math — Page 2

→ May 24, 2018
→ By keith

A Brief History of Infinity.

Infinity is a big topic, to put it mildly. The mere concept of a limitless quantity has vexed mathematicians, philosophers, and theologians for over two centuries. The Greeks developed some of the first infinite series, some divergent (they approach infinity) and some convergent (they approach a finite number), with Zeno making use of these concepts in some of his famous paradoxes. Galileo is better known for his observations in astronomy and work in optics, but he developed an early paradox that he argued meant that we couldn’t compare the sizes of infinite sets in a meaningful way, showing that, although we know intuitively that there are more integers in total than there are integers that are perfect squares, you can map the integers to the perfect squares in a 1:1 ratio that appears to show that the two sets are the same size. Georg Cantor later explained this paradox in his development of set theory, coining the aleph terminology for infinite sets, and then went mad trying to further his theories of infinity, a math-induced insanity that later afflicted Kurt Gödel in his work on incompleteness. There remain numerous – dare I say infinite? – unsolved problems in mathematics that revolve around infinity itself or whether there are an infinite number of some entity, such as primes or perfect numbers, in the infinite set of whole numbers or integers.

Science writer Brian Clegg attempts to make these topics accessible to the lay reader in his book A Brief History of Infinity, part of the Brief History series from the imprint Constable & Robinson. Rather than delving too far into the mathematics of the infinite, which would require more than passing introductions to set theory, the transfinite numbers, and integral calculus, Clegg focuses on the history of infinity as a concept in math and philosophy, going back to the ancient Greeks, walking through western scholars’ troubles with infinity (and objections from the Church), telling the well-known story of Newton and Leibniz’s fight over “the” calculus, and bringing the reader up through the works of Cantor, Gödel, and other modern mathematicians in illuminating the infinite both large and small. (It’s $6 for the Kindle and $5 for the paperback as I write this.)

Infinity can be inconvenient, but we couldn’t have modern calculus without it, and it comes up repeatedly in other fields including fractal mathematics and quantum physics. Sometimes it’s the infinitely small – the “ghosts of departed quantities” called infinitesimals that Newton and Leibniz required for integration – and sometimes it’s infinitely large, but despite several millennia of attempts to argue infinity out of mathematics, there’s no avoiding its existence and even the necessity of using it. Clegg excels when recounting great controversies over infinity from the history of math, such as the battle between Newton and Leibniz over who invented the calculus, or the battle between Cantor and his former teacher Leopold Kronecker, who disdained not just infinity but even the transcendental numbers (like π, e, or the Hilbert number) and actively worked to prevent Cantor from publishing his seminal papers on set theory.

Clegg’s book won’t likely satisfy the more math-inclined readers who want a crunchier treatment of this topic, especially the recent history of infinity from Cantor forward. Cantor developed modern set theory and published numerous proofs about infinity, proving that there are at least two distinct sets of infinities (the integers, aleph-null, are infinite, but not as numerous as the real numbers, aleph-one; aleph notation measures the cardinality of infinities, not the quantity of infinity itself). I also found Clegg’s discussion of Gödel’s incompleteness theorems rather … um … incomplete, which is understandable given the theorems’ abstract nature, but also meant Gödel earned very little screen time in the book other than the overemphasized parallel between his own descent into insanity and Cantor’s. I was disappointed that he didn’t get into Russell’s paradox*, which is a critical link between Cantor’s work (and Hilbert’s hope for a resolution in favor of completeness) and Gödel’s finding that completeness was impossible.

Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then it must be a member of R … but that produces a contradiction by the definition of R.

Clegg does a much better job than David Foster Wallace did in his own book on infinity, Everything and More: A Compact History of Infinity, which tried to get into the mathier stuff but ultimately failed to make the material accessible enough to the reader (and perhaps exposed the limits of Wallace’s knowledge of the topic too). This is a book just about anyone who took one calculus class can follow, and it has enough personal intrigue to hold the reader’s attention. My personal taste in history of science/math books leans towards the more technical or granular, but I wouldn’t use that as an indictment of Clegg’s approach here.

Next up: I’m reading another Nero Wolfe mystery, after which I’ll tackle Michael Ondaatje’s Booker Prize-winning novel The English Patient.

Filed Under: Uncategorized Tagged With: history of science, math, non-fiction, physics

→ October 27, 2017
→ By keith

Everybody Lies.

Seth Stephens-Davidowitz made his name by using the enormous trove of data from Google search inquiries – that is, what users all over the world type in the search box – to measure things that researchers would typically measure solely by voluntary responses to surveys. And, as Stephens-Davidowitz says in the title of his first book, Everybody Lies, those surveys are not that reliable. It turns out, to pick one of the most notable results of his work (described in this book), that only 2-3% of men self-report as gay when asked in surveys, but the actual rate is probably twice that, based on the data he mined from online searches.

Stephens-Davidowitz ended up working for a year-plus at Google as a data scientist before leaving to become an editorial writer at the New York Times and author, so the book is bit more than just a collection of anecdotes like later entries in the Freakonomics series. Here, the author is more focused on the potential uses and risks of this enormous new quantity of data that, of course, is being collected on us every time we search on Google, click on Facebook, or look for something on a pornography site. (Yep, he got search data from Pornhub too.)

The core idea here is twofold: there are new data, and these new data allow us to ask questions we couldn’t answer before, or simply couldn’t answer well. People won’t discuss certain topics with researchers, or even answer surveys truthfully, but they will spill everything to Google. Witness the derisive term “Dr. Google” for people who search for their symptoms online, where they may end up with information from fraudsters or junk science sites like Natural News or Mercola, rather than seeing a doctor. What if, however, you looked at people who reveal through their searches that they have something like pancreatic cancer, and then looked at the symptoms those same people were Googling several weeks or months before their diagnosis? Such an approach could allow researchers to identify symptoms that positively correlate with hard-to-detect diseases, and to know the chances of false positives, or even find intermediate variables that alter the probability the patient has the disease. You could even build expert systems that really would work like Dr. Google – if I have these five symptoms, but not these three, should I see a real doctor?

