de Gennes enthuses about Chemistry and skewers Comte

Pierre-Gilles de Gennes (1932-2007) was arguably the founder of soft matter as a research field, as recognized by the Nobel Prize in Physics in 1991. After this de Gennes gave many lectures in French high schools, which were then published as a book, Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery. Previously, I mentioned the book with regard to whether condensed matter physics is too abstract.

 One of many fascinating sections of the book is a chapter entitled, The Imperialism of Mathematics. de Gennes sings the praises of chemistry, and rants about the weaknesses of the French system, laying the blame at the feet of his compatriot Auguste Comte (1798-1857). Comte was one of the first philosophers of modern science and a founder of sociology and of positivism.

Below I reproduce some of the relevant text. When reading it bear in mind that de Gennes was a theoretical physicist and did work that often involved quite abstract mathematics and concepts.

        THE "AUGUSTE COMTE" PREJUDICE

I now come to a prejudice typical of French culture, inherited from the positivism of Auguste Comte. This nineteenth-century philosopher achieved some degree of fame by inventing a classification system of the sciences. 

At the top of his hierarchy was mathematics; at the bottom was chemistry, which according to him "barely deserved the name of science"; in the middle were astronomy and physics. This classification dismissed out of hand geography and mineralogy, sciences which were declared concrete and descriptive, retaining only those that were theoretical, abstract, and general. The tone was set! It is ironic that this philosophical concept came from an individual who had once written in a letter "The only absolute truth is that everything is relative," and who claimed to be steeped quasi-religiously in factually observable laws, in other words, laws verifiable by experiments. 

The "Auguste Comte" prejudice corrupts to this day the teaching of the sciences, the scientific disciplines, and even the scientists themselves. It also contains the seed of contempt for manual labor, which has interfered for years by curbing every attempt at reform to revalue the manual trades and their apprenticeship... 

An example comes to mind, of some graduates of the Polytechnic School of Paris attending an advanced program at Orsay to learn solid-state physics. They would often show up convinced that they knew everything on the basis of calculations. 

... But the typical Polytechnic graduate I inherited at the time would remain stumped in front of his bare blackboard. One of them finally blurted out (I will never forget his comment): "But, sir, what Hamiltonian should I diagonalize?" He was trying to hang on to theoretical ideas which had no connection whatsoever with this practical problem. This kind of answer explains, in large part, the weakness of French industrial research.

Among all the catastrophes brought about by the positivist prejudice, none is worse than the widespread contempt for chemistry. I have already pointed out the importance of this discipline for our industrial future, the importance of chemists, these marvelously inventive sculptors of molecules, to whom the French teaching establishment does not do nearly enough justice. An undergraduate math major once told me about a teacher who, on opening day, announced: "I personally dislike chemistry, but I have to talk about it. So, I will start by giving you two hours of chemical nomenclature: what the name of an obscure and com- plex molecule is, and the like." At the conclusion of the two hours, the entire class was turned off chemistry for life!

When Lucien Monnerie, the director of studies, and I took over re- sponsibility for courses at the Institute of Physics and Chemistry, we had to wage a determined battle to overcome the antichemistry prejudice. Just before our arrival, the students had organized a strike: they all wanted to become physicists. Slowly, we climbed back up the slope with a series of measures: changing labels, opening up several new channels, turning the entire curriculum upside down, and launching a verbal propaganda campaign. It was rather easy for me to sound persuasive; being a theoretical physicist, nobody could accuse me of protecting my own turf. But it took us 10 years to restore the proper balance. 

To anyone who wants to form a more precise idea of chemistry, of the life of a typical chemical engineer, I would advise reading the magnificent collection of essays by Primo Levi, The Periodic Table. They recount real-life stories. They possess an authenticity and a vitality which give a universal impact to the account of an ordinary fact, the description of minute events. It is an excellent antidote to the poison spread by Auguste Comte's classification scheme.

Can emergent properties be explained?

