Introducing universality and particularity

Every person is unique. No two people on earth are identical. We differ in physical appearance, personality, fingerprints, heartbeat, gait, and DNA. Such differences are used to identify criminals and in the surveillance of citizens by nation states. Yet in other ways all humans are the same. We all have brains, hearts, and lungs. All our bodies use the same biochemistry to stay alive: whether to breathe oxygen, digest food, or fight infections. Arguably, on some level, we all have common aspirations: to survive, to be loved, to be happy, and to find meaning and purpose. Yet these aspirations find many particular expressions. All humans have certain universal qualities and properties, from the biomolecular to the social. Yet at a finer level of detail, there is a particularity of each of these properties. This paradox of ``same and not the same’’ can be viewed as a tension between universality and particularity.

All academic disciplines search for universals; they are used to categorise, to conceptualise, and to theorise. Biologists classify species of plants and animals and types of cells and viruses. All of these different biological systems make use of the same biomolecules (DNA, RNA, and proteins), and biochemical reactions. The same genetic code uses the information encoded in a piece of DNA to make proteins with a specific function. Anthropologists study the immense diversity of human cultures and societies. This diversity can be understood in terms of certain universal concepts such as kinship, sexual relations, family, ritual, community, economics, and religion. Linguists study the structure and grammar of the thousands of different human languages.  Given the diverse world that we live in many of us find the universality that different academic disciplines have discovered over the past century surprising and exciting.

Condensed matter physicists study the incredible diversity of different states of matter and the transitions between them. A surprising discovery is that there is much more universality than might be expected. In this chapter, I will discuss the nature of this universality, the different associated length scales associated with phase transitions, and how this universality emerges. The insight of Landau (chapter 4) was correct: many of the chemical and structural details of materials are irrelevant to understanding phase transitions. Furthermore, a precise classification of different types of phase transitions (universality classes) can be made. Even superconducting and superfluid and a subset of some magnetic transitions are in the same class. The determinants of the universality classes are the symmetry of the order in a state of matter and the spatial dimensionality of the system.

In society today there is significant public debate about morality; what is universal and what is particular to specific individuals, societies, or situations? Philosophers have debated universals for centuries. Many academic disciplines have discovered certain universal patterns, yet struggle to understand how universality does or does not emerge in the presence of particularity.  This struggle is due to the complexity of the systems of interest, including the many different scales present. Condensed matter physics provides a concrete and beautiful example where we do understand how to relate universality and particularity.

Would your non-scientist friends and relatives find this interesting? comprehensible?

I welcome suggestions.