Sex, like medical topics, is another subject people don’t like to discuss with strangers, and it happens to sell books too, so Stephens-Davidowitz spent quite a bit of time looking into what people search for when they’re searching about sex, whether it’s pornography, dating sites, or questions about sex and sexuality. The Pornhub data trove reveals quite a bit about sexual orientations, along with some searches I personally found a bit disturbing. Even more disturbing, however, is just how many Americans secretly harbor racist views, which Stephens-Davidowitz deduces from internet searches for certain racial slurs, and even shows how polls underestimated Donald Trump’s appeal to the racist white masses by demonstrating from search data how many of these people are out there. Few racists reveal themselves as such to surveys or researchers, and such people may even lie about their voting preferences or plans – saying they were undecided when they planned to vote for Trump, for instance. If Democrats had bothered to get and analyze this data, which is freely available, would they have changed their strategies in swing states?

Some of Stephens-Davidowitz’s queries here are less earth-shattering and seem more like ways to demonstrate the power of the tool. He looks at whether violent movies actually correlate to an increase in violent crime (spoiler: not really), and what first-date words or phrases might indicate a strong chance for a second date. But he also uses some of these queries to talk about new or revived study techniques, like A/B testing, or to show how such huge quantities of data can lead to spurious correlations, a problem known as “the curse of dimensionality,” such as in studies that claim a specific gene causes a specific disease or physical condition that then aren’t replicated by other researchers.

Stephens-Davidowitz closes with some consideration of the inherent risks of having this much information about us available both to corporations like Google, Facebook, and … um … Pornhub, as well as the risks of having it in the hands of the government, especially with the convenient excuse of “homeland security” always available to the government to explain any sort of overreach. Take the example in the news this week that a neighbor of Adam Lanza, the Sandy Hook mass murderer, warned police that he was threatening to do just such a thing, only to be told that the police couldn’t do anything because his mother owned the guns legally. What if he’d searched for this online? For ways to kill a lot of people in a short period of time, or to build a bomb, or to invade a building? Should the FBI be knocking on the doors of anyone who searches for such things? Some people would say yes, if it might prevent Sandy Hook or Las Vegas or San Bernardino or the Pulse Orlando or Columbine or Virginia Tech or Luby’s or Binghamton or the Navy Yard. Some people will consider this an unreasonable abridgement of our civil liberties. Big Data forces the conversation to move to new places because authorities can learn more about us than ever before – and we’re the ones giving them the information.

Next up: J.M. Coetzee’s Waiting for the Barbarians.

Filed Under: Uncategorized Tagged With: data science, highly recommended, math, non-fiction

→ September 25, 2017
→ By keith

For the love of algebra.

I have always loved math, and I don’t think there’s any field within math I love more than algebra. I certainly enjoyed calculus, and there are parts of number theory that still fascinate me (Goldbach’s conjecture, an unproven hypothesis that dates back to 1742, more than anything else), but algebra just speaks to me like nothing else in the domains of math or science. So when I saw this week’s FiveThirtyEight Riddler problem, which boils down to solving two equations for two unknowns, I might have dropped everything I was doing and spent about a half an hour solving it – messily, but I think ultimately getting the right answer.

My own personal love of algebra dates back to when I was ten years old, and my junior high school, lacking an honors math class for sixth grade, decided instead to bump me up to the regular eighth grade math course, where I met a wonderful teacher and some awful kids. (I was three years younger than they were, and of course small for my age anyway.) I was told very little about the move but somehow understood that I’d be learning algebra, so I went to the school library and found a book, long out of print now, called Realm of Algebra, by an author I’d never heard of at the time but would later grow to know very well through his science fiction writing, Isaac Asimov. I devoured the book, which I credit to Asimov’s ability to make even abstruse concepts clear to readers, in a weekend, and ended up ahead of where I needed to be for the class. Algebra felt to me like another language, as easy to comprehend as English, maybe even more so – like this was my native tongue and everyone had been hiding it from me. I could always “think” in numbers, but algebra gave me an entire framework for it, and everything I learned that year, especially from Asimov’s book, still directs much of how I think about problems today.

It has also made me an easy mark for puzzles and games that revolve around algebraic questions. I often check FiveThirtyEight’s Riddler questions, but I rarely try to solve them – some look too hard or involved, some just don’t grab me. This week’s question, about finding the area of a missing rectangle, hooked me from the start. (I suppose I should disclose that FiveThirtyEight is part of the ESPN network of sites, and thus I am connected to it as well.) Here’s the question in brief: Find the missing area in the picture below, bearing in mind that it is not to scale.

I tweeted the link to the article last night and got a slew of responses from readers, some right, some I don’t think were right, and a few that gave me more insight into the problem – one of which made me realize my first answer was impossible – so I decided to take a few minutes and explain my method, in case it’s useful to anyone or still contains a mistake.

To figure out the area of the lower-left rectangle, you need to know its height and width, so this is a problem of two unknowns, which means you need (at least) two equations containing those unknowns to be able to solve it. To make the math a little less messy, I defined the height (vertical axis) of the target area as 11-x and the width (horizontal axis) as 14-y, meaning that the height of the upper-left area is x and the width of the lower-right area is y. We know the area of the lower right rectangle is 45, and the area of the upper left rectangle is 32, so using the formula for the area of a rectangle we get the following two equations:

(14 – y)x = 14x – xy = 32
y(11 – x) = 11y – xy = 45

You can then solve one equation for one variable in terms of the other, substitute that back into the second equation, and solve for one of the two variables. I chose to solve the first equation for x, yielding:

x(14 – y) = 32
x = 32/(14 – y)

11y – y(32/(14 – y)) = 45

11y – 32y/(14 – y) = 45
11y(14 – y) – 32y = 45(14 – y)
154y – 11y² – 32y = 630 – 45y
–11y² + 167y – 630 = 0

That, my friends, is a quadratic equation, and if you remember your quadratic formula – where you take the two coefficients and the constant and plug them into the formula to get the two possible solutions – you can solve it from here, or you can just plug them into this site and get your two answers for y, which in this case are 7 or 90/11.

