Nobel Prize in Physics & Chemistry 2024 (Part I)

I will elaborate my thoughts in a later post. For now, this is meant as a stub addressing some misunderstanding of the relevance, or lack of, of "AI" (but not LLMs!) in these respective fields.

Let's start with the Nobel award for chemistry.

AlphaFold won the CASP competition in 2018 & 2020. The thing is that's a recurrent competition in Computational Biology seeking new methods/models for determining protein structure. These may have multiple applications, e.g, in protein design, where you want to optimize an amino acid sequence starting with a given structure. If I remember correctly, David Baker was the first in coming up with a new design and successfully synthesizing it -can't find the reference right now.

Biology not having a Nobel prize on its own makes it a candidate for either the Chemistry or Medicine categories. As I'm sure you know, Structural biology, as a part of biochemistry, is like "usual" chemistry but on steroids.

All this makes the award in chemistry meaningful to me: They all made important contributions to the field of Structural Biology.

It's hard to say the same of any impact of Hopfield, or even less Hinton, on Physics though. It's specially insidious in the case of the latter.

Let's now switch to the Nobel award for Physics that went to Hopfield and Hinton.

Hopfield, with his Associative Memory model, and McCulloc & Pitts, with their perceptron model, can be consider among the forefathers of Neural Networks (NN), in the shadow of Martin Minsky; Hinton made those NN "deep", and in doing so he ignited the "AI" fever of nowadays.

Hinton played first with a model similar to that of Hopfield, both of these based on what's called the Ising model in Physics. This was initially invented as a simple model of a ferromagnet. Let's see what how it works.

A ferromagnet is a material that behaves as a magnet on its own, after having it exposed to an external magnetic field. Kind of, "you charge it" and it becomes a magnet. It can "discharge" as well, again in the presence of an external magnetic field. Remember, the earth is a magnet, so expect some progressive discharge with time.

The transition from "normal" (non-magnetic) to magnetic state, or vice-versa, is the prototypical example of what in physics is called a second-order phase transition (PT). These are a special case of very "smooth" (in a precise mathematical sense) transitions. Many materials and systems, having nothing to do with magnetism, may exhibit such a PT. So the magnetism of the Ising model is, in principle, just a distracting, anecdotical feature. The ice-liquid transition of water is NOT an example of 2nd order phase transition, but a "less smooth" one, boringly called 1st order PT.

It turns out that in these 2nd-order phase transitions all the microscopic details of the different materials and systems become completely irrelevant for describing the overall features of the transition. There are differences on the exact value of when the PT happens, or how effectively it extends over the whole sample, etc. But, you can say that they all behave the same way if you "shift the graphs results" compensating for those numerical differences. To put an analogy, both alcohol and water evaporate at different temperatures, but both two transitions are first-order PT. You can perfectly overlap their graph results if you rescale them appropriately based on those numerical differences. Think of all instances of the character "s" in the previous sentence. They all are located at different positions along the sentence. However, you'd say "it's the same "s"' because you can "rescale" (translate) their position so as to overlap them perfectly. The rescaling you may do for second-order PT is different than that for first-order PT. This is a type of symmetry difference that puts those two types of transitions apart.

OK, so we have a ferromagnet that gets (de)magnetized in the presence of a magnetic field. Can we model this transition so as to convey those "universal features" of it? The Ising model is the first and simplest of models doing just that. This models the ferromagnet as a collection of "spins" that can be in only two positions, up or dow. Think of them as microscopic magnets having their "north" either up or down. When all spins are randomly up and down, the material shows no magnetization. But if all were pointing in the same direction, the piece of macroscopic sample you are holding in your hands would behave as a magnet.

Incidentally, Physics has a systematic procedure for removing all microscopic details of a fine-grained model. In doing so we obtain what's called an effective Hamiltonian (aka, model), e.g., capturing only some basic, coarse-grained features of the system. Clearly, any such model, by its simpler nature, may describe other systems of a completely different nature say like a physical system, a geometric problem or a combinatorial one. The Ising model can be described as such an effective "model".

As we often do in Physics, we describe the state of a system as that of minimum energy. That is, finding the properties of the system entails solving an optimization problem using a given model. For high temperatures all spins point randomly and the minimum energy of the Isign model gives exactly that, i.e., no magnetization. But fir low enough temperatures the minimum-energy solution of the Ising model shows practically all spins pointing along the same direction, i.e., spontaneous magnetization.

There you go, we used an optimization technique (mathematics) on a model (mathematics too, but with inspiration in Physics) with the goal of describing a phase transition (physical phenomenon).

Say you improve the optimization technique, f.i. by making it 10x faster, or tweak the model so as to describe a different material, but keep the goal of describing the PT. Clearly, you would still be making a contribution to physics.

Use the same technique and model but aim at storing and retrieving an image...and you are NOT making a direct contribution to the understanding of physical phenomena. You would be contributing to... you guessed it, Machine Learnig.

Emphasis in "direct" in that last paragraph. If you want to argue that all our knoledge is connected or that our reality might be digital, that's a whole different discussion that you are a free to pursue.

Let's recapitulate. The fact that you can use methods and models initially developed for Physics to study problems in domains far away from it may be surprising and lead you to think there is some substance to the award. But, as you can infer now from the previous discussion on the Ising model, on one hand, that's a feature of Physics and its language, Mathematics. On the other hand, that fact leads to a, currently still a philosophical, question of what is the ultimate object of study of Physics.  Landauer's principle directly connecting Physics and information (erasure) opens the door to interesting speculations, as it makes information a "traditional" physical observable that can be measured in principle.

So, no, I don't think Hopfield, and specially not Hinton, deserve the Nobel prize in Physics.

Note added in proof: If the Nobel committee just wanted to "sell" us something I can understand. That's what I did in assigning labels to this post.

https://www.nobelprize.org/prizes/physics/2024/advanced-information/

Insomnia: van Aubel's Theorem

I woke up in the middle of the night and stumbled upon this post in mathstodon about a simple theorem in Euclidean geometry. So I thought it was a good time to dust off my Geogebra app.

Van Aubel's theorem states that if you start with a convex quadrilateral and construct a square on each side, externally to the quadrilateral, then the line segments connecting the centers of opposite squares will be equal in length and perpendicular to each other.

The following images provide a synthetic proof of this theorem. The line segments mentioned are colored in green and red.

The green and red circumference cross on point $O_1$, which is the center of the blue circumference. By construction, the blue circumference contains points $M_1$ and $K_1$. Hence the red and green segments are of equal length.

The purple line is the perpendiculat to the green line that passes through $P_1$. As can be seen, the purple line contains the red segment. Hence the green and red segments are perpendicular.

This concludes the proof of this theorem.