How Not to Be Wrong: The Power of Mathematical Thinking, by Jordan Ellenberg

Who wants to be wrong? What a great reason to learn math! How Not to Be Wrong is excellently summarized in this review, so take a minute and read that so you can not be wrong anymore. Then you can come back here, and I'll give you some of my examples. (NB: the math herein is very rough. Numbers have been wildly approximated. I tried not to write about anything I didn't understand, but I may have failed. If you want really elegant, clean math and blameless explanations, read the book.)

First of all, math is everywhere, and it turns out that if you know just as much math as you did in the fourth grade, it can be a great party trick. If there are 20 people in the room, and we want to divide into groups that are not too big and not too small, what are our options? What if there are only 19? If your lunch was $7.50 plus tax and tip, what do you owe the person who put down her credit card? If you are having an Easter egg hunt with three kids, and it turns out you have 31 eggs, how many should each one find?

All of these everyday math problems hinge on the beautiful way numbers separate and combine. 4 groups of 5 people can be reorganized into 5 groups of 4 people, and once you know that, you know that 19 people will make 3 groups of 5 and one group of 4, or 4 groups of 4 and one group of 3. $2 is kind of a minimum tip and tax exists and is always more than you think it should be, so $10 would not be too much to contribute towards your $7.50 lunch. And the oldest kid can have the extra Easter egg, because he's the only one who can reliably count that high anyway.

On a more sophisticated level, there's a discussion somewhere in the middle of the book about probabilistic situations that divide into four categories rather than two. For example, there are people who are terrorists and people who are not terrorists, and there are people Facebook flags as possible terrorists and people it does not. In such a situation, the question, "What are the chances that my neighbor is a terrorist?" is completely different from the question, "What are the chances that my neighbor, who was flagged as a possible terrorist, actually is one?" The first question is binary: She is or she isn't. The second is only looking at one quadrant of a four-way possibility matrix, because I am looking at the intersection of people who are actually terrorists and people Facebook identifies as suspicious.

One reason this situation is interesting is the principle that the more extreme a number is, the less useful it's going to be to try to change it by what sounds like an impressive proportion. In our home, that's sometimes known as the Ralph Lauren effect. A half-price sale sounds amazing until you realize that regular price is $125. Even half off just isn't enough to make the shirt affordable.

In our example about terrorists, the chances that anyone is a terrorist are tiny-- like there are 7 billion people in the world, and by the broadest definition there might not be more than a few million terrorists among us. That's if most of them are pretty ineffectual: according to my minutes of research, in 2014, there were about 44,000 deaths and 16,000 injuries as a result of terrorist attacks worldwide. Out of 7 billion people. So the chances of finding a terrorist just by picking a person at random is, let's say, 1 million out of 7 billion, or 1/7000, or .00014%. If I say I can double your chances of picking a terrorist out of the crowd, that sounds great, right? But sadly, that only puts your chances up to 2/7000 or .00028%, which are still terrible odds. Now you see  why we have the NSA and so forth.

So here's some more fun with percents. If I say I'm "doubling" your chances, they will go up by 100%. Which is not the same as going up to 100%! A percent is only as good as its starting point-- remember the Ralph Lauren problem? Here's another example. I have to write surveys for work. Getting people to fill out the surveys is a big problem. My survey provider sent me an email recently asking, "If you could improve survey response rates by 50%, would you do it?" Wow! That sounded great! But when I looked more closely, here's what was really happening, more or less (remember, my numbers are rough). Typical survey response rate was only 25%. So, add 50% of 25% (12.5%), and that new, improved shiny response rate was now... 37.5%! That's not so exciting. Less than half my group would be responding, even with my snazzy new strategy. Furthermore, watch this trick: I still have 62.5% not responding (because P plus NOT P equals 100%). Previously I had 75% not responding. So I only reduced not responding rates by 16.67%! Only 16.67% of my not-responders responded to my new bells and whistles! So here's where things get weird: Increasing the response rate by 50% only decreased the non-response rate by 16.67%! That's because so few people were responding in the first place. If half the people were responding, it would work out more nicely: I would go from 50/50 answer/no answer to 75/25, which would be a tidy 50% increase in what we want and 50% decrease in what we don't want. But a percent is only as good as its starting point!