It turns out that both answers produce whole-number, positive results for the area of the lower left rectangle. If y is 7, x is 32/7, and the area is 45. If y is 90/11, x is 11/2 (5.5) and the area is 32. A reader pointed out that the first answer is impossible, however, because of the one number I haven’t mentioned yet: the truncated, upper-right rectangle’s area, which is 34. Because the area of the whole shebang has to be less than 154 (11 * 14), since there’s a piece missing at the extreme upper right, then the lower left area has to be less than (154 – 32 – 34 – 45), which is 43. That leaves 32 as the only possible answer. (EDIT: Fixed the second sentence, where I transposed the two answers.)

I think.

Filed Under: Uncategorized Tagged With: math, puzzles

→ September 9, 2017
→ By keith

Stick to baseball, 9/9/17.

I wrote two Insider pieces this week, naming ESPN’s 2017 Prospect of the Year (hint: it’s Vlad Jr.) and covering and on the strange saga of Juan Nicasio over the last ten days. I held a Klawchat on Thursday.

Last week, I wrote about the major Game of Thrones-themed boardgames for Vulture. My next boardgame review for Paste will come this week.

My book, Smart Baseball, is out and still selling well (or so I’m told); thanks to all of you who’ve already picked up a copy. And please sign up for my free email newsletter, which is back to more or less weekly at this point now that I’m not traveling for a bit.

And now, the links…

This week’s top longread is one of the longest I’ve posted, and it seems likely to garner a slew of awards for the Houston Chronicle: They told the stories of five Houston residents through Hurricane Harvey, from prelude to aftermath as the storm dropped over 51 inches of rain on the country’s fourth-largest city.
Jacobin forecasts a Republican-led attempt to remake state government, schools, and the social support system in Texas in the wake of Harvey, and they don’t like what they see.
That article discusses Betsy DeVos’ war on public schools, and the Atlantic looks deeper at myths that poison our view of public education in America.
At the other end of the spectrum, New York City public schools will now offer free lunch for all students. Given the connection of adequate nutrition and caloric intake to students’ long-term success, this isn’t just compassionate – it’s sound educational and social policy. We should see enough savings and/or economic growth in the long run to more than pay for this program.
Ta-Nehisi Coates’ “The First White President” piece was deservedly trending this week. Our President is a de facto white supremacist, and one of our two major political parties is going along with it so they can get the tax breaks they want.
A two-decade campaign by “conservative” science-denial groups fueled the U.S. exit from the Paris climate accord earlier this year.
Richard Branson owns Necker Island in the British Virgin Islands, and his home there was completely destroyed by Hurricane Irma. If a luxury home, likely built with top-end materials and to a sophisticated design, gets wiped out by the storm, what chance did lesser structures on other islands stand?
I tweeted this link last night, but it’s worth repeating: Tim Duncan wrote asking Americans not to forget the U.S. Virgin Islands, two of which (St. Thomas and St. John) were devastated by the storm. (St. Croix is far enough south that it escaped the worst impact.)
I linked to Rachel Kaadzi Ghansah’s profile of Dylan Roof a few weeks ago, and this week she appeared on the Longform podcast to discuss it. The conversation is enlightening for the first 2/3 but loses some speed, and I was surprised to hear Ghansah misuse or mispronounce so many words.
From May, Jalopnik posted this hard-to-believe story about a man who became “addicted” to buying BMWs, to the point that he embezzled money from his employers and lost his job, house, family, and freedom.
A youth hockey coach who stood accused of raping one of his former players is going free after the player in question died of a drug overdose. This story is more about the former player, David Gove, and how the abuse led him into a descent of heroin addiction and homelessness, but the world needs to know that this accused predator remains at large.
A former Florida State professor who lost her job for blowing the whistle on favoritism granted to football players in their so-called “classes” died of an accidental drug overdose, the result of a mix of medications for pain after back surgery and anti-depressants she was taking in the wake of FSU officials damaging her career.
FiveThirtyEight looks at the U.S./North Korea war of tweets (and missiles) and decides it’s time for some game theory.
New York is about to vote on whether to hold a Constitutional Convention. If they don’t do so, their next chance to hold one will come in 2037.
Two House Republicans say they only signed an anti-gerrymandering amicus brief by mistake and later removed their signatures from it. How bad is our climate when a politician can endorse gerrymandering like that and suffer no consequences?
Eater profiles Milk Bar CEO and mastermind Christina Tosi as she and David Chang try to take the dessert-bar brand to other markets.
Forbes profiles a 23-year-old woman who makes $60K a month as an online consultant and claims she has advice to help others do the same. The counsel she offers is trite, she almost certainly started life with some huge advantages, and the whole thing reads like unintentional comedy to me.
The Nib gives us a graphic essay in defense of Twitter. I agree with the positives the author identifies here; Twitter has been tremendous for my career, and several people I now consider close friends were originally Twitter acquaintances.
Malaria had been considered eradicated in Italy, but a four-year-old girl died there from malaria last week. The biggest concern here is that climate change may allow the spread of disease-bearing insects to latitudes previously unaffected by those pathogens.
Chaldean-Americans in Michigan, who voted overwhelmingly for Donald Trump, are now at risk of deportation due to his policies.
Aeon goes into the information-theory work of polymath Claude Shannon, whose insights on the probabilistic nature of much information paved the way for modern data-compression techniques.
The Broward County Republican Party Secretary refuses to resign even after officials discovered he tried to kill a girl in 2007. I’d love to know how he managed to plead out to a misdemeanor on this. Maybe because his grandfather was rich and well-connected?
Chinese law says that a woman can’t have a C-section without her family’s permission; when one very pregnant woman didn’t get that permission, she killed herself in the hospital. The U.S. hasn’t been tough on China’s human rights violations in decades; it’s certainly not going to get any better under the current Administration, given the Trump family’s business dealings in the autocratic state.
The Economist looks at the toxic relationship between Angola and the D.R. Congo, where the smaller, oil-rich former Portuguese colony can’t stop meddling in the larger, failed state that separates Angola from its main oil-producing region of Cabinda.
I linked last week to a story about Google pulling funding from a think tank that published opinions contrary to Google’s interests in European antitrust matters; Gizmodo ran a related piece after that, from a writer who says Google pressured her to pull a critical column, saying she had violated an NDA her bosses had signed before the meeting. She claims the NDA didn’t exist. It’s unclear what the whole story is here, but the subject of her original article doesn’t reflect well on the company regardless of whether it should have been published.
The New Yorker managed to dig up Jared Kushner’s Harvard admissions essay!

