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?

What does learning to ride a bicycle teach us?

How do you learn to ride a bicycle? How do you teach someone to ride a bicycle? It is not easy to put this into words and that is an important point in itself. It may help to have some knowledge of the parts of the bicycle and their respective functions. It may help to know something about relevant physics such as inertia, the centre of gravity, and balance. It may help to have some practical advice about seat height, posture, the appropriate speed at which to pedal, and where to look when riding. 

Nevertheless, all that information may not help much. Some young children learn to ride without knowing any of this. They just watch other children doing it, get on bike, try it, and learn by trial and error. The more passionate they are about learning the more likely they may be to succeed.

The mind and body of a bicyclist focus on just a few things: looking where they are going, pedalling, steering, and a sense of balance. This information is integrated together, and the rider adjusts their direction, pedalling, and posture. Furthermore, that process of integration and adjustment involves much that is not the rider’s focus, and they may not even be directly aware of. A person’s sense of body awareness and coordination is shaped by biology, physique, experience, and training.

This example of bike riding illustrates several important things.  First, we can have the ability to do something without necessarily being able to articulate how we do it. Second, knowing requires personal commitment. It involves trust and risk. If a person is unwilling to trust or take risks, they may miss out on something good, such as the joy of riding a bicycle. Third, knowing requires integration of multifaceted information. Fourth, knowledge and understanding come from integrating our focus into an implicit background we may not even be aware of.

The example of riding a bike is valuable for understanding how we know (epistemology) because it is simpler and less fraught and emotionally charged than how we come to an understanding and make decisions about history, ethics, politics, religion, and the meaning of scientific knowledge. 

These observations draw on Michael Polanyi, including his book, The Tacit Dimension, published in 1966, but based on lectures he gave at Yale in 1962. He referred to the first point as tacit knowing, and the fourth point as the subsidiary-focal interaction. The relationship of the subsidiary and the focus is like the whole and the parts. Polanyi considered the idea of tacit knowledge his most important discovery.

Aside: Chapter 2 of The Tacit Dimension is entitled "Emergence" and discusses ideas similar to those that Phil Anderson promoted in 1972 in More is Different, without using the word "emergence." According to Google Scholar, The Tacit Dimension has been cited 45,000 times.

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.

Should Ph.D. students choose to teach?

In Australia, most Ph.D. students are fully funded by scholarships to allow them to focus on their research. This is unlike in the USA where many students must be TAs (teaching assistants) to be paid. 

In most Australian universities, such Ph.D. students can earn extra income by being tutors (same as TAs) for undergraduate courses. Many do, as earning extra money is attractive. Ph.D. students doing teaching saves universities tons of money as it means they don't need to hire and pay permanent academic staff to do this tutoring.

What is my advice to students who have this option? Here are some of the advantages and disadvantages for a Ph.D. student doing such tutoring.

Advantages

You earn additional income.

Having teaching experience listed on your CV may help you get a faculty position at some institutions. For example, in Australia, this seems to be almost a pre-requisite these days. Furthermore, if you can be innovative, and get high student evaluations, that may be viewed favourably. But that really concerns lecturing and not tutoring.

You usually learn a lot from teaching, even lower-level courses.

It can be enjoyable and satisfying. It can provide a break from thinking just about your Ph.D. research.

If you are fortunate enough to eventually get a faculty position this experience will make it easier to handle the formidable challenges of starting out teaching.

It may create some goodwill towards you in your department. You may be seen as a team player and a good departmental citizen.

You may need the money. For example, if you are supporting a family or if you are from a Majority World country and want to send money home to extended family.

Disadvantages

Foremost, it can consume a large amount of time and energy that reduces your research productivity. It reduces your mental space. You may lose research momentum and not complete your Ph.D. on time.

There can be a significant financial opportunity cost. Suppose that doing the teaching delays you completing your Ph.D. by six months. The lost six-month salary will probably be much greater than the amount you earned from doing the teaching.

It can be frustrating to deal with students who are not that interested in learning and are only concerned with grades. Furthermore, there may be the added stress of having to deal with students who make formal complaints about your teaching or their grades.

