29 April 2020

On Infinite (1950-1959)

"It is indeed wrong to think that the poetry of Nature’s moods in all their infinite variety is lost on one who observes them scientifically, for the habit of observation refines our sense of beauty and adds a brighter hue to the richly coloured background against which each separate fact is outlined. The connection between events, the relation of cause and effect in different parts of a landscape, unite harmoniously what would otherwise be merely a series of detached sciences." (Marcel Minnaert, "The Nature of Light and Colour in the Open Air", 1954)

"The infinite in mathematics is always unruly unless it is properly treated." (James R Newman, "The World of Mathematics" Vol. III, 1956)

"It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium." (Ivan P Pavlov, "Experimental psychology, and other essays", 1957)

"[…] observation and theory are woven together, and it is futile to attempt their complete separation. Observation always involve theory. Pure theory may be found in mathematics, but seldom in science. Mathematics, it has been said, deals with possible worlds - logically consistent systems. Science attempts to discover the actual world we inhabit. So in cosmology, theory presents an infinite array of possible universes, and observation is eliminating them, class by class, until now the different types among which our particular universe must be included have become increasingly comprehensible." (Edwin P Hubble, "The Realm of the Nebulae", 1958)

"The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite." (Werner K Heisenberg, "Physics and Philosophy: The revolution in modern science", 1958)

"Mathematics has, of course, given the solution of the difficulties in terms of the abstract concept of converging infinite series. In a certain metaphysical sense this notion of convergence does not answer Zeno’s argument, in that it does not tell how one is to picture an infinite number of magnitudes as together making up only a finite magnitude; that is, it does not give an intuitively clear and satisfying picture, in terms of sense experience, of the relation subsisting between the infinite series and the limit of this series." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)

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