"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck
"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)
******************************************************************** Rob Gluck
2) Finally, since I often tout books here, I’ll add another, just not a math book — haven’t read it myself, but a well-read friend of mine tells me that Robert Sapolsky’s (evolutionary biologist) “Behave” is THE best book, bar none, he has ever read. That’s good enough for me to give it a look. Just passing it along.
…also, currently reading/enjoying “The Jazz of Physics,” by Stephon Alexander, newly out in paperback.
While Congressional Republicans were busy mugging America, and the Trumpster occupied himself sticking pins into his Bob Mueller doll, I found these math stories to pass along:
1) Some of what John Baez is thinking about lately:
9) I’ve been reading a little more foundational and analytical philosophy lately, so this end-of-year book, "Exact Thinking In Demented Times" on such, looks interesting (and Douglas Hofstadter writing the Preface is a pretty good endorsement):
(Anyone already read it and care to comment on it?)
10) I re-posted a fun logic problem/riddle yesterday at Math-Frolic.
11) Shinichi Mochizuki’s controversial/difficult proof of the ABC conjecture continues its wild ride, having been submitted to a prestigious math journal… which Mochizuki himself edits!... what one writer calls “poor optics.” So even if refereed properly this could taint its wider acceptance. Stay tuned.
2) I enjoy videos of “Canon Rock” performances (the rock version of Pachelbel’s Canon) and recently someone sent me this YouTube of a young female Japanese drummer joyously going-to-town with it. So will sign off with this:
While you were sleeping, and Aryan Anti-Christ Donald was busily colluding, obstructing, and weeping over fellow-harasser Roy Moore’s loss, I was once again hard at work pulling together another Friday math potpourri:
1) Great New Yorker profile of Jim Simons, mathematician and billionaire hedge fund manager, and his Flatiron Institute:
Off on a curmudgeonly rant today… inspired by a recent Jim Propp piece, but stripped of any math.
I told Jim that his latest post is one of my very favorites, because it is such an “everyman” posting — we have all experienced it, and the math involved is simple but aggravating (I’m happy to finally have a name for it, “fence-post error”). Jim specifically pinpoints an experience with Verizon to make his case, taking them to task, but I’ll cast the net wider when it comes to the behavior of (predatory?) corporate America (I had my own run-in with Verizon many years ago and dropped them forever… but as I told Jim that only means I had to shop around for a different slimy, deceptive carrier). Deceit and fraud are such an ingrained part of modern corporate fabric we largely accept it unblinkingly. Cable and phone companies, Internet giants, food companies, car dealers, airlines, insurance companies, credit agencies, drug-makers, banks (seriously, how does Wells Fargo even remain in business — oh yeah, I forgot, “too big to fail”), the list goes on-and-on of companies that actively con the public as a routine part of doing business — indeed, they probably couldn’t compete successfully in America if they didn’t do so. Lawyers are paid a boatload to keep corporate words and behavior just this legal side of fraud, but let’s be honest, when you do things to deliberately hoodwink or confuse people, thereby boosting your own profits, you’ve committed fraud, by the spirit of the law if not the letter.
There’s a lot of talk these days on starting early to teach young people critical thinking skills (you know, so we don't end up with a certain kind of President). I’m all for it -- I find it egregious that we still force young people to read Shakespeare, but not study basic modes of reasoning/evaluating. It doesn’t have to be scientific or mathematical thinking, just critical/skeptical analysis. In high school I had to take a semester that included a popularized version of General Semantics (also here) which I've oddly regarded as the most important academic time I ever spent, even as simple as it was. It lends one an awareness of how language manipulates and short-circuits our thought processes and behavior; of how advertisers, propagandists, demagogues/politicians, sales people, promoters, plutocrats, etc. operate… but it even applies to ALL of us in our daily interactions to some extent. And since a lot of it will never change, it is important to be aware of it and self-inoculated.
“Advertising” and “marketing,” unfortunately, essentially become nice, innocuous words for deceit and manipulation. I’ve wished at times that present-day advertising was outlawed and reduced to just putting out technical specification sheets on individual products. Wanna buy a car, here are all the specs imaginable, no glossy pics, sexy models, vroom-vroom video. Wanna buy toothpaste, just the specs please, no guys and gals with blinding smiles and radiant testimonials or clever animations. As Joe Friday used to say, “Just the facts, Ma’am.” But of course that will never happen — I accept that truth-in-advertising is a pipedream; images and emotions are what it's all about. And I’ll even admit a lot of advertising is hugely fun and entertaining; just questioning how truly informative and honest it is... heaven-forbid that honesty and full-disclosure should creep into capitalism. The buyer must beware… always.
