Wednesday, 20 June 2018

Review: Lost in Math by Sabine Hossenfelder

This is an interesting book by a theoretical physicist about how the field has gone astray by relying on subjective aesthetic criteria to judge theories in the absence of evidence. It was a weird reading experience as usually my popsci books are more of a survey of a broad area e.g. The Gene by Siddhartha Mukherjee, I Contain Multitudes by Ed Yong, whereas this one was pretty much entirely about a problem faced by theoretical physics, but it was quite good. I'd recommend it for people interesting in the scientific method  and problems facing it because that's really what it's about; don't go in expecting to learn physics. 

(I apologise in advance: this review doesn't have much of a structure as I mostly just want to record interesting bits.)

4 stars: the approach to explaining the actual physics was poor, but that wasn't the main point of the book and the main point - about how big an issue this is - was good. She's also funny.

Thesis: Theoretical physics (TP) is lost in maths; they use the aesthetic beauty of mathematical theories (in terms of simplicity, elegance, naturalness - not needing to fine-tune things and having all your unitless numbers near 1, and explanatory closure - unexpected insights) to assess theories without experimental evidence because they're so starved for evidence.

Strong points:

  • introduced me to a problem that I didn't really know much about (though I did tease theoretical physics people for their fear of evidence) and convinced me that it's a serious issue
  • funny way of writing and lots of pithy lines
    • "What the heck is an internal space?" you ask. Good question. The best answer I have is "useful".
    • On searching for dark matter particles: experimentalists working with a detector originally developed to catch neutrinos reported in 1986 on the first "interesting bounds on galactic cold dark matter and on light bosons emitted from the sun." In plain English, "interesting bounds" means they didn't find anything. Various other neutrino experiments at the time also found interesting bounds.
  • seemed to have access to lots of big names in the field
  • Her list of suggestions in the appendix seemed very good and original (at least to me)
  • I respect her for coming out and saying this stuff. I was expecting a lot of opposition (in fairness it's only out this month) but I haven't actually found much criticism online...but still. Hopefully it leads to some change in how funding is applied for and given out in foundational physics.

Weak points:

  • It's not clear who she's writing for - it's ostensibly for the public going by the book format, but it seems like it's actually for scientists in her field and the public was added as an afterthought. She didn't explain theoretical physics concepts well - and that's understandable, since I'm sure it takes a huge amount of difficult maths - but then she acted as if she had, where she'd give an explanation that was technically there but really didn't explain things, and then just refer to it by name. Some things that happened with that: U(1), SU(5), fine-tuning, gauge coupling, group. I appreciated the Kirkus review saying 'Even educated readers will struggle to understand the elements of modern physics'. 

Many of the people she spoke of seemed to be to some degree aware of but ignoring the problem, which is weird. Surely that's a lot of cognitive dissonance.

I'm really enjoying how much my mind is stretching over the last while, what with Schols and books like this and the research I'm doing in Genetics at the moment. It's difficult but very rewarding.

She seems to be a very incisive and snarky interviewer, which must make her fairly unpopular with her interviewees. She'll record someone saying something and then be like 'Isn't that exactly what you do?' but maybe only in the text of the book rather than immediately in the interview. That said there were perhaps a bit too many interviews - there just seemed to be an awful lot of them and it wasn't great for the book's structure. 

Cool Quotes

To derive a probability for a theory rather than a constraint, you need a probability distribution, which then needs a metatheory that tells you how probable each theory is. The attempt to get rid of human choice just moves the choice elsewhere

In our search for new ideas, beauty plays many roles. It's a guide, a reward, a motivation. It's also a systematic bias. Ooooh.

Supersymmetry is the largest possible symmetry that can be accommodated in the existing theories - and how could nature not make use of such a beautiful idea? 


One prominent TP said that historically as you go down the scales, things have always gotten simpler. Chemistry has all these weird molecules, then you classify them into the elements, then you get simpler and simpler with atoms and quarks etc. But Hossenfelder points out that this is because he conveniently started with chemistry instead of, say, galaxies, which get more complicated as you go down the scale because you hit biochemistry (my love). Also, Garrett says the idea of the laws of nature being fundamentally ugly is 'abhorrent' to him. I mean, so what? It's not his business to think they're pretty or not, scientists are supposed to find out the truth whatever it is.


According to this TP she interviewed called Weinberg, Copernicus came up with heliocentrism not because of evidence but because he thought that was more attractive than the Ptolemaic system, and that Newton was able to revolutionise force with his theory of gravity because he didn't find force acting at a distance ugly whereas Descartes did.

