The Joy of X

Metadata

• Author: [[Steven Strogatz]]
• Full Title: The Joy of X
• Category: #books

Highlights

• Just as numbers are a shortcut for counting by ones, addition is a shortcut for counting by any amount. This is how mathematics grows. The right abstraction leads to new insight, and new power. (Location 132)
• math always involves both invention and discovery: we invent the concepts but discover their consequences. As we’ll see in the coming chapters, in mathematics our freedom lies in the questions we ask—and in how we pursue them—but not in the answers awaiting us. (Location 136)

New highlights added February 3, 2023 at 6:29 PM

• Notice something magical here: as the numbers inside the logarithms grew multiplicatively, increasing tenfold each time from 100 to 1,000 to 10,000, their logarithms grew additively, increasing from 2 to 3 to 4. Our brains perform a similar trick when we listen to music. 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. (Location 852)
• Mathematicians and conspiracy theorists have this much in common: we’re suspicious of coincidences—especially convenient ones. There are no accidents. Things happen for a reason. While this mindset may be just a touch paranoid when applied to real life, it’s a perfectly sane way to think about math. In the ideal world of numbers and shapes, strange coincidences usually are clues that we’re missing something. They suggest the presence of hidden forces at work. (Location 1059)
• Whenever a state of featureless equilibrium loses stability—for whatever reason, and by whatever physical, biological, or chemical process—the pattern that appears first is a sine wave, or a combination of them. Sine waves are the atoms of structure. They’re nature’s building blocks. Without them there’d be nothing, giving new meaning to the phrase “sine qua non.” (Location 1157)
• Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan—and so are its textbooks. Many exceed a thousand pages and work nicely as doorstops. (Location 1253)
• Roughly speaking, the derivative tells you how fast something is changing; the integral tells you how much it’s accumulating. (Location 1257)
• So we’re long overdue to update our slogan for integrals—from “It slices, it dices” to “Recalculating. A better route is available.” (Location 1393)