An important question about emergent properties is whether they can be explained solely in terms of the properties of the components of the system. Here I explore the question from the point of view of Hempel's covering law of scientific explanation, discussed in my last post.

According to Hempel, a scientific explanation E of a specific phenomena P is a logical argument that starts with some premises, at least one of which is a scientific law L, and which logically implies P.

I now give a version of this that describes a microscopic scientific explanation of some emergent property.

Suppose that a macroscopic system S has property X. S is composed of many interacting microscopic components whose properties, including their interactions, have a finite enumeration x1, x2, x3,...xn. None of these properties is X. Hence, in the sense of novelty, X is an emergent property of S. Let l1, l2, l3,.., lm be a finite number of microscopic laws. Then X has a microscopic scientific explanation if it can be deduced from the x's and l's.

A possible problem with most microscopic "explanations" of emergent properties may be whether they at some point implicitly assume some "emergent" scientific law, such as spontaneous symmetry breaking, or the existence of X. Let me illustrate this possible problem with some examples.

Irreversibility. Microscopic laws are invariant under time-reversal. But macroscopic systems exhibit irreversible behaviour such as the mixing of two distinct fluids. This is encoded in the second law of thermodynamics. This problem of the "arrow of time" is nicely discussed by Tony Leggett in The Problems of Physics, in a chapter entitled "Skeletons in the Cupboard." An alternative perspective is that of Joel Lebowitz, who claims Boltzmann solved the problem.

Superconductivity. One could claim that BCS theory provides a microscopic explanation of superconductivity. We start with the properties of electrons, ions, Coulomb's law, quantum mechanics, and statistical mechanics. These properties and microscopic laws can be used to show that there is an effective attractive interaction between electrons. One then considers the BCS variational wavefunction and calculates the properties of the macroscopic system. They are consistent with experimental observations of superconductivity. It is explained!

However, there are several problems on the way, which all in some sense involve assuming that superconductivity does occur. First, investigating the variational wave function only shows that the superconducting state has lower energy than the normal metallic state. This does not prove it is the true ground state. In fact, in one dimension it is not.

But potentially more fatal to the claimed microscopic explanation is that it assumes that spontaneous symmetry breaking is allowed, including (in some subtle sense that people still argue about) the breaking of the gauge symmetry of electromagnetism. One of the major points that Phil Anderson was trying to make in More is Different is that spontaneous symmetry breaking is a law of nature that should be viewed as of similar status to microscopic laws such as Schrodinger's equation. 

Mean-field theory of antiferromagnetism. One might claim that one can start with a classical Heisenberg or Ising model, and classical statistical mechanics, crank the mathematical handle and get antiferromagnetic. If one does mean-field theory, then one is not really doing statistical mechanics as one is considering a weird ensemble and a Hamiltonian that is no longer microscopic. Suppose instead one does the exact solution of the Ising model. That can give the magnetic state and all the critical exponents. But, it is not clear to me that when one takes the thermodynamic limit, one assumes that the broken symmetry state is allowed. Similar questions arise for me if one does a computer simulation on large lattices and uses clever finite-size scaling techniques to deduce physical properties of the emergent state. Does the assumption of the validity of these techniques amount to some extra (macroscopic) law of nature?  

I wonder whether some of these issues would be clarified (or just muddied) by considering the Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics by David Ruelle. In particular, does he make clear how an equilibrium broken symmetry magnetic state is fundamentally different from the microscopic equilibrium state associated with a finite number of spins.

I welcome ideas on how to clarify these issues.

What is a scientific explanation?

An important issue concerning emergent phenomena is whether part of their definition should be that they "cannot be explained/predicted" solely in terms of the properties of the components of the system.  As I have discussed before, there are several alternatives such as difficult to explain, extremely difficult to explain, impossible to explain, and possible to explain in principle, but not in practice...

