A Beautiful Math: John Nash, Game Theory, and the Modern by Tom Siegfried

By Tom Siegfried

Millions have obvious the motion picture and millions have learn the ebook yet few have totally liked the maths built by means of John Nash's appealing brain. this present day Nash's attractive math has turn into a common language for learn within the social sciences and has infiltrated the nation-states of evolutionary biology, neuroscience, or even quantum physics. John Nash received the 1994 Nobel Prize in economics for pioneering study released within the Fifties on a brand new department of arithmetic referred to as online game idea. on the time of Nash's early paintings, video game thought was once in short well known between a few mathematicians and chilly conflict analysts. however it remained vague till the Nineteen Seventies whilst evolutionary biologists started utilising it to their paintings. within the Nineteen Eighties economists started to embody online game thought. on the grounds that then it has stumbled on an ever increasing repertoire of functions between a variety of clinical disciplines. at the present time neuroscientists peer into online game avid gamers' brains, anthropologists play video games with humans from primitive cultures, biologists use video games to give an explanation for the evolution of human language, and mathematicians take advantage of video games to raised comprehend social networks. a typical thread connecting a lot of this study is its relevance to the traditional quest for a technological know-how of human social habit, or a Code of Nature, within the spirit of the fictitious technology of psychohistory defined within the recognized beginning novels by means of the overdue Isaac Asimov. In a stunning Math, acclaimed technology author Tom Siegfried describes how online game idea hyperlinks the existence sciences, social sciences, and actual sciences in a manner which can carry Asimov's dream in the direction of reality.

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Additional info for A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature

Sample text

Let’s revisit Alice and Bob and see what happened after Alice refused to play Bob’s stupid game. Knowing that she was unlikely ever to get her whole $10 back, she proposed another game that would cause Bob to scratch his head about what strategy to play. In Alice’s version of the game, they go the library every weekday for a month. If they both ride the bus, Bob pays Alice $3. If they both walk, Bob pays Alice $4. If Bob rides the bus and Alice walks, arriving second, Bob pays $5. If Bob walks and Alice rides the bus, arriving first, Bob pays $6.

In a book published in 1928, the same year as von Neumann’s minimax paper, Morgenstern discussed problems of economic forecasting. ” This, Morgenstern knew, was a problem peculiar to the social sciences, including economics. When a chemist predicts how molecules will react in a test tube, the molecules are oblivious. They do what they do the same way whether a chemist correctly predicts it or not. But in the social sciences, people display much more independence than molecules do. In particular, if people know what you’re predicting they will do, they might do something else just to annoy you.

Meanwhile a fly flies back and forth between the bicycles at 15 miles an hour. How far has the fly flown by the time the bicycles meet? You can solve it by adding up the fly’s many shorter and shorter paths between bikes (this would be known in mathematical terms as summing the infinite series). If you detect the trick, though, you can solve the problem in an instant—it will take the bikes an hour to meet, so the fly obviously will have flown 15 miles. When jokesters posed this question to von Neumann, sure enough, he answered within a second or two.

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