I will start with a couple of quotes from the Chapter 2, The Disunity of Science, Paul Feyerabend, The Tyranny of Science
“After Newton had found his law of gravitation, he applied it to the moon and to the planets. It seemed that Jupiter and Saturn, when treated in this way, slowly moved away from each other – the planetary system seemed to fall apart.”
“Newton concluded that it was being kept stable by an additional force and he assumed that God from time to time intervened in the course of planets. That agreed with his theological views. God, Newton believed, was not just an abstract principle.”
“Laplace showed a century later, that the planetary system did not fall apart but oscillated with a very large period. ‘I do not need this hypothesis’, he said, when Napoleon asked him about the need for a divine being.”
“But this was not yet the end of matter. … A precise calculation would have given infinities. … But this meant that Newton’s theory gave correct results only when used in an ad hoc way.”
“Poincaré did care. Using a new type of mathematics, he recast the problem of stability – and now, it seems, we have at last a satisfactory solution.”
I liked that story a lot and below there are results of my search in Google.
In German. Aufsatz von Prof. Roman Sexl, Universität Wien. Isaac Newton korrigiert Descartes. Siehe Gott als kosmischer Gastarbeiter
Newton: “Es ist keine Herabsetzung Gottes, sondern die wahre Verherrlichung seiner Werke, wenn man sagt, dass nichts ohne seine immerwährende Leitung und Aufsicht vor sich geht. Der gegenwärtige Bau des Sonnensystems wird nach den jetzt geltenden Bewegungsgesetzen im Laufe der Zeit in Verwirrung geraten und dann vielleicht verbessert werden.”
Jacques Laskar, Astronomie et Systèmes Dynamiques, Paris, France
Stability of the solar system
“In Newton’s view, the perturbations among the planets were strong enough to destroy the stability of the solar system, and divine intervention was required from time to time to restore planets’ orbits to their place.”
“Although the constants required for the application of Arnold’s theorem correspond to extremely small values of the planetary masses, this result reinforced one more time the idea that the Solar System was stable, by any reasonable acceptance of this term, on a time comparable to its age.
The results obtained through numerical integration in the past decade will show the contrary.”
“This observation leads then to the concept of marginal stability for the Solar system: the Solar system is unstable, but catastrophic phenomena leading to the destruction of the System in its current form can take place only in a time comparable with its age, that is to say approximately 5 billion years.”
Is the Solar System Stable?
“Newton’s comment on this problem is worth quoting: “the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted, which may have arisen from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation.” Evidently Newton believed that the solar system was unstable, and that occasional divine intervention was required to restore the well-spaced, nearly circular planetary orbits that we observe today. According to the historian Michael Hoskin, in Newton’s world view “God demonstrated his continuing concern for his clockwork universe by entering into what we might describe as a permanent servicing contract” for the solar system.”
Discussion (see Deism and Newton):
Some my quotes are below:
“Ancient Babylonian records showed that the planetary system had been stable for a considerable time.”
“At any rate, there was a clash between the facts and Newton’s law of gravitation used without additional assumptions.”
You may want to find Leibniz’s critics of Newton.
“Leibniz ridiculed Newton’s god for being an incompetent universe-maker and declared that what god does once, he does in a perfect way.”
It depends on how you define fact. Imagine that at Newton’s time the ideal scientific standards would have been accepted. Then his idea and his paper have been just rejected. “Okay, your idea is nice but you have to work on it some more to make it scientific.” Don’t you agree?
This is Feyerabend’s point, that the Newton laws have been just ad hoc hypotheses, nothing more. You cannot say that they come from observations, as they have contradicted to the observations at that time.
The most interesting that “Who cares?”. The Newton laws have been accepted by the scientific community long time before they have been brought in agreement with observations.
“But this meant that Newton’s theory gave correct results only when used in an ad hoc way. It did not reveal a feature of universe. Did scientists give up? No. The theory was plausible, it had astonishing successes so it retained despite the fact that, taken literally, it led to absurdities. Besides, many scientists were interested in predictions only and did not care about a metaphysical notion like ‘reality’.”
So, to state that a theory is driven by the facts is actually wrong. In the historical context, the facts are actually driven by a theory.
It happens the same way nowadays. Take for a example the superstring theory. It is has not been driven by facts in any way. Or this notion that information is equivalent to the thermodynamic entropy. It has nothing to do with facts at all.
By ‘ideal scientific standards’ I have meant for example this statement from Wikipedia
‘The Oxford English Dictionary says that scientific method is: “a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.”‘
Yet, if we consider how science has been done according to historical facts (not how it could have been done), then there are discrepancies. After all Newton has called in God who from time to time corrects the planets to preserve stability of the Solar system. It is written in his book and this is a historical fact. According to statement above one can even say that this was a result of systematic observation, measurement and experiment.
As for entropy and information, I may missed some your arguments. Yet, in all papers you gave me there was written that the equivalence of the thermodynamic entropy and information follows from similarity of the two equations. There were no experiments, observations and measurement to this end. Even more, people who have made this statement have not applied it to typical thermodynamics problems and have not shown how conventional thermodynamic problems (heat engines and computing phase equilibria) benefit from such a statement. My examples to this end are here