Tag: Richard Dawid

• String theory and reconciliations

  According to particle physics, the fundamental building blocks of the universe are point-like particles, essentially small dots of energy with no dimension. String theory posits that these dots are actually minuscule vibrating loops of energy. A violin string vibrating at different frequencies produces different musical notes; similarly these filaments are said to be able to vibrate at different frequencies, each one creating a different particle of our universe. One note is an electron, another is a photon, and so on.

  String theory hasn’t been proven — it hasn’t made any testable predictions so far, in fact. Yet it exists because scientists are looking for a ‘theory of everything’: a single theory that can explain both gravity and quantum physics. At present these two theories together explain their particular domains very well but scientists don’t know how they fit together. String theory is one of a few theory programmes trying to reconcile them; others include loop quantum gravity and twistor theory.

  On January 7, scientists from Hungary, Israel, and the US published a curious paper in Nature. Stumped by the complex shapes of neurons, they reportedly found a solution in some arcane equations in string theory and, according to them, the equations also describe how blood vessels and neurons branch.

  If you were an engineer designing the wiring for a brain or a vascular system, you’d probably try to save money by using the least amount of wire possible. For a long time, biologists assumed nature ‘thought’ the same way. According to this paper, however, it doesn’t, at least not necessarily. The researchers analysed high-resolution 3D scans of neurons, blood vessels, and fungi and showed that biological networks don’t care about minimising length but about minimising surface area. And to figure out the complex geometry of how these tubelike structures connect, the researchers borrowed the maths of interacting strings.

  The scientific method says that if you can’t prove something with an experiment, it isn’t science. The problem for string theory is that it describes a part of space so small and so fleeting that no machine we can currently build could ever study it. Yet many physicists have stuck with it because, even though it remains entirely mathematical, they’ve glimpsed deep connections between its equations and structures and other branches of mathematics and physics. According to the physicists these connections are signs that string theory contains ‘truths’ worth exploring more and due to which it can’t simply be dismissed out of hand.

  On the other hand we also have scientists like Peter Woit who have lamented, repeatedly, that string theory is a dead-end, that despite all of its mathematical elegance and structure the fact that it hasn’t made a testable prediction, and doesn’t seem like it will for the foreseeable future, it’s been a drain on physicists’ time and intelligence. Over the years however, neither side has been able to persuade or dissuade the other, and today many criticisms have hardened into denial and vitriol.

  Stockholm University philosopher Richard Dawid published a provocative book in 2013 that, despite its seemingly reconciliatory premise, entrenched these divisions. In the text, titled String Theory and the Scientific Method, based on a small conference he’d conducted a short while earlier, Dawid argued that the history of science is witness to a revolution in how scientific truth can be redefined. (American philosopher and biologist Massimo Pigliucci’s essay in Aeon on the conference and how philosophy can help with science’s demarcation problem is also worth a read.) He proposed that in the absence of empirical data, experts must rely on non-empirical evidence, like the sheer mathematical elegance of a theory or the fact that no one can find a better alternative. That is, he seemed to say, a theory could be true because it’s too ‘good’ to be wrong.

  I’m partial to criticisms of the book, especially those advanced by George Ellis, Joe Silk, Sabine Hossenfelder, and Carlo Rovelli, rather than the book itself.

  Ellis and Silk, both cosmologists, argued that Dawid’s push for “non-empirical theory assessment” (which he prefers to “post-empirical science”) is dangerous for suggesting that a theory can be validated by its ‘elegance’ or its power to explain something post facto. The danger here is that if you move these goalposts you also let in pseudoscience. Hossenfelder, a physicist, took aim at Dawid’s argument that string theory must be true because scientists haven’t found another option that’s equally good. According to her, claiming there are no alternatives is a sociological observation rather than scientific proof, i.e. that scientists can’t imagine an alternative today doesn’t mean one doesn’t exist. It may simply be a lack of imagination, of funding for rival approaches or even of groupthink within the academic community.

  Third, Rovelli, also a physicist and a cofounder of loop quantum gravity, argued that the history of science is littered with beautiful, mathematically coherent theories that turned out to be wrong. He also posited that Dawid’s “unexpected explanatory coherence”, i.e. when a theory solves problems it wasn’t built to solve, is often a result of confirmation bias and that once a community is deeply invested in a mathematical framework, it will inevitably find internal connections that look ‘miraculous’ but have no bearing on physical reality.