It may not add a lot to your CV, particularly if your student evaluations are average. They will probably be average or even below average since you are starting out.

If you don't do a stellar job and/or there are a few disgruntled students your reputation in the department may suffer, perhaps unjustly.

On balance, I think it depends on the individual: their personal financial situation, personality, career goals and stage in the Ph.D. In some cases, I encourage people to do this, although only for one or two semesters. In other cases, I discourage it. The main thing is to make a well-informed decision which takes into account the pros and cons. 

Students also need to be wary of the vested interests of faculty and university management that will push them towards teaching, possibly against the student's best long-term interests.

Aside. I often forget what posts I have written in the past. I really thought I had written this post before. All I could find is one on Should postdocs teach?

I welcome comments, particularly from current and former Ph.D. students who have negotiated this issue. What would you advise?

David Mermin on his life in science: funny, insightful, and significant

 David Mermin has posted a preprint with the modest title, Autobiographical Notes of a Physicist

There are many things I enjoyed and found interesting about his memories. A few of the stories I knew, but most I did not. He reminisces about his interactions with Ken Wilson, John Wilkins, Michael Fisher, Walter Kohn, and of course, Neil Ashcroft.

Mermin is a gifted writer and can be amusing and mischievous. He is quite modest and self-deprecating about his own achievements.

He explains why we should refer to the Hohenberg-Mermin-Wagner theorem, not Mermin-Wagner.

One of his Reference Frame columns in Physics Today, stimulated Paul Ginsbarg to start the arXiv.

I was struck by how Mermin's career belongs to a different era. The community was smaller and more personal. Doing physics was fun. Time was spent savouring the pleasure of learning new things and explaining them to others. Colleagues were friends rather than competitors. His research was curiosity-driven. This led to Mermin making significant contributions to quantum foundations. And, he only published about two papers per year!

Teaching was valued, enjoyable, and stimulated research. It was also a way to learn a subject, regardless of the level at which it was taught. For eight years, Mermin and Ashcroft spent half their time writing their beautiful textbook!

I look forward to hearing others' reflections.

The joys and frustrations of making video recordings in powerpoint

 I have recently been doing something that many of you are probably already doing thanks to online teaching in the pandemic: using PowerPoint to make a video recording of a slide presentation. Particularly for online courses that are not live this can make a lecture more engaging.

First, I will share a few helpful things I learned. To get the best quality video it is best not to use regular room lighting and the camera on your laptop or desktop monitor. It turns out, for reasons I still do not fully understand, that generally, the quality of the video from your phone is much better than from your laptop camera. So I am using my phone with free Irium software to do the recording. I have the phone mounted on a tripod that includes a ten-inch LED ring light. The picture quality really is a lot better.

Now, I come to the weird, frustrating, and random problems that I am having. At first, ppt would not do video recording on my regular MacBook, but it would on my old MacBook, even though they are basically running the same software. Then a few days later it did start to work on the regular laptop, but only for a few days. For the first few days, the recordings went fine, then I experienced the following random and unpredictable outcomes, even though I had not (knowingly) changed anything.

a. Video and sound recording is fine.

b. There is no recording.

c. Video records fine but there is no sound.

d. Video records fine but the sound only starts working at some random point in the video. Usually, it is out of sync with the video.

I have asked Dr. Google for solutions but found little that is relevant or effective. I have tried changing cameras and microphones but this never provides a lasting solution.

I welcome ideas and suggestions.

Here are two things that I have wondered about.

a. the ppt files are very large (half a gigabyte). Are the different components a bit slow talking to each other?

b. IT services at UQ now has remote control of our laptops and can force updates and restarts. Sometimes when I am not using my laptop it has shut down and rebooted.

Has anyone had similar experiences?

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?

 

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...

How much background material do beginning graduate students need to master?

I am working with a graduate student beginning research and she has asked this important question. I don't think there is a simple universal answer.

Background material includes review articles of a field, details of an experimental technique or computer code, details of derivations, seminal articles on the topic, ....

