Condensed concepts

It is rather amazing that many complex systems, ranging from proteins to stock markets to cities, exhibit power laws, sometimes over many decades. A critical review is here , which contains the figure below. Complexity theory makes much of these power laws. But, sometimes I wonder what the power laws really tell us, and particularly whether for social and economic issues they are good for anything. Recently, I learnt of a fascinating case. Admittedly, it does not rely on the exact mathematical details (e.g. the value of the power law exponent!). The case is described in an article by Dudley Herschbach , Understanding the outstanding: Zipf's law and positive deviance and in the book Aid at the Edge of Chaos , by Ben Ramalingam. Here is the basic idea. Suppose that you have a system of many weakly interacting (random) components. Based on the central limit theorem one would expect that a particular random variable would obey a normal (Gaussian) distribution. This means

Almost three years ago I posted  about the controversy concerning whether the photoactive yellow protein has low-barrier hydrogen bonds [for these the energy barrier for proton transfer is comparable to the zero-point energy]. I highlighted just how difficult it is going to be, both experimentally and theoretically to definitively resolve the issue, just as for an enzyme I recently discussed. A key issue concerns how to interpret large proton NMR chemical shifts. Two recent papers weigh in on the issue The Low Barrier Hydrogen Bond in the Photoactive Yellow Protein: A Vacuum Artifact Absent in the Crystal and Solution  Timo Graen, Ludger Inhester, Maike Clemens, Helmut Grubmüller, and Gerrit Groenhof A Dynamic Equilibrium of Three Hydrogen-Bond Conformers Explains the NMR Spectrum of the Active Site of Photoactive Yellow Protein  Phillip Johannes Taenzler, Keyarash Sadeghian, and Christian Ochsenfeld I think the caveats I have offered before need to kept in mind. As with un

Are you looking for Christmas gifts? I think that scientists should be writing popular books for the general public. However, I am disappointed by most I look at. Too many seem to be characterised by hype, self-promotion, over-simplification, or promoting a particular narrow philosophical agenda. The books lack balance and nuance. We should not be just explaining about scientific knowledge but also give an accurate picture of what science is, and what it can and can't do. (Aside: Some of the problems of the genre, particularly its almost quasi-religious agenda, is discussed in a paper by my UQ history colleague, Ian Hesketh.) There is one book I that I do often hear non-scientists enthusiastically talk about. A Short History of Nearly Everything by the famous travel (!) writer Bill Bryson. There is a nice illustrated edition. I welcome comments from people who have read the book or given it to non-scientists.

Today I am giving a talk in the Applied Physics Department at Stanford. My host is Sri Raghu . Here is the current version of the slides.

Carbonic anhydrase is a common enzyme that performs many different physiological functions including maintaining acid-base equilibria. It is one of the fastest enzymes known and its rate is actually limited not by the chemical reaction at the active site but by diffusion of the reactants and products to the active site. Understanding the details of its mechanism presents several challenges, both experimentally and theoretically. A key issue is the number and exact location of the water molecules near the active site. The most recent picture (from a 2010 x-ray crystallography study ) is shown below. The "water wire" is involved in the proton transfer from the zinc cation to the Histidine residue. Of particular note is the short hydrogen bond (2.4 Angstroms) between the OH- group and a neighbouring water molecule. Such a water network near an active site is similar to what occurs in the green fluorescent protein and KSI. Reliable knowledge of the finer details of t

My wife and I are often looking for new science demonstrations to do with children. The latest one she found was "bouncing soap bubbles". For reasons of convenience [laziness?] we actually bought the kit from Steve Spangler. It is pretty cool. A couple of interesting scientific questions are: Why do the gloves help? The claim is that the grease on your hands makes bursting the bubbles easier. Why does glycerin make the soap bubbles stronger? Why does "ageing" the soap solution for 24 hours lead to stronger bubbles? Journal of Chemical Education is often a source of good ideas and science discussions. Here are two relevant articles. Clean Chemistry: Entertaining and Educational Activities with Soap Bubbles  Kathryn R. Williams Soap Films and the Joy of Bubbles Mary E. Saecker

Previously, I posted about a historical precedent for managing by metrics: economic planning in Stalinist Russia. I recently learnt of a capitalist analogue, starting with Ford motor company in the USA. I found the following account illuminating and loved the (tragic) quotes from Colin Powell  about the Vietnam war. Robert McNamara was the brightest of a group of ten military analysts who worked together in Air Force Statistical Control during World War II and who were hired en masse by Henry Ford II in 1946. They became a strategic planning unit within Ford, initially dubbed the Quiz Kids because of their seemingly endless questions and youth, but eventually renamed the Whiz Kids , thanks in no small part to the efforts of McNamara.   There were ‘four McNamara steps to changing the thinking of any organisation’: state an objective, work out how to get there, apply costings, and systematically monitor progress against the plan . In the 1960s, appointed by J.F. Kennedy as Secre

The challenge of understanding phase transitions and proton ordering in hydrogen-bonded ferroelectrics (such as KDP, squaric acid, croconic acid ) and different crystal phases of ice has been a rich source of lattice models for statistical physics. Models include ice-type model s (six-vertex model, Slater's KDP model), transverse field Ising model, and some gauge theories. Some of the classical (quantum) models are exactly soluble in two (one) dimensions. An important question that seems to be skimmed over is the following: under what assumptions can one actually "derive" these models starting from the actual crystal structure and electronic and vibrational properties of a specific material? That quantum effects, particularly tunnelling of protons, are important in some of the materials is indicated by the large shifts (of the order of 100 percent) seen in the transition temperatures upon H/D isotope substitution. In 1963 de Gennes argued that the transverse fi

On Friday I am giving a talk in the Chemistry Department at Berkeley. Here is the current version of the slides. There is some interesting local background history I will briefly mention in the talk. One of the first people to document correlations between different properties (e.g. bond lengths and vibrational frequencies) of diverse classes of H-bond complexes was George Pimentel.  Many correlations were summarised in a classic book, "The Hydrogen Bond" published in 1960. He also promoted the idea of a 4-electron, 3 orbital bond which has similarities to the diabatic state picture I am promoting. There is even a lecture theatre on campus named after him!

Here is a helpful quote from William Bialek. It is a footnote in a nice article,  Perspectives on theory at the interface of physics and biology . The Boltzmann distribution is the maximum entropy distribution consistent with knowing the mean energy, and this sometimes leads to confusion about maximum entropy methods as being equivalent to some sort of equilibrium assumption (which would be obviously wrong). But we can build maximum entropy models that hold many different expectation values fixed, and it is only when we fix the expectation value of the Hamiltonian that we are describing thermal equilibrium. What is useful is that maximum entropy models are equivalent to the Boltzmann distribution for some hypothetical system, and often this is a source of both intuition and calculational tools. This type of approach features in the statistical mechanics of income distributions. Examples where Bialek has applied this includes voting patterns of the USA Supreme Court , flocking of b