Customer Reviews

From the Closed World to the Infinite Universe (Hideyo Noguchi Lecture)

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Korye's decades-old book is still a pleasure and a marvel to read. The ideas developed in this first-rate work are lucidly and extensively developed and contain such subtle gems of thought that one could not possibly discover all of them with a single reading. Anyone with even but a passing interest in the history and philosophy of science should add this book to his library. A true classic!

Of all the tomes I read during my years studying the history of science, this is the one I tend to come back to the most.

Koyre describes the thinking of such diverse figures as Giordano Bruno, Nicholas of Cusa, Galileo, Henry More, and Johannes Kepler regarding the possibility that the universe might be of unlimited extent. As such, the discussions, particularly early on, deal more with scholastic philosophy, with heavy emphasis on religious implications. They deal with abstract notions, and some of the thinking of these early figures is quite bold, startling even, and beautiful, after a fashion.

It is apropos to recall that science was long known as "natural philosophy"...and indeed, as the former figures give way to the analyses of Newton and Leibniz, we find Koyre's work limning the disentangling of these two threads, philosophy and science, at least with respect to cosmology.

In particular, Koyre underlines one of the most ironical developments in all the history of ideas at the very end of the book, in recounting how the triumph of Newtonian physics rendered superfluous the God that it had been Newton's purpose to honor through his science.

Not for everyone; but for me, magnificent.

Readers of this book beware, its themes are huge! It contains lucid narrative of the competition from Cartesians to Newtonians for the best model of the universe and the nature of time and space. There are scarcely any baggy corners into which the reader will turn unwillingly. However, there is not terribly much about the science or the methods of discovery employed by these thinkers in their shared pursuit of important results. Koyre has written a classic study of intellectual history. Discussion of divinity and its aspects is abundant because this presence was one that the scientists were working diligently to situate without offending the authorities and employers of the age. The universe is a source whose study has profoundly metaphysical and ontological implications. Koyre brings these alive for the reader and shares the tumult of ideas that produced much of what we consider now to be a satisfactory vision of the universe.

This is a fantastic book; unfortunately, this version is almost unreadable. There is no indentation or italicization, and quotation marks are often misplaced. This makes it awfully difficult to tell the lengthy quoted passages apart from the author's own text. Definitely read this book--just buy it from a different publisher.

To get a true sense of the Copernican Revolution, it is necessary to understand both:
1) Christian Europe's theological transformations, primarily , from 1400 to 1517 (Protestant Reformation & Catholic response), to 1687
2) an astronomical paradigm shift as result of instruments, discoveries & theories, 1400 to 1687. Kepler, Tycho, Galileo, & Newton.


Koyre has done the hard part of Task 1 for the scholar / scientist / theologian. Koyre has meticulously laid out logically the competing arguments (by originator) for:

the medieval geo-centric closed world / Chain of Being (Scholastics, mostly),
early Renaissance's helio-centric closed world (1543, Copernicus) which undermined the divine Chain / divine right of Kingship, etc
the 17th century mathematically-exact, mechanical, infinite universe that resulted from the astronomy of Kepler, Tycho, Galileo, & Newton.

This theological transformation was a gradual shift from:

1) an infinite, omnipotent, transcendent Christian God that was WHOLLY different from finite Man & his cosmos
to
2) an immanent & infinite 'Deist clock-maker' God who expressed His infinite power through the 'plentitude' of an infinite universe.
Koyre considers the transference of earlier attributes of God -- Absolute power & divine infinity, to the physical description of Newton's Absolute Space -- the 'divinization of Space'! This transformation also revitalized the place of Mankind in the cosmos as 'Renaissance Humanism'.

These changes did not progress without the pain of inquisitions, self-exiles & house arrests, and the occasional martyr. Giordano Bruno was burned at the stake around 1600 for his heresy of an infinite, immanent God. As a priest, his infatuation with infinity was too close to the Church, and, too soon, lacking the support of Galileo & Newton's observations. Cardinal de Cusa, on the other hand, theologized an 'indeterminate cosmos' as a transition from Copernicus to infinite cosmologists and profoundly influenced the theological transformation from medieval to Renaissance.
I would recommend first reading The Sleepwalkers by Koestler, as a generalist summary of the astronomical paradigm shift. With this astronomical background, Koyre will be much easier to understand. Then try Kuhn, The Structure of Scientific Revolutions, which was deeply influenced by Koyre.

I was interested only in the scientific half of the story. I shall summarise it here.

Anti-science was the norm before the scientific revolution. Nicholas of Cusa, for example, "denies the very possibility of the mathematical treatment of nature" (p. 19). By thinking your way out of empiricism and sense-data, "'with the intellect, which alone can practice learned ignorance, you will see that the world and its motion cannot be represented by a figure.'" (p. 17). "'And [if] we are surprised when we do not find the stars in the places where they should be according to the ancients, [it is] because we believe [wrongly] that they were right in their conceptions concerning the centers and poles as well as in their measurements.'" (p. 14). "'The ancients did not arrive at the things we have brought forth, because they were deficient in learned ignorance." (p. 17). Giordano Bruno agreed that "learned ignorance" is the way forwards since sense-perception "advertiseth and confesseth its own feebleness and inadequacy by the impression it giveth us of a finite horizon, an impression moreover which is ever changing. Since then we have experience that sense-perception deceiveth us concerning the surface of this globe on which we live, much more should we hold suspect the impression it giveth us of a limit to the starry sphere." (p. 45).

Kepler, by contrast, makes sense-perception the core of his beautiful discussion of the problem. He argues that our solar system has a unique place in the universe, because the night sky would never look anything like ours from the vicinity of any other star. Assuming first that all the stars "'were placed on the same spherical surface of which we are the center,'" and considering for example two stars in Orion, then "'the eye located on one of them would see the other as having angular magnitude of about 2 3/4°; [a magnitude] that for us of the earth would not be occupied by five suns placed in line and touching each other'" (p. 63). But what if the stars were not on a fixed sphere but rather spread out over much greater distances away from us? That would not help, "'for the more you remove the stars to an infinite altitude, the more monstrous you imagine their dimensions'" (p. 68), i.e., if their distances are very different then so are their sizes, so that, again, the universe would look different from suns other than our own. All this seems to weigh against the infinitude of the universe. However, "'astronomy makes no judgement, because in such an altitude it is deprived of the sense of seeing'" (p. 84). Kepler's arguments are of course faulty since he mistakenly assumes that a star's apparent magnitude is proportional to its distance and size, but no scientific arguments against this assumption were possible at the time.

One person was in a better position than anyone to take the next step: Galileo, with his telescope. But, in his usual cowardly manner, he has nothing to say on the matter and refuses to take part at all in the discussion at all (p. 95).

With Descartes science is abandoned in favour of philosophy. He "denies that there is such a thing as 'space,' and entity distinct from 'matter' that 'fills' it. Matter and space are identical and can be distinguished only by abstraction." (p. 102). Thus "to assign boundaries to [the universe] becomes not only false, or even absurd, but contradictory. We cannot posit a limit without transcending it in this very act." (p. 104).

Newton too was no stranger to philosophical and theological arguments, but he also made scientific contributions to the issue: his 'proof' of the existence of absolute space (p. 168), the law of inertia and its implications (p. 169), and an argument that a finite universe would collapse under gravity: "'it seems to me that if the matter of our sun and planets, and all the matter of the universe, were evenly scattered throughout all the heavens, ... and the whole space throughout which this matter was scattered was but finite; the matter on the outside of this space would, by its gravity, tend towards all the matter on the inside, and, by consequence, fall down into the middle of the whole space, and there compose one big spherical mass'" (p. 185).