Boardgame news will return next week; I know of two significant Kickstarters to launch on Tuesday, but at least one of them is currently covered by an embargo so I can’t talk about it just yet.

Filed Under: Uncategorized Tagged With: africa, climate change, dessert, links, math, stick to baseball

→ September 2, 2017
→ By keith

Stick to baseball, 9/2/17.

For Insiders this week, I wrote four pieces. I broke down the Astros’ trade for Justin Verlander and the Angels’ trade for Justin Upton. I put up scouting notes on prospects from the Yankees, Phillies, Jays, and Rangers. And I looked at five potential prospect callups for September. I also held a Klawchat on Thursday.

At Vulture this week, I looked at five major Game of Thrones-themed boardgames, not just reskinned games but several original titles like the excellent GoT Card Game. For Paste, I reviewed the Tour de France-themed boardgame La Flamme Rouge, which is light and good for family play. And here on the dish I reviewed the strong app version of the two-player game Jaipur, a steal at $5.

I’m trying something new this week, and if you find it useful I’d appreciate your feedback. I get a lot of press releases on boardgames from publishers, so I’m including the best of those at the end of this run of links along with boardgame-related news items. These will include Kickstarter announcements that look interesting to me, and if I’ve seen a game at all I’ll indicate it in the blurb.

This is your regular reminder that my book Smart Baseball is available everywhere now in hardcover, e-book, and audiobook formats. Also, please sign up for my free email newsletter, as my subscriber count is down one after I removed that one guy who complained about the most recent edition and called me a “tool.”

