When the Math is Pretty But the Truth Ain’t

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It’s an old, familiar idea: Truth is beauty. Beauty is truth. They go together, inextricable, like friendship and laughter, or road work and traffic. Gazing at the universe will always satisfy your aesthetic itch—and if not, then you probably suck at gazing.

In her new book Lost in Math, physicist Sabine Hossenfelder lofts a very skeptical eyebrow at this orthodoxy.

Confession: I know about as much physics as the average squirrel. (Less, in fact; they, at least, reach birdfeeders via daring feats of applied mechanics.) Still, I found the book accessible, informative, and compellingly argued. Plus, the writing is great—a delicious mix of journalistic balance and iconoclastic snark.

Hossenfelder’s argument, in brief:

  1. There’s no reason to think nature cares what we find beautiful.

“Why should the laws of nature care what I find beautiful?” she writes on page 3. “Such a connection between me and the universe seems very mystical, very romantic, very not me.” Later, on page 189, she elaborates:

mathematics is full of amazing and beautiful things, and most of them do not describe the world. I could belabor until the end of eternal inflation how unfortunate it is that we don’t live in a complex manifold of dimension six because calculus in such spaces is considerably more beautiful than in the real space we have to deal with, but it wouldn’t make any difference. Nature doesn’t care.

The “beauty = truth” dogma isn’t a priori obvious. It’s worth asking why we find such a connection, and if the link says more about the universe, or about our unreliable perceptions of beauty.

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  1. A lot of the beauty narrative is just that—narrative.

We’re storytelling creatures. And our “truth = beauty” conviction seems to rest on cherry-picked anecdotes. On p. 161, Hossenfelder relates a conversation:

“So why are you convinced that mathematics can describe everything?”

“All our successful theories are mathematical,” Garrett says.

“Even the unsuccessful ones,” I retort.

Another key factor: our notion of “beauty” shifts over time. Hossenfelder cites a historian named James McAllister, who argues that “every revolution in science necessitates overthrowing the concepts of beauty that scientists have developed.” Maybe it’s not so much that truth follows beauty, but that we rewrite the laws of beauty to match our latest understanding of truth.

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  1. With new data so hard to come by, our beauty instinct runs amok.

These days, fundamental physics is like San Francisco real estate: wildly and forbiddingly expensive. Experimental data is slow and hard to come by. This creates a danger—that in the absence of empirical data, scientists will get lost in dreamy speculation. Hossenfelder pulls no punches on page 108:

I can’t believe what this once-venerable profession has become. Theoretical physicists used to explain what was observed. Now they try to explain why they can’t explain what was not observed. And they’re not even good at that.

Because “beauty = truth” is such a pretty and pleasing idea, Hossenfelder worries that bad ideas can hide behind it, avoiding the scrutiny they deserve. “Where experimentalists go to great lengths to account for statistical biases,” she writes, “theoreticians proceed entirely undisturbed, happily believing it is possible to intuit the correct laws of nature.”

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Hossenfelder knows that she’s one scientist, writing from a particular angle. Perhaps, she worries on page 96, “I shouldn’t psychoanalyze a community that neither needs nor wants my therapy.”

Still, I’m glad she did. I’m fond of mathematical beauty, and fascinated by its role in intellectual life—including the ways it might steer the car into the pond like a malevolent GPS. I leave physicists to judge the merits of Hossenfelder’s case; as an outsider, I enjoyed the window into a live scientific debate.

12 thoughts on “When the Math is Pretty But the Truth Ain’t

  1. On the other hand, to devise a hypothesis which to test, sometimes it is both possible and necessary to intuit the laws of nature.

    Eliezer Yudkowsky writes:

    “Rather than observe the planets, and infer what laws might cover their gravitation, Einstein was observing the other laws of physics, and inferring what new law might follow the same pattern. Einstein wasn’t finding an equation that covered the motion of gravitational bodies. Einstein was finding a character-of-physical-law that covered previously observed equations, and that he could crank to predict the next equation that would be observed.

    Nobody knows where the laws of physics come from, but Einstein’s success with General Relativity shows that their common character is strong enough to predict the correct form of one law from having observed other laws, without necessarily needing to observe the precise effects of the law.”

    I would keep on quoting, but you should just go and read the essay.

  2. It’s a bit like Occam’s Razor… it’s a nice idea, and very compelling, but I’ve never felt certain it’s actually how the world operates. And both ‘beauty’ and ‘simplicity’ may tend toward being in the eye of the beholder.

