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.

Topological defects determine the strength and growth rate of crystals

 The quantum theory of solids developed in the 1920s provided a theoretical estimate of the ideal strength of crystals. The problem was that this estimate was a thousand times greater than the measured strength of metals. This paradox was resolved in 1934, when Egon Orowan, Michael Polanyi and G. I. Taylor, independently proposed that plastic deformation could be explained in terms of the theory of dislocations. Aside: this is an example of how macroscopic properties can be determined by structures at the mesoscale rather than microscopic properties.

By 1940 the accepted theory of crystal growth was that it occurred by nucleation of successive close-packed layers of the crystal and this provided algebraic expressions for growth rates that were consistent with experiment. However, around 1950 Keith Burton estimated the parameters in the theory and pointed out that it predicted a growth rate that was smaller than observed growth rates by a factor 10^1000, i.e., 1000 orders of magnitude!

This quantitative discrepancy was resolved by Burton, Nicolas Cabrera and Charles Frank in 1951 who showed the central role played by screw dislocations. A crystal does not grow by the independent nucleation of separate layers. Rather it grows from just one layer that heloicoidally overlapping itself. A signature of this growth mode is the presence of spiral steps on crystal surfaces and they were subsequently observed.

This history is beautifully recounted in the introduction to a review article on Snow Crystals published by Charles Frank in 1982. It was reprinted in 2009 with an introduction by Andrew Fisher.

Following the introduction Frank discusses how snow is an important example of crystal growth that is not attributable to the presence of screw dislocations.

In 2015, D.P. Woodruff wrote a commentary on the classic 1951 paper by Burton, Cabrera, and Frank.

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.

Polanyi and Emergence before "More is Different"

The common narrative in physics is that the limitations of reductionism, the importance of emergence, and the stratification of scientific fields and concepts were first highlighted in 1972 by P.W. Anderson in a classic article, "More is Different", published in Science. Anderson nicely used broken symmetry as an example of an organising principle that occurs at one strata and as a result of the thermodynamic limit.

The article was based on lectures Anderson gave in 1967.
The article actually does not seem to contain the word "emergence". He talks about new properties "arising".

I recently learned how similar ideas about emergence and the stratification of fields was enunciated earlier by Michael Polanyi, in The Tacit Dimension, published in 1966, based on his 1962 Terry Lectures at Yale. The book contains a chapter entitled "Emergence".

Here is a quote:

you cannot derive a vocabulary from phonetics; you cannot derive the grammar of language from its vocabulary; a correct use of grammar does not account for good style; and a good style does not provide the content of a piece of prose. ... it is impossible to represent the organizing principles of a higher level by the laws governing its isolated particulars.

Much of the chapter focuses on biology and the inadequacy of genetic reductionism. These ideas were expanded in a paper, "Life's irreducible structure," published in Science in 1968.

I recently learned about Polanyi's contribution from
The concept of emergence in social sciences: its history and importance 
G.M. Hodgson

Here is a bit of random background.

Before turning to philosophy, Polanyi worked very successfully in Physical Chemistry. Some readers will know him for his contributions to reaction rate theory, the transition state, a diabatic state description of proton transfer, the LEPS potential energy surface based on valence bond theory, ...

Polanyi was the Ph.D. advisor of Eugene Wigner. Melvin Calvin, a postdoc with Polanyi, and his son, John Polanyi, went on to win Nobel Prizes in Chemistry.

Google Scholar lists "The Tacit Dimension" with almost 25,000 citations.
The book was recently republished with a new foreword by Amartya Sen, Nobel Laureate in Economics.

Simple valence bond model for a chemical reaction

Valence bond theory provides an intuitive picture of not just chemical bonding but bond breaking and making. For a reaction ab + c -> ac + b, one can write done the energy of the total system in terms of pairwise exchange J and coulomb integrals Q. This can be used to produce semi-empirical potential energy surfaces and/or diabatic states and coupling between them. This is at the heart of the treatment of coupled electron-proton transfer by Hammes-Schiffer and collaborators, discussed in previous posts. I struggled a bit to find the background of this. It goes back to London-Eyring-Polanyi-Saito (LEPS). A nice summary is the paragraph below taken from a paper by Kim, Truhlar, and Kreevoy. It provides a way to parametrise the Qs and Js in terms of empirical Morse potentials for the constituent molecules. At the transition state the gap to the next excited state is related to a singlet-triplet gap, a point emphasized by Shaik and collaborators.

More background is in material in the old text, Theoretical Chemistry by Glasstone (1944).

One of my scientific heroes: John R. Platt (1918-1992)

John R. Platt has featured on this blog before because of his paper in Science about "Strong Inference" and the "method of multiple alternative hypotheses". This stimulated my New Year's resolution.

Platt also wrote a really nice theory paper about organic dyes that will feature soon because Seth Olsen has a paper about to appear in Journal of Chemical Theory and Computation which gives a rigorous quantum chemical basis for Platt's theory.

I was wondering what happened to Platt and found an interesting 1992 Obituary in the New York Times.

I also found that Platt was on a panel discussion with Michael Polanyi about the interplay of reductionism and emergence in biology, physics, and chemistry.

Emergence in molecular biology

A key framework for molecular biophysics is that structure determines property which in turn determines function. But `function’ is not a reducible concept (something Michael Polanyi emphasized).
John Hopfield is a Professor of Molecular Biology at Princeton University and also was recently President of the American Physical Society. In a helpful piece in Nature about physicists working in molecular biology Hopfield states, ``The word `function’ does not exist in physics, but physicists need to learn about it, otherwise they will be in a sandbox playing by themselves.’’

In molecular biology, a dramatic, puzzling, and fascinating manifestation of emergence is how differences in a string of letters (the nucleotides A,G,T, and C) encoded at the molecular level in DNA lead to different cell types, different acquired characteristics, and even different species.