And now, the links…

Longread of the week: GQ sent essayist Rachel Kaadsi Ghansah to South Carolina to look for answers in the background of mass murderer Dylan Roof, although I don’t know that she found any. This was a severely mentally ill man with a criminal background who was allowed to purchase a gun.
Another longread from Lapham’s Quarterly, published a few years ago: On the brief career and unsolved disappearance of Barbara Follett, a child novelist who published two novels and wrote two more before her still-mysterious vanishing at age 25.
A German mathematician claimed he has solved the P vs. NP problem, and done so with the negative (but most likely correct) answer that P does not equal NP – that is, that there are some computational problems (NP) that cannot be reduced to equivalence with other problems (P) that we know can be solved in polynomial time. Norbert Blum has since posted a comment on the proof’s page saying “The proof is wrong,”, so perhaps we’re still not there yet.
The planet is warming, including the oceans, and that latter temperature increase could lead to much smaller fish.
Consumers are increasingly demanding antibiotic-free meat, including chicken, but can chicken producers “afford” to make the switch? Of course they can, and maybe meat will cost more in the end, but the cost of doing nothing – of continuing prophylactic use of antibiotics and dealing with the multi-drug resistant bacteria that will result – is far greater.
Eight of the 28 members of a DHS advisory panel on cybersecurity quit en masse last week, arguing that the President is ignoring threats to critical infrastructure.
Meanwhile, Trump continues to fill the swamp with political appointees, often taking people from industry and putting them in regulatory positions overseeing those businesses, as ProPublica continues to investigate these unreported hirings.
Presidential adviser (and son-in-law) Jared Kushner is hundreds of millions of dollars in debt to foreign investors on a building he sort-of owns in Manhattan. Bloomberg investigates Kushner & associates’ attempts to solicit new investments from foreign sources as well as the troubled finances of his real estate firm.
A reader passed along this 2007 study of New Orleans residents who chose not to evacuate before Hurricane Katrina hit, looking at reasons why they didn’t leave. The “Perceived Barriers to Action” section of the conclusions is the money part – literally, as financial barriers were a significant issue.
Jay Caspian King looks at why some new sports stats catch on and others don’t for the NY Times. I think he undersells the point in his last paragraph about our obsession with round numbers, though.
One of my colleagues, Ed Cunningham, walked away from his job as a football announcer because he was concerned about the impact of brain injuries in the sport.
Awful Announcing looks at Joe Sheehan and his subscription-only newsletter, and how he’s managed to make a living charging for content in an era where free content was still king. Disclaimer: Joe’s a good friend of mine dating back to the early days of Baseball Prospectus.
A Yemeni social media star who’d reported on and criticized both sides in that country’s devastating civil war has been abducted by Houthi rebels, the forces loyal to Yemen’s deposed dictator. The civil war has led to countless deaths and a cholera epidemic.
Parents of autistic children have become targets for a host of unproven or dangerous “treatments” for the genetic condition, a situation exacerbated by what the writer calls “online filter bubbles” of shared junk science stories.
The University of Tampa fired a professor who suggested Hurricane Harvey was karma for Texas Republicans. I can’t blame them – it was stupid, insensitive, and obviously false. You can have those thoughts, you may even be entitled to share them in your classroom, but once you put that on social media for the world to see, you’ve changed the stakes.
Speaking of Harvey, the Washington Post asked Texas Republicans who voted against aid for victims of the ‘superstorm’ Sandy in 2013 to defend their votes; only one answered, and he did so with a lie about the Sandy bill. The Republicans also failed to answer the Post‘s questions about Harvey and climate change.
Trevor Noah offered a ridiculous, specious criticism of the “antifa” movement in what seemed to me like some sort of weak-ass attempt to satisfy a fairness doctrine. In fact, law enforcement authorities, including the FBI and CIA, appear to place the blame for so-called “antifa” attacks on Trump himself, due to the “inflammatory rhetoric and policies” he’s espoused as candidate and now president.
A size-10 model has returned her beauty pageant crown after the event organizers told her to lose weight. There are several pictures of the woman in the article, and if that woman needs to shed some pounds, then I’d say 99% of the planet is obese.
A first-time author appears to have gamed the NYT Bestseller list largely through bulk sales of her own book. The author, Lani Sarem, has denied any shenanigans. I found it surprising that the Times‘ bestseller lists are still assembled in such an ad hoc fashion more than 20 years after the music industry went to hard sales data collected by SoundScan.
The Guardian asked three authors to discuss their favorite Philip K. Dick novels ahead of this fall’s release of a sequel to Blade Runner, which was based on Dick’s novel Do Androids Dream of Electric Sheep? I was surprised none of them discussed The Man in the High Castle, my favorite PKD novel and his lone book to win the Hugo Award.
The Guardian also ran an op ed this week arguing that Google, Facebook, and amazon should be “nationalized” because of their quasi-monopoly status. This is a pretty terrible idea across the board.
But it does appear that Google dropped the hammer on a think tank it supports, leading it to fire several of its experts, as one of the deposed academics writes in the Washington Post. This seems to go against Google’s “don’t be evil” policy.
The NY Times ran a quirky op ed this week in praise of memorizing poems. This used to be common practice, and it’s evident if you read novels from across the last 150 years or so that the practice has gone away, as quotes and allusions to classical poetry have declined.
Also from the Grey Lady, editorial writer Bret Stephens shared fifteen tips for aspiring op ed writers – but most of these are just good tips for writers, period.
I’ve never tried the video game franchise Overwatch in part because I hear it’s a lot of first-person shooting, and Paste opines that it’s time for the designers to give players something else to do. I never cared for the earliest generation of FPS games, like Castle Wolfenstein or Doom, and that’s around the time I started to fade out of video gaming.
Boardgame news: Kotaku looks deeper at Photosynthesis, one of the biggest buzz games at GenCon this year. I ranked Photosynthesis seventh on my list of the best new games at GenCon.
Playing boardgames with other people can make you a nicer person with better relationships.
There’s a new virtual reality version of Catan coming out for the holidays. I’m really not sure what the market for this is; how will VR add to the Catan gaming experience?
Plan B Games, founded by former Z-Man owner/head Sophie Gravel, announced Azul, an upcoming game with a Moorish theme and artwork, due out in October. They didn’t have this out at GenCon, so it’s new to me as well.
Greenbrier Games has reopened its Kickstarter for the fantasy/adventure boardgame Champions of Hara, which will also include some miniatures and upgraded artwork.
Greater than Games announced a Legends of Sleepy Hollow boardgame (PDF link), with a Kickstarter beginning on October 17th.

Filed Under: Uncategorized Tagged With: boardgames, chicken, climate change, links, math, philip dick, stick to baseball, unsolved problems, writing

→ July 8, 2017
→ By keith

Stick to baseball, 7/8/17.

For Insiders this week, I previewed the Futures Game and broke down some of the worst omissions from the All-Star rosters. I held a Klawchat on Friday.

On the non-baseball front, I reviewed the high-strategy boardgame Great Western Trail for Paste this week. I also have a new piece up at Vulture looking at how the TV show Orphan Black has used boardgames as an integral part of several episodes.

Thanks to everyone who’s already bought Smart Baseball; sales spiked this month between Father’s Day and the positive review in the Wall Street Journal. I’ve got book signings coming up:

* Miami, Books and Books, today at 3 pm
* Harrisburg, Midtown Scholar, July 15th
* Berkeley, Books Inc., July 19th
* Chicago, Volumes, July 28th, 7:30 pm
* GenCon (Indianapolis), August 17th-20th

If you’re with an independent bookstore and would like to host a signing, please contact Danielle Bartlett at HarperCollins; we’re trying to accommodate everyone we can within my work schedule. I’m talking to one store about a signing/talk in Brooklyn (along with another author) in August or early September.