Apparently Kepler originally thought the orbits were in Ptolemaic geometrical solids. Also, an issue with people supporting heliocentrism was that until the ninteenth century astronomers couldn't detect the parallax of the stars and so either the Earth had to be stationary during the year or the planets would have to be very far away, much further than the Sun and other planets in the solar system, and this introduced an unacceptably large number.

When Kepler said that the planets moved in elliptical, rather than circular, orbits, his idea was met with opposition from people who said it was absurd because that's not what a perfect creator would have done, and it was too ugly. He was told to just add epicycles, smaller circles to fix the ellipses so they could be circles. Coz circles are pretty.

Tidbit: in a 1916 book called Harmony of the World, Kepler derived the tunes of the planet and said that Earth sings Mi-Fa-Mi. Which is yknow, odd.

Talking about the parrotfish shaping landscapes with its feces and unsubtly alluding to the state of TP: 'if you pile up enough of it, even shit can look beautiful.'

Imagine a website where you can order door signs with numbers: 1, 2, 3, 4,.  and so on, all the way up to infinity. Then you can also order an emu, an empty bottle, and the Eiffel Tower. That's how awkwardly the exceptional Lie groups sit beside the orderly infinite families

Apparently Enrico Fermi replied to a question on what he thought about the discovery of a particle called K02 with 'Young man, if I could remember the names of these particles I would have been a botanist.' Seems too polished to be true but anyway. [Side note: wooot with my recent exam results I know I won't have to do botany!]

The Multiverse

Cosmologist Martin Rees bet his dog that the multiverse is right, Andrei Linde bet his life, and Steven Weinberg had "just enough confidence about the multiverse to bet the lives of both Andrei Linde and Martin Rees's dog."

The multiverse is presented as an alternative to having to come up with parameters for theories - if you can't find a parameter that's natural i.e. close to one, and you don't find it aesthetically pleasing to just pick a parameter that works, you can avoid having to choose one at all by positing a multiverse where there's a universe with each possible parameter. Newton, for example, could have refused to just measure the gravitational constant and instead argued that there must be a universe for each possible value...You can create a multiverse for every theory -- all you have to do is drop a sufficient amount of assumptions or ties to observation. 

The idea of 'fine-tuning', and TPs hating it, is central to the book; apparently TPs hate very large or very small numbers because then the numbers aren't 'natural' and need an explanation. 

There's also a more radical 'mathematical multiverse' which is like the mother of all multiverses: any theory that describes our universe relies on the selection of some mathematics to describe it, and you can't justify that maths because it would require other maths (apparently, since TPs love maths), so the only logical final theory is one in which all maths exists. Gosh this book got awfully philosophical.

Quantum Mechanics: Interpretations

Quantum mechanics refers to observations mattering -- so telescopes and brains matter; it assumes the existence of macroscopic objects. This is bad for reductionism. 

Learned a bit about the conflict between general relativity and quantum theory, which I knew nothing about before: general relativity is not a quantum theory, but it has to react to matter and radiation, which have quantum properties. If an electron is in two places at once, which one should spacetime curve around? Its curvature can't be in two places at once.

According to the Copenhagen interpretation, quantum mechanics is a black box: we enter an experimental setup and push the math button, and out comes a probability. What a particle did before it was measured is a question you're not supposed to ask. In other words, "shut up and calculate". This is something that really bothered me about my quantum mechanics lectures last year; there was no interpretation at all, just derivations.

I do kinda like the sound of QBism (with the caveat that I know very little really about the maths of quantum mech) - it says that the wave function is a device to collect an observer's information about the real world, which is updated when the person makes a measurement.

An interesting and bizarre interpretation is the 'many-worlds' or 'many-histories' version, which says that instead of the wave function ever collapsing, it actually branches into parallel universes, one for each measurement outcome. 

Someone she interviews describes a friend of theirs describing a graduate student (phew) whose career essentially disintegrated, and I asked what went wrong and he said "He tried to understand quantum mechanics'. He could have had a perfectly good career without it. But getting into the fundamentals of quantum mechanics is a losing game. She also pre-empted me by saying: If you quote this, you can be the first person to quote someone quoting someone quoting himself quoting someone.

There followed an interesting description of how, while aesthetics are a bad metric to use for judging theories, consistency is a good one - the standard model without the Higgs boson becomes internally inconsistent at LHC energies. 

No proof is ever better than its assumptions


"Yes, there was this story that the LHC should find supersymmetry," I say. "Gordy Kane still thinks gluinos have to show up in run two."

"Ack," Garrett says. "The most egregious thing was his claim of predicting the mass of the Higgs, after all the rumors were already flying. And two days before the official announcement, he put out this paper. And then the announcement confirms the rumors and he calls it a prediction from string theory!"