At the UQ condensed matter theory group meeting, we had a brief discussion about the question.
Answers from students, both beginning and advanced, were helpful. It also underscored how important the question is because students really do struggle with this issue. One shared how he developed some mental health problems because at the beginning of his Ph.D. he was too obsessive about understanding all the details. The question and discussion underscored to me how we need to have more discussions of this nature.

Beginning research is a difficult transition for most graduate students. When they were undergraduates they often could understand all the details and work through all the derivations.
(They are unlike a significant fraction of undergraduates who just don't seem to realise that the details DO matter.)
However, the painful reality is that what was possible for a gifted and motivated undergraduate is simply not possible for most Ph.D. research.
Research fields are so vast and have so much foundational material a student simply does not have the time to check everything and understand everything in full.
The question is painfully relevant in Australia because Ph.D. students do not do coursework (or a Masters degree) and the government continues to reduce the number of years of funding.
Furthermore, the "publish or perish" culture puts pressure on students and advisors to be cranking out papers, which means there is pressure for students not to ``waste time'' on slow and deep learning of background material.

Like many things in life, I think answers to the question require some balance and need to allow for differences in personality, learning styles, personal goals, and nature of the research topic.

Here are some composite pictures to illustrate the extremes and the associated problems and potential.

Sanjay loves to understand and master details. He is also interested in the big foundational questions the research might address. When he reads an article he likes to work through all the details of the mathematical derivations. He would prefer to write his own computer code so he really knows what is going on. He has a large stack of papers on his desk, waiting to be read, consisting of many of the papers related to his research topic. After a year he is still learning background material. However, in his third year, he has a big breakthrough because he realises that one a key assumption/derivation in the field is wrong in certain cases. He not only corrects it but opens up a new avenue of research.

Priya just wants to get on with research and is not a detail oriented person. Following her advisors request she reads a few background articles superficially and dives into research. However, she does not really grasp the big picture or understand the limitations of the technique she is using. Consequently, she wastes a lot of time making mistakes, producing dubious results, and getting help for things she should have worked out for herself. However, this approach actually suits her learning style and she does eventually learn the essential things she needs to know and understand what is going on. Furthermore, because she has "dived in'' early, by the end of her Ph.D. she has produced several nice papers.

What do you think?
It would be good to hear from beginning graduate students, advanced graduate students, and faculty advisors.
What did you do? What do you wish you had done?

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.

Broken symmetry, order, and entropy

One of the greatest joys of teaching is having students ask questions that you do not know the answer to. In the last week of the course PHYS2020 Thermodynamics and Condensed Matter Physics for second year undergrads at UQ, I give two lectures about critical points, universality, critical exponents, broken symmetry, order parameters, and Landau theory.

Many students find this quite challenging. However, I think it is important that students be exposed to two of the most important ideas of theoretical physics from the twentieth century: broken symmetry and universality. Furthermore, there is no technical reason why second year undergrads cannot learn this material. Since the text, Thermal Physics by Schroeder, does not cover this material we have finally settled on a chapter from a book by Hoch.

After my last lecture, a student asked an excellent question along the lines of
"Why is it that broken symmetry occurs at lower temperatures?
How is this related to entropy and order?"

This led me to wondering whether there were any rigorous results that answer the question. I could not find anything in a quick search.
Do you know of anything?

I was wondering whether something like the following conjecture was true:

Conjecture. Consider a physically reasonable Hamiltonian H for an infinite system. Suppose H is invariant under some symmetry group G. Let rho(T) be the equilibrium density matrix at temperature T. Then for sufficiently large T, rho(T) is also invariant under G.

Maybe this is equivalent to

Lemma. At sufficiently high temperatures, the von Neumann entropy S (rho) = - Tr( rho ln (rho)) is maximal if rho is invariant under G. 

This looks to me like the kind of thing that people like Elliot Lieb, David Ruelle, Y. Sinai, ... might have tackled at some point.

I welcome ideas and suggestions.

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?

Rethinking On-Line courses

About five years ago Massive On-Line Courses (MOOCs) were all the rage among politicians and university managers. Like most hyped up fashions, they have lost their gloss as reality has set in. There are no simple panaceas, particularly technological ones, for the complexities of tertiary education. I have previously expressed skepticism and concern about MOOCs, but recently I have rethought some of my views.

