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The Joy of X: A Guided Tour of Mathematics, from
One to Infinity
by Steven H. Strogatz.
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Table of Contents worth reading, unlike most books, what with the witty comments of the authir, who's done his best to make a subject seen with fear and aversion by mist, especially so in U.S.; he continues this from first chapter on, where he introduces the topic with numbers and history thereof.
But it isn't that easy, if one has an aversion rooted in lack of comprehension, and it doesn't go away by a professional indulging in a discourse that takes in important concepts attempting to be folksy. For those that do understand the topic a bit, yes, it's a marvel that he can be so entertaining.
Of special note are his chapters on some of the favourite topics - from quadratic equations to geometry, proofs, conic sections, to infinity and Cantor, and of course, Mobius bands or strips. His anecdote about the children, very endearing. (I've had kids entertained, and if grown enough, engrossed in the why, but none crying!)
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(Actually, languages can be very tricky in this respect. The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive but none in which a double positive makes a negative — to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.”)
Binary chapter, nicely done.
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Square roots chapter introduces something very interesting.
" ... In 600 B.C. a manual written in Sanskrit for temple builders in India gave detailed geometric instructions for computing square roots, needed in the design of ritual altars. More than 2,500 years later, in 1976, mathematicians were still searching for roots, but now the instructions were written in binary code."
Why do they always imagine its about an alter? India had stupendous architecture, amongst other spheres of knowledge.
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"THE QUADRATIC FORMULA is the Rodney Dangerfield of algebra. Even though it’s one of the all-time greats, it don’t get no respect."
(WHY? It's beautiful. As is polynomial theorem!)
"Professionals certainly aren’t enamored of it. When mathematicians and physicists are asked to list the top ten most beautiful or important equations of all time, the quadratic formula never makes the cut. Oh sure, everybody swoons over 1 + 1 = 2, and E = mc2, and the pert little Pythagorean theorem, strutting like it’s all that just because a2 + b2 = c2. But the quadratic formula? Not a chance."
"In our own time, the quadratic formula has become an irreplaceable tool for practical applications. Engineers and scientists use it to analyze the tuning of a radio, the swaying of a footbridge or a skyscraper, the arc of a baseball or a cannonball, the ups and downs of animal populations, and countless other real-world phenomena. For a formula born of the mathematics of inheritance, that’s quite a legacy."
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Compound interest and folding paper! Who knew they were related!
"The challenge was thought to be impossible until Britney Gallivan, then a junior in high school, solved it in 2002. She began by deriving a formula that predicted the maximum number of times, n, that paper of a given thickness T and length L could be folded in one direction. Notice the forbidding presence of the exponential function 2n in two places — once to account for the doubling of the wad’s thickness at each fold, and another time to account for the halving of its length."
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Geometry, proofs, conic sections, lovely stuff.
"So many people I’ve met over the years have expressed affection for that subject. Is it because geometry draws on the right side of the brain, and that appeals to visual thinkers who might otherwise cringe at its cold logic? Maybe. But some people tell me they loved geometry precisely because it was so logical. The step-by-step reasoning, with each new theorem resting firmly on those already established — that’s the source of satisfaction for many.
"But my best hunch (and, full disclosure, I personally love geometry) is that people enjoy it because it marries logic and intuition. It feels good to use both halves of the brain."
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Sine waves in nature!
"Dave liked to chart the times of the glorious sunrises and sunsets he could watch from his deck all year long. Every day he marked two dots on his chart, and after many months he noticed something curious. The two curves looked like opposing waves. One usually rose while the other fell; when sunrise was earlier, sunset was later."
Who knew that the intrinsically amusing trigonometry had applications beginning with beautiful sunrises and sunsets!
" ... 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. Astronomers have probed the spectrum (the pattern of sine waves) of the cosmic microwave background and found that their measurements match the predictions of inflationary cosmology, the leading theory for the birth and growth of the universe. So it seems that out of a featureless Big Bang, primordial sine waves — ripples in the density of matter and energy — emerged spontaneously and spawned the stuff of the cosmos."
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He introduces calculus beautifully.
