cubes, which Gamow discussed. In the same book, he told this story. (The grains doubled on each square, not just added one more.) In Gamow’s telling, the Persian King Rashid wished to reward his vizier for inventing and presenting to him the game of chess, and this was the vizier’s request. (Gamow also tells a glamorized story of the rings on the three pegs that you have to shift from one peg to another, one ring at a time. We commonly call this the Tower of Hanoi, but Gamow sets the story in India, at the Great Temple at Benares, center of the Hindu universe. There are 64 rings of gold, three diamond pegs, set into a platinum base. The Brahmin priest on duty must shift the rings, one at a time; the task is handed down from father to son through the generations. When the task is completed, according to prophecy, then rings, priest, and temple will all disappear, and with a great thunderclap the universe will end. He called this the Tower of Brahma. Gamow attempts to compare this prophecy with an actual estimate of the lifetime of the universe. Assuming the priests make their moves at the speed of atomic vibrations, and make no mistakes, and have no downtime at all, Gamow finds that the task will still take vastly longer than the estimated lifetime of the universe.) ETA: [Get your copy here!](http://www.amazon.com/One-Two-Three-Infinity-Speculations/dp/0486256642) ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [December 15, 2015, 7:13am UTC](https://boards.straightdope.com/t/paper-folding-math/740397/22 "2015-12-15T07:13:55Z")
[Full text of _One, Two, Three . . . Infinity_ by George Gamow on-line here!](http://www.google.com/url?q=http://selfdefinition.org/science/25-greatest-science-books-of-all-time/10.%2520George%2520Gamow%2520-%2520One%2520Two%2520Three...%2520Infinty%2520(1947)(1988).pdf&sa=U&ved=0ahUKEwifnMKUpt3JAhUHxmMKHXXFCMQQFggYMAE&usg=AFQjCNG9IWYwsIB6_Y9u4CDdlxocf_4FAA) (Big PDF file.) Story of the grains of rice on the chess board starts on page 7. (I had the names wrong – it was King Shirham of India, wishing to reward his vizier Sissa Ben Dahir for chess.) Story of the Tower of Brahma begins on page 9. (Various minor details wrong there too – the base is brass, not platinum; other minor details wrong too.) Hey, so sue me. I read that when I was in 6th grade, about 50 years ago! Story of the printing press that prints every possible line starts on page 11. (This is the one where he assumes _every atom in the universe_ is a separate printing press, printing at the speed of atomic vibrations, since the beginning of the universe. By now, the job would be one thirtieth of one percent done.) Note this differs from the hypothetical monkeys banging at typewriters, as the printing press prints every possible line in an organized systematic sequence, not randomly. A few pages after that, he gets into counting different sizes of infinity. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [December 15, 2015, 9:03am UTC](https://boards.straightdope.com/t/paper-folding-math/740397/23 "2015-12-15T09:03:49Z")
penultima thule writes: \> As to the number of cuts needed then the answer provided by Colophon would be \> a reasonable starting point Actually, no, it isn’t the same thing. Colophon is talking about a piece of paper one atom thick. The number of atoms in an apple pie would be much different than the number of atoms in a one-atom-thick piece of paper that’s the same circumference as the pie. In post #8 my rather sloppy estimate of the number of atoms in an apple pie was that it was about 2 ^ 90. I know that some of my figures were rather imprecise guesses. Could someone refine that estimate and tell us a more exact figure? ---
**Author:** ![penultima\_thule](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/penultima_thule/32/3833_2.png) [@penultima\_thule](https://boards.straightdope.com/u/penultima_thule)\ **Post date:** [December 15, 2015, 9:38pm UTC](https://boards.straightdope.com/t/paper-folding-math/740397/24 "2015-12-15T21:38:38Z")
Obviously all this high falootin technical stuff is confusing because you asked two questions. One was how many atoms, the other how many cuts. > [@Colophon](#): > > If we assume the paper is 0.1mm thick then that is about 600,000 atoms high. Colophon answered the question that is you cut/fold a piece of paper 64 times you’d have it’s length down to within an order of magnitude of a single atom. As to the number of atoms in an apple pie; Since a recipe hasn’t been provided let’s take a 1kg apple pie at a molecular level. 45% is water, 55% is carbohydrate in a multitude of forms e.g. sugar, starch, lipid, fibre, [with addition of nitrogen] protein etc. 450 g H20 = 24.9 moles 550g CH20 = 18.3 moles Which is 24.9x2 moles H + 24.9 moles O + 18.3moles C + 18.3x2 moles H + 18.3 moles O =148 moles \* 6.022 x 10^23 = 9 x 10^25 per kg 2^90 is a very large number. [Previous page](https://boards.straightdope.com/t/paper-folding-math/740397.md?page=1)