To further consider this issue, it is helpful to back up and consider the general question, "What is a scientific explanation of a specific natural phenomena?" This has received a lot of attention over the past century from philosophers of science. A nice accessible introduction is found in Philosophy of Science: A Very Short Introduction by Samir Okasha. In chapter 3, he discusses at length the Covering Law model of explanation, developed by Carl Hempel.

Here are the basic elements of the model. Hempel observed that "scientific explanations typically have the logical structure of an argument, i.e., a set of premises followed by a conclusion." More specifically, 

1. The argument should be a deductive one. The conclusion is the phenomena to be explained.

2. All the premises must be true.

3. One of the premises should be a scientific law.

Here is an example:

Premise a. Astronomical data about planetary motion.

Premise b. Kepler's laws of planetary motion can describe the data.

Premise c. Newton's theory of gravity.

Conclusion. The motion of planets can be described by Newton's theory of gravity.

Hempel considered that explanation and prediction were two sides of the same coin. 

Okasha also discusses some weaknesses of the covering law, namely that it is too broad allowing "explanations" that are not really scientific. Specifically, there is the problem of symmetry and the problem of irrelevance.

In the next post, I will explore how this model for scientific explanation might help frame discussions about whether emergent phenomena can be predicted.

A model for light-induced spin-state trapping in spin-crossover materials

 An important challenge required to understand the physical properties of materials that are chemically and structurally complex is to ascertain which microscopic details are important. A related question is at what scale (length, number of atoms, energy) models should be developed.

A specific example is understanding the magnetic properties and state transitions of spin-crossover materials. This is difficult for equilibrium properties, let alone for non-equilibrium properties such as Light-Induced Excited Spin-State Trapping (LIESST). At low temperatures irradiation with light can induce a transition from the equilibrium low-spin state to a long-lived high-spin state, which is only an equilibrium state at higher temperatures. (LIESST gets a lot of attention because of the potential to make optical memories for information storage).

Some of my UQ colleagues recently published a nice paper that elucidates some of the key physics with the proposal and analysis of a (relatively simple) model that captures many details of the experimental data.

Toward High-Temperature Light-Induced Spin-State Trapping in Spin-Crossover Materials: The Interplay of Collective and Molecular Effects

M. Nadeem, Jace Cruddas, Gian Ruzzi, and Benjamin J. Powell

Panel on mental health

 In the School of Mathematics and Physics at UQ there is an Early- and Mid-Career Academic group who organise activities to support one another. Today they organised a panel discussion on "Mental Health, Wellness and Resilience".

I commend them for their initiative. Before covid, they organised a single forum which I spoke at and thought was particularly good.

I am one of the panelists. As someone who has struggled with mental health for four decades now, here are a three of the points I want to make.

Practise the basics: eat and drink healthy, sleep, rest, exercise, control screen time, and connect to community.

Get professional help, sooner than later. Be open to medication, counselling, and expertise. 

Live according to your own personal values, rather than those that your boss or university management may want you to have.

One of my fellow panelists, Marissa Edwards, brought to our attention this recent article in The Conversation, Where has the joy of working in Australian universities gone? It is pretty disturbing, but unfortunately not surprising.

The financial state of Australian universities

On Saturday the Australian Financial Review had a good, but disturbing, article, Uni chiefs reap million-dollar salaries, record surpluses as jobs cut. It is behind a paywall, but a hard copy photo is below.

Of particular note is how the Vice Chancellors (Presidents) of regional universities (which are like community colleges in rural parts of the USA), which most readers outside of Australia will never even have heard of, are given salaries around one million AUD. Given the relatively low cost of living in their locations, those salaries are even more spectacular.

An issue that is not discussed in the article is how at each university there is a whole cabal of senior managers, not just the VC, who are on exorbitant salaries and packages. For example, if you look at this organisational chart for UQ, I count four deputy VCs and 8 pro-VCs. In addition, there are more than ten Executive Deans and Directors of Institutes. That means there are probably about twenty people on packages in the range of $500K to $1M. None of this is public information, as far as I am aware, even though these are public institutions. For comparison, the Prime Minister of Australia receives a salary of around $600K.

