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Square Roots Quotes

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Square Roots Quotes

“How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.”

“That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.”

“The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.”

“You see, gentlemen, reason is an excellent thing, there’s no disputing that, but reason is nothing but reason and satisfies only the rational side of man’s nature, while will is a manifestation of the whole life, that is, of the whole human life including reason and all the impulses. And although our life, in this manifestation of it, is often worthless, yet it is life and not simply extracting square roots.”

“For Rat Kiley, I think, facts were formed by sensation, not the other way around, and when you listened to one of his stories, you'd find yourself performing rapid calculations in your head, subtracting superlatives, figuring the square root of an absolute and then multiplying by maybe.”

“The anceints devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point. Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial?”