Erwin Schrödinger , talking about the diffusion process in his historical book "What is life?" , writes
"[...] its physical exactitude must nevertheless be challenged in every particular application. Being based on pure chance, its validity is only approximate. If it is, as a rule, a very good approximation, that is only due to the enormous number of molecules that co–operate in the phenomenon. The smaller their number, the larger the quite haphazard deviations we must expect and they can be observed under favourable circumstances."
In this sentence Schrödinger puts together almost all the profound concepts characterizing a complex system: probability (chance), fluctuations (deviations) and a huge number of molecules doing something all together (cooperation, emergence).
("What is life?" is available here in free download!)
"[...] its physical exactitude must nevertheless be challenged in every particular application. Being based on pure chance, its validity is only approximate. If it is, as a rule, a very good approximation, that is only due to the enormous number of molecules that co–operate in the phenomenon. The smaller their number, the larger the quite haphazard deviations we must expect and they can be observed under favourable circumstances."
In this sentence Schrödinger puts together almost all the profound concepts characterizing a complex system: probability (chance), fluctuations (deviations) and a huge number of molecules doing something all together (cooperation, emergence).
("What is life?" is available here in free download!)
Pierre-Simon, marquis de Laplace in his book "A Philosophical Essay on Probabilities" says
"Given for one instant an intelligence which could comprehend all the forces by which nature is animated [...], it would embrace in the same formula the movements of the greatest bodies in the universe and those of the lightest atom"
Laplace introduces the emergence of noise and random phenomena as the result of the human ignorance about the full characterization of a given process (lack of information). Indeed, if we "[...] could comprehend all [...]".
("A philosophical Essay on probabilities" is available here in free download!)
"Given for one instant an intelligence which could comprehend all the forces by which nature is animated [...], it would embrace in the same formula the movements of the greatest bodies in the universe and those of the lightest atom"
Laplace introduces the emergence of noise and random phenomena as the result of the human ignorance about the full characterization of a given process (lack of information). Indeed, if we "[...] could comprehend all [...]".
("A philosophical Essay on probabilities" is available here in free download!)
A beautiful sentence from an Italian Book, "Personaggi e scoperte della Fisica", by Emilio Segrè (here I give the translation in English):
"Thermodynamics, during the subsequent conceptual revolutions in Physics in the twentieth century, has been stable like a rock [...] The great masters, Planck and Einstein, used it as an anchor when everything seemed to be in doubts "
(Italian version) “La termodinamica, durante le successive rivoluzioni nella fisica del XX secolo, è rimasta stabile come una roccia, e [...] i grandi innovatori, Planck ed Einstein, la usarono come un’ancora quando tutto sembrava dovere essere messo in dubbio.”
"Thermodynamics, during the subsequent conceptual revolutions in Physics in the twentieth century, has been stable like a rock [...] The great masters, Planck and Einstein, used it as an anchor when everything seemed to be in doubts "
(Italian version) “La termodinamica, durante le successive rivoluzioni nella fisica del XX secolo, è rimasta stabile come una roccia, e [...] i grandi innovatori, Planck ed Einstein, la usarono come un’ancora quando tutto sembrava dovere essere messo in dubbio.”
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"The mathematical concept of probability arose from the endeavour to render objective, as far as possible, the subjective expectation of a single event. To do this the expectation must be replaced by the objective average frequency of an event when it is repeated under like conditions.”
Wolfgang Ernst Pauli in Writings on Physics and Philosophy |
"Probability does not exist !"
Bruno de Finetti in Theory of Probability, Vol. 1. New York: John Wiley and Sons (1974) |
Albert Einstein, in his historical paper "Investigation on the Theory of Brownian Movement", writes
“If the movement discussed here can actually be observed (together with the laws relating to it that one would expect to find), then classical thermodynamics can no longer be looked upon as applicable with precision to bodies even of dimensions distinguishable in a microscope: an exact determination of actual atomic dimensions is then possible”
With the above sentence, Einstein is actually anticipating the result of the celebrated fluctuation-dissipation relation, introduced by him in his paper for the first time in the human history. The Einstein's result provided, for the first time, an operative way to determine the atomic dimensions and thus definitively prove the atomic hypothesis (Yes: Einstein has been more than the Relativity Theory!). Studying fluctuation - dissipation relations is still today an intense and highly interesting field of research.
("Investigation on the Theory of Brownian Movement" is available here in free download!)
“If the movement discussed here can actually be observed (together with the laws relating to it that one would expect to find), then classical thermodynamics can no longer be looked upon as applicable with precision to bodies even of dimensions distinguishable in a microscope: an exact determination of actual atomic dimensions is then possible”
With the above sentence, Einstein is actually anticipating the result of the celebrated fluctuation-dissipation relation, introduced by him in his paper for the first time in the human history. The Einstein's result provided, for the first time, an operative way to determine the atomic dimensions and thus definitively prove the atomic hypothesis (Yes: Einstein has been more than the Relativity Theory!). Studying fluctuation - dissipation relations is still today an intense and highly interesting field of research.
("Investigation on the Theory of Brownian Movement" is available here in free download!)
"there are broadly speaking two problems: I. Is it possible to reconcile both time reversibility and recurrence with 'observable' irreversible behavior? II. Is it possible to achieve such a reconciliation in the realm of classical mechanics?"
Marc Kac in Probability and Related Topics in Physical Sciences
Marc Kac in Probability and Related Topics in Physical Sciences
"While examining the form of the particles immersed in water , I observed many of them very evidently in motion. These motions were such to satisfy me [...] that they arose neither from currents in the fluid nor from its gradual evaporation, but belonged to the particle itself"
Robert Brown in A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies.
(available here in free download!)
Robert Brown in A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies.
(available here in free download!)