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.
Filterworld.
In his new book Filterworld: How Algorithms Flattened Culture, journalist Kyle Chayka details the myriad ways in which we are thrust towards homogeneity in music, television, movies, books, and even architecture and travel because, in his view, of the tyranny of the algorithm. The book is more of a polemic than a work of research, filled with personal anecdotes and quotes from philosophers as well as observers of culture, and while Chayka is somewhat correct in that a small number of companies are now determining what people watch, listen to, and read, that’s always been true – it’s just happening now by algorithm when technology was supposed to democratize access to culture.
Chayka’s premise is sound on its surface: Major tech companies now depend on maintaining your attention to hold or increase revenues, and they do that via algorithm. Netflix’s algorithm keeps recommending movies and shows it believes you’ll watch – not that you will like, but that you will watch, or at least not turn off – thus keeping you as a customer. Spotify’s auto-generated playlists largely serve you artists and songs that are similar to ones you’ve already liked, or at least have already listened to, as I’ve learned recently because I listened to one song by the rapper Werdperfect that a friend sent me and now Spotify puts Werdperfect on every god damned playlist it makes for me. Facebook, Twitter, Instagram, Tiktok, and their ilk all use algorithms to show you what will keep you engaged, not what you asked to see via your following list. Amazon’s recommendations are more straightforward, giving you products its algorithm thinks you’ll buy based on other things you’ve bought.
Chayka goes one further, though, arguing that algorithmic tyranny extends into meatspace, using it to explain the ubiquity of Brooklyn-style coffee shops, with sparse décor, subway tiles, exposed wood, and industrial lighting. He uses it to explain homogeneity in Airbnb listings, arguing that property owners must determine what the algorithm wants and optimize their spaces to maximize their earnings. He is ultimately arguing that we will all look the same, sound the same, wear the same clothes, live in the same spaces, drink the same expensive lattes, and so on, because of the algorithms.
To this I say: No shit. It’s called capitalism, and the algorithm itself is not the disease, but a symptom.
Businesses exist to make money, and in a competitive marketplace, that’s generally a good thing – it drives innovation and forces individual companies to respond to customer demand or lose market share to competitors. These market forces led to the advent of mass production over a century ago, a process that depended on relatively uniform tastes across a broad spectrum of consumers, because mass-producing anything economically depends on that uniformity. You can’t mass-produce custom clothes, by definition. Companies that have invested heavily in capital to mass produce their widgets will then work to further expand their customer base by encouraging homogeneity in tastes – thus the push for certain fashions to be “in” this year (as they were twenty years prior), or the marketing put behind specific books or songs or movies to try to gain mass adoption. Coffee shops adopt similar looks because customers like that familiarity, for the same reason that McDonald’s became a global giant – you walk into any McDonald’s in the world and you by and large know what to expect, from how it looks to what’s on the menu. This isn’t new. In fact, the idea of the algorithm isn’t even new; it is the technology that is new, as companies can implement their algorithms at a speed and scale that was unthinkable two decades earlier.
Furthermore, we are living in a time of limited competition, closer to what our forefathers faced in the trust era than what our parents faced in the 1980s. There is no comparably-sized competitor to Amazon. Spotify dominates music streaming. Each social media entity I listed earlier has no direct competition; they compete with each other, but each serves a different need or desire from consumers. The decline of U.S. antitrust enforcement since the Reagan era has exacerbated the problem. Fewer producers will indeed produce less variety in products.
However, the same technology that Chayka decries throughout Filterworld has flattened more than culture – it has flattened the hierarchy that led to homogeneity in culture from the 1950s through the 1990s. Music was forced, kicking and screaming, to give up its bundling practice, where you could purchase only a few individual songs but otherwise had to purchase entire albums to hear specific titles, by Napster and other file-sharing software products. Now, through streaming services, not only can any artist bypass the traditional record-label gatekeepers, but would-be “curators” can find, identify, and recommend these artists and their songs, the way that only DJs at truly independent radio stations could do in earlier eras. (And yes, I hope that I am one of those curators. My monthly playlists are the product of endless exploration on my own, with a little help from the Spotify algorithm on the Release Radar playlists, but mostly just me messing around and looking for new music.) Goodreads is a hot mess, owned by Amazon and boosting the Colleen Hoovers of the world, but it’s also really easy to find people who read a lot of books and can recommend the ones they like. (Cough.) Movies, food, travel, television, and so on are all now easier to consume, and if you are overwhelmed by the number and variety of choices, it’s easier to find people who can guide you through it. I try to be that type of guide for you when it comes to music and books and board games, and to some extent to restaurants. When it comes to television, I read Alan Sepinwall. When it comes to movies, I listen to Will Leitch & Tim Grierson, and I read Christy Lemire, and I bother Chris Crawford. I also just talk to my friends and see what they like. I have book friends, movie friends, game friends, coffee friends, rum friends, and so on. The algorithms, and the companies that deploy them, don’t decide for me because I made the very easy choice to decide for myself.
So I didn’t really buy Chayka’s conclusions in Filterworld, even though I thought the premise was sound and deserved this sort of exploration. I also found the writing in the book to be dull, unfortunately, with the sort of dry quality of academic writing without the sort of rigor that you might see in a research paper. I could have lived with that if he’d sold me better on his arguments, but he gives too little attention to points that might truly matter, such as privacy regulations in the E.U. and the lack thereof in the U.S., and too much weight to algorithms that will only affect your life if you let them.
Next up: Angela Carter’s The Magic Toyshop.