Friday, December 27, 2019

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.

Thursday, December 12, 2019

John Wilkins (1936-2019): condensed matter leader

I was sad to hear last week of the death of John Wilkins. He was a mentor to a whole generation of condensed matter physicists and a generous servant, both individuals and institutions. This obituary and memories from some colleagues gives a nice description of his many contributions.

I was privileged to do a postdoc with Wilkins at Ohio State University in the early 1990s. He had a significant influence on me, both scientifically and professionally. Much of the practical advice I write on this blog relating to jobs, writing, and giving talks, I learned from Wilkins. Even ten years after I worked with him I would still occasionally phone him for advice, particularly with negotiating and deciding on job offers.

Real leadership does not involve having a position, but rather having influence. Servant leaders are not concerned with advancing their own interests, but rather those of others in their community. They do this by investing in people and institutions. Wilkins did this in many ways. He invested heavily in his own graduate students and postdocs. He advised and mentored countless other students, postdocs, and young faculty, for whom he had no formal responsibility or anything to gain from their success. He was proud of the fact that he never held an administrative position in a university. Nevertheless, his influence was far greater than most department chairs and deans. He served the American Physical Society in countless ways, particularly their publishing activities and the Division of Condensed Matter Physics. He wrote innumerable reference letters, referee reports, and grant reviews.

Reflecting on Wilkins, I was reminded of these recent words of David Brooks, written in a different context.
I had a feeling of going back in time. Why did it feel so strange? It was because I was looking at people who are not self-centered. They’ve dedicated themselves to the organization that formed them, and which they serve.
A few other basic but important things I learned from Wilkins:
Write clearly. Rewrite. Talk to people. Theory should relate to real materials and real experiments. Defining the problem clearly can be an important contribution. A concrete calculation on a concrete model is valuable.

Wilkins did have significant scientific achievements, but they tend to get dwarfed in comparison to his influence over people. Perhaps, the most significant relate to the Kondo problem. This began with his student Krishnamurthy, who used Wilson's numerical renormalisation group to understand all the different regimes of the Anderson single impurity model. Later with his students Dan Cox and Gene Bickers, Wilkins applied slave boson techniques to describe a wide range of experimental properties of valence fluctuation associated with magnetic impurities in metals.

In classic Wilkins style, he convened a group of distinguished theorists to meet in Los Alamos one summer to write a definitive early review article on heavy fermions.

Wilkins was larger than life. He laughed a lot and was a tease. He could also be intimidating. Before his groups' annual pilgrimage to the APS March meeting, everyone had to give a practice talk to the group and Wilkins. A fellow postdoc confided to me that each year he was more nervous about giving the practice talk than the real talk! One time, Wilkins got frustrated that too many of us had small fonts on our overhead transparencies. He made us all chant together: ``22 point type is the smallest! 22 point type is the smallest! ...."  again and again until we got the point.

It was well known that Wilkins did not like his picture taken. On his department web page he put a picture of another John Wilkins, one of the founders of the Royal Society. However, my wife did not know his aversion. In 1992? Kevin Ingersent hosted a group Thanksgiving dinner at his house. Later to my shock, I discovered my wife took the photo below. ``What?! You took a photo of Wilkins?!"


Wilkins was a great role model as a scientist, a faculty member, and a servant of a professional community.

Tuesday, December 10, 2019

Mathematics, biology, and emergence

Last night I heard a model public lecture about science. The School of Mathematics and Physics at UQ hosted a public lecture at the Queensland State Library. Holly Krieger, a pure mathematician at Cambridge, spoke on the Mathematics of Life. This is part of a biannual lecture series endowed by Kurt Mahler.

The lecture was amazing, both in content and presentation. It was engaging for high school students, and stimulating for experts. I wish I had a video or a copy of the slides. Krieger is well known to some through her Numberphile videos on YouTube.
Here are a few things I learned in the lecture.

Mathematics is the language of relationships and patterns.

We forget how even the concept of numbers is abstract. The notion of functions even more so.

An underlying theme of the lecture was that of emergence: a simple rule describing the interactions between the components of a system lead to collective behaviour (complexity) of the whole system.

Examples were given from biological systems that raise the question: how does the system know to do this?

Swarms of starlings were shown in the short film, The art of flying by Jan van IJken.
How do they move in concert when there is no leader?



Other examples included ant bridges, an experiment with a slime mould that was able to replicate the Japanese transport network (here is the Canadian version), stripes and spots on animals (pattern formation explained by with coupled reaction-diffusion equations by Alan Turing).

To illustrate how simple rules lead to complex behaviour, several cellular automata were demonstrated starting with Pascal's triangle and Sierpinski triangle. The latter was connected to biology through the pattern on the shell of a (poisonous) cone snail.

Rule 30 produces patterns similar to those found on the shell. It has periodic patterns such as stripes and aperiodic chaotic patterns.
It seems the new Cambridge train station also has this pattern!


Rule 184 can describe traffic including jamming for medium traffic densities.
The occurrence of a traffic jam does not depend on the initial state or a particular car, but only depends on the density of cars and the interaction (rule) between cars.

A nice video was shown of a traffic shockwave.
When water flows from a tap (faucet) and hits a flat sink bottom at right angles it may produce a "hydraulic jump" such as that shown below.



That is just the first half of the lecture. I may blog later about the second half which concerned chaos,
defined as small initial changes leading to significant changes in outcome.

