As the natural sciences have developed to encompass increasingly complex systems, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical neo-Darwinism, information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, wave functions, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos.
Nick LandRelated topics
century classical complex complexity early edge entropy late later mechanics natural quantum trend gene sciencesRelated quotes
I reproach myself for a gross error. But I would reproach myself more if I had persisted in an error after observations revealed it clearly to be that. I made a deal of money in the late 1940s on the bull side, ignoring Satchel Paige's advice to Lot's wife, "Never look back.” Rather I would advocate Samuelson's Law: "Always look back. You may learn something from your residuals. Usually one's forecasts are not so good as one remembers them; the difference may be instructive.” The dictum "If you must forecast, forecast often,” is neither a joke nor a confession of impotence. It is a recognition of the primacy of brute fact over pretty theory. That part of the future that cannot be related to the present's past is precisely what science cannot hope to capture. Fortunately, there is plenty of work for science to do, plenty of scientific tasks not yet done.
Paul Samuelson
Personally, I never met Knut Wicksell. I saw him once when he delivered a lecture in Oslo, but being an unassuming student at the time, I did not have the courage to talk to him. So my knowledge of his theory came only through his writings. That, however, was a very intense and absorbing form of making his acquaintance. Already from my early student days, I read his writings (in German and Swedish) avidly. And I continued to do so later.
When I started my study on Wicksell, I found that his works were not easy reading. Often it was only at the third or fourth reading that I grasped his ideas. Invariably, each new reading made me more and more enthusiastic. Sometimes it happened that I thought I had finally caught him in an inconsistency or in unclear thinking. Every time this happened, it turned out, however, that the error was mine.
Ragnar Frisch
This new quantum mechanics promised to explain all of chemistry. And though I felt an exuberance at this, I felt a certain threat, too. "Chemistry,” wrote Crookes, "will be established upon an entirely new basis.... We shall be set free from the need for experiment, knowing a priori what the result of each and every experiment must be.” I was not sure I liked the sound of this. Did this mean that chemists of the future (if they existed) would never actually need to handle a chemical; might never see the colors of vanadium salts, never smell a hydrogen selenide, never admire the form of a crystal; might live in a colorless, scentless, mathematical world? This, for me, seemed and awful prospect, for I, at least, needed to smell and touch and feel, to place myself, my senses, in the middle of the perceptual world.
Oliver Sacks
A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. ...But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.
Hermann Weyl
The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.
George Klir