You can probably sense I’m not much of a consumer… at least not on bigger ticket items (I do sometimes nickel-and-dime myself to death foolishly on small stuff -- OK, I have more pairs of Crocs than I'll ever admit to). And in this country, where conspicuous consumption is the national religion, that pretty much makes me a baaaad American. Worse yet, I pay my Visa bill off on time, every month — as you may know, that literally makes me, in the eyes (and labels) of the credit card industry, a “deadbeat” for never paying my share of the ongoing interest charges they depend upon. Yeah, I’m one of their most despised customers… ‘cuz I actually pay my bill. Such is the world we live in where frugality and timely payments are venial if not mortal sins.
Any rational human knows that the widespread advertising of drugs, in 60-second spots, to unsuspecting Americans is a dreadful idea (and at one time illegal). And don’t you just love the way those ads spend 55 seconds describing the wonder of their product with pictures of a meadow full of butterflies and ducks on a pond... before spending the last five seconds in rapid-fire, barely-intelligible English deigning to mention that the drug just might also cause dizziness, depression, baldness, suicidal thoughts, heart attacks, liver failure, incontinence, and the heartbreak of psoriasis, or whatever other afflictions some poor tortured experimental rats experienced in their brief, beleaguered lives.
Or how about the contracts we all read and sign in order to receive some service… contracts that we don’t actually read (but falsely sign, saying we’ve read and understood). The companies know that we don’t read them, we know the companies know we don’t read them, and they know we know they know we don’t read them… if you get my drift.
Or take one of my pet peeves: fruit juice products. There have been many outright fruit juice scandals over the years which I won’t even cite (except to say that often you’re not getting what you think you’re getting when you buy a bottle of say orange juice). But, as bad as the contents may be, my big beef is with the labelling.
The label may say Grape (or some other variety) Juicebeverage, drink, blend, or cocktail, but of course “GRAPE JUICE” is scrawled in BIG catchy letters across the label, while the ‘drink,’ ‘beverage,’‘blend,' or 'cocktail" notation is added in smaller and different lettering below — disguising the fact that the contents may actually contain surprisingly little grape juice, but a whole lot of additives. There are other tricks they employ, as you likely know, yet still sometimes fall for. Why this is legal I don’t have a clue; except well, lobbyists and money don’t ya know. And of course the grocery shelves are chockfull of other examples of packaging chicanery and labeling hype.
I grew up admiring/trusting corporate America, before joining the swelling ranks of those distrustful of big companies in particular. I’m constantly amazed by folks who are peeved with big government for all its ills and incompetencies, but who give the corporations who really run our lives and treat us like guinea pigs a free ride. Meanwhile the income gap between CEOs, and their employees and customers, increases obscenely, while the shrinking middle class stands by helplessly. Besides, at least I have a chance to vote in or out the scoundrels of government; the heads and management of corporations are unelected and I have little sway with.
People roil over all the regulations that government imposes, but many of those regulations are merely the result of trying to prevent in the future the very ways companies have shafted people in the past — all have to be regulated in order to insure a few bad actors stop doing what they’re doing (same reason we have laws against murder — in order to have a mechanism for dealing with the small percentage of people who actually commit murder). Anyone who walks into Verizon, Comcast, Wells Fargo or Time Warner or Best Buy or, or, or… and doesn’t realize you’re about to get played needs to wake up and smell the cash register.
Reminds me a bit of the current focus on sexual harassment — a situation that has been around for millennia, but held under-the-radar until at long-last being taken seriously and critically. We need such a spotlight on the treatment (abuse?) of customers by corporations, as well. On Twitter, the sex harassment headlines led to a #MeToo hashtag for women to add their relevant experiences. I feel like James Propp's storyline could be given a #MeToo followup for all who feel they've been screwed by businesses at one time or another.
Jim cleverly calls these corporate foes “errorists” in his post (because of mathematical mistakes they make), but actually or more broadly I don’t think they are errorists at all, rather primarily knaves who know exactly what they’re up to -- indeed, they pay people good money to derive the marketing, algorithms, wording, and sales techniques aimed specifically at exploiting people.