One of the most interesting things for me about the lecture was Krieger's claim that ``Emergent complexity isn't everywhere. It can be hard to detect or confirm.'' i.e. just because we see complex behaviour (patterns) does not mean that it is due to emergence. In question time she said that this was in response to some of Wolfram's grand claims in A New Kind of Science, along the lines that everything (consciousness, gravity, continuity, free will, ...) could be explained in terms of discrete computational models such as cellular automata.

I think a more nuanced view is necessary. I agree, along with many others, that Wolfram's grand claims are not justified. But, I do not equate emergent complexity solely with simple rule-based computational models such as cellular automata. Different people do define emergence differently. For example, Sophia and Steve Kivelson propose the following definition.

An emergent behavior of a physical system is a qualitative property that can only occur in the limit that the number of microscopic constituents tends to infinity.

This would rule out classifying most of the phenomena described in the lecture as emergent. I disagree with this definition. On the other hand, I am not sure I agree with Krieger's claim. I do think almost anything interesting is emergent: consciousness, critical phenomena, the vacuum in quantum field theory, superconductivity, ...

Wednesday, December 4, 2019

A culture of fear in universities?

Following the fall of the Berlin Wall, one incredible revelation was the expansive role of the secret police, vast network of informers, and level of personal surveillance. This was underscored to me in movies such as The Lives of Others, novels such as The Day of the Lie, and a seminar I attended about human rights abuses in Syria.

The survival of totalitarian regimes is facilitated by the regime creating a culture of fear at every level of society and institutions, from factories to families. You do not dare to question or criticise the regime. Even making a joke at work may send you to the gulag.

Over the last decade, I have noticed a cultural shift in universities where there seems to be a culture of fear in many different aspects. A few examples are below.
I should be clear that I am not suggesting that universities today are anything like Syria, China, or the former Soviet Union.
Nevertheless, it is worth reflecting on whether there is a culture of fear and what its implications are for productivity, job satisfaction, and the integrity of the institution.
Some of this fear is created by the hyper-competitive environment. Some results from the lust for power and control of managers.

I won't criticise the new policy just announced by my department chair because I don't want to tick them off before my promotion decision (or request for more lab space, sabbatical request, ...)

I won't ask my supervisor that question because she might think I am dumb.

I won't write that in the paper because Professor X, who may be a referee, won't like it. I need to get this paper in a ``high impact'' journal.

I won't write that on my blog because it may offend potential grant reviewers.

I won't publically criticise the latest crazy scheme of senior management because they may make it difficult for me to get promoted.

If I don't work on the latest fad topic I won't get lots of citations. Then I won't get funding/tenure/job...

If I don't publish in luxury journals I won't get funding/tenure/job...

In my paper, I won't talk about the limitations of my results or techniques because then the paper may not get published.

If I don't engage in hype I won't get funding.

I will do anything my boss wants. If I don't I may not get the superlative letter of reference I need to get my next job.

What do you think?
Is there a culture of fear?
If so, can you think of other examples.

Addendum. I should have made some constructive suggestions. I think that senior faculty have a responsibility to make their research groups safe spaces and environments and to not give way to the climate of fear.

Monday, December 2, 2019

Ising model basics

The Ising model is a paradigm in both statistical mechanics and condensed matter physics. Today for most theorists it is so familiar that some of its historical and conceptual significance is lost.
Previously, I posted about what students can learn from computer simulations of the Ising model.

If you had to talk about the Ising model to an experimental chemist what would you say?
[Last week I had to do this].

The Ising model is the simplest effective model Hamiltonian that can describe a thermodynamic system that undergoes a first-order phase transition and has a phase diagram containing a critical point.

On each site i of a lattice one defines a spin sigma_i= +1 or -1, representing spin up or spin down.

The Hamiltonian H is

J_ij describes the interaction between spins on sites i and j. In the simplest version the interactions are only between nearest neighbours, and have the same value J.
h is the external magnetic field.

If J is positive, the ground state at h=0 is a ferromagnet.
If J is negative, the ground state at h=0 is an anti-ferromagnet for a bipartite lattice.

[Caution: just like for the Heisenberg model, some authors define the Hamiltonian with the opposite sign of J].

For h=0 there is a critical point at a finite temperature Tc, for lattices of dimension two and higher.

The spins sigma_i= +/- 1 defined at each lattice site i, were originally to represent the atomic magnetic moments in a ferromagnetic material. However, the sigma's can represent any two states of the site i. For example, the ``spin'' or pseudo-spin can represent the presence or absence of an atom or molecule in a ``lattice gas'', atom A or atom B in a binary alloy (mixture), or the low-spin and high-spin states in a spin-crossover material.

The mean-field theory of the Ising model is mathematically equivalent to the thermodynamic theory of binary mixtures with an entropy of an ideal mixture.
There is a nice discussion of such mixtures in Section 5.4 [and the associated problems] of Introduction to Thermal Physics by Schroeder.
[Here are the slides for a lecture I have given based on that text].
Chapter 15 of the text by Dill and Bromberg is also helpful as it has more detail.
Neither text makes an explicit connection to the Ising model. Following this paper on alloys, one has

This is shown in Section 8.1.2 of James Sethna's text, Statistical MechanicsEntropy, Order Parameters and Complexity.

When interactions beyond nearest-neighbours are included in the Ising model or when the lattice is frustrated (e.g. fcc or triangular) a richer phase diagram is possible. Examples include the ANNNI model and some models for spin-state ice considered by Jace Cruddas and Ben Powell.