Isn't math fun? Now go read that review, at least, so you can learn more!

Ellenberg closes with a wonderful quote from W.V. Quine that I have used a lot since I read it: "To believe something is to believe that it is true; therefore a reasonable person believes each of his beliefs to be true; yet experience has taught him to expect that some of his beliefs, he knows not which, will turn out to be false. A reasonable person believes, in short, that each of his beliefs is true and that some of them are false." Isn't that great! It doesn't make much sense going around saying, "I could be wrong." For crying out loud, if you think you're wrong, do some more research until you either are pretty sure you're right or have realized the answer is unknowable! But, at the same time, realize that you are perfectly capable of all kinds of errors, even while you are doing your best due diligence to avoid them. That's mathematical thinking!

510-519: Mathematics

Ah, the bedrock of science! Good thing I only had time to go to my little local library, because my book haul was ample-- and heavy to carry home!

Finding Zero, by Amir Aczel. Dr. Aczel begins by describing the pleasures of growing up the son of a ship's captain, and particularly of being introduced to the mystery and joy of numbers by a ship's steward, Laci, who snuck him into a casino and later used playing cards to teach him about Arabic, Hindi and modern Arab numerals. This preschool experience was the first spark of his lifelong fascination with numerals and number theory, and at some point in his life, he apparently had the opportunity to travel the world hunting up the most ancient instances of numeral inscriptions he could find.

The Signal and the Noise, by Nate Silver. Subtitled "Why So Many Predictions Fail-- But Some Don't," it seems not entirely clear how it got in the Math section. It is classified as a book about "Forecasting," which I suppose is a subdiscipline of probability, about "Bayesian Statistical Decision Theory," so there you go, but also about "Knowledge, Theory of..." something that really should be found in the 010's with Black Swan. He opens with a discussion of the crash of 2008 and whether it was predictable or not, and gets very technical very fast, demonstrating how his brand of statistical and stochastic analysis could be applied to a variety of situations. Turns out one of the keystones of Bayesian statistical decision theory is that you have to acknowledge your biases-- your preferred outcome-- before you start, so that seems like a good idea.

Thinking in Numbers, by Daniel Tammet.  I loved Born on a Blue Day, which told the story of how Tammet came to terms with all the things that made him neurologically exceptional. This book, like that one, showcases his warmth and his charming writing style, but doesn't seem as directed. The first essay is a series of musings on the number 9 and on set theory, occasioned by the fact that the set of Tammet children in his family of origin equalled 9. This seems like a good book to pick up and read in odd moments, maybe not straight through.

How Not to Be Wrong, by Jordan Ellenberg. Subtitled The Power of Mathematical Thinking, this book is about how math actually is something we can use to solve all kinds of real-life issues and think through whether we are even asking the right question. There are 18 different "episodes," or examples, one of which deals with Bayesian statistical analysis! Along the way, he's also going to help me understand what "expected value" is, which I've been worrying about ever since it came up on an ACT a while back. I like that he admits that it actually means "average" value. I am curious to see whether he is going to address the fact that the "average" value for almost anything is often the least useful piece of information you can obtain from a data set, as well as to find out about Biblical numerology and whether it is possible to game the lottery.

480-489: Greek. Alpha to Omega, by Alexander and Nicholas Humez

Ostensibly a book about the Greek alphabet, this is really more like a book about Greek culture. The overall effect is not unlike that of Leo Rosten's The Joys of Yiddish, reviewed elsewhere. Following are some of the fun facts I learned from as much of this book as I read.

Gamma is for gyne: In ancient Athens, girls were fed less than boys, but in Sparta they went to school and had property and inheritance rights. Given this cultural heritage, how did Sophocles come to write so sympathetically about the plight of women?

