→ March 30, 2025
→ By
→ 1 Comment

Stick to baseball, 3/30/25.

For subscribers to the Athletic, I posted my annual just-for-fun predictions column and a roundup of a few prospects I saw on the back fields in Florida this week. I also put together a post (with my editor’s help) with the preseason scouting reports and a sentence or two on the 2025 outlook for all top 100 & just missed guys who made Opening Day rosters.

At Paste, I reviewed the Ticket to Ride legacy game, Legends of the Old West, which is one of the best legacy games I’ve tried. It’s true to the original game and doesn’t load it up with too many new rules or twists (there are some, of course).

I appeared on NBC News This Morning and NPR’s All Things Considered on Thursday to discuss Opening Day and the upcoming MLB season; I was also on CNN that evening but I don’t think it’s online. I also discussed the Guardians on WHBC 1480.

And now, the links…

  • Hamilton Nolan writes in his Substack that the federal government is going to destroy labor unions if we don’t stop them, after Trump signed an executive order (which, to be clear, is just that, not a law) saying the federal government won’t recognize the unions that represent most of its employees.
  • Republicans in North Carolina continue their legal fight to steal a state Supreme Court seat, arguing that the right to vote is not absolute as they try to invalidate over 65,000 votes.
  • Mathematicians solved another century-old puzzle, this one on whether you can divide a triangle into fewer than four pieces and assemble those into a square. The answer is that you can’t – four is the lowest number.
Filed Under: Uncategorized Tagged With: , , , , , , , , , , , ,
→ March 24, 2025
→ By
→ 7 Comments

Fantastic Numbers and Where to Find Them.

Prof. Antonio Padilla is a theoretical physicist and cosmologist at the University of Nottingham who has also appeared numerous times on the Numberphile Youtube series, including this incredibly popular video where he shows how the sum of all natural numbers (1 + 2 + 3 + 4 + … ?) is actually -1/12. It’s ridiculous – Padilla concedes that it looks like “a bit of mathematical hocus-pocus”, but the pudding is in the proof, or something, and he points out that 1) this only works if you’re adding all of the natural numbers, which means you don’t stop at any point, and 2) this sum appears in physics, where we don’t see infinities (and if we do, it’s a problem).

Padilla describes the interplay between physics and some numbers at both extremes of the mathematical scale, both the very small and the very large, in his book Fantastic Numbers and Where to Find Them: A Journey to the Edge of Physics, an intense but mostly accessible book that runs through nine distinct numbers, from zero to a googolplex to 10-120 to infinity, and uses them to explain some key concepts or findings about the nature of everything. He waltzes through the history of math – just about every famous figure there makes an appearance at some point, which will make you realize just how many great mathematicians ended up losing their marbles – and just about always finishes up somewhere in the realm of quantum physics, whether it’s things we know or things we think we know, or occasionally things we still don’t know. There’s even a chapter on the cosmological constant, which was in the news just this past week with the revelations that dark energy isn’t as immutable as we believed, which implies that the cosmological constant is, in fact, inconstant.

When Padilla is talking physics and cosmology, at either end of the scale, he’s engaging and by and large easy to follow, other than perhaps near the end of the book when he’s introduced the panoply of particles that populate the quantum world – all the quarks, leptons, and gauge bosons that we know or think exist – where keeping any of them straight was a bit more than I could handle. It doesn’t end up mattering much to the narratives of those chapters, as Padilla’s point is the relevance of the numbers in question, although I ended up a little frustrated that I didn’t entirely know what was going on at some points.

It’s the mathy stuff where Padilla struggles to communicate in a way that a typical reader might follow, and perhaps that’s just a function of the size of the numbers he’s discussing. The chapter on the number TREE(3), which is so large that we can’t even notate it, let alone comprehend it, ultimately lost me not in its prose but in its sea of notation. TREE(3) is much larger than the number of atoms scientists believe exist in the entire universe (around 1080, itself a number that we can’t easily envision), a number so big that the universe won’t “allow” it to exist – according to the Poincaré recurrence theorem, at least, which says that the universe will “reset” before TREE(3) happens in any sense of the word. Padilla uses TREE(3) to explain that theorem and the possibility that the universe is a hologram, that we live in two dimensions and only think we perceive the third, but by the end of that chapter I didn’t understand why TREE(3) got us there in the first place. (It doesn’t help that Padilla discusses all of this several chapters before he gets into string theory, which underpins the holographic principle, so we’re walking without a net for a while.)

