Emergence matters

Reality is stratified and science is hierarchial: from physics to chemistry to biochemistry to biology to psychology. Generally, as one goes up the strata the complexity of the system under study increases and the relevant length and time scales become greater. At each strata or level of hierarchy, science seeks to illuminate what are the principles that describe the phenomena under study. Sometimes principles can be reduced to and understood in terms of principles from the strata below. For example, genetics can be understood in terms of molecular biology. Rules of chemical bonding can be understood in terms of quantum physics. However, it should be stressed that there are very few specific cases where phenomena at one strata have been predicted solely from a knowledge of the laws underlying strata below. In almost all cases, one observes (n.b., not deduces) phenomena at one level, develops concepts to understand them at that level, and then a posteriori tries to understand them in terms of the laws from the level below.

Perhaps is not appreciated enough just how hard it is to predict properties of quantum many-body systems. New phases of matter continue to be discovered: liquid crystals, quasicrystals, antiferromagnets, superfluids, …. Yet I am only aware of one case where a new state of matter was predicted and then discovered; that is Bose-Einstein condensates in dilute atomic gases were predicted.

Quantum chemistry involves using Schrodinger’s equation to calculate properties of molecules. It has many successes at calculating observed properties of small molecules. However, a measure of its limitations is the citation that one of the world leaders in the field, Fritz Schaefer, received for award of the Centenary Medal of the Royal Society of Chemistry in 1992: ``the first theoretical chemist successfully to challenge the accepted conclusions of a distinguished experimental group for a polyatomic molecule, namely methylene.”


In his classic More is Different paper, Phil Anderson emphasised that the success of methodological micro-reductionism does not imply a constructivist hypothesis: if we know the laws of one strata we can deduce the laws of the next strata above. Since making predictions from one strata to the next is so difficult, if not impossible, an a posteriori approach rather than an a priori approach is often necessary.