Quotes from P.W. Anderson's paper published in Science, 1972.
The reductionist hypothesis may still be a topic for controversy among philosophers, but among the great majority of active scientists I think it is accepted without question. The workings of our minds and bodies, and of all the animate or inanimate matter of which we have any detailed knowledges are assumed to be controlled by the same set of fundamental laws. if everything obeys the same fundamental laws, then the only scientists who are studying anything really fundamental are those who are working on those laws. In practice, that amounts to some astrophysicists, some elementary particle physicists, some logicians and other mathematicians, and few others. The main fallacy in this kind of thinking is that the reductionist hypothesis does not by any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other. One may array the sciences roughly linearly in a hierarchy, according to the idea that the elementary entities of science X obey the laws of science Y.
| X | Y |
|---|---|
| Solid state or many-body physics | Elementary particle physics |
| Chemistry | Many-body physics |
| Molecular biology | Chemistry |
| Cell biology | Molecular biology |
| …. | ….. |
| …. | …. |
| Psychology | Physiology |
| Social sciences | Psychology |
But this hierarchy does not imply that science X is “just applied Y”. At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry.
The reason why we see different properties when considering large scale and complex systems is related to broken symmetry. There are at least three inferences to be drawn from this. One is that symmetry is of great importance in physics. By symmetry we mean the existence of different viewpoints from which the system appears the same. It is only slightly overstating the case to say that physics is the study of symmetry. The first demonstration of the power of this idea may have been by Newton, who may have asked himself the question: What if the matter here in my hand obeys the same laws as that up in the sky that is, what if space and matter are homogeneous and isotropic? The second inference is that the internal structure of a piece of matter need not be symmetrical even if the total state of it is. A third insight is that the state of a really big system does not at all have to have the symmetry of the laws which govern it, in fact, it usually has less symmetry. The outstanding example of this is the crystal: Built from a substrate of atoms and space according to laws which express the perfect homogeneity of spaces the crystal suddenly and unpredictabIy displays an entirely new and very beautiful symmetry. The general rule, however, even in the case of the crystal, is that the large system is less symmetrical than the underlying structure would suggest: Symmetrical as it is, a crystal is less symmetrical than perfect homogeneity.
The essential idea is that in the so called N -> Infinity limit of large systems; (on our own, macroscopic scale) it is not only convenient but essential to realize that matter will undergo mathematically sharp, singular ‘phase transitions’ to states in which the microscopic symmetries, and even the microscopic equations of motion, are in a sense violated. In this case we can see how the whole becomes not only more than but very different from the sum of its parts.
In closing, I offer two examples from economics of what I hope to have said. Marx said that quantitative differences become qualitative ones, but a dialogue in Paris in the 1920’s sums it up even more clearly: FITZGERALD: The rich are different from us. HEMINGWAY: Yes, they have more money.