Padilla is a gifted communicator, clearly, and his enthusiasm for the subject comes through everywhere in the book – it’s just that the topic itself is abstruse and assumes some familiarity with physics and/or with some branches of math like infinite series and set theory. He’s better at explaining concepts like particle spin, which he points out isn’t spin like what we’re talking about in baseball but an innate characteristic of a particle (any more than red or green quarks have those actual colors), than at explaining concepts like the nested powers of TREE(3) or Gödel’s incompleteness proof. It all left me with the sense that I’d enjoyed the book, but that the audience for it might be very narrow – you have to know enough to follow him through his various rambles through math and physics, but not so much that you already know all of this stuff. I was at least lucky enough to mostly be in the first camp, even though I got lost a few times, but that’s just because I love these topics and have read a lot of books about them. It’s not the physics I learned in high school, and not really the math I learned there either.

Next up: Michael Swanwick’s Stations of the Tide, winner of the 1991 Nebula Award for Best Novel.

Filed Under: Uncategorized Tagged With: , , , ,
→ October 21, 2023
→ By

Stick to baseball, 10/21/23.

My second Arizona Fall League notebook went up on Monday, covering everyone of note whom I hadn’t written up in the first one. I also held a Klawchat on Thursday.

I appeared on TSN 1050 in Toronto to talk about the League Championship Series and the Blue Jays, including prospect Ricky Tiedemann and the controversial decision to replace José Berrios with Yusie Kikuchi in what turned out to be their last playoff game.

And now, the links…

Filed Under: Uncategorized Tagged With: , , , , , , , , , , , , , , , , , , , ,
→ January 22, 2023
→ By

Stick to baseball, 1/21/23.

No new content for subscribers to the Athletic as I’ve continued writing capsules for the top 100 prospects ranking, which will run on January 30th. Please stand by.

My podcast did return this week, with guest Seth Reiss, who co-wrote the screenplay for the film The Menu. You can listen and subscribe via iTunes, Spotify, Stitcher, amazon, or wherever you get your podcasts.

I’m planning to send out another issue of my free email newsletter on Sunday, now that I’m back on track with the prospect stuff. I was fairly stressed about it as recently a few days ago, but I’ve caught up enough that I can finish everything with a reasonable daily output of words.

And now, the links…

  • Longreads first: A 17-year-old woman in Texas wanted an abortion. A judge decided she wasn’t “mature” enough to make that choice. ProPublica looks at the ramifications of that decision.
  • The San Francisco Chronicle has the heartbreaking story of a mother’s attempts to help her daughter, a 35-year-old opioid addict living on the San Francisco streets, touching on the city’s lack of services for addicts and for homeless people. There’s a sad baseball connection: The daughter’s boyfriend, Abdul Cole, was a Marlins minor leaguer for three years, but died last April.
  • The School Board of Madison County, Virginia, voted to ban 21 books from its libraries, including The Handmaid’s Tale and four books by Nobel laureate Toni Morrison, because Christian groups complained.
  • Meanwhile, two Christian activists in Crawford County, Arkansas, are trying to remove the library director and defund the system over the display of LGBTQ+ books, calling it an “alternative lifestyle.” Sexual orientation is not a lifestyle, or a choice. Gender identity is not a lifestyle, or a choice. Religion is a lifestyle, and a choice.
  • Iowa Republicans are trying to defund public schools by allowing parents to use vouchers for private schools, including religious schools, which would seem to violate the principle of separation of church and state. You can send your kids to a parochial school, but only without my tax dollars.
  • A couple of Eagles players recorded a Christmas album for charity, hoping to raise about $30,000. It raised $250,000 and will help fund two toy drives and a summer camp for Philly kids with serious behavioral problems. (We have a copy.)
Filed Under: Uncategorized Tagged With: , , , , , , , , , , , , , , , , , ,
→ May 14, 2022
→ By

Stick to baseball, 5/13/22.

For subscribers to The Athletic, I posted a minor league scouting notebook, with comments on players from the Red Sox, Orioles, Rays, and Nats systems. My first mock draft for 2022 will go up on Thursday, May 19th, and I’ll do some sort of chat or Q&A around it that afternoon.

At Polygon, I reviewed Ark Nova, the best new game I’ve played so far this year, a more complex title that draws heavily on Terraforming Mars but with streamlined rules and better art.

I sent out a new edition of my free email newsletter yesterday, and I have to thank all of you who’ve sent such kind replies. I mentioned the possibility of an in-person event in London in August, and it looks like we’re going to be able to make that happen, with the help of a reader who works at a bookshop there. Speaking of books, Smart Baseball and The Inside Game are both available in paperback, and you can buy them at your local independent book store or at Bookshop.org.