And now, the links…

The headline may be salacious, but the problem is serious: Antibiotic-resistant gonorrhea is spreading, due in large part to unprotected sex (including oral sex), resulting in some patients with untreatable cases. And given what we know about horizontal gene transfer in bacteria, this should terrify you even if you aren’t at risk of contracting this particular disease.
Longread of the week: Nathan Fenno, who wrote the definitive piece on Rays prospect turned accused murderer Brandon Martin, has another, similar piece, on former NFL player De’von Hall, who killed his mother during an argument, apparently after a quick decline into mental illness and homelessness.
Digg has a riveting first-person account of post-partum psychosis. The girl who grew up next door to me, two years my senior, took her own life about a decade ago a few days after giving birth, the result of post-partum psychosis.
James Beard winner Sean Brock, the celebrity chef behind Husk (Charleston, Nashville, and soon two more locations), opened up to the New York Times about getting sober after friends staged an intervention around his drinking.
Bloomberg profiled a strange, remote, popular hotel on Newfoundland’s Fogo Island in a piece from May of 2016. The photos are as incredible as the story.
WIRED looks at the unlikely rise of mathematician June Huh, who didn’t come to mathematics until college and is doing his best work now at age 34, well past the typical peak years of most mathematicians. Clearly we should be testing him for Proof Enhancing Drugs.
From Gizmodo, why people with implanted medical devices should fear automatic doors and the general rise of devices operating in the same frequency ranges as, say, brain implants or pacemakers.
Austin is a rare bastion of progressive thought and policy in Texas, a state with one of the country’s most reactionary governments, leading to conflict between the citizens of the state’s capital and the politicians working in it, particularly over “preemption laws,” whereby states tell cities and counties they can’t pass certain ordinances or enact policies that might run counter to what the state governments want.
A white man shot and killed an 18-year-old black woman in a road rage incident in Pennsylvania last week. It doesn’t appear their races played a role in the crime, but they seem to have affected the news coverage of the incident. David Desper had a permit for the 40-caliber semi-automatic he (is alleged to have) used to kill Bianca Robertson.
A Kenyan woman told the BBC how she missed her own wedding because she’d been abducted and gang-raped outside of Nairobi.
Flights in the southern US (and beyond) are increasingly facing high-heat delays due to climate change, which our current federal Administration still denies even exists.
John Le Carré gave a speech, transcribed in the Guardian, extolling the virtues of learning German in a post-Brexit world, although I think his points can apply to anyone learning any foreign language. Not only does it facilitate communication, but different languages can express different concepts and can give the speaker new perspectives.
Are humans insignificant in the cosmos, and if so, does life have meaning? A fellow of philosophy and epistemology examines a question often reserved for clergy and theologians.
Eighteen states are suing the Department of Education for delaying implementation of a rule aimed at helping students conned by for-profit universities. For-profit colleges aren’t necessarily bad, but the field is certainly ripe for scams, particularly since federal aid is so easy to come by.
The Guardian‘s editorial page also came out in favor of mandatory childhood vaccinations, while accurately comparing modern anti-vaccine movements to the religious fundamentalists – the article mentions the Taleban, but Christian Scientists have the same bad beliefs – who also oppose vaccinations.
Lindy West, who deleted her Twitter account in January due to the service’s refusal to deal with abusive trolls, writes about how the same class of trolls threatens free speech rights.

Filed Under: Uncategorized Tagged With: charleston, climate change, links, math, stick to baseball, texas, vaccines

→ September 15, 2016
→ By keith

Gödel’s Proof.

My latest Insider post covers eight top 100 prospects who took a step back this year. I’ll also hold a Klawchat here at 1 pm ET.

I read Rebecca Goldstein’s biography of Kurt Gödel, Incompleteness, last summer, and I believe it was within her book that I read about James Newman and Ernest Nagel’s book Gödel’s Proof that attempts to explain the Austrian logician’s groundbreaking findings. The 114-page volume does a great job of building up to the final proof, but I have to concede that the 19-page section near the end that reveals the fatal blow Gödel delivered to Bertrand Russell, David Hilbert, and others who believed in the essential completeness of mathematical systems lost me in its nested language and ornate symbols. (The newest edition includes a foreword by Douglas Hofstadter, who wrote about the proof in Gödel, Escher, Bach, which won the Pulitzer Prize for Non-fiction.)

Gödel was himself a fascinating figure, a philosopher, mathematician, and logician who wrote a paper with two theorems at age 25 that stunned the world of mathematics in their method and conclusions, proving that any axiomatic system of arithmetic that is consistent cannot be complete. Completeness here means that every true formula that can be expressed within the system can be proven within the system. Gödel’s trick was to create an entire system of expressing logical formulas via what is now called Gödel numbering, and then to craft a formula that says itself that it is unprovable within the system. His proof further stated that even if you could add an axiom to this system of mathematics to cover this new exception, the formula could always be rephrased to pose a new exception, and thus the system is essentially incomplete.

Nagel and Newman do a great job of getting the reader – or at least in getting this reader – to the edge of understanding by building up the history of the question, giving a lay explanation of Gödel’s basic method of numbering and delineating what a simple axiomatic system like that of Russell’s Principia Mathematica (the system Gödel targeted in his proof) would look like. Russell and other logicians of the time were convinced that systems of mathematics were complete – that we could define any such system in terms of a finite number of axioms that would cover all possible formulas we could craft within that system. Any formula that could be proven true at all could then be proven true using only the axioms of that system. Gödel’s proof to the contrary was scarcely noticed at first, but when it spread and others in the field realized it might be true, it blew apart a fundamental assumption of number theory and of logic, while also making Gödel’s name as a major figure in the history of mathematics and logic.

All of which is to say that I just couldn’t follow the nested statements that constitute Nagel and Newman’s explanation of Gödel’s proof. I haven’t read Gödel’s original paper, because it is a truth universally acknowledged that you’ve got to have some serious math background to understand it, so I will accept the claim that Nagel and Newman made it much easier to grasp … but I still only get this at a superficial level. When the authors compare this to Richard’s Paradox, an earlier device that Gödel cited in his paper, I could understand it; these are all descendants of the “This statement is false” type of logical trick that causes an inherent contradiction. Gödel appears to have done the same thing for arithmetic. I just couldn’t quite get to the mental finish line on this one. I guess you could say my understanding of the topic remains ….

…incomplete.

Next up: I finished and will review Laurent Binet’s HHhH, and have begun Clifford Simak’s Hugo-winning novel Way Station.

Filed Under: Uncategorized Tagged With: history of science, logic, math, non-fiction, philosophy

→ July 30, 2016
→ By keith

Stick to baseball, 7/30/16.

It’s been a busy week already and I assume the next 52 hours will be even more so; here are my three Insider posts on trades from the last seven days:

• The Aroldis Chapman trade
• The Texas/Atlanta trade and the Blue Jays’ two deals
• The Andrew Cashner and Eduardo Nunez trades

I also have a draft blog post up on last week’s Under Armour Game, and I held my regular Klawchat on Thursday.

