Lost in Math

I recently read Sabine Hossenfelder's Lost in Math and recommend it. The backbone of the text is a series of interviews with fellow theoretical physicists, punctuated by the author's own typically gimlet observations and reflections. I don't intend to review the book here, but merely to provide a few highlights.

Some of the people interviewed:

• Nima Arkani-Hamed
• Steven Weinberg
• Chad Orzel
• Frank Wilczek
• Garrett Lisi
• Joseph Polchinski
• Xiao-Gang Wen
• Katherine "Astrokatie" Mack
• George Ellis

Hossenfelder's thesis is that the dearth of data in high-energy physics over the past few decades has left theorists with little guidance, so they end up selecting among the many possible theories using criteria spun largely out of thin air. "Beauty" is how many refer to that inarticulate quality that supposedly characterizes a good theory. Hossenfelder particularly takes issue with "naturalness": the idea that dimensionless constants in physics should have a value of order of magnitude 1. Simplicity, elegance, and symmetry are other criteria.

Chapter 2's catalog of where "beauty" has failed physics should be required reading for aspiring theorists. A primal example is Kepler's inscribing the planetary orbits in the Platonic solids; she also cites Galileo's preference for circular orbits over elliptical. Here's a choice line:

The historian Helge Kragh concluded his biography of Dirac with the observation that "after 1935 [Dirac] largely failed to produce physics of lasting value. It is not irrelevant to point out that the principle of mathematical beauty governed his thinking only during the later period." (p. 21)

In chapter 5, she names the types of proposed multiverses: Eternal Inflation, String Theory Landscape, Many Worlds, and The Mathematical Universe. All of these seek to avoid fixing the values of mathematical parameters in theories by positing that every value of every parameter is actualized somewhere or in some way. The weakness of the justification for such theories becomes evident when she undermines the uniqueness of the present need for them: "Since every theory requires observational input to fix parameters or pick axioms, every theory leads to a multiverse when it lacks input" (106). Throughout all of physics we could have speculated about a multiverse, but we didn't.

She talks with Steven Weinberg at length. The most interesting part was this remark on quantum foundations:

If you had a theory that said that, well, particles move around and there's a certain probability that it will go here or there or the other place, I could live with that. What I don't like about quantum mechanics is that it's a formalism for calculating probabilities that human beings get when they make certain interventions in nature that we call experiments. And a theory should not refer to human beings in its postulates. You would like to understand macroscopic things like experimental apparatuses and human beings in terms of the underlying theory. You don't want to see them brought in on the level of axioms of the theory. (124)

Aristotle's dictum that form precedes matter makes perfect sense of this irreducibility. The truth of two facts is no mere coincidence: that Weinberg doesn't understand this aspect of quantum theory and that he would be one of the last people to admit that Aristotle had anything meaningful to say about the world.

I typically find George Ellis insightful, and Hossenfelder's interview with him does not disappoint. He's especially good in observing how atheists' baseless claim that science disproves the existence of God actually contributes mightily to undermining the authority of science (214). The conversation also fruitfully turns to the value of philosophy, including this exchange:

"Yes—when we have an infinity appearing in a function, we assume it's not physical," I explain. "But there's no good mathematical reason why a theory should not have infinities. It's a philosophical requirement turned into a mathematical assumption. People talk about it but never write it down. That's why I say it gets lost in math. We use a lot of assumptions that are based on philosophy, but we don't pay attention to them."

"Correct," George says. "The problem is that physicists have been put off philosophy by a certain branch of philosophers who spout nonsense—the famous Sokal affair and all that. And there are philosophers who—from a scientific viewpoint—do talk nonsense. But nevertheless, when you are doing physics you always use philosophy as a background, and there are a lot of good philosophers—like Jeremy Butterfield and Tim Maudlin and David Albert—who are very sensible in terms of the relationship between science and philosophy. And one should form a good working relationship with them. Because they can help one see what are the foundations and what is the best way to frame the questions. (218)

Recognizing a value to philosophy is certainly a significant step, but does it go far enough? I have at best a passing familiarity with the work of the three philosophers named, but I daresay that they are the typical "safe" philosophers that physicists typically turn to, the kind that never question the central idea of modernity that philosophy has no meaningful access to the natural world except through "science." This kind is a far cry from recognizing that what we call physics today is actually a subset of a much larger field called natural philosophy, whose axioms are as certain and as immediately graspable as your presence in the place where you read this; which can draw on physics without being wholly dependent on it for data about the real world; and on which physics is wholly dependent if only implicitly. I would delight to be proven wrong about these three philosophers: please comment below with citations.

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Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (New York: Basic Books, 2018).

Big Screen Conventions

The big screen (not to mention the small screen) is not only a screen that presents the world, but it is also a screen that obscures the world. Below is a list of some prominent big-screen conventions that we need to see past to see the world rightly.

Bop on the head

It's a convenient way to get someone out of the way without killing him. By convention, the person comes to without any lasting damage. In reality, being knocked unconscious is a serious injuring, possibly accompanied by a concussion.

No helmet

The good don't wear helmets, at least ones that would obscure their faces. For example, in Lone Survivor (2013), the heroes repeatedly throw themselves down the side of a mountain to escape the Taliban forces pursuing them. Somehow their heads sustain no injuries, despite the lack of protective headgear. Why? Movies are a visual medium, and the audience has to be able to tell the protagonists apart, and seeing their faces also helps us to identify with them. What's also interesting is how often the bad guys are anonymized by wearing helmets, e.g., the Star Wars stormtroopers. That way we don't mind their being killed.

Sleeping around

Many modern romantic comedies and situation comedies have characters sleeping around. But no one gets pregnant or contracts a venereal disease. I suppose the reason is that if something like that happened, the movie would take on a deeper moral dimension and no longer be a (light) comedy. Of course, in a slasher film, the convention is exactly the opposite: the teen couple that transgresses this moral boundary is usually the first to suffer at the hands of the supernatural antagonist.

Anachronistic sexual morals

The characters in relationships portrayed as taking place in a previous age often hold assumptions about the nature of sexual intercourse that are manifestly characteristic of the modern, anything-goes age. For example, in Sky Captain and the World of Tomorrow (2004), the action takes place in 1939, but the characters in the love triangle at its center talk as if casual relations were nothing remarkable. The Amazon series Man in the High Castle (2015–) takes place in an alternative 1962, but two central characters, Frank and Juliana, live together unmarried, with no one around them making any special note of the fact. The assumption behind these anachronisms is that the upside-down situation that has prevailed since the advent of the Pill is how things have always been. At best, this is shorthand for allowing us moderns to identify with the characters of the past. At worst, it's a kind of cultural imperialism: the present conquering the past, notionally if not in fact, in order to justify itself.

Significant details

Any detail shown is significant to the story. In part, this is just a limitation of story-telling: there's only limited time to convey the action and make it understandable to the audience. But it has the potential to mislead. What's significant to our lives very often we only realize in retrospect, whereas any given detail of our day-to-day lives (e.g., an unexpected coincidence), is unlikely to have a tremendous significance to our life story.

The End is The End

Another story-telling convention. Stories are finite, they must end. But the end carries with it the implication that the character's state at the end is what prevails from that time on, "ever after." In reality, the only real end is death and the end of a story is the beginning of another story—or rather another point in the continuum of life. Episodes of The Twilight Zone have significant endings in this sense, though often the end conveys a notion of Justice that echoes that Final Judgement we all must face.

What are some other conventions? I'd be interested to hear in the comments.