  Hossenfelder’s and Rovelli’s criticisms also help to see the problems with using the new Nature paper to claim it verifies or legitimises the pursuit of string theory in any meaningful way. Its authors show that the mathematics of string theory handles problems in which you need to minimise the surface area very well, but this shouldn’t be surprising, as Rovelli has argued. Complex maths is often useful in disparate fields but just because calculus describes both the orbit of planets and the marginal cost of gizmos doesn’t mean gravity holds the economy together.

  Similarly, that string theory describes the branching of neurons doesn’t mean the universe is fundamentally made of vibrating strings. The only way to know the latter is if the theory unifies the principles of quantum mechanics with gravity and makes a testable prediction.

  The paper’s authors themselves, while taking care to temper their claims regarding the physical reality of string theory, have also expressed optimism about its mathematical necessity. They’ve called their finding a “formal mapping between surface minimisation and high-dimensional Feynman diagrams” and say they’re taking “advantage of a well-developed string-theoretical toolset”. They also clarify that they’re removing the fundamental physical properties usually associated with string theory as a ‘theory of everything’ and instead treating the matter at hand as a very difficult geometry problem. Then, however, they strongly imply that the mathematics of string theory is essential to solving this problem.

  Now, is it possible to reconcile the (demonstrated) usefulness of the string theory toolkit with Rovelli’s and Hossenfelder’s criticisms? Specifically, setting aside for a moment the fact that the new study treats the maths of string theory as a toolkit: while solving the problem doesn’t ‘prove’ string theory in any meaningful way, how does one reconcile the notion that string theorists indeed developed this mathematical toolkit with Rovelli’s criticism? Is it possible to argue that only string theory could have discovered this toolkit despite Hossenfelder’s criticisms or is it possible to conclude in a reasonable way that we simply use the complex mathematics and discard the rest?

  I think this entails distinguishing between the mathematical machinery and the physical claims. Rovelli’s position isn’t that string theory mathematics are ‘wrong’ or ‘useless’ but rather that internal consistency and mathematical elegance alone don’t constitute empirical proof of quantum gravity. So the fact that string theorists developed a toolkit that can solve problems in biology doesn’t contradict Rovelli, in fact it arguably supports his view that string theory has become a rich mathematical framework. The act of reconciliation lies here in accepting that string theorists spent decades exploring the geometry of interacting surfaces (which they call “worldsheets”).

  Second, vis-à-vis Hossenfelder’s pushback to Dawid’s argument that there are no equally good alternatives to string theory, it also seems physically as well as historically risky to argue that only string theory could have discovered these tools. A mathematician focusing purely on topology or differential geometry could likely have arrived at similar tools without positing 10 dimensions or supersymmetry. In this sense string theory has simply been a historical catalyst, an ‘engine’ that seems to have accelerated humans’ approach to the toolkit that they subsequently used to solve a particular problem in brain biology.

  I’m generally wary of non-empirical assertions, so perhaps a scientifically robust position for me to take is the instrumentalist rather than the realist view: i.e. to conclude we can use the mathematics and discard the physical dogma. This way I retain the formalism, which is the calculus of optimising 3D surfaces, because it works for the data, while rejecting the ontology, i.e. the idea that the universe is fundamentally composed of strings.

  2026.01.15

• Getting ahead of theory, experiment, ourselves

  Science journalist Laura Spinney wrote an article in The Guardian on January 9, 2022, entitled ‘Are we witnessing the dawn of post-theory science?’. This excerpt from the article captures its points well, I thought:

  Or take protein structures. A protein’s function is largely determined by its structure, so if you want to design a drug that blocks or enhances a given protein’s action, you need to know its structure. AlphaFold was trained on structures that were derived experimentally, using techniques such as X-ray crystallography and at the moment its predictions are considered more reliable for proteins where there is some experimental data available than for those where there is none. But its reliability is improving all the time, says Janet Thornton, former director of the EMBL European Bioinformatics Institute (EMBL-EBI) near Cambridge, and it isn’t the lack of a theory that will stop drug designers using it. “What AlphaFold does is also discovery,” she says, “and it will only improve our understanding of life and therapeutics.”

  Essentially, the article is concerned with machine-learning’s ability to parse large amounts of data, find patterns in them and use them to generate theories – taking over an important realm of human endeavour. In keeping with tradition, it doesn’t answer the question in its headline with a definitive ‘yes’ but with a hard ‘maybe’ to a soft ‘no’. Spinney herself ends by quoting Picasso: “Computers are useless. They can only give you answers” – although the para right before belies the painter’s confidence with a prayer that the human way to think about theories is still meaningful and useful:

  The final objection to post-theory science is that there is likely to be useful old-style theory – that is, generalisations extracted from discrete examples – that remains to be discovered and only humans can do that because it requires intuition. In other words, it requires a kind of instinctive homing in on those properties of the examples that are relevant to the general rule. One reason we consider Newton brilliant is that in order to come up with his second law he had to ignore some data. He had to imagine, for example, that things were falling in a vacuum, free of the interfering effects of air resistance.