I’ll be on ESPN’s trade deadline show on Monday from 1 to 4 pm ET, after which I’m taking a few days off to work on my book and on some other personal projects.

And now, the links…

Dr. Mike Sonne, an injury prevention researcher and a baseball fan, argues that pitch clocks may increase pitcher injury risk by reducing recovery time for fatiguing muscles. So maybe pace of game isn’t such a huge problem.
If you missed this on Twitter you really should read Eireann Dolan’s story about her autistic brother, from how he was bullied as a kid to the nightmare they all just went through with him.
Iowa Republican Steve King says racist stuff on a regular basis and keeps winning re-election. The Iowa Starting line blog looks at why.
As always, I’m nobody’s expert on these matters, but I feel like the rejection of state “vote fraud” laws, including this week’s invalidation of North Carolina’s law as racist, is the biggest story of this election cycle. One, with African-American voters favoring Clinton in historic proportions, it seems like striking down these laws could help her in several critical states, including the swing state of North Carolina. Two, killing these laws – based on the entirely fraudulent fear of fraudulent voting – will have an effect on many elections to come, and, one might hope, will slow efforts to disenfranchise entire demographic groups.
BuzzFeed political editor (and longtime reader of mine) Katherine Miller wrote a great longread on how Trump “broke” the conservative movement.
Trump has faced multiple allegations of sexual assault from women over the last several decades, including one from his ex-wife Ivana. Everyone dismissed such claims against Bill Clinton in 1991-92, but a quarter-century later, the climate around rape and sexual assault is, or seemed to be, much changed. Perhaps Hannibal Burress needs to joke about it before it’ll go anywhere.
A large Swedish study on the environmental impacts of organic agriculture versus conventional found differences in each direction, with neither side clearly favored. This is especially important for consumers, in that food labeled “organic” isn’t going to be more nutritious or necessarily better for the environment. But there’s a problem within the problem here – the term “organic” has itself been watered down (pun intended) from what the term meant when Lord Northbourne coined it in 1940. So-called “natural” pesticides aren’t going to automatically better for the environment, for example, and dumping organic fertilizers into the soil won’t have the same effect as using compost and working in crops (like clover or legumes) that increase nitrogen content in the soil.
Those “recyclable” disposable coffee cups aren’t recyclable at all, not unless you have access to one of the very few facilities capable of doing so. This means tons of cups end up in landfills every year, so why don’t we demand better?
Scientific American explains a card trick that relies on a simple cipher and the cooperation of a partner.
A tough longread on a 20-year-old unsolved missing persons case on the Isle of Wight. The police seem to have botched the earliest stages of the investigation, which may render the case unsolvable.
German scientists found a bacterium living inside human noses that produces a chemical toxic to Staphylococcus aureus, the bacterium that causes MRSA. Now if only it worked against gonorrhea, the bacterium behind which has evolved resistance to all known antibiotics.
Joe Biden has to acknowledge the LIQUID SWORDS tweet at some point, right? If I see him around here I’m going to ask him.
Why are police officers enforcing Trump’s ban on Washington Post reporters? They’re claiming it’s a security issue, but that’s clearly not the case.
I wrote about a year ago about an essay I read on the unsolved abc problem in mathematics and the abstruse proof offered by a Japanese mathematician, Shinichi Mochizuki, who created a whole new branch of math to solve it – which meant no one was sure if he actually had solved it at all. Scientific American offers an update and some new commentary, including criticism of Mochizuki’s unwillingness to travel or work with others on the proof.
In a new book, Innovation and its Enemies, Calestous Juma explains why people often hate new stuff, and talks about what variables affect adoption rates or drive opposition.
The National Post gave the fraudumentary Vaxxed zero stars and an admonition not to see it.
Speaking of fraud, anything that claims it can “boost your immune system” is lying and even they worked, it’s a terrible idea. If you pay for these “enhanced” water products, or for useless supplements like Airborne, you might as well flush your money down the toilet.
The elusive DC-area chef Peter Chang is opening what he calls the restaurant of his dreams in Bethesda. I’ve been to his place in Charlottesville, and I thought it was excellent but have very little history or knowledge of Sichuan cuisine to compare it to.
Congrats to Pizzeria Vetri, our favorite pizzeria in Philly and just one of our favorite restaurants there period, for winning Philly magazine’s Best Soft-Serve Ice Cream nod for 2016.
Seth Meyers on “Bernie or Bust” twits:

Have a ton of respect for Bernie and supporters but also have this msg for "or bust" crew https://t.co/3dQVrG6gqB

— Seth Meyers (@sethmeyers) July 27, 2016

Filed Under: Uncategorized Tagged With: baseball, environment, ice cream, links, math, organic agriculture, vaccines

→ July 22, 2016
→ By keith

Infinitesimal.

Amir Alexander’s Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World is less a history of math (although there is quite a bit) than a history of the people and institutions who fought a protracted philosophical battle over something we now consider a trivial bit of precalculus. The idea of infinitesimals, at the time of their development called “indivisibles,” sparked vociferous opposition from the supposedly progressive Jesuits in the 1600s, becoming part of their vendetta against Galileo, leading to banishments and other sentences against Italian mathematicians, and eventually pushing the progress of math itself from Italy out to Germany, England, and the Netherlands.

If you’ve taken calculus at any point, then you’ve encountered infinitesimals, which first appeared in the work of the Greek mathematician Archimedes (the “eureka!” guy). These mathematical quantities are so small that they can’t be measured, but their size is still not quite zero, because you can add up a quantity (or an infinity) of infinitesimals and get a concrete nonzero result. Alexander’s book tells the history of infinitesimals from the ancient Greeks through the philosophical war in Italy between the Jesuits, who opposed the concept of indivisibles as heretical, and the Jesuats, a rival religious order founded in Siena that included several mathematicians of the era who published on the theory of indivisibles, including Bonaventura Cavalieri. When the Jesuits won this battle via politicking within the Catholic hierarchy, the Jesuats were forced to disband, and the work involved in infinitesimals shifted to England, where Alexander describes a second battle, between Thomas Hobbes (yep, the Leviathan guy) and John Wallis, the latter of whom used infinitesimals and some novel work with infinite series in pushing an inductive approach to mathematics and to disprove Hobbes’ assertion that he had solved the problem of squaring the circle.