Delta is for diagignesthai, to discern, from which we get diagnosis. Dr. Benjamin Lee Gordon points out that the Persians "resorted more frequently to spells than to drugs on the grounds that, although spells might not cure the disease, they at least would not kill the patient." Hippocrates seems to have originated the doctor-as-God problem that we still have in Western medicine. He said, "The physician must wear an expression of sympathy and understanding, never showing the slightest perplexity.... by predicting-- and making explicit-- who will live and who will die, the physician will ensure himself against censure."

Zeta is for zoon ("living thing), from which zoo. The first recorded zoo in the Western world was that of the Egyptian Queen Hatshepsut, 16th c BC, focusing on animals of Africa. Aristotle's groundbreaking work, Inquiries on Animals, full of Nature Channel-type behavioral observations, was written at the urging of his pupil, Alexander the Great.

Theta is for theater and Thespis, a legendary, possibly mythological innovator credited by Aristotle with introducing the individual actor to drama, which had previously been confined to the choral recital of mythology. It was Sophocles who increased the number of individuals all the way to 4!

Iota is for isos, meaning equal: isosceles triangles, which have two equal sides; isotopes ("equal places"), elements that share the same space on the periodic table; isobars, lines on a weather map denoting areas of the same barometric pressure.

Kappa is for kentron, a pointed object, from which "center", as of a circle when you draw it with a peg and a piece of string. Not to be confused with the Latin cingere, to cinch, from which we get the more specialized meaning of "center" as in the curved wood that supports a stone arch as it is being built. In the 5th c BC, Pythagoras said everything in the sky spun around a central fire. In the 3rd C BC, Aristarchos said the earth and planets circled round the sun.

Lambda is for Logos, the "Word" of John 1. Actually "word" usually refers to epos, from which we get "epic" (originally told by the spoken word) or rhema, from which "rhetoric" (another kind of spoken word). Logos refers simultaneously to the outward expression of a concept, as opposed to a mere name, and to the actual concept itself, and is a combination of the thought and its verbal expression. It could be akin to the Latin ratio, meaning thought, as opposed to oratio, meaning the expression of thought. The logos is the whole sentence, the complete thought, or the power and process of reasoning itself. It refers to whatever is said: a fable, a story, a thing spoken of, a principle, or an explanation. It comes from the verb legein (to gather, select), which also gives us lexis, which refers both to words (as in "lexicon") and manners of speaking (as in "dialect").

500-509: General Science. A Short History of Nearly Everything, by Bill Bryson

Okay, I've finally emerged from the 400s with one big takeaway: my Spanish is improving all the time as I read with a pencil and dictionary and boldly speak every chance I get. On to the 500s, which is all hard science, all the time. "Everything under the sun"... or rather "everything in creation," as all the stuff beyond the sun is also included. The first decade is, as usual, for general introductions, and Bill Bryson seems like he would be an entertaining guide to life, the universe, and (almost) everything. I should have known better when I didn't read him in the 390's, and again when I so didn't read him in the 420's that he didn't even get a mention. Maybe I should confine myself to his travel books, having listened to both A Walk in the Woods and The Road to Little Dribbling with great enjoyment.

To be fair, A Short History is also a travel book of sorts... if time travel counts. Not only time travel as in, "I will begin the story of the Universe at the beginning of the Universe," as Dickens might have said, but also and even more time travel through the development of our ideas about the development of the Universe. Because, as it turns out, Bryson doesn't really want to write about neutrinos. He wants to write about how they were discovered-- and, more importantly, he wants to gossip about their discoverers.

He starts innocently enough, by detailing how the sound of the background radiation resulting from the Big Bang was simultaneously heard by two Bell Labs employees and described theoretically by a team of Princeton researchers. So, that's a pretty interesting story, and along the way you get a very clear idea of what this noise is and how much it matters. But one thing leads to another, and the next thing Bryson knows, the book has really become a series of anecdotes about the wacky antics of geologists, astronomers and the like, which is not exactly what I wanted. I was looking for a popularization of science, not a popularization of scientists. Oh well.