Earlier this year, polymath Eric Weinstein was so concerned about the way language is being used to sway people he actually made the little-referenced “Russell conjugation” (or “emotive conjugation”) his selection in response to the 2017 annual Edge question, “What scientific term or concept ought to be more widely known?”
These “conjugations,” made famous by Bertrand Russell (and studied by myself back in General Semantics) are rhetorical devices for expressing similar ideas but with very different connotations. Some famous ones below:
I am firm. You are obstinate. He is a pig-headed fool.
I am righteously indignant. You are annoyed. He is making a fuss about nothing.
I am a creative writer. You have a journalistic flair. He is a prosperous hack.
You can easily invent many more, often very creative ones, at will. It’s a bit reminiscent of how many people in polls tended to support “the Affordable Care Act” but oppose “ObamaCare,” not realizing they were the same thing (or "illegal aliens" versus "undocumented immigrants" is a similar example from Weinstein's piece). Anyway, his brief essay is worth a gander.
I could go on and on about shameful practices in big business, but I don’t even entirely fault them for manipulating us so regularly, given the cut-throat competitive world they inhabit (and perhaps I should be clear that many of their worst foibles don't apply as readily to small business and entrepreneurs). I do wish though, through enlightened education, the citizenry could be placed on guard against the very techniques being used to connive them, yielding a more even playing field. Worse yet, the managed demagoguery/skulduggery of corporate America is being transferred to the highest levels of government (and a President who worships at the altar of the dollar sign). But hey, don’t get me started…
p.s.... Merry Christmas (...or, Festivus, as the case may be)
Black Friday has arrived so time for some end-of-year stocking-stuffer book recommendations:
My two favorites for the year were “The Mathematics Lover’s Companion” by Edward Scheinerman and “Foolproof” by Brian Hayes. I’m a sucker for what I call “buffet” books (that cover several different topics briefly, instead of focusing on a single theme), and these both fall in that category. Even though Scheinerman’s book covered mostly well-worn topics in math I really enjoyed his writing and approach. Despite topping my own list, I didn't see the volume get a lot of publicity, and suspect that is only because the publisher, Yale University Press, may not spend much time/effort on promotion. I definitely recommend it, especially for young up-and-coming math enthusiasts and teachers.
Brian Hayes’ book is as well, a sort of “buffet” of more quirky, unpredictable topics (essays he had previously written), given Hayes’ excellent analytical treatment. Your ‘mileage may vary’ but I have to believe most math lovers will enjoy these two selections, covering a variety of topics, that top my picks.
The rest of the mentions I’ll list in no particular order…
More “buffet” offerings arrive via Mircea Pitici’s “Best Writing on Math” series. This year we actually got two from him, with “The Best Writing on Mathematics in 2016” showing up early in the year and the 2017 edition appearing recently. Pitici’s selections are always so broad and varying that in addition to the pieces I really enjoy there are always some others I don’t care for, making it hard for him to compete with my top two choices. But so glad he’s there offering this smorgasbord year-after-year.
Many 2017 books had a greater focus on niche areas, of interest to certain readers, but with perhaps less broad appeal. Two that I’ll mention dealt with subjects I think inherently interesting to most math lovers:
“A Most Elegant Equation” from David Stipp is an entire volume on Euler’s famous identity, e^(iÏ€)+1=0 , generally considered the most beautiful equation in all of mathematics. Though a few curmudgeons argue the equation is not that beautiful or inspiring (and Stipp deals with such claims in the book), most I suspect, think otherwise and for that reason alone will enjoy the volume. I especially liked the final, more philosophical chapter where Stipp deals with what ‘beauty’ even means in mathematics.
“Unsolved” by Craig Bauer could probably be organized or written a little better, but again the topic, unsolved codes/cryptograms over time, is so inherently fascinating it will likely pull most folks in, especially with some of the more familiar ones that readers have encountered and wondered about at one time or another.
Moving on, statistics and probability continued to be popular topics in 2017. I’ll only note two volumes:
From Persi Diaconis and Brian Skyrms came “Ten Great Ideas About Chance.” I thought this was going to be another popularized account of probability for lay people, of which there have been several recently, but it’s actually a more technical work, better as an adjunct text in a class than for a general audience. Once again I especially liked the final chapter on Hume, Bayes, and induction, but every chapter has value often touching on ideas not always stressed in probability courses. There is also an excellent probability tutorial in the Appendix. If probability is a major area of interest for you, you will want to look at this take.
