Quotations and notes from "The Joy of X" - A Guided Tour of Math, from One to Infinity by Steven Strogatz
"... numbers have lives of their own. ..Even though they exist in our minds, once we decide what we mean by them,..They obey certain laws and have certain properties, .. and ways of combining with one another ...they are eerily reminiscent of atoms and stars, the things of this world ...except that those things exist outside our heads."
"The Babylonians ..numerical system was based on 60 ...Sixty is the smallest number that can be divided evenly by 1, 2, 3, 4, 5, and 6{besides 10, 12, 15, 20, and 30}. ..Because of its promiscuous divisibilty, 60 is much more congenial .. for any sort of calculation or measurement that involves cutting things into equal parts"{such as hours or minutes or circles}.
"Quantum mechanics describes real atoms, and hence all of matter, as packets of sine waves. Even at the cosmological scale, sine waves form the seeds of all that exists."!
"...vector calculus is helping to explain how dragonflies, bumblebees, and hummingbirds can fly - something that had long been a mystery to conventional fixed-wing aerodynamics."
"With the notions of divergence and curl ...{Using mathematical maneuvers equivalent to vector calculus} Maxwell's equations .. express" the four fundamental laws of electric and magnetic fields: how electricity and magnetism are related to their sources of charged particles and currents and how they interact over space and time to produce undulating waves.
The laws of probability turn individual randomness into collective regularity.
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