The stories I read were very entertaining, I'll give Bryson that, and along the way I did learn some very fun facts. My favorite fact is that good old Bishop Ussher, who dated the six-day Creation of Earth to October 23, 4004 BC, had long since ceased to hold sway over the thinking of even deeply religious scientists before Darwin made his discoveries. In 1770, for example, George-Louis Leclerc tried to estimate the earth's age based on patterns of heat loss, arriving at a figure very roughly in the neighborhood of 100,000 years. By the middle of the nineteenth century most educated people were thinking in terms of millions or tens of millions of years. Darwin did not knock down the "young Earth" theory--that had already been done. What he did do, along with Lord Kelvin, was turn the millions of years into hundreds of millions of years (current estimates are running about 4.6 billion). So that's an interesting little tidbit.

So, I guess what I'm saying is that what Bryson really wants to do in this book is what he did so well in the books I enjoyed-- he wants to tell human stories. He wants to talk about people, not ideas. So if you want to meet a lot of very smart, very odd people, and get a whirlwind tour of life, the universe and everything, I guess this is the book for you. As for me, nearly everything turned out to be a little too much.

490-499: All Those Other Languages

Was Melville Dewey a genuinely unpleasant person, or just a product of his times, as we all are? I don't know or even care any more. What I do know is that the more I use the Dewey Decimal System, the more I see how arbitrary it is. In the 200s, Christianity gets 9/10ths of the numbers. In the 400s, many European languages get 10 full digits, while all the languages native to all the other continents are left to smash into this area, 490-499. Of course, through the magic of decimals, it's not hard to create a classification for Tagalog, but it's not going to be 407. (It's 499.211, by the way. Nearby are Vietnamese, 495.922, and Lenape, 497.3.) The problem is that to make a substantive revision to the system, thousands of poor assistants and pages would have to scrape millions of numbers off book spines, so we just keep lumping along.

Speaking of lumping along, in the local library I have most ready access to, the only volumes in the 490-499 range are Russian dictionaries, and I think I've mentioned before how much I am not going to read a dictionary, even in the service of my noble quest. Oh well-- when in doubt, I resort to the children's section. (Hey, look-- last time this happened was at the beginning of the 400s!) That's where I found something on a topic I could actually get behind: The Rosetta Stone!

The Riddle of the Rosetta Stone: Key to Ancient Egypt, by James Cross Giblin, is just what it sounds like: a summary of the discovery and importance of the Rosetta Stone. It is beautifully and generously illustrated with photos of hieroglyphic and hieratic (demotic) Egyptian writing. If you don't know the significance of the Rosetta Stone, here's what happened:

In the 7th century AD, Greek scholars began to get curious about the meaning of the carvings they saw all over tombs and statues, which they called "hieroglyphs," meaning "sacred writing." They asked around, but by this time Egypt had been conquered by the Arabs, and anyone who had used this formal script was long gone. That didn't prevent people from forming theories, of course, but it wasn't until the 1700s that CJ De Guignes made an astute observation (that certain patterns of hieroglyphs were often enclosed in a border, which he called a cartouche), followed by an accurate and useful guess: that these patterns represented names. This insight proved to be one of the keys to the Rosetta Stone, which, in turn, unlocked both forms of Egyptian written records and enabled us to have all the Egyptian history we know and love today. 

Because the Egyptians intersected with other groups that kept written historical records, such as the Jews and the Greeks, and, I suppose, because they must have had their own oral history about the spectacular artifacts amongst which they lived, it's not like nothing was known. But it really wasn't until Napoleon's armies ran across this inscription that contained the same decree in three scripts, two mostly unknown and one extremely familiar, that the writings so generously provided on and in every statue and tomb in Egypt could be deciphered and a detailed history of that ancient civilization pieced together. 

One thing that takes this book to the next level, in my opinion, is that it provides extensive excerpts from the translated text of said decree. The style is not actually very gripping, any more than the ones we write today proclaiming "National Jam Day" or whatever, but the content is a bit startling to modern ears. It basically boils down to the idea that King Ptolemy is really great, has done a lot of good things, will hereafter be known as "the well-favored God revealed on Earth," and welcomes the worship of all people. I don't know how much of that he got, but he certainly deserves our thanks for leaving behind this handy linguistic breadcrumb trail!