One VC whose salary is not listed in the table is Brian Schmidt from ANU (Australian National University). This is because, last year he negotiated his salary down to $484,000, about half that of the other VCs. Refreshing!

Emergence matters (in a nutshell)

Emergence is one of the most important concepts in the sciences: from physics to biology to sociology. Most of the big questions in science involve emergence. Yet there is no consensus about what emergence is, how to define it, or why it matters. This is my attempt to clarify some of the important issues and questions. For reasons of brevity, I give no references and only a few examples. They can come later. Here I am trying to take a path that is intermediate between the precision of philosophers and the looseness of condensed matter physicists' discussion of emergence. My goals are clarity and brevity.

Characteristics of emergent phenomena

Consider a system that is composed of many interacting parts. If the properties of the system are compared with the properties of the individual parts, a property of the whole system is an emergent property if it has the following characteristics.

1. Novelty 

An emergent property of the system is a property that is not present in the individual parts of the system.

2. Modification of parts 

An emergent property of the system is associated with a modification of the properties of and the relationships between the parts of the system. 

3. Universality

An emergent property is universal in the sense that it is independent of many of the details of the parts. As a consequence, there are many systems that can have the emergent property.

4. Irreducibility

An emergent property cannot be reduced to properties of the parts.

5. Limited predictability

An emergent property is difficult to predict solely from knowledge of the properties of the parts and how they interact with one another.

Here are a few issues to consider about the five characteristics above. 

First, “emergent property” could possibly be replaced with emergent phenomenon, object, or state.

Second, for each of the five characteristics is it necessary and/or sufficient for the system property to be emergent?

Third, one of the most contested characteristics concerns predictability. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity, which provided a posteriori, rather than a priori, understanding. A keyword in the statement above is “solely”.

Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties. The property of the system is simply the sum of the properties of the parts.

Scales and hierarchies

Central to emergence is the idea of different scales. Emergent properties only occur when scales become larger. Scales that are simply defined, and might be called extrinsic, are the number of parts, length scale, and time scale. A more subtle scale, which might be called intrinsic, is a scale associated with the emergent property. This emergent scale is intermediate between that of the parts and that of the whole system.

Emergent scales lead naturally to hierarchies, such as those associated with different scientific disciplines, as shown below. Hierarchies also occur within individual disciplines.

At each level there are distinct phenomena, concepts, theories, and scientific methods.

Another important scale is that of complexity. Generally, as one goes up the hierarchy one says that the level of complexity increases. Giving a precise version of such statements is not simple.

Complexity

Simple rules can lead to complex behaviour. This is nicely illustrated by cellular automata. It is also seen in other systems with emergent properties. For example, the laws describing the properties of electrons and ions in a crystal or a large molecule are quite simple (Schrodinger’s equation plus Coulomb’s law). Yet from these simple rules, complex phenomena emerge: all of chemistry and condensed matter physics!

There is no agreed universal measure for the complexity of a system or with many components. One possibility is the Kolmogorov measure. Using such measures to elucidate emergence, such as how complexity changes with other scales, is an important challenge.

Other issues

There are a host of other issues and topics that enter discussions about emergence. Some of these are of a more philosophical nature. Here I just list them: robustness, quality vs. quantity, objective vs. subjective, universality vs. particularity, ontology vs. epistemology, discontinuities, incommensurability, theory reduction, asymptotic singularities, top-down causation, supervenience, differentiation and integration (not calculus) of system parts, reductionism, foundationalism, fundamentalism, strong versus weak emergence, and criteria for theory acceptance.

Discussion of some of these issues can be quite abstract but to make the discussion above more precise they may need to be considered. 

Emergence is relevant to practical matters such as scientific strategy, priorities, allocation of resources, and our dispositions as scientists. Too often views on these issues are implicit and not reflected upon. 

The practical matter of scientific strategy

When studying a system, the first choice that must be made is what scale or scales to focus on. For example, in materials science, the options range from the atomic scale to the macroscopic. This choice determines the tools and methods, both experimental and theoretical, that can be used to study the system. In different words, the scientist is making a choice of ontology: the object they choose to study. This then determines epistemology: the concepts, theories, and organising principles a scientist may use or hope to discover. Effective theories and toy models enter here. 

When systems have been studied by a range of methods and at a range of scales, a challenge is the synthesis of the results of these studies. Value-laden judgements are made about the priority, importance, and validity of such attempts at synthesis. Often synthesis is relegated to a few sentences in the introductions and conclusions of papers.

For known systems and emergent properties, there is the possibility of creating new methods and probes to investigate them at appropriate scales.

New systems can be created and investigated in the hope of discovering new emergent properties (e.g., new states of matter) or more modestly, that manifest an emergent property that is more amenable to scientific study or technological application.

As emergent properties involve multiple scales they are often of interest to and amenable to study by more than one scientific discipline. This creates opportunities and challenges for interdisciplinary collaboration.

Individual scientists must and do make decisions about the relative priority of the different strategies outlined above. Research groups, departments, institutions, professional societies, and funding agencies must and do also make decisions about such priorities. The decision outcomes are also emergent properties of a system with multiple scales from that of the individual scientist to global politics. I claim that too often these weighty decisions are made implicitly, rather than explicitly following debate and deliberation.

The disposition of the scientist

All scientists are human. In our professional life, we have hopes, aspirations, values, fears, attitudes, expectations, and prejudices. These are shaped by multiple influences from the personal to the cultural to the institutional. We should reflect on the past century of our study of emergent systems from physics to biology to sociology. If we honestly evaluate our successes and failures I think this may lead us to have certain dispositions that are interrelated.

Humility. There is so much we do not understand. Furthermore, we fail abjectly at predicting emergent properties. This is not surprising. Unpredictability is one of the characteristics of emergent properties. There is a hubris associated with grand initiatives such as “the theory of everything”, the Human Genome Project, “materials by design”, and macroeconomic modelling. 

Expect surprises. There are many exciting discoveries waiting. They will be found by curiosity and serendipity.

Wonder. Emergent phenomena are incredibly rich and beautiful to behold, from physics to biology to sociology. Furthermore, the past century has seen amazing levels of understanding. But this is a “big picture” and “coarse-grained” understanding, not the description that the reductionists lust for and claim possible. 

Realistic expectations. Given the considerations above I think we should have modest expectations of the levels of understanding possible, and what research programs, from that of individual scientists to billion-dollar initiatives, can achieve. We need to stop the hype. Modest expectations are particularly appropriate with respect to our ability to control emergent properties.

The holy grail

“The philosophers have only interpreted the world, in various ways. The point, however, is to change it.”

Karl Marx

Understanding complex systems with emergent properties is an ambitious scientific challenge. This enterprise has intrinsic intellectual merits. But a whole other dimension and challenge is to use this understanding to modify, manipulate, and control the properties of systems with emergent properties. This enticing prospect appeals to technologists, activists, and governments. Such promises feature prominently in grant applications, press releases, and reports from funding agencies. Diverse examples of this control goal include chemical modification of known superconductors to produce room-temperature superconductivity, drug design, social activism, the leadership of business corporations, and governments attempting to manage the economy. 

However, we should honestly reflect on decades of “scientifically informed” and “evidence-based” initiatives in materials science, medicine, poverty alleviation, government economic policy, business management, and political activism. Unfortunately, the fruit from these initiatives is disappointing, particularly compared to what has often been promised.

My goal is not to promote despair but rather to prevent it.  With more realistic expectations, based on reality rather than fantasy, we are more likely to make significant progress in finding ways to make some progress (albeit modest but worthwhile) in learning how to manipulate these complex systems.

This post contains many claims that require discussion, refinement or abandonment. I welcome suggestions on how to improve these ideas.