Max Weber on the evolution of institutions

Max Weber is one of the founders of sociology. This post is about two separate and interesting things I recently learned about him.

A while ago I discussed Different phases of growth and change in human organisations, based on a classic article from Harvard Business Review. [Which had no references or data!]
My friend Charles Ringma recently brought to my attention somewhat related ideas from Max Weber.
According to Wikipedia

Weber distinguished three ideal types of political leadership (alternatively referred to as three types of domination, legitimisation or authority):^[52][111]

1. charismatic domination (familial and religious),
2. traditional domination (patriarchs, patrimonialism, feudalism) and
3. legal domination (modern law and state, bureaucracy).^[112]

In his view, every historical relation between rulers and ruled contained such elements and they can be analysed on the basis of this tripartite distinction.^[113] He notes that the instability of charismatic authority forces it to "routinise" into a more structured form of authority.^[79]

I also learnt that Weber had a long history of mental health problems. According to Wikipedia

In 1897 Max Weber Sr. died two months after a severe quarrel with his son that was never resolved.^[7][37] After this, Weber became increasingly prone to depression, nervousness and insomnia, making it difficult for him to fulfill his duties as a professor.^[17][26] His condition forced him to reduce his teaching and eventually leave his course unfinished in the autumn of 1899. After spending months in a sanatorium during the summer and autumn of 1900, Weber and his wife travelled to Italy at the end of the year and did not return to Heidelberg until April 1902. He would again withdraw from teaching in 1903 and not return to it till 1919. Weber's ordeal with mental illness was carefully described in a personal chronology that was destroyed by his wife. This chronicle was supposedly destroyed because Marianne Weber feared that Max Weber's work would be discredited by the Nazis if his experience with mental illness were widely known.^[7][38]

This puts Weber in a similar class to many other distinguished scholars who had significant mental health problems: Boltzmann, John Nash, Drude, Michel Foucault, ...

Spin-crossover in geophysics

Most of my posts on spin-crossover materials have been concerned with organometallic compounds. However, this phenomena can also occur in inorganic materials. Furthermore, it may be particularly relevant in geophysics. A previous post discussed how strong electron correlations may play a role in geomagnetism and DMFT calculations have given some insight.

A nice short overview and introduction is
Electronic spin transition of iron in the Earth's deep mantle 
Jung‐Fu Lin Steven D. Jacobsen Renata M. Wentzcovitch

[It contains the figure below]
The main material of interest is magnesiowüstite, an alloy of magnesium and iron oxide,
(Mg1−xFex)O



Experimental studies and DFT calculations suggest that as the pressure increases the iron ions undergo a transition from high spin to low spin. The basic physics is that the pressure reduces the Fe-O bond lengths which increases the crystal field splitting.
In geophysics, the pressure increases as one goes further underground.

DFT+U calculations are reported in
Spin Transition in Magnesiowüstite in Earth’s Lower Mantle 
Taku Tsuchiya, Renata M. Wentzcovitch, Cesar R. S. da Silva, and Stefano de Gironcoli

The main result is summarised in the figure below.

There is a smooth crossover from high spin to slow spin, as is observed experimentally. However, it should be pointed out that this smoothness (versus a first-order phase transition with hysteresis) is built into the calculation (i.e. assumed) since the low spin fraction n is calculated using a single site model.  On the other hand, the interaction between spins may be weak because this is a relatively dilute alloy of iron (x=0.1875).
Also, the vibrational entropy change associated with the transition is not included. In organometallics, this can have a significant quantitative effect on the transition.

The elastic constants undergo a significant change with the transition. This is important for geophysics because these changes affect phenomena such as the transmission of earthquakes.

Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth’s Lower Mantle 
Suyu Fu, Jing Yang, and Jung-Fu Lin

A previous post considered changes in the elasticity and phonons in organometallic spin-crossover. Unfortunately, that work did not have the ability to resolve different elastic constants.

Is this an enlightened use of metrics?

Alternative title: An exciting alternative career for Ph.Ds in condensed matter theory!