On The Keith Law Show, I got the band back together with Eric Karabell for a show last week. I was on the move most of this week (and then traveled again Thursday night) and didn’t have a recording window until Thursday morning morning, so I recorded next week’s episode with guest Jonathan Higgs of Everything Everything.

And now, the links…

Filed Under: Uncategorized Tagged With: , , , , , , , , , , , , , , ,
→ November 19, 2021
→ By

Infinite Powers.

I’m a sucker for a good book about math, but a lot of books about math aren’t that good – either they’re dry, or they don’t do enough to explain why any of this matters. (Sometimes it doesn’t matter, as in Prime Obsession, but the author did such a good job of explaining the problem, and benefited from the fact that it’s still unsolved.) Steven Strogatz’s Infinite Powers: How Calculus Reveals the Secrets of the Universe manages to be entertaining, practical, and also educational, as the author builds up the reader through some essentials of pre-calculus before getting into the good stuff, to the point that I recommended that my daughter check it out before next year when she takes calculus in school.

Calculus underlies everything in the universe; it is the foundation upon which the universe, and everything in it, functions. It is also one of humanity’s most remarkable discoveries, one that required multiple leaps of mathematical faith to uncover hidden truths about the universe. Physicist Richard Feynman quipped that it is “the language that God talks,” although he meant it in a secular sense, while mathematician Felix Klein said that one could not understand “the basis on which the scientific explanation of nature rests” without at least some understanding of differential and integral calculus.

 The story of how both Isaac Newton and Gottfried Wilhelm Leibniz simultaneously discovered calculus in the late 1600s, doing so both with their own remarkable insights and by building on the discoveries of mathematicians before them, going back to the ancient Greeks, would by itself be enough for an entertaining history. Strogatz does start with that, and uses the history as scaffolding to bring the reader up from algebra through geometry and trigonometry to the mathematics of limits, which is the essential precursor to calculus, before getting to the main event.

Or I should say “events,” as differential and integral calculus, while two sides of the same analytical coin, were discovered at separate times, with separate methods, and Strogatz tells their stories separately before bringing them together towards the end of the book. Differential calculus is what we learn first in schools, at least in the United States. It’s the mathematics of the rates of change; the rate at which a function changes is the derivative of that function. Acceleration is the derivative of velocity – that is, the rate at which velocity is changing. Velocity, in turn, is the derivative of position – the rate at which an object’s position changes. That also makes acceleration the second derivative of position, which is why you see a 2 in the formula for the acceleration of an object falling due to Earth’s gravity (9.8 m/s2): a position might be measured in meters, so velocity is measured as the change in position (meters) by time (seconds), and acceleration is the change in velocity (meters per second) by time (seconds, again).

Integral calculus goes the other way – given an object’s acceleration, what is its velocity at a given point in time? Given its velocity, what is its position? But Leibniz and Newton – I expect to hear from Newton’s lawyers for listing him second – conceived of integration as a way to solve an entirely different problem: How to determine the area under a curved function. Those two didn’t think of it that way – the concept of a function came somewhat later – but they understood the need to find out the area underneath a curve, and came up, independently, with the same solution, which broke apart the space into a series of rectangles of known heights and near-zero widths, giving rise to the infinitesimals familiar to any student who’s taken integral calculus. They aren’t real numbers, although they do appear in more arcane number systems like the hyperreals, yet the sum of the areas of this infinitesimally narrow rectangles turns out to be a real number, giving you the area under the curve in question. This insight, which was probably Leibniz’s first, opened the world up for integral calculus, which turns out to have no end of important applications in physics, biology, and beyond.

Strogatz grounds the book in those applications, devoting the last quarter or so of Infinite Powers to discussing the modern ways in which we depend on calculus, even taking its existence for granted. GPS devices are the most obvious way, as the system wouldn’t function without the precision that calculus, which GPS uses for dealing with errors in the measurements of distances, offers – indeed, it’s also used to help planes land accurately. Yet calculus appears in even less-expected places; biologists used it to model the shape of the double helix of strands of DNA, treating a discrete object (DNA is just a series of connected molecules) as a continuous one. If your high school student ever asks why they need to learn this stuff, Infinite Powers has the answers, but also gives the reader the background to understand the author’s explanations even if you haven’t taken math in a few decades.

Next up: David Mitchell’s The Thousand Autumns of Jacob de Zoet.