Mathematical consistency can't be the only requirement for a theory; there are tons of theories that are mathematically consistent but don't have any relation to reality.

For it hardwired in my brain, it ought to have been beneficial during natural selection. Not sure this is true - could've just got there by drift or by common descent I imagine.


The idea of supersymmetry (though this wasn't really made clear in the book, just the partners bit) is a relationship between fermions and bosons that means every particle in one group has a 'superpartner' from the other group, with spins differing by a half-integer (thanks Wikipedia). Supersymmetry is called 'susy' for short, and people are very attached to it.
When I was a student, in the late 1990s, the simplest susy [supersymmetry] models had already run into conflict with data and the process of designing more complicated but still viable models had begun. To me it looked like a field where nothing new could be said without first detecting the predicted particles [superpartners]. I decided to stay away from susy until that happened. It hasn't happened. Not in the LEP which ran until 2000, not at the Tevatron which reached higher energies and ran until 2011, and not at the still more powerful LHC.

Apparently TP is a very mature field, and thus has very strong constraints already from old experiments, which rule out almost everything you can try (according to Nima). He seems to imply that this means you don't need to check things with new experiments. It's an odd concept - can biology just find out enough things and then extrapolate from there forever?

She talks about how weird it is that TPs don't like assumptions that "are selected 'merely' to explain observations, since there are already so many of those that just don't get talked about, like the stability of the vacuum, which could occur in many theories that don't match the world but is included because it does happen to match the world.

I thought the description of how scientists testing SU(5) unification by just getting a big vat of water and waiting for one of its protons to decay was cool, because at least they were actually looking to experiment.

Some bullshitty sounding supersymmetry (very aware that I don't understand the maths): It didn't take long until it was noted that, even if broken at high energy, supersymmetry would lead to disagreement with exxperiment by enabling interactions that are forbidden in the standard model, interactions that hadn't been seen. And so was invented R-parity, a symmetry that, when combined with supersymmetry, simply forbids the unobserved interactions because they would conflict with the new symmetry postulate.

She gave a nice understandable description of symmetry with something like: you could say something is blue in the west, and east, and north, and south, and northwest, etc, or you could just say it's blue everywhere (rotational symmetry). 

String theorists had for a long time used a cosmological constant that was negative; when it was found to be positive they had to quickly adjust things. String theorists appear to have abandoned the idea that their idea would uniquely determine the laws of nature and instead embraced the multiverse, in which all the possible laws of nature are real somewhere. They are now trying to construct a probability distribution for the multiverse according to which our universe would at least be likely.
...String theorists' continuous adaptation to conflicting evidence has become so entertaining that many departments of physics keep a few string theorists around because the public likes to hear about their heroic attempts to explain everything. Also, they're apparently a cheap way to get a physics department since no experiments.

I did have a few 'people get paid for this?' moments, I will admit.

Ars Technica's review has a good description of the issue with supersymmetry: 'Supersymmetry was attractive because it was natural and beautiful. Unfortunately, results from the Large Hadron Collider have eliminated natural versions of supersymmetry. If it turns out that the world is supersymmetric, the theory will not be natural; it will be fine tuned, with some unusual numbers that are just baked in.'

Two sides of string theory

Good: string theory fits naturally with supersymmetry (unsure whether this is really good); there are thought to be an infinite number of string theories that are collected together in M-theory; their theory was able to predict the thermodynamics of black holes and matched the already known laws; invented some interesting maths; gauge-gravity duality; apparently showed that our universe can in theory be squeezed into 2D? Not sure what that means.

Bad: no evidence and no testable hypotheses thus kinda raising doubts about whether it's science at all

The Energy Desert

The energy desert is the 12 orders of magnitude between the LHC energies (around a thousand GeV) and the energies of grand unification and the Planck scale (10^15 GeV). This would be a pretty impossibly enormous undertaking to develop experimental equipment to bridge, but they do need experimental evidence soon.

When some scientist she interviewed discovered something that involved the multiverse, he had to go to a psychiatrist for it he was so upset.

There was a bit about how physicists can't actually solve the equations of the Standard Model so they use perturbation theory and just hope the refinements, the adjustments to the bumps of things off each other, will keep getting smaller. But they don't, and it's an issue that fundamentally physicists don't understand the theory. 

Foundational physics is the canary in the coalmine when it comes to non-empiricial theory assessment, or figuring out which ideas are worth pursuing, because its ideas are the hardest to test -- but Hossenfelder says this will affect other fields too. Theories are cheap and plentiful but experiments are expensive and few. 