Then from Steven Miller, comes the prodigious (700 pg.) “The Probability Lifesaver” — again suited more for the classroom than a general readership. An impressive compendium of probability topics and problems for anyone specializing in that area.
Next, how about some biographies. I’m still waiting for someone to top Siobhan Roberts’ 2015 treatment of John Conway ("Genius At Play"), but these are worth consideration:
Keith Devlin dug deep into history, and clearly had fun doing so, to tell the story of Fibonacci in “Finding Fibonacci.” Meanwhile Ian Stewart, never allowing a year to pass without producing a book, gave us “Significant Figures,” a historical look sketching 25 great mathematicians. I found the second half of the volume more engaging than the first half, but if you lack short bios of many famous mathematicians on your bookshelf this one will do nicely.
A tangential book I enjoyed was “A Man For All Markets” by and about successful stocktrader Edward O. Thorp. Some, but limited, math — in fact the math is some of the drier, duller material — but many interesting anecdotes about life on Wall Street and elsewhere from a very intriguing individual.
A book I haven’t yet read, but looks good, is “A Mind At Play” by Jimi Soni and Rob Goodman, a biography of Claude Shannon.
Two other books I haven’t read but don’t mind citing are “Arithmetic” by the always interesting Paul Lockhart, and “The Joy of Mathematics: Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Class” from Alfred Posamentier (again someone who churns out at least a book per year, and this one appears to overlap much of his previous output).
Two other popular books worth noting are “Beyond Infinity” from Eugenia Cheng (especially if you need a good primer on infinity for your bookshelf), and “The Calculus of Happiness” a quirky, practical, self-help guide from Oscar Fernandez.
And finally, I can’t let an offering from Marcus du Sautoy go unnoticed. “The Great Unknown” is a slightly encyclopedic volume covering a wide range of science topics and questions. In its scope, it reminds me a bit of Sean Carroll’s “The Big Picture,” if you are familiar with and enjoyed that volume.
Even with all this, I’ve left out dozens of math-related popular books from the year, but hope you or a few folks on your list will enjoy some of the above.
End of year is always a good time for lists (which make for good space-fillers too) ;)
So here a list of some websites I'm especially thankful for -- the math-related writers that excite me most when they show up in my RSS feed (in alphabetical order):
Scott Aaronson — love Scott’s unpredictable topics, his honesty, and step-by-step thought processes (even when I don’t understand half of what he’s laying out). Primarily a computer scientist, he also blogs about math, physics, philosophy, culture, politics, and more:
Keith Devlin — NPR “math guy” (and Stanford professor); love his ability to write about math expertly for a mass audience; long-time favorite at my blog; he has several writing venues, the one below being a main one:
Brian Hayes — award-winning essayist; unpredictable what and when he’ll post; a non-mathematician writing often about quirky, math-related subjects, but crisp and interesting whatever topic he chooses:
Evelyn Lamb — has developed into one of the finest math expositors on the Web, suitable for students and professors alike; again with several outlets, but perhaps the main one below for Scientific American:
Fawn Nguyen — what can I say about Fawn that hasn’t been said long before! I don’t follow a lot of primary/secondary education blogs but always perk up when I see she’s posted a new piece for her “Finding Ways” blog; it’s not even the math I enjoy so much, as her passion and wit! (made all the more delicious, knowing that English wasn’t even her native tongue):
Ben Orlin — never would’ve guessed math could be this funny, let alone cartoonish. Have grown to love Ben’s simple, round-faced offspring; but the amazing thing is not how much they make me laugh, but how regularly they make me think!:
Jim Propp — more strictly mathematical, but often on topics I don’t see elsewhere or at least with a different approach; richer and longer posts than most popular blogs, and almost always including ideas one could use in a classroom:
Quanta Magazine — not a blog, and not exclusively math, but some of the best doggone consistent popular science and math writing anywhere on the Web from a stable of great writers (sometimes I shake my head that we get this for free!):
I hope every one of these is already among your favorites, but if not, be sure to check 'em out. Wish I'd had some of these folks as teachers when I was growing up!
[...And feel free to mention below the Internet blogs/writers you are especially grateful for, or excited by, at this thankful time of year.]
