Steven Strogatz Quotes
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The frequencies of the notes in a scale—do, re, mi, fa, sol, la, ti, do—sound to us like they’re rising in equal steps. But objectively their vibrational frequencies are rising by equal multiples. We perceive pitch logarithmically.
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In mathematics, our freedom lies in the questions we ask — and in how we pursue them — but not in the answers awaiting us.
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Change is most sluggish at the extremes precisely because the derivative is zero there.
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When you create something new, you're breaking tradition - which is an act of defiance.
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To grasp how different a million is from a billion, think about it like this: A million seconds is a little under two weeks; a billion seconds is about thirty-two years.
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One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
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Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.
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Those of us who teach math should try to turn this bug into a feature. We should be up front about the fact that word problems force us to make simplifying assumptions. That’s a valuable skill—it’s called mathematical modeling.
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Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.
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When you love a problem, its contours, obstacles and resistances are all just part of its character.