Dark matter

The second rule for inventing a new particle is that you need an argument for why it's just about to be discovered, because otherwise nobody will care. This doesn't have to be a good argument - everyone in the business wants to believe you anyway - but you have to give your audience an explanation they can repeat. The common way to do this is to look for numerical coincidences and then claim they hint at new physics for a planned experiment, using phrases like 'natural explanation' or 'suggestive link'. She says the WIMP miracle (weakly-interacting massive particles), in which a calculation based on the WIMPs' mass and interaction rate gives roughly the right amount of dark matter in the early universe, is an example.

Hossenfelder mentions a large number of experimental setups - I counted 25 - that found "interesting bounds" on dark matter -- and the parameter range in which the WIMP miracle holds has meanwhile been excluded


Hossenfelder briefly turns her attention to other areas of research, particularly economics. Apparently in economics, to get into a good journal your theory has to be selfish agents maximising their preferences, and that getting one paper in one of the five top journals is enough to get you tenure at a good university. The guy she's talking to, Doyne, says it's even worse than string theory because at least string theory is making interesting contributions to mathematics, but econ is just using standard maths and even then it's not empirical. So what is it? I'm sure econ has some good things, but if it's not empirical what is the actual point of it? Do we just keep it around because we find money intrinsically interesting?


Where experimentalists go to great lengths to account for statistical biases, theoreticians proceed entirely undisturbed, happily believing it is possible to intuit the correct laws of nature. 

On the sunk cost fallacy: The more time and effort you've spent on supersymmetry, the less likely you are to call it quits, even though the odds look worse and worse. We keep on doing what we've been doing long after it's stopped being promising, because we already invested in it, and we don't like to admit we might have been wrong. It's why Planck quipped, "Science advances one funeral at a time."

On the broken process of science funding

Scientists seem to exaggerate in grant applications, especially about the future impact of their work, because they have to get funded. We have failed to protect our ability to make unbiased judgments. We let ourselves be pushed into a corner, and now we are routinely forced to lie if we want to continue our work.

Three lessons

1. If you want to solve a problem with math, first make sure it really is a problem.
2. State your assumptions. (These assumptions include naturalness and simplicity - simplicity doesn't necessarily increase as you go down scales, as in the biochemistry example). 
3. Observational guidance is necessary. Because even with good problems and clearly stated assumptions, there can still be many mathematically possible solutions. 

Flashes in the Pan

Near the end of the book, she writes a quick but depressing timeline. The diphoton anomaly, something that theorists hoped pointed to new physics at the LHC, disappeared with new data. The LUX dart matter experiment found no WIMPs. No sign of supersymmetry was found at the LHC. No axions have been found. How long is too long to wait for a theory to be backed up by evidence? ... whether or not we will find something, it is already clear that the old rules for theory development have run their course. Five hundred theories to explain a signal that wasn't and 193 models for the early universe are more than enough evidence that current quality standards are no longer useful to assess our theories. 

Suggestions for Improvement 

Here are some of my favourite of her suggestions: 

  • Be careful with peer reviewers (of research papers): of a reviewer's continued funding depends on the well-being of a certain research area, that person has a conflict of interest and should not review papers in that area.
  • Make commitments: not all science can be done by post-docs on two-year fellowships. Tenure is important. She argues that tenure should be given to a higher proportion of scientists, even if that means fewer scientists in general. I'm not sure if I agree here; tenure would be great but y'know so would being able to get into the field.
  • Encourage a change of field: Scientists have a natural tendency to stick to what they already know. If the promise of a research area declines, they need a way to get out; otherwise you'll end up investing money in dying fields. Therefore, offer reeducation support, one- to two-year grants that allow scientists to learn the basics of a new field and to establish contacts. During that period they should not be expected to produce papers or give conference talks.
  • Hire full-time reviewers, scientists who specialise in providing objective reviews in certain fields. These reviewers should not themselves work in the field and should have no personal incentive to take sides. This one is interesting because (I imagine) there's a tradeoff between objectivity and knowledge of the field, so if you're not working in the subfield you can review it more objectively but you might not actually understand the paper as well because you're not following all the advances as closely. Maybe.
  • Support publication of criticism of others' work and negative results - criticism doesn't feel nice but is essential for the scientific method. 

So what to do about the physics in general? Now, I'm not sure it's legitimate for me to agree with Hossenfelder's criticisms when I don't actually understand the maths of TP at all, but it definitely seems like the current approach of making bigger and bigger detectors trying to find the same things isn't working, and maybe scientists should step back from that area until they make progress in related fields and can come up with better ways to test these things? I don't know, but something has to give. 

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