Filed Under: Uncategorized Tagged With: , , ,
→ September 21, 2021
→ By

Seven Bridges.

Seven Bridges is a “stroll-and-write” game based on the famous mathematical problem, eventually proved unsolvable by Leonhard Euler: Can a pedestrian walk through the German city of Königsberg, crossing each of its seven bridges exactly once? Euler’s proof became a foundational one in the history of graph theory, but that’s beyond the scope of the game. (The game is currently unavailable, but I’ll update this post when Puzzling Pixel gets the next print run.)

In Seven Bridges, all players begin by marking in the same square on their pages, showing a grid map of the city with, indeed, seven bridges, along with thirteen ‘landmarks,’ some trees, lots of buildings, and numbers around the map’s edge. On each player’s turn, they roll the game’s six dice, which the players then draft, one at a time. The dice show seven different shapes of roads: a straight line, a cross, a T, an elbow, a half-street, a 2 with a straight line, or a 3 with a straight line. You must fill in roads on your map using the shape of the die you select, connecting one of the edges of the shape your existing network of roads. (In rare instances when you can’t legally do so, you may ‘downgrade’ to a less valuable shape.) The 2 | and the 3 | die faces mean you may draw a continuous line up to that many spaces long; you can go shorter than that, but you can’t break it apart or turn its direction. Each player gets to roll five times over the course of the game.

Passing landmarks, which are marked with single letters on the board, earns you the choice of eleven bonuses, seven immediate and four you can use later. The immediate bonuses match the shapes on the dice, so you can fill in one of those shapes on your board, following the usual rules. One of the extra bonuses allows you to fill in the handful of footpaths – bordered by dashed lines rather than solid ones – on the map. The other three are re-rolls, which either let you roll all remaining dice again, or stop the draft and distribute all remaining dice to players as you see fit.

You don’t have to cross all seven bridges to win this game, but you do get more points for crossing more bridges. You score for crossing bridges and passing by landmarks; the more of each, the more each subsequent one is worth. You score for the largest closed loop of roads/footpaths you completed by multiplying its number of bridges cross by the number of 90 degree turns in it; I think five is the maximum number of bridges you can possibly get, but you can absolutely get 8 or more right angles into a loop. You score a point for each building you pass, and for each tree you pass. You score for each road you take to the edge of the map, worth a number of points from 1 to 6 that is shown at that edge. And you score points for each bonus you received and used during the game, again from 1 to 6.

The game is kind of mathy under the hood, which strongly appeals to me; there’s a spatial relations aspect, and a clear push-your-luck aspect to the way you place your roads. You can go big, and end up without the shapes you need to complete a major route, or you can play it safe and hope no one else completes something larger. You can also head to certain areas of the map that are dense with trees but don’t promise you much in the way of other bonuses. There seem to be a lot of ways to win here, and just as many ways to screw it up.

I’ve only played this with two players, several times, however, and with a different opponent each time. Games took maybe 20-30 minutes, and if both players already know the rules, it could easily come in under 20. With two players, since you draft three dice on each roll, you only have ten total rolls over the course of the game. With the maximum of 6 players, you’d have 30 rolls, and that’s going to take some more time. Seven Bridges was first released at the very end of 2020, after my year-end list, so it qualifies for this year’s, and it has a very good chance to make my best of 2021 list. It’s quick to teach, offers very little downtime between turns, and does a fantastic job of bringing a mathematical puzzle into a board game format. It might be the best roll-and-write I’ve ever played.

Filed Under: Uncategorized Tagged With: , , , ,
→ October 17, 2020
→ By

Stick to baseball, 10/17/20.

Just one piece this week for subscribers to the Athletic as I work on the top 40 free agents ranking, which will run a few days after the World Series ends: Nick Groke, our Rockies beat writer, asked me a bunch of questions about Colorado’s farm system, and I dutifully answered them. Klawchat, board game reviews, and dish posts should return next week.

My guest on this week’s episode of The Keith Law Show was my old partner-in-crime Eric Karabell, although Bias Cat did not make an appearance. My podcast is now available on Amazon podcasts as well as iTunes and Spotify.

I’m due to send out a fresh edition of my free email newsletter this weekend as well. We’ll see how that works out for me.

As the holiday season approaches, I’ll remind you every week that my books The Inside Game and Smart Baseball make excellent gifts for the baseball fan or avid reader in your life.

