A digest of P. W. Anderson’s “more is different”

A digest of P. W. Anderson’s “more is different” ,
Broken symmetry and the nature of the hierarchical structure of science.


Yu Lim Chen
Philip W. Anderson noted that collective behavior is not only more than but very different from a simple sum of individual behavior. Anderson tried to illustrate his argument about the paradox of reductionist hypothesis citing the theory of “broken symmetry” in his own field of many-body physics. He coined the phrase "More is different" while formulating his contention that all fields of physics, indeed all of science, involve equally fundamental insights.
A huge and complex aggregates composed of large number of elementary particles can not be described via the simple extrapolation of the particles’ nature.
In each level, there are always new and exciting universal principles, which can not be automatically derived from a more basic science. We can enumerate the representative and the importance of these scientific conclusions, such as: the genetic law, the double helix, quantum mechanics, nuclear fission.
In physics research, the reductionist hypothesis means that the complex phenomena can be reduced to a simpler and more basic phenomenon. For example, in classical physics, thermodynamics can be reduced to the kinetic theory, acoustics can be reduced to the movement of molecules.
   An obvious corollary of reductionism reveals that 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. This actually means that scientists are nothing more than astrophysicists, elementary particle physicists, logicians and mathematicians who can investigate the fundamental laws governing the whole universe. P. W. Anderson proposed the idea, “more is different”, to put forward his point of view against the reductionist hypothesis.
   Anderson suggests that “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 scale and complexity are dual difficulties for constructionist assumptions will be naturally untenable.
We look at the more complex molecules, because the constituent molecules become more, the law of symmetry is not abolished, but breaking. Three inferences can be drawn. First, the symmetry in physics is extremely important. Second, even the total state of a substance is symmetrical, its internal structure is not necessarily symmetrical. In other words, step-by-step attempt to derive the nature results by these basic laws is extremely difficult. 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.
  Anderson quotes Marx’s words, quantitative differences become qualitative ones, and a dialogue in Paris in the 1920's to clarify his inght of hierarchical structure of science.