  I’m personally cynical about such claims. If we think we are going to be obsolete, there must be a part of the picture we’re missing.

  There was an idea partly similar to this ‘post-theory hypothesis’ a few years ago, and pointing the other way. In 2013, philosopher Richard Dawid wrote a 190-page essay attempting to make the case that string theory shouldn’t be held back by the lack of experimental evidence, i.e. that it was post-empirical. Of course, Spinney is writing about machines taking over the responsibility of, but not precluding the need for, theorising – whereas Dawid and others have argued that string theory doesn’t need experimental data to stay true.

  The idea of falsifiability is important here. If a theory is flawed and if you can design an experiment that would reveal that flaw, the theory is said to be falsifiable. A theory can be flawless but still falsifiable: for example, Newton’s theory of gravity is complete and useful in a limited context but, for example, can’t explain the precession of the perihelion of Mercury’s orbit. An example of an unfalsifiable theory is the one underlying astrology. In science, falsifiable theories are said to be better than unfalsifiable ones.

  I don’t know what impact Dawid’s book-length effort had, although others before and after him have supported the view that scientific theories should no longer be falsifiable in order to be legitimate. Sean Carroll for one. While I’m not familiar enough with criticisms of the philosophy of falsifiability, I found a better reason to consider the case to trust the validity of string theory sans experimental evidence in a June 2017 preprint paper written by Eva Silverstein:

  It is sometimes said that theory has strayed too far from experiment/observation. Historically, there are classic cases with long time delays between theory and experiment – Maxwell’s and Einstein’s waves being prime examples, at 25 and 100 years respectively. These are also good examples of how theory is constrained by serious mathematical and thought-experimental con- sistency conditions.

  Of course electromagnetism and general relativity are not representative of most theoretical ideas, but the point remains valid. When it comes to the vast theory space being explored now, most testable ideas will be constrained or falsified. Even there I believe there is substantial scientific value to this: we learn something significant by ruling out a valid theoretical possibility, as long as it is internally consistent and interesting. We also learn important lessons in excluding potential alternative theories based on theoretical consistency criteria.

  This said, Dawid’s book, entitled String Theory and the Scientific Method, was perhaps the most popular prouncement of his views in recent years (at least in terms of coverage in the non-technical press), even if by then he’d’ been propounding them for nine years and if his supporters included a bevy of influential physicists. Very simply put, an important part of Dawid’s arguments was that string theory, as a theory, has certain characteristics that make it the only possible theory for all the epistemic niches that it fills, so as long as we expect all those niches to filled by a single theory, string theory may be true by virtue of being the sole possible option.

  It’s not hard to see the holes in this line of reasoning, but again, I’ve considerably simplified his idea. But this said, physicist Peter Woit has been (from what little I’ve seen) the most vocal critic of string theorists’ appeals to ‘post-empirical realism’ and has often directed his ire against the uniqueness hypothesis, significantly because accepting it would endanger, for the sake of just one theory’s survival, the foundation upon which almost every other valid scientific theory stands. You must admit this is a powerful argument, and to my mind more persuasive than Silverstein’s argument.

  In the words of another physicist, Carlo Rovelli, from September 2016:

  String theory is a proof of the dangers of relying excessively on non-empirical arguments. It raised great expectations thirty years ago, when it promised to [solve a bunch of difficult problems in physics]. Nothing of this has come true. String theorists, instead, have [made a bunch of other predictions to explain why it couldn’t solve what it set out to solve]. All this was false.

  From a Popperian point of view, these failures do not falsify the theory, because the theory is so flexible that it can be adjusted to escape failed predictions. But from a Bayesian point of view, each of these failures decreases the credibility in the theory, because a positive result would have increased it. The recent failure of the prediction of supersymmetric particles at LHC is the most fragrant example. By Bayesian standards, it lowers the degree of belief in string theory dramatically. This is an empirical argument. Still, Joe Polchinski, prominent string theorist, writes in that he evaluates the probability of string to be correct at 98.5% (!).

  Scientists that devoted their life to a theory have difficulty to let it go, hanging on non-empirical arguments to save their beliefs, in the face of empirical results that Bayes confirmation theory counts as negative. This is human. A philosophy that takes this as an exemplar scientific attitude is a bad philosophy of science.

  2022.01.14