"LONG BEFORE I knew what calculus was, I sensed there was something special about it. My dad had spoken about it in reverential tones. He hadn’t been able to go to college, being a child of the Depression, but somewhere along the line, maybe during his time in the South Pacific repairing B-24 bomber engines, he’d gotten a feel for what calculus could do. Imagine a mechanically controlled bank of antiaircraft guns automatically firing at an incoming fighter plane. Calculus, he supposed, could be used to tell the guns where to aim."
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How he jumps from exponential functions and e, to dating - and "finding a mate" problem!
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About statistics, if one didn't dislike it, one would like these chapters more; but it's far too applied a part of mathematics!
"President Bush made use of this property when he stated that his 2003 tax cuts had saved families an average of $1,586 each. Though that is technically correct, he was conveniently referring to the mean rebate, a figure that averaged in the whopping rebates of hundreds of thousands of dollars received by the richest 0.1 percent of the population. The tail on the far right of the income distribution is known to follow a power law, and in situations like this, the mean is a misleading statistic to use because it’s far from typical. Most families, in fact, got less than $650 back. The median was a lot less than the mean."
Reminds one about the three kinds of lies!
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O. J. Simpson's defence had mathematics?
"The prosecution spent the first ten days of the trial introducing evidence that O.J. had a history of violence toward his ex-wife Nicole Brown. He had allegedly battered her, thrown her against walls, and groped her in public, telling onlookers, “This belongs to me.” ... As one of the prosecutors put it, “A slap is a prelude to homicide.”"
"Alan Dershowitz countered for the defense, arguing that even if the allegations of domestic violence were true, they were irrelevant and should therefore be inadmissible. He later wrote, “We knew we could prove, if we had to, that an infinitesimal percentage — certainly fewer than 1 of 2,500 — of men who slap or beat their domestic partners go on to murder them.”"
"The real question is: What’s the probability that a man murdered his ex-wife, given that he previously battered her and she was murdered by someone? That conditional probability turns out to be very far from 1 in 2,500. "
"To see why, imagine a sample of 100,000 battered women. Granting Dershowitz’s number of 1 in 2,500, we expect about 40 of these women to be murdered by their abusers in a given year (since 100,000 divided by 2,500 equals 40). We also expect 3 more of these women, on average, to be killed by someone else (this estimate is based on statistics reported by the FBI for women murdered in 1992; see the notes for further details). So out of the 43 murder victims altogether, 40 of them were killed by their batterers. In other words, the batterer was the murderer about 93 percent of the time."
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Groups he introduces by flipping mattresses and doesn't tell the reader he's brought them to a group of quaternions! Or close.
“spin in the spring, flip in the fall.”
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" ... Einstein showed that light beams follow geodesics as they sail through the universe. The famous bending of starlight around the sun, detected in the eclipse observations of 1919, confirmed that light travels on geodesics through curved space-time, with the warping being caused by the sun’s gravity. "
Another favourite topic, geodesics!
"At a more down-to-earth level, the mathematics of finding shortest paths is critical to the routing of traffic on the Internet. In this situation, however, the relevant space is a gargantuan maze of addresses and links, as opposed to the smooth surfaces considered above, and the mathematical issues have to do with the speed of algorithms — what’s the most efficient way to find the shortest path through a network? Given the myriad of potential routes, the problem would be overwhelming were it not for the ingenuity of the mathematicians and computer scientists who cracked it."
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Cantor, finally, and unexpectedly!
" ... He defined a rigorous way to compare different infinite sets and discovered, shockingly, that some infinities are bigger than others. At the time, Cantor’s theory provoked not just resistance, but outrage. Henri Poincaré, one of the leading mathematicians of the day, called it a “disease.” But another giant of the era, David Hilbert, saw it as a lasting contribution and later proclaimed, “No one shall expel us from the Paradise that Cantor has created.”"
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April 24, 2021 - December 09, 2021.
Purchased August 03, 2018.
Kindle Edition, 336 pages
Published November 1st 2012
by Atlantic Books
(first published October 2nd 2012)
Original Title The Joy of x
ASIN:- B00A25NMO4
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Hardback
ISBN: 978 84887 843 3
Trade paperback
ISBN: 978 1 84887 844 0
Ebook ISBN: 978 0 85789 845 6
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https://www.goodreads.com/review/show/4378924483
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https://www.goodreads.com/review/show/4378927304
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