Last year I was visiting some friends in a small Majority World college and I noticed that one of the administrators had a copy of the book Poor Economics on his desk. I told him how much I liked it and he said that he had really enjoyed and benefited from taking the associated on-line course at MIT. Then he said, "But the online course I really like is the Oxford one, From Poverty to Prosperity, by Paul Collier.'' Wow!

To me, this represents the best of on-line courses; when they provide access to educational opportunities that were inconceivable a decade ago.

I have also been helping another friend with an on-line Masters course. A positive here is that it is not a substitute for regular classes for traditional students in physical classrooms but a course for students who are in life situations (family, jobs, location, ...) that do not afford them the luxury of full-time study in a traditional setting. I think a big positive is having an excellent on-line tutor who actively engages with the students.

Overall, I think the key issue here is that On-line courses are not a desirable substitute for traditional courses, but rather can complement them. Similarly, I think within traditional contexts (i.e. students on physical campuses) "blended courses" (i.e. ones with a mixture of face-to-face and on-line interaction) can be superior to traditional ones. For example, I have found that an on-line quiz about pre-lecture reading seems to increase the quality of the experience for students who then come to the lecture.

However, I want to emphasize a basic claim: the ideal educational environment and strategy for most students (particularly young undergraduates) is one where you have a group of students and a teacher in a physical classroom interacting with each other. People are relational and learning best happens in the context of relationships.

I welcome comments.

Postscript (Feb. 13).
I forgot to link to this excellent NYT article.

Online Courses Are Harming the Students Who Need the Most Help Economic View, by Susan Dynarski

Who was the greatest theoretical chemist of the 19th century?

Dimitri Mendeleev, who proposed the periodic table of the elements, purely from phenomenology and without quantum mechanics!
He even successfully predicted the existence of new elements and their properties.

A friend who is a high school teacher [but not a scientist] asked me about how he should teach the periodic table to chemistry students. It is something that students often memorise, especially in rote-learning cultures, but have little idea about what it means and represents. It makes logical sense, even without quantum mechanics. This video nicely captures both how brilliant Mendeleev was and the logic behind the table.



A key idea is how each column contains elements with similar chemical and physical properties and that as one goes down the column there are systematic trends.
It is good for students to see this with their own eyes.
This video from the Royal Society of Chemistry shows in spectacular fashion how the alkali metals are all highly reactive and that as one goes down the column the reactivity increases.



The next amazing part of the story is how once quantum theory came along it all started to make sense!

Entering the strange world of Kurt Godel

The picture below is of Godel's rotating universe. It represents an exact solution to Einstein's gravitational field equations and has the strange property of closed timelike curves (i.e. one can travel into the past!). This mathematical solution was found by Kurt Godel while he was employed by the Institute for Advanced Study at Princeton.

I think I first encountered this picture in my final undergraduate year in the classic book, The Large Scale Structure of Space-Time by Hawking and Ellis, while working on a research project in general relativity.

Godel's universe is just one example of the fascinating science and stories recounted in the book
Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study by Ed Regis, first published 30 years ago.

I only read the book this past week and loved it. It is a captivating blend of science, mathematics, personalities, history, philosophy, humorous anecdotes, gossip, eccentricities ...
I was so captivated that I read it during two situations I would not normally read something so "heavy": during a long flight [normally I watch reruns of The Big Bang Theory or Upper Middle Bogan [need to laugh!] or recently a Warren Buffett documentary... sorry better not mention that again...], and during "down time" in the evening after a busy day.

Regis nicely describes the continuum hypothesis, Einstein-Podolsky-Rosen (EPR) "paradox" in quantum theory, von Neumann machines, cellular automata, the Bourbaki seminar, parity violation, the solar neutrino problem, fractals, the stability of matter, ...

The personalities covered include Godel, Einstein, Herman Weyl, John von Neumann, J. Robert Oppenheimer, Freeman Dyson, T.D. Lee,  C.N. Yang, Andre Weil, John Bahcall, Stephen Wolfram, Ed Witten, .....

