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Sometimes it all adds up

“Mathematics is not a body of facts arranged and justified by a stringent logical structure.  To give a dynamic metaphor that stems from the related field of fluid flow, it is like a turbulent river.  The flow of the water is extremely complex, but every now and again you see the appearance of stable structures, eddies and whirlpools.  These stable structures correspond to the propositions and theorems of mathematics.  It is the logical structure of mathematics that gives these theorems their stability, but when we look at things in this way we see that the stability is not absolute.  The data can be structured in many different ways corresponding to what we are interested in and in the mathematical ideas that arise to do the structuring.  These ideas arise in response to the question, ‘What is going on here?’—that is, from the attempt to make sense of the phenomena in question.” – William Byers, How Mathematicians Think

Published inMathematics

2 Comments

  1. One of the deep regrets of my life is the inability to understand even rudimentary mathematics. Physics holds the same fascination for me that the Bible must hold for a Christian: all the answers are within, but I just don’t understand.

    • my brother was a math wiz from early on, which may be why i was not. i needed to chart a different course. math always gave me trouble. my way of understanding the world was not compatible with what math needs. it wasn’t until i was an undergraduate in my early 20s and studying symbolic logic that i found the key that works in my math lock: approach it as learning the rules to a very boring game.

      last year and earlier this year i returned to the study of math and logic as a precursor to reading nietzsche. i read texts in symbolic logic, geometry, and trigonometry. i found it fascinating, particularly if i didn’t get bogged down in the formulas but satisfied myself enough to recognize the crystalline beauties before me.

      before me now is not crystalline beauty but mundane task. it is tax season and my boss thinks i should be his bookkeeper and even his first-string accountant. i work as a paralegal–i have no training–none, nada, zilch–as a bookkeeper or an accountant. he seeks the short-term savings of a false economy. i seek the shelter of continued employment so i go now to keep books and accounts, flailing about in a subject whose terms and conditions are all but opaque to me.

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