470-479: Lingua Latina. Carpe Diem: Put a Little Latin in Your Life, by Harry Mount

I decided to major in French in college because of Baudelaire:

"Mon enfant, ma soeur,
Songe à la douceur
D'aller là-bas vivre ensemble!
Aimer à loisir,
Aimer et mourir
Au pays qui te ressemble!
Les soleils mouillés
De ces ciels brouillés
Pour mon esprit ont les charmes
Si mystérieux
De tes traîtres yeux,
Brillant à travers leurs larmes."

-From L'invitation au voyage

*Swoon*. What adolescent could resist that?

I almost changed to Classics, but I can't remember why exactly. It might have been my first instructor, who was only a few years older than me. It might have been Catullus or Virgil. It might even have been the time we went around campus at Christmastime singing "Gaudete"-- despite the fact that my instructor was a Bhuddist. 

I can't imagine it was the declension charts... but those are what I remember best. "Hic, haec, hoc, hunc, hanc, hoc, huius, huius, huius, huic, huic, huic, hoc, hac, hoc"... I recited it on the way to classes and in the shower. I made these pig noises so many times I still pretty much remember this chant, the way you could rattle off: "I say, you say, he, she or it says, we say, you say, they say." 

Latin conjugates its verbs, declines its nouns, and goes into moods that are barely remembered in English, like the subjunctive. Our closest equivalent is the almost prissy-sounding "If I were..." (but I'm not) or "I wish you would..." (but you never will). And if you spend the first semester of your freshman year memorizing all these tenses and cases and moods, by winter of your sophomore year you will be able to sing medieval Christmas carols, and by spring of your sophomore year you will be reading Virgil. The Aeneid. In the original. And understanding it! Take that, fourth semester French or Spanish! We sure didn't read Victor Hugo or Don Quixote in fourth semester! I suppose the fact that we did not need to spend any time learning to actually speak the language (or write original sentences) saved a lot of time.

All of this to say that Carpe Diem brought back fond memories of those college days. Even the (rather too lengthy) list of commonly used phrases, which felt more like a dictionary than I would have preferred, contained some old friends it was nice to see again... as well as some rather dated references to celebrities from John McEnroe to Juvenal. Well, what do you expect from a book about a dead language? Highly recommended, if your goal is to brush up your rusty Latin-- and why wouldn't it be?

460-469: Spanish. Dios habla hoy.

You guys! Inspired by Juhmpa Lahiri's example, I said I would translate Bible passages from the Spanish, and I'm doing it! I also checked out a SAT-II Spanish prep book, just as an example of my other thrilling options, but I just tested out of it here, so I am excused from wading through that.

I am using Dios habla hoy instead of the classic Reina Valera. I already owned an RV, but I got tired of fighting with the antiquated language. Since my goal is to improve my conversational Spanish (without having to actually take the risk of actually conversing-- yet), I didn't want to end up walking around sounding like the Spanish equivalent of a King James Bible.

I translate about a paragraph a day, more or less. I do it in writing, which forces me to be honest about the words I don't know. Sometimes I just reread what I have already done and see how many of the new words I still remember. Sometimes, when a passage is very familiar, I just translate as I read.

I find the vocabulary of the Epistles is pretty manageable, since any unusual, theological words are probably cognates of English. The Psalms, though, are really teaching me a lot of great vocabulary for weather phenomena, weaponry, and emotions. I'm also getting some practice recognizing idioms: "tener presente" (to keep in mind), "hacer pedazos" (to tear into pieces),  "tocar en suerte" (a transitive for "to luck into").

I kind of love this one: instead of saying "I lucked into a beautiful home," in Spanish one says "A beautiful home touched me in luck." The Spanish language is very good at removing human agency from events: it's not "I forgot my homework" but "Se me olvido la tarea" (The homework forgot itself to me). I was just standing there, and that darn homework went and forgot itself! What could I do? There I was, and a beautiful house reached out with a lucky touch!

Before I can learn what the idioms mean, though, I have to realize that's what they are, that is, that even though I know the individual words, I can't translate word for word, but that the combination means something else. I've watched English language learners struggle with this phenomenon, so it's good for me to have the same experience.