Book review: Phase Transitions

Phase Transitions by Ricard Solé was one of those books that nurtured my curiosity and motivated me to carry on with my PhD. Ana, my girlfriend at the time (2011), always suggested me to bring nice books for holidays that would distract me from work, books with stories or authors from the places we were visiting . But with Solé it was difficult to leave it at home. Most of the book was read in 2012-13 on the beaches and bars of Barcelona, Solé’s home; and believe or not, it did distracted me from work by making me looking it from a different perspective.

Phase Transitions is the concept that physicist like Solé use to describe changes in dynamic systems with bifurcations – changes between different states of organisation in complex systems. It’s the same as ‘critical transitions’ or critical phenomena, as other authors like Marten Scheffer prefer to use; or ‘regime shifts’ as ecologist often call them. But that’s just jargon. I read the book too long ago to be able to give a fair summary and highlight its most important lessons. However, this review will be more from an emotional perspective, what I like and dislike from that bunch of math.

The book is an amazing resource for teaching. It’s structured in 16 very short chapters, most of them don’t exceed the 10 pages. Yet they cover as many disciplines as you can imagine, it’s like brain candy for an interdisciplinary inclined mind. Chapter 1-5 set up the basics: what are phase transitions, analysis of stability and instability, bifurcations, percolations and random graphs. Solé keeps the mathematics to a minimum, any student without a strong maths background like me follows and enjoy more the story that the mathematical subtleties. He also guide you on how the math or the set of equations that helps you understand something, say percolations, are also useful to understand what looks like unrelated topics  such as cancer dynamics or lexical change in a language.

And that is exactly what I like of the book. Chapters 6 – 16 takes you on a journey of where phase transitions have applications in different fields in science: the origins of life (6), virus dynamics (7), and cell structure (8) for the biology inclined.  For the medicine inclined: epidemic spreading (9), gene networks (10), and cancer (11). For someone like me: ecological shifts (12), social collapse (16), information and traffic jams (13) and collective intelligence (14). And my absolute favourite: language (15) because it surprised me how phase transitions can be used to understand change in language, and also because it introduced a very peculiar model called the hypercube. Now what I dislike of the book was the incomplete list of references, imagine if the one missing is the one you want to follow up!

I took the book out of the shelf today and look at it with nostalgia. Last week I read a paper that studies depression as a critical transition using models of symptoms networks with thresholds (co-authored by Scheffer, the author of the book that inspired this blog), and today I accidentally ended up watching the video below on how music can also have basins of attraction. That feeling of déjà vu, that two disparate fields can have something fundamental in common, that we can learn music and better understand depression or cancer and viceversa; that’s what makes me in love with science. That’s what I enjoyed the most of Solé’s book, it opened the horizon of what I was actually doing on my PhD and helped me feel less afraid of exploring; otherwise how does one make the nice connections?

 

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