Infinite Powers Quotes

“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.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“In mathematical modeling, as in all of science, we always have to make choices about what to stress and what to ignore. The art of abstraction lies in knowing what is essential and what is minutia, what is signal and what is noise, what is trend and what is wiggle. It's an art because such choices always involve an element of danger; they come close to wishful thinking and intellectual dishonesty.”
― Steven Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Calculus succeeds by breaking complicated problems down into simpler parts. That strategy, of course, is not unique to calculus. All good problem-solvers know that hard problems become easier when they’re split into chunks. The truly radical and distinctive move of calculus is that it takes this divide-and-conquer strategy to its utmost extreme — all the way out to infinity.”
― Steven H. Strogatz, Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics

“Infinity lies at the heart of so many of our dreams and fears and unanswerable questions: How big is the universe? How long is forever? How powerful is God? In every branch of human thought, from religion and philosophy to science and mathematics, infinity has befuddled the world’s finest minds for thousands of years. It has been banished, outlawed, and shunned. It’s always been a dangerous idea.”
― Steven H. Strogatz, Infinite Powers: The Story of Calculus - The Language of the Universe

“Naturally, the place to start is at infinity.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be, because nonmathematical universes can’t harbor life intelligent enough to ask the question. In any case, it’s a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“First comes intuition. Rigor comes later.”
― Steven H. Strogatz, Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics

“The study of algebra in its own right, as a symbolic system apart from its applications, began to flourish in Renaissance Europe. It reached its pinnacle in the 1500s, when it started to look like what we know today, with letters used to represent numbers. In France in 1591, François Viète designated unknown quantities with vowels, like A and E, and used consonants, like B and G, for constants. (Today’s use of x, y, z for unknowns and a, b, c for constants came from the work of René Descartes about fifty years later.) Replacing words with letters and symbols made it much easier to manipulate equations and find solutions.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Galileo was elated to discover that a parabola, an abstract curve studied by his hero Archimedes, was out there in the real world. Nature was using geometry.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Articles aside, the word calculus itself has stories to tell. It comes from the Latin root calx, meaning a small stone, a reminder of a time long ago when people used pebbles for counting and thus for calculations. The same root gives us words like calcium, chalk, and caulk. Your dentist might use the word calculus to refer to that gunk on your teeth, the tiny pebbles of solidified plaque the hygienist scrapes off when you go for a cleaning. Doctors use the same word for gallstones, kidney stones, and bladder stones.”
― Steven H. Strogatz, Infinite Powers: The Story of Calculus - The Language of the Universe

“More important, it’s the most accurate theory anyone has ever devised . . . about anything. With the help of computers, physicists are still busy summing the series that arise in QED,”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Quinto and I are studying these topics because they are interesting in their own right as mathematical problems, and that is what science is all about.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Before we look at how far Newton got on it, let me try to clarify why it’s so hard. Local Versus Global”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“The evening of August 16, 2008, was windless in Beijing. At ten thirty, the eight fastest men in the world lined up for the Olympic finals of the 100-meter dash. One of them, a twenty-one-year-old Jamaican”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“According to the Americans with Disabilities Act, a wheelchair-accessible ramp must not rise by more than 1 inch for every 12 inches of horizontal run. For a ramp with this maximum permissible gradient, the relationship between rise and run is y = x/12, where y is the rise and x is the run.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“There it will be revealed that the forward problem and the backward problem, as different as they seem, are twins separated at birth, a shocker called the fundamental theorem of calculus.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“At their deepest level, the laws of nature are expressed in terms of derivatives. It’s as if the universe knew about rates of change before we did.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Of all the various rates of change that exist, the slope of a curve in the xy plane is the most important and useful, because it can stand in for all the rest.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Wavelets were ideal for the job. By representing fingerprints as combinations of many wavelets and by turning the knobs on them optimally using calculus, mathematicians from the Los Alamos National Lab teamed up with the FBI to shrink their files by a factor of more than twenty.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Together, though, algebra and geometry were unstoppable. Algebra gave geometry a system. Instead of needing ingenuity, it now demanded tenacity. It transformed difficult questions requiring insight into straightforward, if laborious, calculations. The use of symbols freed the mind and saved time and energy.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“The processes of algebra could be soothingly repetitive, like the pleasures of knitting.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“With geometry, there was often no clue about where to start a proof. Beginning an argument required strokes of genius. Algebra, however, was systematic. Equations could be massaged almost mindlessly, peacefully; you could add the same term to both sides of an equation, cancel common terms, solve for an unknown quantity, or perform a dozen other procedures and algorithms according to standard recipes.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“It’s as if nature keeps returning to the same motif again and again, a pendular repetition of a pendular theme.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Unfortunately, Galileo never managed to derive this rule mathematically. It was an empirical pattern crying out for a theoretical explanation. He worked at it for years but failed to solve it. In retrospect,”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“Galileo was particularly intrigued—and frustrated—by a curious fact he discovered about pendulums, the elegant relationship between its length and its period (the time it takes the pendulum to swing once back and forth).”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“In any case, Galileo’s assertion that a pendulum’s swing always takes the same amount of time is not exactly true; bigger swings take a little longer. But”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“To spell out this law of odd numbers more explicitly, let’s suppose the ball rolls a certain distance in the first unit of time. Then, in the next unit of time, it will roll three times as far. And in the next unit of time after that, it will roll five times as far as it did originally. It’s amazing; the odd numbers 1, 3, 5, and so on are somehow inherent in the way things roll downhill.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“The strategy is to reimagine the circle as a pizza. Then we’ll slice that pizza into infinitely many pieces”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“With these ingredients alone, he could cook up any curve he wanted by putting in a pinch of x and a dash of x2 and a heaping tablespoon”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe

“After the interview, as they were parting, Feynman asked Wouk if he knew calculus. No, Wouk admitted, he didn’t. “You had better learn it,” said Feynman. “It’s the language God talks.”
― Steven H. Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe