Statistical mechanics in just one equation

 This semester, I am giving four lectures in a third-year undergraduate course on statistical mechanics. Last year, I gave a guest lecture on the Ising model.

The first thing I want to emphasise is that the whole course is built around just one equation.

exp(−F(T, V)/kT) = ∑_s exp(−E_s/kT) ≡ Z(T, V)

This connects macroscopic thermodynamic properties (contained in the Helmholtz free energy F(T,V)) to microscopic properties (the energies E_s of all possible states s of the system).

[Note that from equilibrium thermodynamics, partial derivatives of F(T,V) give the entropy (and specific heat capacity) and the pressure (equation of state)].

I think that we are so used to this equation that we may miss just how amazing and profound it is.

First, the equation is incredibly simple.

Second, it is universal. It applies to any system in thermodynamic equilibrium regardless of its chemical or physical composition.

Third, in the context of the theory of emergent phenomena, it is exceptional because it provides a robust, tested way to connect the microscopic to the macroscopic. Biology, neuroscience, economics, sociology, and computer science have nothing like it.

Fourth, although the above three points are impressive, the basis of its validity remains an outstanding problem (a mystery?). One can "derive" it and "justify" it by drawing on assumptions such as the fundamental postulate ("in an isolated system all accessible microstates are equally probable"), the principle of maximum entropy, and the validity of equilibrium thermodynamics. But why are they true?

Although the equation is simple, implementing it, particularly for systems of interacting particles, is challenging. This challenge can be broken into five steps. One can get stuck on any one of the steps. People build whole careers on them.

1. For a system of interest, propose microscopic states of each particle and a Hamiltonian for the whole system.

2. Enumerate all possible microscopic states of the system.

3. Evaluate the energy of each of these microstates.

4. Perform the sum over all states in the partition function Z.

5. Take the thermodynamic limit where the system size becomes infinite.

Scandals in Australian universities

In Australia, scandals about the management of public universities continue to be covered in the media. A recent one is the use of billions of dollars to pay consulting firms to tell management which staff to sack and courses to cut because they are not making a profit.

Below is a recent episode of an ABC (Australian equivalent of BBC or PBS in USA) show on the topic, Chaos on Campus.

I tend to avoid engaging too much with media lamenting the state of unversities as I find it too disturbing. However, I was asked to reference the show in something I was asked to write and so felt I should watch it. It was painful.

This is definitely a scandal. However, it got me reflecting on something that I think gets virtually no media coverage and when I talk to people outside the university, they are pretty surprised and shocked. Anecdotal evidence from my colleagues is that attendance at lectures is now typically around 10-30 per cent of enrolment. Even before COVID-19, lectures at UQ were all recorded. Faculty have no choice. But only a few per cent of students watch the videos. This is quite demoralising for faculty.

What does this low level of student engagement mean for learning outcomes?

What is happening elsewhere? 

Here are some links from Google AI. 

I did not find them that insightful.

One link is an article from The Guardian in Australia from last year. It highlights how moving things to online and lowering standards is driven by financial incentives. This ties in with the scandals in the video. The values of Australian universities are money, marketing, management, and metrics.

What is your own experience with the level of disengagement? How do you think this is affecting student learning? How are you and your colleagues adapting? Are academic standards being lowered? Any suggestions on ways forward?

Why is the state of universities such an emotional issue for me?

It all about values!

Universities have changed dramatically over the course of my lifetime. Australian universities are receiving increasing media attention due to failures in management and governance. But there is a lot more to the story, particularly at the grassroots level, of the everyday experience of students and faculty. It is all about the four M's: management, marketing, metrics, and money. Learning, understanding, and discovering things for their own sake is alien and marginalised. I have stopped writing posts about this. So why come back to it?

I am often struck how emotional this issue is for me and how hard it is to sometimes talk about it, particularly with those with a different view from me. Writing blog posts (e.g. this one) about it has been a somewhat constructive outlet, rather than exploding in anger at an overpaid and unqualified "manager" or one of their many multiplying minions.

A few weeks ago, I listened to three public lectures by the Australian historian Peter Harrison. [He is my former UQ colleague. We are now both Emeritus. I benefited from excellent seminars he ran at UQ, some of which I blogged about].

The lectures helped me understand what has happened to universities and also why it is a sensitive subject for me. Briefly, it is all about values and virtues.

The lectures are nicely summarised by Peter in the short article, 

How our universities became disenchanted: Secularisation, bureaucracy and the erosion of value

Reading the article rather than this blog post is recommended. I won't try and summarise it, but rather highlight a few points and then make some peripheral commentary.

I agree with Peter's descriptions of the problems we see on the surface (bureaucracy, metrics, and management features significantly). His lectures are a much deeper analysis of underlying cultural changes and shifting worldviews that have occurred over centuries, leading universities to evolve into their current mangled form.

A few things to clarify to avoid potential misunderstanding of Peter's arguments.

Secularisation is defined broadly. It does not just refer to the decline in the public influence of Christianity in the Western world. It is also about Greek philosophy, particularly Aristotle, and the associated emphasis on virtues and transcendence. Peter states:

"The intrinsic motivations of teachers, researchers and scholars can be understood in terms of virtues or duties. According to virtue ethics, the “good” of an activity is related to the way it leads to a cultivation and expression of particular virtues. These, in turn, are related to a particular conception of natural human ends or goals. (Aristotle’s understanding of human nature, which informs virtue ethics, proposes that human beings are naturally oriented towards knowledge, and that they are fulfilled as persons to the extent that they pursue those goals and develop the requisite intellectual virtues.)"

The virtue ethics of Aristotle [and Alisdair MacIntyre] conflicts with competing ethical visions, including duty-oriented (deontological) ethics, consequentialist ethics, and particularly utilitarianism. This led to a shift away from intrinsic goods to what things are "good for", i.e., what practical outcomes they produce. For example, is scientific research "good" and have "value" because it cultivates curiousity, awe, and wonder, or because it will lead to technology that will stimulate economic growth?

Peter draws significantly on Max Weber's ideas about secularisation, institutions, and authority. Weber argued that a natural consequence of secularisation was disenchantment (the loss of magic in the world). This is not simply "people believe in science rather than magic". Disenchantment is a loss of a sense of awe, wonder, and mystery.

Now, a few peripheral responses to the lectures.

Is secularisation the dominant force that has created these problems for universities? In question time, Peter was asked whether capitalism was more important. i.e., universities are treated as businesses and students as customers? He agreed that capitalism is a factor but also pointed out how Weber emphasised that capitalism was connected to the secularising effects of the Protestant Reformation.

 I think that two other factors to consider are egalitarianism and opportunism. These flow from universities being "victims" of their own success. Similar issues may also be relevant to private schools, hospitals, and charities. They have often been founded by people of "charisma" [in the sense used by Weber] motivated by virtue ethics. Founders were not concerned with power, status, or money. What they were doing had intrinsic value to them and was "virtuous". In the early stages, these institutions attracted people with similar ideals. The associated energy, creativity, and common vision led to "success." Students learnt things, patients got healed, and poverty was alleviated. But, this success attracted attention and  the institution then had power, money, status, and influence.

The opportunists then move in. They are attracted to the potential to share in the power, money, status, and influence. The institution then takes on a life of its own, and the ideals and virtue ethics of the founders are squeezed out. In some sense, opportunism might be argued to be a consequence of secularisation. 

[Aside: two old posts considered a similar evolution, motivated by a classic article about the development of businesses.]

One indicator of the "success" of universities is how their graduates join the elite and hold significant influence in society. [Aside: ignoring the problem of distinguishing correlation and causality. Do universities actually train students well or just select those who will succeed anyway?]  Before (around) 1960, (mostly) only the children of the elite got to attend university. Demands arose that more people should have access to this privilege. This led to "massification" and an explosion in the number of students, courses, and institutions. This continues today, globally. Associated with this was more bureaucracy. Furthermore, the "iron triangle" of cost, access, and quality presents a challenge for this egalitarianism. If access increases, so does cost and quality decreases, unless you spend even more. It is wonderful that universities have become more diverse and accessible. On the other hand, I fear that for every underprivileged student admitted whose mind is expanded and life enriched, many more rich, lazy, and entitled students suck the life out of the system.

Metrics are pseudo-rational

Peter rightly discussed how the proliferation of the use of metrics to measure value is problematic, and reflects the "rationalisation" associated with bureaucracy (described by Weber). Even if one embraces the idea that "rational" and "objective" assessment is desirable, my observation is that in practice, metrics are invariably used in an irrational way. For example, managers look at the impact factor of journals, but are blissfully oblivious to the fact that the citation distribution for any journal is so broad and with a long tail that the mean number is meaningless. The underlying problem is that too many of the people doing assessments suffer from some mixture of busyness, intellectual laziness, and arrogance. Too many managers are power hungry and want to make the decisions themselves, and don't trust faculty who actually may understand the intellectual merits and weaknesses of the work being assessed.

The problems are just as great for the sciences as the humanities

On the surface, the humanities are doing worse than the sciences. For example, if you look at declining student numbers, threats of job cuts, political criticism, and status within the university. This is because science is associated with technology which is associated with jobs and economic growth. However, if you look at pure science that is driven by curiousity, awe, and wonder, then one should be concerned. There is an aversion to attacking difficult and risky problems, particularly those that require long-term investment or have been around for a while. The emphasis is on low-lying fruit and the latest fashion. Almost all physics and chemistry research is framed in terms of potential applications, not fundamental understanding. Sometimes I feel some of my colleagues are doing engineering not physics. In a similar vein, biochemists frame research in terms of biomedical applications, not the beauty and wonders of how biological systems work. 

Are universities destined for bureaucratic self-destruction?

Provocatively, Peter considered the potential implications of the arguments of historian and anthropologist Joseph Tainter concerning the collapse of complex societies. On the technical side, this reminded me of a famous result in ecology by Robert May, that as the complexity of a system (the number of components and interactions) increases, it can become unstable.

I don't think universities as institutions will collapse. They are too integrated into the fabric of modern capitalism. What may collapse is the production of well-educated (in the Renaissance sense) graduates and research that is beautiful, original, and awe-inspiring. This leads naturally into the following question.

Is the age of great discoveries over?

Peter briefly raised this issue. On the one hand, we are victims of our own success. It is amazing how much we now know and understand. Hence, it is harder to discover truly new and amazing things. On the other hand, because of emergence we should expect surprises.

There is hope on the margins

Peter did not just lament the current situation but made some concrete suggestions for addressing the problems, even though we are trapped in Weber's "iron cage" of bureaucracy.

• Re-balancing the structures of authority
• Finding a place for values discourse in the universities
• Develop ways of resolving differences with a sense of the rationality of Alisdair MacIntyre in mind

On the first, I note the encouraging work of the ANU Governance Project.

Peter also encouraged people to work on the margins. I also think that this is where the most significant scholarship and stimulus for reform will happen. A nice example is the story that Malcolm Gladwell tells in a podcast episode, The Obscure Virus Club.

Undergraduates need to learn about the Ising model

A typical undergraduate course on statistical mechanics is arguably misleading because (unintentionally) it does not tell students several important things (related to one another).

Statistical mechanics is not just about how to calculate thermodynamic properties of a collection of non-interacting particles.

A hundred years ago, many physicists did not believe that statistical mechanics could describe phase transitions. Arguably, this lingering doubt only ended fifty years ago with Wilson's development of renormalisation group theory.

It is about emergence: how microscopic properties are related to macroscopic properties.

Leo Kadanoff commented, "Starting around 1925, a change occurred: With the work of Ising, statistical mechanics began to be used to describe the behaviour of many particles at once."

When I came to UQ 25 years ago, I taught PHYS3020 Statistical Mechanics a couple of times. To my shame, I never discussed the Ising model. There is a nice section on it in the course textbook, Thermal Physics: An Introduction, by Daniel Schroeder. I guess I did not think there was time to "fit it in" and back then, I did not appreciate how important the Ising model is. This was a mistake.

Things have changed for the better due to my colleagues Peter Jacobson and Karen Kheruntsyan. They now include one lecture on the model, and students complete a computational assignment in which they write a Monte Carlo code to simulate the model.

This year, I am giving the lecture on the model. Here are my slides  and what I will write on the whiteboard or document viewer in the lecture.

Remembering the student protestors who died 36 years ago

Memorial plaque in the Great Court of the University of Queensland today.

Who should get to attend elite universities in the USA?

Equitable access to good education is a desirable goal. Yet it rarely happens and debate about how to achieve it can be diluted by focusing on access to elite institutions and on "culture war" rhetoric.

This week The Economist had a leader (editorial) about admission policies for universities in the USA. Below I reproduce some of the leader, highlighting some points I found poignant.

A diversity of backgrounds in elite institutions is a desirable goal. In pursuing it, though, how much violence should be done to other liberal principles—fairness, meritocracy, the treatment of people as individuals and not avatars for their group identities? At present, the size of racial preferences is large and hard to defend. The child of two college-educated Nigerian immigrants probably has more advantages in life than the child of an Asian taxi driver or a white child born into Appalachian poverty. Such backgrounds all add to diversity. But, under the current regime, the first is heavily more favoured than the others.

Racial preferences are not, however, the most galling thing about the ultra-selective universities that anoint America’s elite. ...A startling 43% of white students admitted to Harvard enjoy some kind of non-academic admissions preference: being an athlete, the child of an alumnus, or a member of the dean’s list of special applicants (such as the offspring of powerful people or big donors). 

A cynic could argue that racial balancing works as a virtue-signalling veneer atop a grotesquely unfair system. A study published in 2017 found that most of Harvard’s undergraduates hailed from families in the top 10% of the income distribution. Princeton had more students from the top 1% than the bottom 60%. When this is the case, it seems unfair that it is often minority students—not the trust-funders—who have their credentials questioned. University presidents and administrators who preen about all their diverse classes might look at how Britain—a country of kings, queens, knights and lords—has fostered a university system that is less riven with ancestral privilege.

...Legacy admissions should be ended. Colleges claiming that alumni donations would wither without them should look to Caltech, MIT and Johns Hopkins— ....[who all] ditched the practice..

In some ways, the question of who gets into a handful of elite universities is a distraction from the deeper causes of social immobility in America. Schooling in poorer neighbourhoods was dismal even before covid-19. The long school closures demanded by teachers’ unions wiped out two decades of progress in test scores for nine-year-olds, with hard-up, black and Hispanic children worst affected. Efforts to help the needy should start before birth and be sustained throughout childhood. Nothing the Supreme Court says about the consideration of race in college admissions will affect the more basic problem, that too few Americans from poorer families are sufficiently well-nurtured or well-taught to be ready to apply to college. However the court rules, that is a debate America needs to have.

On a related note, Malcolm Gladwell has a fascinating podcast episode, Outliers, Revisited  that brings out some of the issues including, how privileged parents game the system for their children.

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.

The very human side to universities

My wife and I started watching the series The Chair, a comedy about an English department in an affluent liberal arts university in the Northeastern USA. We thought the first episode was a bit too soapy and stopped watching. But then, I read an article claiming that The Chair Is Netflix’s Best Drama in Years: "The near-perfect show elegantly skewers the subject of free speech on campus." So, we kept watching and were glad we did. But, I think it is really about much more than "free speech".

What I appreciate the most is that it brings out just how human (fallible, creative, caring, contradictory, selfish, egotistical, ridiculous, ...) all the players in the university are: students, faculty, administrators, families, ... There is much to laugh at, to groan about, and to celebrate. And, this is why we need the humanities.

For me, the best scene is the disciplinary hearing in the final episode. The embattled English department Chair says:

“Why should [students] trust us? The world is burning and we’re sitting up here worried about our endowment? Our latest ranking on U.S. News & World Report?”

She then asks the Dean, "when did you last teach a class?" [I think all senior managers should be required to do some teaching.]

Nancy Wang Yuen has a nice article in the LA Times, I’m an Asian American woman in academia. Here’s what ‘The Chair’ gets right

One thing I think the series got badly wrong was how engaged the students were. They came to class, had done the required reading, asked questions, and were not on their phones! Oh, to teach a class in Hollywood!

If you have watched the series, what did you think?

Sweet demonstrations of phase transitions

This week my wife and I did some science experiments with kids, aged about 8-12, at a holiday kids club organised by our church. The first day we did rockets, using the old standbys of baking soda rockets and mentos and coke.

On the second day, we did the science of chocolate. Ten years ago (!) we had done this based on some demonstrations developed at Harvard, described in this paper The Science of Chocolate: Interactive Activities on Phase Transitions, Emulsification, and Nucleation. 

Teaching kids about phase transitions with ice and steam is not quite as exciting or memorable as them melting chocolate in their mouths. An important scientific idea is:

Physical properties of matter (such as melting temperature) change with differences in chemical composition.

This is illustrated by the different melting temperatures of white, milk, and dark chocolate.

We also tried to mix water and oil, with and without the presence of detergent. This illustrates ideas about emulsification, including hydrophobic interactions. This is relevant to the production of nice smooth and uniform chocolate because the cocoa powder can only dissolve in the cocoa butter when an emulsifier is present.

Discussing chocolate is also an opportunity to discuss Milton Hershey (USA) and the Cadbury family (UK). They were not only philanthropists but were proactive in taking care of employees and their families, e.g. constructing schools, parks, and affordable housing. Richard and George Cadbury developed the garden village of Bournville; now a major suburb of Birmingham. I particularly like this sentence in the Wikipedia entry on George Cadbury, showing how he was far ahead of his time.

In 1901, disgusted by the imperialistic policy of the Balfour government and opposed to the Boer War, Cadbury bought the Daily News and used the paper to campaign for old age pensions and against the war and sweatshop labour.^[4]

Other scientific articles of interest include the following. The first two discuss how there are six different polymorphs (crystal structures) of chocolate. The competition between these states comes into play with tempering, snapping, shine, and smoothness. [Aside: In general, calculating the relative energies of different polymorphs of molecular materials is a major scientific challenge.]

Chocolate: A Marvelous Natural Product of Chemistry, Ginger Tannenbaum

Using Differential Scanning Calorimetry To Explore the Phase Behavior of Chocolate Michael J. Smith

The kitchen as a physics classroom Amy C Rowat, Naveen N Sinha, Pia M Sörensen, Otger Campàs, Pere Castells, Daniel Rosenberg, Michael P Brenner and David A Weitz

Condensed matter physics is not axiomatic

 When I was an undergraduate I loved taking courses in pure mathematics and physics. I never took the "Solid State Physics" course because the person who taught it was a hopeless teacher. In my honours year (final year) I wrote a thesis on "Gravitational Lenses" that involved proving some theorems in General Relativity. I wanted to do a PhD in mathematical physics, which is why I chose to take an offer from Princeton rather than Cornell. Nevertheless, I am very glad I ended up doing condensed matter.

I only just realised that there is a basic and fundamental thing about condensed matter that distinguishes it from all the physics courses I took and loved as an undergraduate. In simple and loose terms, CMP is not axiomatic. I don't meet this in a rigorous mathematical sense, but rather the following. Consider classical mechanics, thermodynamics, statistical mechanics, electromagnetism, special relativity, general relativity, and quantum mechanics. For all of them, particularly at the undergraduate level, you can write down just a few equations  (or laws) and everything else follows. It can almost become an exercise in applied mathematics. At least that is how I viewed it. This is why undergraduate physics can be quite easy for nerds who are good at calculus and linear algebra. 

On the positive side, this "axiomatic" character to these physics subjects is rather beautiful because of the simplicity of the fundamental laws/equation. Furthermore, in some cases, one can argue that one subject can be largely summarised in a single variational principle, such as the extrema of the action.

In contrast, CMP really does not have comparable "axioms" or laws. All it has are certain organising principles such as spontaneous symmetry breaking, emergence, quasi-particles, topological order, ...

Perhaps, I mean CMP is not reductionist or "fundamental", rather than not axiomatic. 

CMP is hard for undergraduates because it involves drawing together practically everything they have learnt: mechanics, electromagnetism, quantum, statistical mechanics, thermodynamics, .. 

This lack of an axiomatic character may be a second reason why CMP is hard for undergraduates, particularly for those like me who have found other physics subjects "easy".

What do you think?

 

The Classics matter

Some people might expect me to be enthused that the Australian government recently announced that the tuition costs for university degrees in the humanities and social sciences would increase and the costs of undergraduate degrees in mathematics and sciences has decreased. This is based on three unquestioned assumptions and values. First, university is a job-training program. Second, all these extra mathematics and science graduates will get employment in the area that they study. Third, there is no need to address the massive other problems that Australian universities are facing, further accentuated by covid-19.

The central purpose of a university education is to learn to think.

Why study the classics? Recently, I read the following letter to The Economist written by Robert Machado, a PhD student in classics at Cambridge.

As a teacher and researcher in classics, I care profoundly about the subject’s purpose (Johnson, May 2nd). Too many of my colleagues rely on the guff that it teaches grammatical rigour or fall back onto vague assertions about the origins of Western civilisation. Although it is good to have a knowledge of ancient societies, the study of classics or indeed any ancient peoples offers one important transferable skill. When studying any ancient civilisation, one quickly brushes up against the reality that 99.9% of the information one would like to have is already lost. This forces any student or researcher to reflect hard on what data can be used. We must carefully analyse and argue over every scrap, while avoiding the temptation to come to conclusions that the data do not justify. In an age where we are faced with a glut of data, knowing what they can or cannot be used to say is vital.

Rodney Stark was a well-established sociology professor at the University of Washington when he made the bold move to work on the history of early Christianity, making use of methods and concepts from sociology. In the Preface to his book, The Rise of Christianity, he notes

my effort to reconstruct the rise of Christianity has been a cherished hobby - a justification for reading books and articles that now fill an entire wall of my study. It would be impossible to express adequately how much pleasure I have gained from these authors. I am convinced that the students of antiquity are on average the most careful researchers and the most graceful writers in the world of scholarship. 

Parenthetically, I note that Stark's work and attitude provides a model of how to successfully break into a new field.

The 90% University

A helpful starting point for me when considering universities after the pandemic is the cover story of The Economist, from two weeks ago, The 90% Economy. They were reflecting on the world economy will change in the coming years, suggesting three key characteristics.

 1. the economy will be more fragile 
 2. there will be less innovation 
 3. there will be even greater inequality 

The reason that it is called the 90% economy is because in the next few years rather than growing a few percent each year it will decrease in size by about 10%. 
Now on one level that doesn't sound too bad, but the problem is that it is not a uniform decrease across every sector, company, and individual. The changes will be quite heterogeneous. Rather, there will be significant gaps, that because of the interconnectedness of everything there will be problems. 

Just like the economy going back to ``normal'' universities will continue to have students, continue to do teaching, continue to graduate people but things, won't be quite the same, in some quite significant ways. It is not just a matter of possible 10-20 percent budget cuts.

1. Universities will be more fragile

Less stability and predictability is particularly bad for universities. Key ingredients for universities to achieve their real purpose are time and stability. Significant research, teaching, and learning all require time to build up knowledge, explore different possibilities, make mistakes, and not be distracted by crises, whether personal, institutional, or societal. Economic uncertainty is just one of many dimensions to the forthcoming fragility.

2. There will be less innovation in universities

Research is all about innovation, discovering new things, and exploring new ideas.  Drawing on The Economist article. More virtual meetings, less international travel, and fewer face-to-face meetings mean less brainstorming. Less random meetings and informal interactions will mean fewer new ideas. There will also be less money available for discretionary funding for new initiatives and fewer startup funds for new faculty, even if hiring freezes end.
After any crisis, people are more cautious and more risk-averse. A problem before the pandemic was that science was increasingly being done in a very risk-averse manner. People, particularly those without tenure, focus on low-lying fruit, working on problems that they are pretty sure they can solve in a year or less. Even senior people can only get funding if they have a ``track record'' in an area. This means they will just keep doing the same thing and not move into new areas. 
In reviewing his scientific life, Tony Leggett recently made the following comments.

Indeed, when I look back on ... a 60-year career in physics, I think I have been fortunate in many ways. I have had a marvelous constellation of graduate students and postdocs, from all corners of the globe... But if I had to pick out one thing that made all the difference, particularly in the early stages, it would be the tolerant and relaxed environment that I experienced at Sussex when starting there in the late 1960s. When I recall this and then look around at the current environment for people at the postgraduate, postdoc or junior faculty level, I feel quite concerned ... I get the impression that many of them feel that there will be no hope of obtaining the kind of postdoctoral/faculty/tenured position .. unless they have not only published three or four papers but published them in high-impact journals... I fear that one almost ineluctable outcome is that there is a strong temptation to focus all one’s energy on problems that can be reasonably guaranteed to yield results within the relevant time frame, typically two or three years. And almost by definition, these are not the really worthwhile problems! ...  the best advice I can give to any younger colleagues who seek my opinion is deliberately to put aside some fraction (30%, 25%, even 20%) of their research time for problems that they not only are not sure they can solve within the two- or three-year deadline but are not even sure that they (or anyone) can solve at all.

A similar conclusion can be drawn from a brilliant podcast, The Obscure Virus Club, by Malcolm Gladwell.

3. There will be more inequality, both within universities and between universities

This is part of the social tragedy that the rich get richer and the poor get poorer, particularly during and after a crisis, such as a pandemic. The poor do not have the resources to adapt and survive. If you live in a slum you can't practice social distancing. If you don't have access to clean running water or disinfectant it is hard to practice personal hygiene.  If you lose your job you can't use your savings to go and get training for a new job. In contrast, if you are wealthy and have significant cash reserves you can wait things out, see your competitors fail, and snap up cheap investments. Similarly, with universities, it's hard for me to believe that institutions such as Harvard with massive endowments won't come out of the pandemic relatively stronger. Weak institutions will fold. Others will really struggle to survive and go through periods of stagnation.

There will also be inequality within institutions related to access, gender, and seniority. Because of the background of an economic downturn it will be harder for students from poorer backgrounds to afford tuition or access scholarships. Furthermore, poor job prospects will make the financial cost and risks of student loans not seem worthwhile. There will also be a push within universities to increase the number of adjunct faculty (i.e. people on short-term teaching contracts with no benefits). People with tenure who are well established will do fine because they also have a good strong social and professional networks. In a more online environment, it's harder to build those professional networks and so disparities may increase. The Economist article mentions a study that found the productivity of female economics faculty, as measured by the production of research papers, fell relatively to male ones, since the pandemic. That's arguably because women are more likely to have to take care of homeschooling and entertainment of bored children during the lockdown.

All this is a bit depressing. However, with a crisis, there are always opportunities. There will be plenty of opportunism (where people exploit a situation without regard to moral considerations and the impact on others). But, there will also be opportunities for the wealthy, powerful, and privileged to do good and facilitate much-needed changes in universities. For example, large philanthropies and wealthy universities can make long-term investments that others won't or can't. Well-established faculty can provide support/cover to junior faculty, students, and postdocs. In the longer term of decades, these will likely be the institutions and individuals at the forefront of what universities really should be about: thinking, writing, teaching, and learning, at the deepest level.

Universities after the pandemic

There is a growing discussion of what changes might result from the pandemic: changes in societies, in institutions, and to us as individuals.

What will happen to universities? Will they change for the better or for the worse?

First, I want to acknowledge that there's a lot of heterogeneity, due to the diversity of institutions and their different contexts. The effect of the pandemic on Harvard, on the University of Queensland, and on a small state university in Sri Lanka, could be vastly different.

Any change produces both challenges and opportunities. There are many immediate questions: which universities will survive financially? How many staff will be sacked?  To what extent will universities move to online learning, or to some hybrid? A few years from now will we be back to largely face-to-face teaching?

Although important, we should also ask be asking bigger questions.

An epidemic provides a mirror on society: its values, its strengths, and its weaknesses. This idea is emphasized by Frank Snowden, a historian at Yale University. Last year he published “Epidemics and Society: From the Black Death to the Present,” and there is an insightful interview with him in The New Yorker.
David Brooks in the New York Times also picks up on this idea.

Thus, it's worth thinking about how universities respond to the pandemic may tell us something about them. What do you think?

The Chronicle of Higher Education had an interesting series, How will the pandemic change higher education? (in the USA). They asked about a dozen different faculty, administrators, and analysts. It's worth looking at the article as they present a range of perspectives on a range of issues, some pessimistic and some optimistic. One scary suggestion is that the crisis will be used by managers as a pretext for various cost-savings, such as moving to more online learning and an even greater increase of adjunct faculty (i.e. in the USA this means faculty on short-term and part-time contracts and with few benefits). Will the humanities die or experience a resurgence? Will grades be abandoned? Will research become less esoteric? Will students' personal needs be better addressed? Will universities give up on risky expansion plans and expensive fancy buildings?

I would welcome responses to some of these articles.

There are questions about the mechanics of universities such as financial sustainability, modes of teaching, and virtual graduation ceremonies. These are important. However, these mechanics are really means to an end. One can do all the mechanics: recruiting, enrolling students, offering courses, assessment, and graduation, without actually achieving anything. Doing these things does not mean students actually get an education.

 I would like to see more discussion of big questions about what universities are actually for and how can they do those things better, not just in the next few years but also in the longer term. We need to keep coming back to what universities are all about: thinking! Teaching is about students learning how to think and the discipline of learning to think in the manner of certain disciplines. Learning to think like an economist, learning to think like a historian, or learning to think like a physicist or an engineer. Secondly, universities are about research. Again this means thinking, discovering new things, and synthesizing ideas.

What do you think might be significant changes that will occur in the coming years in your own context?

Question your intuitions and preconceptions

 My economist son often listens to the podcast, Conversations with Tyler Cohen. We recently listened to a conversation with Esther Duflo, who shared the 2019 Nobel Prize in Economics. Like most episodes it covers a wide range of territory, from development economics to Indian classical music to parenting. I highly recommend it.

Perhaps, the bit that was most striking for me was the following.

What advice do you give to your talented undergraduates that differs from the advice your colleagues would give them?  

I give almost all of them the advice to take some time off, in particular if they have any interest in development, which is generally the reason why they come to see me in the first place. But even if they don’t really, to spend a year or two in a developing country, working on a project. Not necessarily inner city. Any project spending time in the field.  

It’s only through this exposure that you can learn how wrong most of your intuitions are and preconceptions are. I can tell it to them till they are blue in the face to not let themselves be guided by what seems obvious to them. But until they’ve confronted what they think is obvious to something entirely different, then it’s not clear.

I think this relates to profound differences (cultural and economic and experiential) between rich countries and Majority World countries. Culture is what you assume is normal and unquestioned.

Thinking skills for scientists (and engineers)

I keep coming back to the basic claim that the key ingredient of education is learning to think in particular ways. [n.b. In science, I am not at all playing up theory over experiment. You have to learn to think about what experiment to do and how to think about your results.].

In the past year, several people brought to my attention that MIT recently reviewed their engineering curricula. It is interesting that a key element is to teach students 11 ways of thinking. The list is worth reading and contemplating.

I have two minor comments. Although I affirm this as an admirable goal. I think the list is incredibly ambitious (even for MIT students) both in scope and content. But, maybe that is a good thing.
What do you think?

One of the 11 ways is Systems Thinking

Predicting emergence of the whole by examining inter-related entities in context, in the face of complexity and ambiguity, for homogeneous systems and systems that integrate multiple technologies.

Again, I love it. But, some would even argue you cannot predict emergence...

Some basic ideas about teaching

Over the past few decades, I have taught a wide range of courses in diverse contexts. Perhaps I have been slow to learn how to be a better teacher. Since I began teaching things have changed dramatically. Our goals and the content of most curricula have changed little, and should not. However, advances in technology provide new opportunities but also challenges and potential distractions. The social context has changed significantly in terms of the expectations of both students and institutions.

Here are a few of the ideas that I think are important to keep in mind.  Some seem obvious, particularly in hindsight. On the other hand, practical implementations are a challenge. I think keeping the ideas in mind is also important for maintaining your sanity and motivation.
The ideas are listed in no particular order and many are interconnected.

The amount of learning that happens is correlated with the level of student engagement.
Engagement happens at many levels and in many ways: through attendance, listening carefully, taking notes, asking questions, reading texts, talking to classmates about content, working on problems, watching relevant videos, thinking about content, ...
Consequently, a good teacher explores strategies to increase student engagement. However, there is a limit to what you can do. This is why I despair of the situation in most beginning undergraduate classes in Australia. For example, in the last course that I taught there were about 100 students enrolled. Only about 30 actually showed up for class, and only about 20 used clickers in class to engage. Videos of the lectures are available (because of mandatory university policy), increasing the temptation of students to not attend. But most videos have viewed a handful of times. This is quite representative. It sadly contrasts to some different contexts I have taught where there is a very high level of student engagement.

The curriculum should be your servant not your master.
Textbooks get thicker and thicker with time. More and more content gets crammed into curricula. This increases the pressure to "cover material", even if students learn little. I recently had the opportunity to teach a whole course and took the liberty to reduce content and focus on depth of understanding. I think the outcomes were much better.

Accept and work with the hand of cards you that have been dealt.
We all have fantasies of teaching a class with students that are all gifted, well prepared, highly engaged, highly motivated, and appreciative. However, it never happens! We need to accept who they are, where they are at and adapt our expectations, strategies and academic level.

Flip, blend and mix the classroom.
On the one hand, there is a lot of hype about the value of "flipping the classroom",  online courses, and peer instruction. On the other hand, I am told (and I have my own anecdotal experience) that there is significant research that does show that a "blended" class [i.e. a combination of online and face-to-face] instruction is effective. I find that regular online quizzes and reflections do increase student engagement and give me helpful feedback about learning progress. But, expect some student resistance and complaints. If you reduce traditional lecturing a few students will complain that you aren't "teaching them" or that they are ``not getting their money's worth''!
Different students have different learning styles. Furthermore, today's students are more video oriented than text-oriented and have shorter attention spans. Hence, in a single class hour, there is value in a mixture of traditional lecture, short video clips, small group discussion, ...

Be mindful of the undercurrent of complex social and psychological dynamics in the classroom.
Students are human! They come to class with a lot of emotional and intellectual "baggage",  both good and bad: aspirations, gifts, expectations, insecurities, prejudices, excitement, preconceived ideas, fears, hopes, ...
Furthermore, they are not just individuals but a social unit. Your students have a relationship with you and with one another: positive, negative, ambivalent, or non-existent.
All this complex dynamics has the potential to enhance or to hinder learning. Unfortunately, much of it we have no control over. On the other hand, if we can discern some of the dynamics and respond appropriately it can enhance learning significantly.

Learning is enhanced through personal relationships.
Even extreme introverts are wired to be relational and yearn for meaningful relationships. They just want a few select relationships.

Accept that you will never make everyone happy.
It never ceases to amaze me how polarised student feedback and teaching evaluations are. You are the best/worst teacher they have ever had. This is the best/worse course they have taken. The course is too hard/easy... This is all for the same course and teacher! Don't take the feedback so personally.

What do you think?
Any other things that you think are important.

The mental health crisis among university students is going to get worse

For the past few months I have been travelling in North America and the UK, for a mixture of work and holiday. In a range of professional and social settings I have had conversations with different people associated with universities: faculty, students, parents, and NGOs. It is amazing (and disturbing) how many times one subject keeps coming come up: student mental health problems. It was never me who brought up the subject and I don't think any of the people who did bring it up knew that I am interested in the issue, partly because of my own struggles. Two important questions people have asked are:

Has the incidence of student mental health problems increased or is it just that reporting of problems has increased?

Is the situation likely to improve in the near future?

Unfortunately, I think the problems have substantially increased and that they unlikely to decrease in the near future. I hope I am wrong. But, I think that there are a multitude of inter-related social, economic, and political changes that form a toxic cocktail for students.

To illustrate the extent of the problem and some of the compounding issues it is worth reading these two articles, both of which almost have a (tragic) surreal feel.

Why are suburban super-students burning out in college? These Main Line therapists say anxiety is high – and all around us
Philadelphia Inquirer

Feeling Suicidal, Students Turned to Their College. They Were Told to Go Home
New York Times
[Comments are worth reading too]

What are the origins of the crisis?
I think it may be a combination of the factors below. In isolation I doubt one or two of them would create such a large problem, but when you put many together, life starts to get very difficult. To what extent you think some of them is a problem may also depend on what you believe is "normal" and "healthy". The factors are listed in random order. Some are inter-related.

A winner takes-all society.
Everyone wants to be a winner and a celebrity. But most people are not. At the crass level, this cultural shift is reflected in TV shows involving singing or cooking competitions. It is also reflected in increasing economic inequality,  where the wealth of the upper class (the one per cent) is increasing dramatically and the lower middle class is ballooning, including graduates with massive debts from student loans. The pressure to succeed is immense and the despair of "failure" is greater.

Social media.
Students are comparing themselves to their "friends" and struggling to project a perfect and successful life. Interpersonal conflict is escalated because social media is a flawed medium for civil and meaningful communication. Rather that talking to other students before or after class students are staring at their phones.

Frustration from or fear of unfulfilled expectations.
University marketing departments portray life on campus as a collection of beautiful young people sitting around on lawns on bright sunny days having meaningful conversations before they graduate to high-paying and fulfilling jobs. A student at an over-crowded state university soon discovers they are sitting in a lecture hall with hundreds of students and no one seems to care whether they are there or not. Although they were told their degree would be a launching pad for a "career", many discover it is actually hard to get any sort of job, let alone something related to their major. No wonder they are depressed!

Excessive screen time.
It is bad for your brain and addictive. You get overstimulated. For some there is addictive content such as on-line games and pornography. It cuts into time for personal relationships.

Breakdown of family life.
Parents are increasingly absent, whether literally, emotionally, or practically, while children are growing up. This decreases students sense of identity, stability, ability to navigate life, including form meaningful relationships, and resolve conflict.

Alcohol and drug abuse.
This may actually be decreasing. However, it is still rampant, and compounds all of the other problems. Furthermore, mental health problems and substance abuse become intertwined.

Sexual harassment and assault.
Reporting has certainly increased. Again, the prevalence of this problem compounds all of the issues above.

What do you think? Have the problems increased? If so, what are the causes?

Big changes in universities?

I was recently asked to give a talk to an NGO about how universities are changing.
There is no doubt that there are rapid changes, many for the worse, happening. For me the biggest change has been the rising influence of neoliberalism (free market ideology) in the values, goals, and decision making within universities. But that is another story...
In the past few weeks some relevant articles "came across my desk" [through my web browser...].

I would be particularly interested to hear readers comments on the first one.
My wife sent me this New York Times piece to read and I really despaired
The iGen Shift: Colleges Are Changing to Reach the Next Generation 
The newest students are transforming the way schools serve and educate them, including sending presidents and deans to Instagram and Twitter.

Why do I despair?
I believe a university education should largely be about two things. The first goal is explicit and the second is implicit.

The first and primary goal of university education is to help students to learn to think: to think about specific disciplines, and to think about anything. Deep and valuable thinking does not come easily. It takes time, concentration, perseverance, and freedom from distractions. It a student is constantly checking their phone or just skimming the first material that comes up on a Google search or in the Twitter (for twits!) feed for their course, it is highly unlikely they are going to do much deep thinking.

Second, a university education is about helping students "grow up":  to move towards adulthood, to learn to be responsible and independent, to create an identity that is more independent of their parents and their peers, to have a sense of direction and purpose, and a desire to be good citizens.
Unfortunately, too many students think "growing up" means getting really drunk and throwing up...
However, too many of the initiatives described in the article seem to be pandering to students (customers) and "hand holding" them through their university experience. For example, at some point in life students are going to have to learn to seek and find relevant information, regardless of whether it is nicely packaged in some cool app with great graphics and lots of "likes".

Oh, the Humanities! 
New data on college majors confirms an old trend. Technocracy is crushing the life out of humanism.
Ross Douhat (NYT op-ed columnist)

The third article is more controversial and political, and raises questions about whether one purported change is as big or significant as often claimed (particularly in the right-wing press)
The free speech panic: how the right concocted a crisis
Snowflake students have become the target of a new rightwing crusade. But exaggerated claims of censorship reveal a deeper anxiety at the core of modern conservatism.
William Davies (A Long Read in The Guardian)
For balance here is a counter-view that there is a problem
The Problem of Hyper-liberalism
John Gray (Times Literary Supplement)

Comments welcome.

Pushing back against the multi-versity

One of the many concerns I have about universities, particularly in Australia, is the trend to compartmentalisation, factionalisation, fragmentation, obscure over-specialisation, ...
Long ago visions of the UNIversity included unity of knowledge, collegiality, and combining breadth and depth, ...
This trend to the multi-versity manifests itself in diverse ways:
- the lack of appreciation for the value of a liberal arts education
- students who are reluctant to see the relevance of previous subjects and course they have studied to the one they are studying right now, and more broadly the value of other majors (e.g. maths to physics, physics to chemistry, chemistry to biochemistry, history to sociology, philosophy to everything, ....)
- departments that ruthlessly compete with one another for student enrolments
- a ridiculous diversity of undergraduate majors, minors, and degrees
- claims that all points of view are equally valid and should not be critiqued
- a lack of interest in big ideas, big questions, and big issues

In light of this I was fascinated to read about an initiative of the current President of Princeton, Christopher Eisgruber. The Pre-Read has now been running for six years. Before they arrive on campus all Freshman are sent a copy of the same academic book to read and discuss.
In a recent short article, Eisberger discusses the criteria he uses for selecting the book each year.

 The Pre-read’s author speaks to the incoming class at the Freshman Assembly during Orientation week. The book also forms the basis of my Opening Exercises remarks, and I lead Pre-read seminars in the residential colleges during the fall semester.

His two primary goals are to "introduce students to Princeton's vibrant intellectual culture" and "to encourage students to reflect on the values that should guide their Princeton educations and their lives after graduation''.

There are many things I like about the initiative. One is that it helps encourage civil, robust, and intellectually rigorous debate among the students.
Another positive is that the university president himself interacts with the undergrads about the book. This not only has benefits for the students but also for the President himself (and consequently the whole university) because he is exposed first hand to "coal face". I emphasised this point earlier in a post All University Managers should have to teach.
[Aside. I am very happy that the UQ Provost is currently helping teach an undergrad physics class.].

There is many things that Princeton does that other universities cannot do due to lack of resources. However, this is actually an initiative that almost any university could do.

Do you know of other similar initiatives?

What were the intellectual highlights of your undergraduate education?

I think one of the greatest moments of being a teacher or student is when the student understands or learns something that they find exciting, satisfying, or stimulating. In this "Ah hah!" or Wow! moment they will say "That is really cool!" or "That is beautiful!" or something similar.
These moments can be so significant that the student can years later even remember the exact time, location, or circumstance in which the event happened.

Did you have any such experiences when you were an undergraduate?

I reflected on my own experience. Even though it is almost 40 years ago I can remember what I learnt and sometimes the place, the book, the person, ...
Here is some of the things that immediately came to mind. They are listed in random order. It is interesting that many involve learning how one result follows from a more fundamental result with a simple mathematical proof. Often it meant there was a deeper reason for something we had previously been told was "just the way it is".
Most of these beautiful moments were in theoretical physics and pure mathematics. None were in chemistry. I think this was partly because of my own interests and orientation and partly because of the quality (or lack thereof) or approach to teaching of different subjects.

Ehrenfest's theorem
The equations of motion of classical mechanics are the average of the equations of motion for position and momentum operators.

Heisenberg's uncertainty relation follows from commutation relations.

The energy eigenvalues for the harmonic oscillator can be derived from the commutation relations of creation and annihilation operators.
No differential equations or Hermite polynomials were required!

Experimental test of time dilation from measurement of the lifetime of cosmic-ray mesons
I read about this in the textbook on Special Relativity by French. The experiments are described here.

van der Waals interaction from the Schrodinger equation
I learnt this derivation from reading my father's copy of Quantum Chemistry (1957) by Walter Kauzmann.

Electromagnetic radiation and the speed of light from Maxwell's equations

The ideal gas equation of state from the partition function

The logical structure of the laws of thermodynamics
I learnt this axiomatic approach from Hans Buchdahl, both from his book and his lectures.

Functional analysis and the equivalence of matrix and wave mechanics
This was in a pure mathematics class. It is really just an isomorphism of Hilbert spaces.

Evaluation of infinite series from residues in complex analysis
Cauchy's residue theorem can be used.

Dimensional analysis in fluid mechanics
It was amazing the physical insights one could gain simply from dimensional analysis.

Newtonian gravity from Einstein's gravitational field equations

What were some examples from your own undergraduate education?
How do we create such moments for students?