It is amazing how much Regis packs into less than 300 pages (in a paperback).

The tragic mental health problems of Godel are described in a sensitive manner.

One pathetic story concerns the endless quibbles of T.D. Lee and C.N. Yang.
(Aside: They actually did their Nobel Prize winning work on parity violation at the IAS. This is in contrast to the countless Nobel laureates who at one time have been affiliated with the IAS but did not do their prize work there.)
Lee and Yang (or is it Yang and Lee?) argued constantly about the order in which their names should be listed, not just as co-authors, and at the Nobel ceremony, but even in newspaper and magazine articles about them. Furthermore, it is crazy to read the wildly different and self-serving accounts of certain concrete events. Great scientists are all too human ......

Some people consider the book is a bit of a "hatchet" job and has a mocking tone that paints the IAS in a poor light and questions its value and existence. I would not agree. I think it does show that the IAS has produced a lot of important scholarship. Regis does raise some important questions I mention below. But, I did think that he did refer to the IAS as "the One True Platonic Heaven" too many times.

Regis is implicitly critical of the fact that there is very little interaction between different research groups and disciplines within IAS. However, there is one important story he missed: when Freeman Dyson and the number theorist Hugh Montgomery were introduced at tea at the IAS and they made a connection between random matrix theory (quantum physics) and zeros of the Riemann zeta function.

Some questions the book raises for me include:

Can you really "manage" genius?

How do you create an institutional environment that increases the likelihood of truly great discoveries and scholarship?

What is the best way to hire "great" people?

What is a good mix of young and old staff?

What is a good mix of permanent faculty, postdocs, and short term senior visitors?

When is the absence of students in a research institute good or bad?

When is the absence of experimentalists in an institution bad/good for theoretical physics?

How do you foster a healthy synergy between pure mathematics and theoretical physics?

How might you foster some constructive interaction between distinct disciplines: philosophy, mathematics, theoretical physics, economics, history, ....?

Here is Feynman's perspective (partly quoted in the book):

I don't believe I can really do without teaching. The reason is, I have to have something so that when I don't have any ideas and I'm not getting anywhere I can say to myself, "At least I'm living; at least I'm doing something; I am making some contribution" -- it's just psychological. 

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves, OK? So they don't get any ideas for a while: They have every opportunity to do something, and they are not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens. Still no ideas come. 

Nothing happens because there's not enough real activity and challenge: You're not in contact with the experimental guys. You don't have to think how to answer questions from the students. Nothing!

Governments have less and less interest in "research for its own sake" and "without constraints" [hallmarks of the IAS]. However, there is an increasing number of generous and wealthy philanthropic organisations who are very interested. These are important questions for them.

Although I lived in Princeton for four years around the time the book was being written I only recall going inside "the Brain Farm" [as a friend called it] once, and that was for a music concert. Nevertheless, I spent many pleasant hours walking, jogging, bird watching, and skiing in the beautiful woods located behind the IAS.

I thank Ben Powell for a conversation about the IAS, stimulating me to remember I had inherited a copy of the book from my parents.

I welcome thoughts on any of the questions and any good IAS stories...

How might we teach students to actually think?

Four important goals to me are to teach students:
1. To think.
2. To think like a physicist.
3. To think like a condensed matter physicist.
4. The specific technical content of the course.

The last one is arguably easier than the others.
I also think it is the least important. Others will disagree.
We don't reflect enough on how we might achieve the other goals.
The biggest challenge of improving education in the Majority World is not lack of material resources but changing the culture of rote learning and teaching critical thinking.
[This is highlighted in a NYTimes piece about China and a very funny video about India ITs].

Last week the UQ School of Maths and Physics Teaching Seminar was given by Peter Ellerton who works for the UQ Critical Thinking project.

The slides from a similar talk are here.
In the talk he mostly walked us through the three graphics shown here.
[If you click on the image you can see a high resolution .pdf]

The main value of all this is it puts names, categories, and questions on what I want to do. I found the third graphic the most helpful because it has some very specific questions we can ask students to get them to reflect more on what they are learning and in the process learn to think more critically.