And now, the links…

  • Now some longreads: ProPublica details the fall of the CDC, undermined from above by the anti-science Trump Administration and from within by craven, spineless leadership.
  • Sara Benincasa’s essay “Fred and Me” is just wonderful and I won’t spoil it in the least.
  • Why has Germany handled COVID-19 better than its neighbors? By following the science, including implementing widescale, frequent testing.
  • QAnon, the batshit-crazy hoax embraced by multiple alt-right figures and now our sitting President, is tearing families apart as people become sucked into this utterly false conspiracy theory and alienate family members with their nonsense.
  • Lauren Witzke, the Delaware GOP candidate for the Senate seat currently held by Democrat Chris Coons, appeared on white-nationalist, anti-immigrant hate site VDare last month, not long before saying the Proud Boys provide security at her events. She has no chance to win, but still, Delaware Republicans should revoke their endorsement of her.
  • Draining the swamp update: A former patent litigator became a federal judge and is openly advising patent trolls to come to his court. This lets those trolls abuse the patent system (which has its own problems, but still) for their own profit, and ultimately American consumers will end up paying the cost.
  • The role-playing game designer outfit Roll20 is holding a 3-day virtual gaming con with proceeds to benefit a charity focused on racial justice.
Filed Under: Uncategorized Tagged With: , , , , , , , , , , , , ,
→ September 5, 2020
→ By

Stick to baseball, 9/5/20.

I had three pieces for subscribers to The Athletic around the trade deadline, wrapping up the Padres’ three moves, the Blue Jays’ and Mets’ moves, and five other trades in separate columns. I also had two new episodes of The Keith Law Show this week, one featuring Jessica Luther and Kavitha Davidson, authors of the new book Loving Sports When They Don’t Love You Back (which you can buy here), and another one with Will Leitch, which we posted Friday morning so you’d have it before the holiday weekend.

On Friday night, September 11th, I’ll be hosting a live talk with author Chuck Palahniuk about his new book The Invention of Sound through Midtown Scholar in Harrisburg. It’s a ticketed event, and with your purchase you’ll get a signed copy of the book as well as a link to the talk. (I just started reading the book about an hour ago.)
 
At Paste, I reviewed the tile-laying and set-collection game Succulent, and then ranked the five best tile-laying games I’ve played, which should include a few titles familiar to longtime readers.

I sent out a fresh edition of my free email newsletter on Friday, describing how I went from someone who hadn’t run in any meaningful way since 1985 to running 5 km without interruption in about four months.

And now, the links…

  • Daniel Thompson, the only full-time Black journalist at The Kenosha News, resigned his position to protest the paper’s use of an incendiary quote that cast protesters in an inaccurate light.
  • Larry Flynt wrote a “final farewell to the Falwells,” and it’s a more nuanced and thoughtful note than you might expect, with kind words about Jerry Falwell, Sr., with whom Flynt waged a very public battle over his First Amendment rights, and damning words about Falwell’s hypocritical son.
  • Online hoaxes, like the myriad ones about COVID-19, are making doctors’ jobs harder – and the blame falls primarily on Facebook and other sites that have let this misinformation fester.
  • Ars Technica reports that Facebook’s “plan” to combat election misinformation is the same as its plan for pretty much everything else that goes wrong on its site – doing nothing at all.
  • Philly Inquirer columnist Will Bunch says that Trump’s “reelection scheme of a civil war” is kicking into high gear as the election approaches. I was always skeptical of those who said Trump wouldn’t leave office willingly, but my view is shifting as his rhetoric changes, and the rest of his party continues to enable him.
  • Three mathematicians have solved a longstanding question about straight paths on the dodecahedron, one of the five Platonic solids and the only one for which this question remained unsolved.
Filed Under: Uncategorized Tagged With: , , , , , , , , ,
→ July 25, 2020
→ By

Stick to baseball, 7/25/20.

I wrote two pieces for subscribers to The Athletic this week – a season preview, with breakout candidates and team predictions; and a look at the top 100 prospects who made Opening Day rosters. I held a live Zoom Q&A via The Athletic’s Twitter account on Thursday.

For Paste, I reviewed the new flick-and-write game Sonora, where players flick discs on to the same board, possibly knocking each others’ discs out of the way, and score on their personal scoresheets based on where the discs end up.

My book, The Inside Game: Bad Calls, Strange Moves, and What Baseball Behavior Teaches Us About Ourselves, is out now. You can order it anywhere you buy books, and I recommend bookshop.org. I’ll also resume my email newsletter this weekend.

And now, the links…

Filed Under: Uncategorized Tagged With: , , , , , , ,