Home > 555. The Golden Thread, C. The Thinker As Hero, I. Books > The Great Equations–A Book Review

The Great Equations–A Book Review

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Some of RT’s worst memories of High School involve staring at blackboards filled with incomprehensible mathematical symbols and graphs, chief among which were logarithms. Such mysteries as the differential co-efficient of log tan were so perplexing that he even obtained a Texas Instruments calculator to help, but to little avail. He slogged through his math courses, squeaking by with a C- or so (usually for effort), a lesson reinforced by his sub-500 math SAT scores.

But RT is an ornery beast. In college, he was able to pursue further study of numbers, this time benefiting from a curriculum not designed to eliminate nonengineer- and nonmath professor-material such as himself from the class roster. Two pleasant memories remain with him from his college math instruction: 1) actually being able to understand (at least parts of) Isaac Newton’s Principia (with the help of excellent tutor notes); and 2) having math majors at other universities want to borrow and study his copy of Lobachevsky’s NonEuclidian Geometry.

His college math triumphs aside, RT will probably never make a significant contribution to mathematical theory, but his ongoing interest in math has convinced him of one thing: there are better ways to teach math (and especially advanced mathematics) than those that have been encountered by the hapless majority of High School students over the last several decades.

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So, despite everything about the nature of this blog, it will come as small surprise that RT has wanted to post on mathematics. At this point in his life, RT has come to believe that there is a deep connection between language and mathematics, between word and number, a suspicion strengthened by his learning over the last year that many animals have the ability to count at a rudimentary level. Word and number are basic aspects of mind, and if we can relate the two aspects more precisely via a word/number system that includes characters that function as both a number and a word, then perhaps we will reach a new (and better) mastery of intellect, ourselves, and the world. Translating between number and word could be the ultimate human intellectual achievement.

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The Great Equations, by Robert P. Crease, is a wonderful book. TGE is structured around discussion (and some mathematical derivation) of ten equations that have greatly advanced scientific knowledge and made a profound impact on society, the first of these being the Pythagorean Theorem and the last Heisenberg’s Uncertainty Principle. RT admires the book’s approach to discussing these mathematical milestones: Crease includes lots of information about the mathematicians/physicists who developed the equations, concentrating on the story behind the development of each equation. He then goes on to explain why the equation was important to advancing scientific knowledge and how it affected human culture. And let it be said, 1) Crease is an excellent writer and 2) the math in the book is accessible to just about anyone who took High School geometry, algebra, and chemistry/science classes.

What is driving this collection of essays is Crease’s conviction that everyone, even the poets among us, must have some familiarity with math and science: he compares someone who doesn’t know what the Second Law of Thermodynamics is to someone who’s never read one of Shakespeare’s plays. Mathematics, in short, is one of the disciplines that must be studied if someone wants to call him- or herself cultured. He discusses the role of mathematics and physics in clarifying how our minds work, and he notes the many improvements in our lives made possible by advances in scientific theory–to name just a few, the radio, TV, and the Internet. And beyond this, he wants us to understand that mathematicians and scientists are people, just as emotionally invested in their work as anyone else, just as likely to fudge here and there to make a claim to creating an equation, just as vulnerable to emotional disorders, overwork, and personality conflicts. Scientists and poets are both creative, in his view.

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Perhaps the most satisfying lesson RT takes away from The Great Equations is that many scientists expect their theories to be visualizable and describable, that is, to be explicable in terms of image and word. Just as the humanities at the moment seem unable to provide the breakthroughs in general understanding and method that will take us to the next level in human development, so too has science left us in a place where we struggle to understand its discoveries. We are waiting for a new insight that combines the ancient analyses of experience into numbers and words to help us appreciate the beauty of the Uncertainty Principle and to guide us away from ignorance, abject poverty, and war.

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GraphPearson Type VII distribution log; User: MarkSweep; WikiCmns; Public Domain.

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  1. mj
    July 26, 2013 at 3:51 pm

    Loved this post. Perhaps you might like to visit a blog I follow: http://poundforabrown.wordpress.com/

    • July 26, 2013 at 11:15 pm

      thanks, mj! i’ve visited and am now following the pfb blog; much worthwhile material there! RT

      • mj
        July 27, 2013 at 3:35 am

        🙂

  2. July 27, 2013 at 4:25 pm

    You make maths sounds so inviting!

    many animals have the ability to count at a rudimentary level
    A factoid, possibly, but I have a memory of a study which suggested that crows (or some such corbid) counted thus: One, two, three … a lot!
    That’s a lot more sensible than shoppers who seem to think that £13.99 (or $13.99 or whatever) is nearer to thirteen than fourteen and therefore a bargain price to pay.

  3. August 8, 2013 at 3:46 am

    Your schooldays anecdote resonates with my own experience of just scraping through maths at high school. What made the big difference for me was the discovery of language-based approaches to mathematics. Having, like you, retained an ongoing interest in matters mathematical, I will be looking into Mr Crease’s book.

  1. August 6, 2013 at 11:40 pm

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