Delusional Donald the Democracy-Subverter has returned from Asia, somehow confusing being laughed-at-behind-his-back with respect, and now re-opening the African elephant trophy trade (because assuredly who among us doesn't need more elephant parts adorning our living rooms)... but oh well, onward:
1) Not sure that there’s any math in this (…you be the judge), but the latest from Scott Aaronson:
8)The latest (and one of my favorites) from Jim Propp at Mathematical Enchantments, about things we've all experienced, and why "the errorists" may be winning:
Been a busy week (even with il Duce Donald out of the country embarrassing us elsewhere) and I didn't gather any math bits for passing along here, so will just offer up some non-math-potpourri links to a few miscellaneous items that caught my interest:
Won’t have time to do adequate blurbs (let alone full reviews) of all the books I’m reading now but will mention just a few of those I’m enjoying most, for a general audience.
Volume I last finished was Ian Stewart’s “Significant Figures,” his new compendium of biographical sketches of a couple dozen famous mathematicians — the writing is not as scintillating as some of Stewart’s other offerings, but adequate, especially if you’re looking for succinct profiles of mathematicians from ancient through William Thurston. The first half of the bios (and they’re in chronological order), had an almost cut-and-paste feel to it (to me), while the writing for the more modern half was more interesting/engaging.
Oddly, after finishing the new Stewart volume I stumbled upon his much older “The Problems of Mathematics” (at a garage sale) which is a wonderful read and overview of mathematics (a bit dated in parts), and highly recommendable.
And 3 more current books in my queue at the moment:
“Ten Great Ideas About Chance” — have barely started it, but coming from Persi Diaconis and Brian Skyrms looks quite good, though I’m tiring a bit of the many popular treatments of chance/probability/statistics in the last 3 years. Still, an important topic, and leafing through it, the volume does appear to have a somewhat fresh take and organization.
“The Best Writing In Mathematics 2017” — Micea Pitici’s latest entry in his ongoing series (the 2016 edition also came out earlier this year, so two in one year!). The volume is, as usual, a very wide-ranging collection of writings/topics from 2016, as Pitici shows again how “panoramic” and “versatile” mathematics really is. Some of your favorite popular math writers from the internet are included, and it is handsomely produced by Princeton University Press. I couldn’t detect a theme or prevalence of topics in this year’s edition, just the usual disjointed variety that Pitici brings together.
He mentions at the end that he has switched his own career focus over to library science now, from mathematics, and I’m not clear if that will affect his production of this volume in the future (though I suspect not).
“A Most Elegant Equation” by David Stipp — How could you go wrong writing about everybody’s favorite equation in mathematics, Leonhard Euler’s e^(iÏ€)+1=0. Even when the writing is a bit dry or stodgy the topic is so inherently interesting as to pull you along.
These are all books that will make my recommended list for end-of-year Holiday shopping, but several other books of a more specialized nature have crossed my desk the last few months, and I’ll probably leave them un-noted.
7) Evelyn Lamb’s “TinyLetter,” covering her doings for the month of October, is now out (hopefully by now most of you are receiving it in your email box each month):
A week with liddle Republicans coming apart at the seams, and Melania Trump, drenched-to-the-bone in irony, speaking of a campaign (LOL) against bullying, and our own Gov’t., in a demonstration of why so many revile it and see neo-fascism as an appealing alternative, deciding that 25 years just wasn’t enough time to figure out how to release a trove of JFK documents as ordered to by law. (What else can’t possibly be accomplished in 25 years? I mean other than healthcare, tax reform, fair re-districting, gun control, banking reform, truth-in-advertising, climate change regulation...). Is it any longer a surprise that so many voters perceive government workers as lazy, incompetent, pencil-pushers, and Steve Bannon thinks his future looks bright... 'This too shall pass'... or, maybe not. Oh well, some bits of math from the week:
5) There are so many fantastic free math instructional videos around these days… and yet Grant Sanderson still seems to have advanced to a league of his own. I hope you all are keeping up with his incredible offerings at 3blue1brown:
It will be interesting to see if we witness a significant increase in math majors and basic math literacy in the future just because of all the great content now freely available online at people’s fingertips.
6) The 150th Carnival of Mathematics is now up at:
(I don’t believe it’s in American bookstores yet, and when it is, may show up under a different title as British math books often do)
2) Just in time for your next cocktail chatter… ;) David Butler tweeted this week: “For every prime after 66600049, you can cross out some of its digits and find a smaller prime.”
