If I could explain it to the average person, I wouldn’t have been worth the Nobel Prize— Richard Feynman

Giorgio Parisi has just been awarded the 2021 Physics Nobel Prize for his work on the disorder in systems of all kinds. At the same time Syukuro Manabe and Klaus Hasselmann won for their joint work on the physical modeling of the Earth’s climate and reliably predicting global warming.

Today Ken and I look at some aspects of this year’s prizes.

Small issue: I do believe in human-caused global warming, but shouldn’t the citation read: for reliably predicting the future temperature of the planet? Currently it reads a bit like for reliably predicting the rise in the global stock market, as if the outcome not the model were primary.

Oh well. Every year there are Nobel prizes awarded for things that have at least some computational aspect. This year’s prize is certainly for something related to computation. One aspect that we are hoping for is Aspect—Alain Aspect. Ken was among those tipping him, John Clauser, and Anton Zeilinger for this year’s prize—for their work demonstrating quantum entanglement and non-classical experimental outcomes. This work spans substantial areas of quantum computing.

General Comments

The Nobel committee’s technical review of the prizewinning trio’s accomplishments ends with an expansive comment:

Clearly this year’s Laureates have made groundbreaking contributions to our understanding of complex physical systems in their broadest sense, from the microscopic to the global. They show that without a proper accounting of disorder, noise and variability, determinism is just an illusion. Indeed, the work recognized here reflects in part the comment ascribed to Richard Feynman (Nobel Laureate 1965), that he “Believed in the primacy of doubt, not as a blemish on our ability to know, but as the essence of knowing.”

Recognizing the work of this troika reflects the importance of understanding that no single prediction of anything can be taken as inviolable truth, and that without soberly probing the origins of variability we cannot understand the behavior of any system. Therefore, only after having considered these origins do we understand that global warming is real and attributable to our own activities, that a vast array of the phenomena we observe in nature emerge from an underlying disorder, and that embracing the noise and uncertainty is an essential step on the road towards predictability.

Ken says about the global-warming part of the last sentence that all you need to do is ask a wine grower, of which there are many in the Niagara region. The latitudes at which certain grape strains thrive have been shifting recently and steadily north.

For some general comments by Parisi, see his interview. He says lots of neat stuff including:

Well, things that Well, my mentor Nicola Cabibbo was usually saying that we should work on a problem only if working on the problem is fun. So, I mean, fun is not very clear what it means, but it’s something that we find deeply interesting, and that we strongly believe that it is I mean you won’t find fun in unclear because one gets a new idea of something unexpected and so on. So I tried to work on something that was interesting and which I believed that had some capacity to add something.

His Trick

The Nobel citation says: “One of the many theoretical tools Professor Parisi has used to establish his theory is the so-called ‘replica trick’—a mathematical method which takes a disordered system, replicates it multiple times, and compares how different replicas of the system behave. You can do this, for instance, by compressing marbles in a box, which will form a different configuration each time you make the compression. Over many repetitions, Parisi knew, telling patterns might emerge.” They point to a paper from talks by Parisi in 2013 also involving Flaviano Morone, Francesco Caltagirone, and Elizabeth Harrison.

The trick has a Wikipedia page, which says that its crux “is that while the disorder averaging is done assuming to be an integer, to recover the disorder-averaged logarithm one must send continuously to zero. This apparent contradiction at the heart of the replica trick has never been formally resolved, however in all cases where the replica method can be compared with other exact solutions, the methods lead to the same results.”

The mathematical identity underlying the replica trick is

The is the partition function of a physical system or some related thermodynamical measure. The power represents independent copies of the system—if is an integer, that is. But instead we treat as a real number going to zero. The formal justification is best seen via a Taylor series expansion:

But on the whole, this strikes me as a silly idea. Suppose that you have a nasty function where . How do you try to understand the behavior of ? Several ideas come to mind:

1. Try to see how grows as ?
2. Try to get an approximate formula for as grows?
3. Try to understand ?

Wait, this is nuts. How can the value help us understand the limit of

Indeed.

The trick here is that instead of letting go to infinity they set to zero. This is crazy. But it is so crazy that it yields a ton of insight into the behavior for large . I wish I could understand this better. Perhaps it could help us with our problems like ?

Indeed, one of Parisi’s main applications is to spin glass models, which are related to the Ising model and likewise have associated problems that are -hard. This applies even to a spin-glass model for which Parisi showed that exact solutions are computable.

Manabe and Hasselmann

The prize for Manabe is well summed by the title to this Italian news article, which translates as, “The scientist who put the climate into computers.” The article’s subhead makes a point that deserves further reflection: “Without his models it would have been impossible to do experiments on the climate.” Stated positively and picking up “reliable” from the Nobel citation, the point is:

Having reliable climate models has made it possible to do experiments on the climate.

Now we cannot actually do experiments on the climate—short of setting off a nuclear winter or erecting a Dyson sphere, maybe. We can observe changes caused by El Niño events and shifts in the jet stream, for instance, and try to build the framework of a controlled experiment around them. But that’s all.

So what is meant is that the models are robust enough, and have proven themselves on predictions at smaller or broader scales, that we can confidently regard computational experiments with them as indicative of real-world outcomes. The article mentions being able to tell what would happen if we made mountains disappear or shuffled the continents around. But in line with what we said in the intro, the logic sounds circular or self-confirming unless its reasonableness is explained more. The Washington Post article on the prizes stops short of saying that Manabe’s modeling of the effect of atmospheric carbon dioxide is a truly confirmed prediction, but it does say that his 50 years of modeling choices have had an almost 1.000 batting average.

Hasselmann is hailed for supplying a different piece that promotes confidence and accounting of causality. This is to demonstrate consistent effects of short-term local weather events on longer-term global climate. To those like us not versed in the background, this might again sound circular: didn’t the global configuration cause the local event? One particular effect Hasselmann traced is of weather events on ocean currents. The chain from atmosphere to storm to ocean sub-surface is non-circular.

Perhaps all this can be put as pithily as John Wheeler’s non-circular explanation of general relativity: “Matter tells space-time how to curve, and curved space-time tells matter how to move.” But until then, we feel a need to hallow a more fundamental story of how computational modeling works and why it is effective.

Open Problems

One day we will see a more computationally-oriented Nobel Prize, but how soon? Until then, best to all working on theory. You are Laureates in our eyes.