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{"id":38990,"date":"2024-01-31T21:58:40","date_gmt":"2024-01-31T21:58:40","guid":{"rendered":"https:\/\/scienceandnerds.com\/2024\/01\/31\/how-to-build-an-origami-computer\/"},"modified":"2024-01-31T21:58:40","modified_gmt":"2024-01-31T21:58:40","slug":"how-to-build-an-origami-computer","status":"publish","type":"post","link":"https:\/\/scienceandnerds.com\/2024\/01\/31\/how-to-build-an-origami-computer\/","title":{"rendered":"How to Build an Origami Computer"},"content":{"rendered":"

Source:https:\/\/www.quantamagazine.org\/how-to-build-an-origami-computer-20240130\/#comments<\/a><\/br>
\nHow to Build an Origami Computer<\/br>
\n2024-01-31 21:58:40<\/br><\/p>\n

\n

In 1936, the British mathematician Alan Turing came up with an idea for a universal computer. It was a simple device: an infinite strip of tape covered in zeros and ones, together with a machine that could move back and forth along the tape, changing zeros to ones and vice versa according to some set of rules. He showed that such a device could be used to perform any computation.<\/p>\n

Turing did not intend for his idea to be practical for solving problems. Rather, it offered an invaluable way to explore the nature of computation and its limits. In the decades since that seminal idea, mathematicians have racked up a list of even less practical computing schemes. Games like Minesweeper or Magic: The Gathering could, in principle, be used as general-purpose computers. So could so-called cellular automata like John Conway\u2019s Game of Life<\/a>, a set of rules for evolving black and white squares on a two-dimensional grid.<\/p>\n

In September 2023, Inna Zakharevich<\/a> of Cornell University and Thomas Hull<\/a> of Franklin & Marshall College showed that anything that can be computed can be computed by folding paper<\/a>. They proved that origami is \u201cTuring complete\u201d \u2014 meaning that, like a Turing machine, it can solve any tractable computational problem, given enough time.<\/p>\n

Zakharevich, a lifelong origami enthusiast, started thinking about this problem in 2021 after stumbling on a video that explained the Turing completeness of the Game of Life. \u201cI was like, origami is a lot more complicated than the Game of Life,\u201d Zakharevich said. \u201cIf the Game of Life is Turing complete, origami should be Turing complete too.\u201d<\/p>\n

But this wasn\u2019t her area of expertise. Although she\u2019d been folding origami since she was young \u2014 \u201cif you want to give me a super complex thing that requires a 24-inch sheet of paper and has 400 steps, I\u2019m all over that thing,\u201d she said \u2014 her mathematical research dealt with the much more abstract realms of algebraic topology and category theory. So she emailed Hull, who studied the math of origami full time.<\/p>\n

\u201cShe just emailed me out of the blue, and I was like, why is an algebraic topologist asking me about this?\u201d Hull said. But he realized he\u2019d never actually thought about whether origami might be Turing complete. \u201cI was like, it probably is, but I don\u2019t actually know.\u201d<\/p>\n

So he and Zakharevich set out to prove that you can make a computer out of origami. First they had to encode computational inputs and outputs \u2014 as well as basic logical operations like AND and OR \u2014 as folds of paper. If they could then show that their scheme could simulate some other computational model already known to be Turing complete, they would accomplish their goal.<\/p>\n

A logical operation takes in one or more inputs (each one written as TRUE or FALSE) and spits out an output (TRUE or FALSE) based on a given rule. To make an operation out of paper, the mathematicians designed a diagram of lines, called a crease pattern, that specifies where to fold the paper. A pleat in the paper represents an input. If you fold along one line in the crease pattern, the pleat flips to one side, indicating an input value of TRUE. But if you fold the paper along a different (nearby) line, the pleat flips onto its opposite side, indicating FALSE.<\/p>\n<\/div>\n

<\/br><\/br><\/br><\/p>\n

Uncategorized<\/br>
\n<\/br>
\nSource:https:\/\/www.quantamagazine.org\/how-to-build-an-origami-computer-20240130\/#comments<\/a><\/br><\/br><\/p>\n","protected":false},"excerpt":{"rendered":"

Source:https:\/\/www.quantamagazine.org\/how-to-build-an-origami-computer-20240130\/#comments How to Build an Origami Computer 2024-01-31 21:58:40 In 1936, the British mathematician Alan Turing came up with an idea for a universal computer. It was a simple device: an infinite strip of tape covered in zeros and ones, together with a machine that could move back and forth along the tape, changing zeros […]<\/p>\n","protected":false},"author":1,"featured_media":38991,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"pagelayer_contact_templates":[],"_pagelayer_content":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38990","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"yoast_head":"\nHow to Build an Origami Computer - Science and Nerds<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/scienceandnerds.com\/2024\/01\/31\/how-to-build-an-origami-computer\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Build an Origami Computer - Science and Nerds\" \/>\n<meta property=\"og:description\" content=\"Source:https:\/\/www.quantamagazine.org\/how-to-build-an-origami-computer-20240130\/#comments How to Build an Origami Computer 2024-01-31 21:58:40 In 1936, the British mathematician Alan Turing came up with an idea for a universal computer. 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