There is a fascinating long article in The New York Times Magazine
How Data (and Some Breathtaking Soccer) Brought Liverpool to the Cusp of Glory 
The club is finishing a phenomenal season — thanks in part to an unrivaled reliance on analytics.

This is in the tradition of Moneyball. Most of the data analytics team at Liverpool have physics Ph.Ds. It is led by Ian Graham who completed a Ph.D. on polymer theory at Cambridge.

On the one hand, I loved the article because my son and I are big Liverpool fans. We watch all the games, some in the middle of the night. On the other hand, I was a bit surprised that I liked the article since I am a strong critic of the use of metrics in most contexts, especially in the evaluation of scientists and institutions. However, I came to realise that, in many ways, what Liverpool is doing is not the blind use of metrics but rather using data as just one factor in making decisions.
Here are some of the reasons why this is so different from what now happens in universities.

1. The football manager (Jurgen Klopp, who has played and managed) is making the decisions, not someone who has never played or has had limited success with playing and managing (a board member or owner).

2. The data is just one factor in hiring decisions. For example, Klopp often spends a whole day with a possible new player to see what their personal chemistry is. Furthermore, he has watched them play (the equivalent of actually reading the papers of a scientist?).

3. A single metric (cf. goals scored, h-index, impact factor) is not being used to make a decision on who to recruit. Rather, many metrics are being used, to develop a complete picture. Furthermore, a major emphasis of the Moneyball approach is finding ``diamonds in the rough'', i.e. players who have unseen potential, because their unique gifts are being overlooked (because they are currently undervalued because they score poorly with conventional metrics) or they would be a potent combination with other current plays. The latter was a decision is recruiting Salah; the data suggested he would be a particularly powerful partner to Firmino. On the former, the article discusses in detail the analysis that led to Liverpool recruiting the Ghanian midfield,  Naby Keita.

Keita’s pass completion rate tends to be lower than that of some other elite midfielders. Graham’s figures, however, showed that Keita often tried passes that, if completed, would get the ball to a teammate in a position where he had a better than average chance of scoring. What scouts saw when they watched Keita was a versatile midfielder. What Graham saw on his laptop was a phenomenon. Here was someone continually working to move the ball into more advantageous positions, something even an attentive spectator probably wouldn’t notice unless told to look for it. Beginning in 2016, Graham recommended that Liverpool try to get him.

What might be an analogue of this approach in science?
A person who does not attract a lot of attention but has a record of writing papers that stimulate or are foundational to significant papers of better-known scientists?
A person who does very good science even though they have few resources?
A person who is particularly good at putting together collaborations?

Other suggestions?

Public talk on emergence

Every year in Australia there is a week of science outreach events in pubs, Pint of Science. I am giving a talk  tomorrow night, Emergence: from physics to sociology.
Here are the slides.

In the past, when explaining emergence I have liked to use the example of geometry. However, one can argue that a limitation of that case is there are not necessary many interacting components to the system. Hence, I think the example of language, discussed by Michael Polanyi is better.

Phonons in organic molecular crystals.

In any crystal the elementary excitations of the lattice are phonons. The dispersion relation for these quasi-particles relates their energy and momentum. This dispersion relation determines thermodynamic properties such as the temperature dependence of the specific heat and plays a significant role in electron-phonon scattering and superconductivity in elemental superconductors. A nice introduction is in chapter 13 of Marder's excellent text. [The first two figures below are taken from there].

The dispersion relation is usually determined in at least one of three different ways.

1. The classical mechanics of balls and harmonic springs, representing atoms and chemical bonds, respectively. One introduces empirical parameters for the strengths of the bonds (spring constants).

2. First-principles electronic structure calculations, often based on density functional theory (DFT). This actually just determines the spring constants in the classical model.

3. Inelastic neutron scattering.

The figure below shows the dispersion relations for a diamond lattice using parameters relevant to silicon, using method 1. I find it impressive that this complexity is produced with only two parameters.

Furthermore, it produces most of the details seen in the dispersion determined by method 3. (Squares in the figure below.) which compare nicely with method 2. (solid lines below).

