A brief history of mathematics - download pdf or read online

By Fink K.

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So Arthur sharpenedhis pencils and went to work. What he wanted was a mathematical framework that incorporated dynamics-that showed explicitly, step by step,how the marketplacechoseamong the multiple possible -"In the real world, outcomesdon't iust happen," he says'"They Lutcomes. The equations were aciually quite general, he says,and applied to essentiallyany kind of increasing-returnssituation. Conceptually, however,they worked something like this: Supposeyou are buying a car. )And suppose,for the sake'ofsimplicity, that there are iust two models to choosefrom.

And now that QWERTY is a standardused by millions of people, it's essentiallylocked in forever. How could this havehappened? Becausethe VHS vendorswerelucky enoughto gain a slightly biggermarket sharein the beginning,which gavethem an enormousadvantagein spite of the technologicaldifferences:the video storeshated having to stock everythingin two differentformats,and consumershatedthe ideaof being stuck with obsoleteVCRs. So everyonehad a big incentive to go with the market leader. Once again, increasingreturns.

But he didn't havethe mathematicaltoolsto do much with it in an analyticalway. And economistsever since have gotten hung up on the same ,,wherever there is more than one equilibrium point possible,, the point. There "End story. of says. he Lutcom. " Somethingsimilar happenedin the 1920s,w-hena number of European economists iried to use increasing-returnsconceptsto explain why cities grew and concentrated the way they did, and why different cities (and lifferent countries)would specializein, say,shoesor chocolatesor fine violins.

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A brief history of mathematics by Fink K.

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