Wallis’ work with infinitesimals extended beyond the controversy with Hobbes into the immediate precursors of the calculus developed by Isaac Newton and Gottfried Leibniz, including methods of calculating the area under a curve using these infinitesimals (which Wallis described as width-less parallelograms). Alexander stops short of that work, however, choosing instead to spend the book’s 300 pages on the two philosophical battles, first in Italy and then in England, that came before infinitesimals gained acceptance in the mathematical world and well before Newton or Leibniz entered the picture. Hobbes was wrong – the ancient problem of squaring the circle, which means drawing a square using only a straightedge and compass that has the same area as that of a given circle, is insoluble because the mathematical solution requires the square root of pi, and you can’t draw that. The impossibility of this solution wasn’t proven until 1882, two hundred years after Hobbes’ death, but the philosopher was convinced he’d solved it, which allowed Wallis to tear Hobbes apart in their back-and-forth and, along with some of his own politicking, gave Wallis and the infinitesimals the victory in mathematical circles as well.

Alexander tells a good story here, but doesn’t get far enough into the math for my tastes. The best passage in the book is the description of Hobbes’ work, including the summary of the political philosophy of Leviathan, a sort of utopian autocracy where the will of the sovereign is the will of all of the people, and the sovereign thus rules by acclamation of the populace rather than heredity or divine right. (I was supposed to read Leviathan in college but found the prose excruciating and gave up, so this was all rather new to me.) But Alexander skimps on the historical importance of infinitesimals, devoting just a six-page epilogue to what happened after Wallis won the debate. You can’t have integral calculus without infinitesimals, and calculus is kind of important, but none of its early history appears here, even though there’s a direct line from Wallis to Newton. That makes Infinitesimal a truncated read, great for what it covers, but missing the final chapter.

Next up: The Collected Stories of Katherine Anne Porter, winner of the Pulitzer Prize for Fiction in 1966.

Filed Under: Uncategorized Tagged With: history of science, math, philosophy, religion, science

→ April 8, 2016
→ By keith

The Unfinished Game.

I’m still playing a bit of catchup on stuff I read during March (and just finished Joe Haldeman’s The Forever War over lunch today), but one title I definitely want to bring to everyone’s attention is the delightful, short book by mathematician (and NPR’s “Math Guy”) Keith Devlin called The Unfinished Game, which explains how one specific letter in the correspondence between Blaise Pascal and Pierre de Fermat opened the door to the world of probability and everything that this branch of mathematics makes possible.

The unfinished game of the book’s title was based on a common, popular controversy of the time surrounding games of chance, which were largely seen as incalculable – our modern, simple way of calculating odds of things like throws of the dice just did not exist at the time. Pascal and Fermat discussed the question of how to divide winnings in a game of two or more players where the players choose to abandon the game before any one player has won the requisite number of matches. (So, for example, they’re playing a best-of-five, but the players quit after three rounds, with one player having won two times and the other one.) The controversy in question will seem silly to any modern reader who’s taken even a few weeks of probability theory in high school math, but Devlin is deft enough to explain the problem in 1600s terms, so that the logical confusion of the era is clear on the page.

The confusion stemmed from the misunderstanding about the frequencies of subsequent events, given that the game would not always be played to its conclusion: You may say up front you’re going to play a best of seven, but you do not always need to play seven matches to determine a winner. If you quit after three games, in the situation I outlined above, it is possible that you would have needed just one more match to determine a winner, and it is possible that you would have needed two more matches. Pascal’s letter to Fermat proposed a method of determining how to split the winnings in such an unfinished game; the letter was the start of modern probability theory, and the problem is now known as the problem of points. (You can read the entire surviving correspondence on the University of York’s website; it also includes their conversations on prime numbers, including Fermat’s surprising error in claiming that all numbers of the form 2^(2ⁿ)+1, which is only true for 0 ≤ n ≤ 4. Those five numbers are now called Fermat primes; Euler later showed Fermat’s hypothesis was wrong, and 2^(2⁵)+1 = 4294967297, which is composite.)

Fermat realized you must count all of the potential solutions, even ones that would not occur because they involved playing the fifth game when it was made unnecessary by the first player winning the fourth match and taking the entire set, so to speak. (The problem they discussed was slightly more involved.) Pascal took Fermat’s tabular solution, a brute-force method of counting out all possible outcomes, and made it generalizable to all cases with a formula that works for any number of players and rounds. This also contributed to Pascal’s work on what we now call Pascal’s triangle, and created what statisticians and economists now refer to as “expectation value” – the amount of money you can expect to win on a specific bet given the odds and payout of each outcome.

Devlin goes about as far as you can when your subject is a single letter, with entertaining diversions into the lives of Pascal and Fermat (who corresponded yet never met) and tangents like Pascal’s wager. At heart, the 166-page book is about probability theory, and Devlin makes the subject accessible to any potential reader, even ones who haven’t gone beyond algebra in school. Given how much of our lives – things like insurance, financial markets, and sports betting, to say nothing of the probabilistic foundations of quantum theory – are possible because of probability theory, The Unfinished Game should probably be required reading for any high school student.

Next up: I just started Eimear McBride’s A Girl is a Half-Formed Thing, winner of the 2014 Baileys Women’s Prize for Fiction.

Filed Under: Uncategorized Tagged With: Economics, highly recommended, history of science, math, philosophy

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