Philip Anderson wrote a well-known article for Science in 1972 entitled "More is Different" whose goal was to refute the "constructionist hypothesis," i.e. the idea that all phenomena can be explained by a small set of fundamental laws. Presumably, these were the laws that govern elementary particle interactions. The constructionist hypothesis states that everything, from cellular biophysics to human thought processes, can be understood in terms of these laws so long as one is sufficiently clever in applying them. This hypothesis also leads many scientists to consider other fields as applied subsets of the fundamentals, such as biology existing as a form of applied chemistry, which would be just applied many-body physics and so-on down the line until particle physics is reached again.
Anderson claimed that, contrary to the constructionist hypothesis, new and "fundamental" science is performed at each level of the logical hierarchy of scientific fields and that this is because of the emergence of unexpected behavior at each level of complexity. His primary arguments lay with many-body physics and the idea of broken symmetry. As a system becomes more complex (that is, it takes on more components or the interactions between components become more intricate), it seeks to minimize the interaction energy between its components, which leads to a reduction in the symmetries of the components and an entirely different behavior of the system.
One example of emergent behavior in many-body physics is a crystal lattice, whereby translational and rotational symmetry is reduced by the ordered arrangement of atoms. Instead of a continuous translation or rotation, space must be shifted by an integer amount before the lattice looks the same again, and so these symmetries are reduced. The behavior that emerges from this is rigidity. If certain regions of the crystal experience a force, then the entire crystal moves as a result.
Another example—which demonstrates the unpredictability of emergent behavior—from many-body physics is the ammonia molecule. The nitrogen atom in ammonia undergoes inversion at a rate of roughly 30 billion times per second, which means that the nitrogen atom flips between its location above and below the plane containing the hydrogen atoms. Quantum mechanically, the stationary state of the molecule is a superposition of the two states representing the location of the nitrogen atom. This stationary state is symmetrical and represents what is actually measurable about the molecule. However, the understanding of inversion as a superposition of two unsymmetrical and unmeasurable states required intellectual machinery that was independent of the fundamental rules of atoms. Anderson's argument here suggests that human intuition led to the understanding of inversion, not the laws of physics, which at the fundamental level deal with symmetries and their consequences.
On a minor level, Anderson notes that scale and complexity are what lead to faults with the constructionist hypothesis. He also cautions that the nature of emergence at one level of complexity may not be the same at other levels.
My only question from this article is exactly what does fundamental mean? He seems to assume that fundamental science is always good science, so with his arguments chemists, biologists, and even psychologists can use the word to describe their work and win back their prestige from the particle physicists. However, it also might suggest that any scientific work is fundamental, thereby reducing the word's value and meaning.
A "lab notebook" about my life in science, programming, and philosophy.