What about organic molecular crystals?
The following paper may be a benchmark.

Phonon dispersion in d8-naphthalene crystal at 6K 
I Natkaniec, E L Bokhenkov, B Dorner, J Kalus, G A Mackenzie, G S Pawley, U Schmelzer and E F Sheka

The authors note that method 3. is particulary challenging for three reasons.

• The difficulties in growing suitable single-crystal samples. 
• The high energy resolution necessary to observe the large number of dispersion curves (in principle there are 3NM modes, where N is the number of atoms per molecule and M is the number of molecules per unit cell). 
• The high momentum resolution necessary to investigate the small Brillouin zone (due to the large dimensions of the unit cell).

The figure below shows their experimental data for the dispersions. The solid lines are just guides to the eye.

The authors also compare their results to method 1. However, the results are not that impressive, partly because it is much harder to parameterise the intermolecular forces, which are a mixture of van der Waals and pi-pi stacking interactions. Hence, crystal structure prediction is a major challenge.

A recent paper uses method 2. and compares the results of three different DFT exchange-correlation functionals to the neutron scattering data above.
Ab initio phonon dispersion in crystalline naphthalene using van der Waals density functionals
Florian Brown-Altvater, Tonatiuh Rangel, and Jeffrey B. Neaton

What I would really like to see is calculations and data for spin-crossover compounds.

Introducing phase transitions to a layperson

I have written a first draft of a chapter introducing phase diagrams and phase transitions to a layperson. I welcome any comments and suggestions. Feel free to try it out on your aunt or uncle!

Fun facts about phonons

Today we just take it for granted that crystals are composed of periodic arrays of interacting atoms. However, that was only established definitively one hundred years ago.
I have been brushing up on phonons with Marder's nice textbook, Condensed Matter Physics.
There are two historical perspectives that I found particularly fascinating. Both involve Max Born.

In a solid the elastic constants completely define the speeds of sound (and the associated linear dispersion relationship). In a solid of cubic symmetry, there are only three independent elastic constants, C_11, C_44, and C_12.
Cauchy and Saint Venant showed that if all the atoms in a crystal interact through pair-wise central forces then C_44=C_12. However, in a wide range of elemental crystals, one finds that C_12 is 1-3 times larger than C_44. This discrepancy caused significant debate in the 19th century but was resolved in 1914 by Born who showed that angular forces between atoms could explain the violation of this identity. From a quantum chemical perspective, these angular forces arise because it costs energy to bend chemical bonds.

The first paper on the dynamics of a crystal lattice was by Born and von Karman in 1912. This preceded the famous x-ray diffraction experiment of von Laue that established the underlying crystal lattice. In 1965, Born reflected

The first paper by Karman and myself was published before Laue's discovery. We regarded the existence of lattices as evident not only because we knew the group theory of lattices as given by Schoenflies and Fedorov which explained the geometrical features of crystals, but also because a short time before Erwin Madelung in Göttingen had derived the first dynamical inference from lattice theory, a relation between the infra-red vibration frequency of a crystal and its elastic properties.... 

Von Laue's paper on X-ray diffraction which gave direct evidence of the lattice structure appeared between our first and second paper. Now it is remarkable that in our second paper there is also no reference to von Laue. I can explain this only by assuming that the concept of the lattice seemed to us so well established that we regarded von Laue's work as a welcome confirmation but not as a new and exciting discovery which it really was.

This raises interesting questions in the philosophy of science. How much direct evidence do you need before you believe something? I can think of two similar examples from more recent history: the observation of the Higgs boson and gravitational waves. Both were exciting, and rightly earned Nobel Prizes.
However, many of us were not particularly surprised.
The existence of the Higgs boson made sense because it was a necessary feature of the standard model, which can explain so much.
Gravitational waves were a logical consequence of Einstein's theory of general relativity, which had been confirmed in many different ways. Furthermore, gravitational waves were observed indirectly through the decay of the orbital period of binary pulsars.

Emergence: from physics to international relations

Today I am giving a seminar for the School of Political Science and International Studies at UQ.
Here are the slides.