  3. A good night’s sleep is, in fact, made of kittens. The more kittens you have, the better you sleep. (It is important to schedule your good night’s sleep for the daytime, though, because kittens are nocturnal.)

  4. Great review of a very interesting book. For sure there is a big problem in physics. It’s not that there are still so many unanswered questions. It’s much worse. We now know that we know very little. 15,000ish theorists out there are struggling with this refusing to acknowledge the problems because reputation and funding are hard won. We need an Enstein or a child to show the way forward. It’s brave, hopefully not foolish of Dr H to stand up and be counted.

  5. Reality check 1

    Dr. Hossenfelder pursuits “ugly” bottom-up phenomenological approach to physics rather than up-bottom “beauty” theories – but the ugly fact is, this approach failed as well.

    Reality check 2

    At least Smolin or Peter Woit wrote their books well before string theory fiasco – but where Dr. Hossenfelder was, when they pointed to its problems? After wit is everyone’s wit… 🙂

    Reality check 3

    Her hypocrisy and opportunism goes even deeper: When string theory was still hyped, Dr. Hossenfelder also jumped into its bandwagon for example by many studies involving extradimensions – but now she bravely pretends, she was never involved into it.


  6. The biggest breakthrough in expirmental physics in recent years was the discovery of the Higgs boson.
    The only reason we were looking for the Higgs was because of a beautiful theory. Physicist latched onto super-symmetry because it was beautiful. But If super-symmetry is true it would suggest that the Higgs exists.

    But then we have the problem with theories that are “not even wrong.” They may be beautiful, but they lack sufficient implications to actually test the theory. Or problems like string theory, where there are so many flavors, just about any observation can be made to fit some flavor of string theory.

  7. zephirawt seems to be arguing that anyone who changes his or her mind is thereby a hypocrite. This makes no sense to me. Personally I would think that someone who tries an approach, or a commercial product for that matter, is the best person to review it. In the book Dr. Hossenfelder gives many caveats and rather than just presenting and then arguing against ideas herself, went around the world interviewing the proponents of those ideas to give them a voice.

    The Higg’s boson was proposed as a mechanism for giving particles mass well before string theory was developed, and its mass as predicted by super-symmetry was off by orders of magnitude, if I recall correctly from reading Dr. Hossenfelder’s book. In so far as a theory with adjustable parameters can be falsified, the LHC results have falsified super-symmetry. It might have worked, but it hasn’t. Trial and error is a valuable mechanism for progress, but only if one is willing to admit the errors and try something else.

    1. To expand on your comment, the prediction of the Higgs Boson was nothing like the rest of the things they were hoping to find.

      If there was either no Higgs Boson or something that filled exactly the same role as the Higgs Boson (and many alternatives had been proposed), the standard model itself, our best theory for the fundamental particles and forces of the universe, would begin to contradict itself in truly strange and logic-destroying ways*. Because the contradictions would begin to come out of the woodwork at energies easily reachable from the LHC, they were dead certain they were going to find something filling that hole; logic and statistics demanded it. Even if they didn’t find the Higgs Boson, they were going to find something.

      Unfortunately, we had and have no guarantees for finding something similar to reconcile gravity and the standard model at any energies we can reach. Gravity is stupidly weak. All of the other things that they were hoping to find in this energy range were much more speculative, driven by, well, beauty, the idea that unitless numbers should be close to 1. However, the theory itself works just fine with a set of parameters that looks like 0.1, 10, 500 and 1e27. It’s just our human revulsion at that last one that makes it feel incomplete, but there are no logical inconsistencies or unphysical behavior, and no guarantees.

      Completely different beasts, from a logical perspective.

      *A typical wavefunction for a particle can produce the chance of that particle being found in any particular place. If you sum up this probability over all space for a particular particle, you get a probability of one (i.e. dead certainty) that it is somewhere. (I am simplifying here slightly; particle collisions can create particles, so it’s more complex than this, but the core idea is true). The essence of the problem is that if there were nothing filling the role of the Higgs boson in the standard model, at high enough collision energy, the probabilities for some measurements occurring would begin to add up to more than one—and nobody knows what that would even mean. The energies at which you would start to get nonsense answers was well within the range of the LHC, so we were certain to find something, even if it was “was does a probability greater than one mean”? Not many people expected that last outcome, BTW. It’s hard to fight definitions.

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