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David Berlinski's A Tour of the Calculus2 has been called "a love letter, or song of praise, that makes difficult theory seem elegant, seductive and desirable. Berlinski reveals, stepby-step, the manner in which calculus, through a system of numbers and equations, gives us the power to represent time and space in a real world.


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  4. Once understood, calculus does more than describe time and space. It allows us to see the past and predict the future. Using calculus, we can determine where things have been and we can discover where they are going. Needless to say, this is what trial lawyers do as well. Just as calculus is an intellectual tool that uses numerical notation to symbolize time and space, so is the common law trial a device to recreate what happened, where, and when. As I will explain shortly, a mathematical function draws a picture of events in a way that allows them to be disassembled and reassembled until they make useful sense.

    A trial does the same thing, using rules of procedure and evidence in the place of numbers. As every schoolchild no longer knows, the calculus was devised simultaneously and independently by Sir Isaac Newton and Gotfried Liebnitz in the winter of Such was the pace of academics in the Seventeenth Century that it was not until that Newton finally got around to publishing his Philosophiae Naturalis Principia Mathematica, commonly known as the Principia, and then only at the urging of the astronomer Edmund Halley.

    It is far less known, though pretty evident once you think about it, that the calculus of Newton and Liebnitz was only a beginning, just the first pass at the fully developed discipline that we know today. As Berlinski puts it, "what Newton and Liebnitz saw in the harsh but thoroughly unfocused dare of their own genius, they never clearly or completely understood. One of Berlinski's great contributions, then, is to convey an understanding of the historical development of the calculus.

    At every stage he shows how ideas rose and fell, how theories were polished and sometimes replaced, how new thoughts led to newer ones.

    A Tour of the Calculus by David Berlinski: | gievoulcairohot.ga: Books

    One good example of this progression is the concept of instantaneous velocity. Speed seems obvious.


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    If you know how long it took to get somewhere, then you can figure out how fast you were going. But this understanding of speed really only yields an average.

    It compresses a series of speeds into a single number, thereby blurring acceleration and deceleration, rates of change, and even the occasional frolic or detour. It is no trick to measure speed over a defined interval.

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    But instantaneous speed-speed at a single moment, with no passage of time now there is another question entirely. Paperback —. Add to Cart. About A Tour of the Calculus Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Also by David Berlinski. See all books by David Berlinski.

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