Johannes Kepler Views an Infinite Universe with Horror

In a previous post entitled Giordano Bruno on the One and the Infinite, I presented Bruno’s (1548-1600) belief that the universe was infinite and that therein were multitudes of stars, all similar to our sun. Here, for example, is Philotheo beginning the Third Dialogue in Bruno’s On the Infinite Universe and Worlds¹:

[The whole universe] then is one, the heaven, the immensity of embosoming space, the universal envelope, the ethereal region through which the whole hath course and motion. Innumerable celestial bodies, stars, globes, suns and earths may be sensibly perceived therein by us and an infinite number of them may be inferred by our own reason. The universe, immense and infinite, is the complex of this [vast] space and of all the bodies contained therein. [p.302, my emphasis]

I also wrote that the infinite universe is not currently in vogue, quoting from Arthur Eddington’s (1882-1944) The Nature of the Physical Universe², in which he violently rejected “the nightmare of infinity”:

Space is boundless by re-entrant form not by great extension. That which is is a shell floating in the infinitude of that which is not. We say with Hamlet, “I could be bounded in a nutshell and count myself a king of infinite space’’.

But the nightmare of infinity still arises in regard to time. The world is closed in its space dimensions like a sphere, but it is open at both ends in the time dimension. [p.83, my emphasis]

The rejection of an infinite universe is not new. For example, Aristotle (384 BCE - 322 BCE) argued against it [the infinite universe] in his De Caelo (On the Heavens). What is striking of Eddington’s words is how they resemble those of Johannes Kepler (1571-1630), who addressed the writings of Bruno and William Gilbert (1544-1603) in Chapter XXI of De Stella Nova in Pede Serpentarii³ [Of the New Star in the Foot of the Serpent], originally published in 1606:

[The infinite universe] was defended by the unfortunate Jord. Bruno. It was also asserted in a by no means obscure way, though he expressed himself as if he doubted it, by William Gilbert in the otherwise most admirable book De magnete. Gilbert’s religious feeling was so strong that, according to him, the infinite power of God could be understood in no other way than by attributing to Him the creation of an infinite world. But Bruno made the world so infinite that [he posits] as many worlds as there are fixed stars. And he made this our region of the movable [planets] one of the innumerable worlds scarcely distinct from the others which surround it; so that to somebody on the Dog Star (as, for instance, one of the Cynocephals of Lucian) the world would appear from there just as the fixed stars appear to us from our world. Thus according to them, the new star was a new world. This very cogitation carries with it I don't know what secret, hidden horror; indeed one finds oneself wandering in this immensity, to which are denied limits and center and therefore also all determinate places. [p.253, my emphasis; English translation of Latin from Koyré⁴, pp.60-61]

Max Caspar, the editor of Kepler’s collected works, wrote the following note:

In long explanations (pp.253-257), Kepler turns with all his insight and with the greatest emphasis against this teaching, which Giordano Bruno had proclaimed a short time before. Since this is an essential part of his astronomical worldview, these statements in the 21st chapter deserve special attention. The idea that the individual fixed stars are worlds like the world of the sun and fill infinite space is unbearable to him, it almost inspires him with “horror”. In his refutation he first tries to prove that it is wrong to assume that the view of the world of fixed stars from the sun is the same as from any fixed star. With a great deal of effort, some of which are of course based on the apparent diameters of the fixed stars, which were assumed to be far too large at the time, he tries to save the idea that the place where the sun and the planets are located has something special about it, that this represents a “praecipuus mundi sinus” [“the main cavity of the world”], that the world has an absolute center in the sun, while the fixed stars should have a spherical arrangement around this center of the world, the outermost limit of which is the Milky Way. If there were stars at infinite distances, their mass would also have to be infinite. The assumption that the infinitely distant stars cannot be seen cannot be held. [pp.453-454, my emphasis; English translation of German by Deepl]

Caspar continues:

[Kepler] does not express here the deepest reason for the “horror” that Giordano Bruno's teachings instilled in Kepler. But it is hinted at in the last sentence of the chapter: “infinita mensura cogitatur nunquam” [“an infinite measure cannot be imagined”]. It reveals itself clearly when one considers the roots of his worldview. Like the Pythagoreans, Kepler sees the perfection of the world in the moderately ordered finite; in contrast, the infinite can be equated with chaos. [p.454, my emphasis; English translation of German by Deepl]

It should be noted that De Stella Nova was published four years before Galileo announced his observations of the heavens with a telescope in Sidereus Nuncius [The Starry Messenger]. Therein, Galileo explained that there are numerous more stars than in the heavens than had previously been known. Two possible conclusions followed therefrom: the newly discovered stars could only be seen with magnification because they were further away from, or because they were smaller than, the known stars. Kepler chose the latter, as he wrote in the Preface of his Dioptrice⁵ [Refraction]:

Pena has noticed how astronomers, using the principles of optics, have by most laborious reasoning removed the Milky Way from the elementary universe, where Aristotle had placed it, into the highest region of the ether; but now, by the aid of the telescope lately invented, the very eyes of astronomers are conducted straight to a thorough survey of the substance of the Milky Way; and whoever enjoys this sight is compelled to confess that the Milky Way is nothing else but a mass of extremely small stars. [p.343, my emphasis; English translation of Latin from Carlos⁶, p.83]

As a result, the discovery that with increased magnification, new stars would be seen, in no way changed Kepler’s refusal of an infinite universe. In fact, Kepler would adhere to this view to the end. In his last astronomical work, Epitome Astronomiae Copernicae⁷ [Epitome of Copernican Astronomy], Kepler wrote:

But what if there were in reality stars, of finite body, scattered upwards in the infinite spaces, [stars] which, be­ cause of so great a distance, were not seen by us?

First, if they are not seen, they in no way concern astronomy. Then [Second], if the region of the fixed stars is at all limited, namely downwards, towards our mobile world, why should it lack limits upwards?

Third, though it cannot be denied that there can be many stars which, either because of their minuteness or because of their very great distance, are not seen, nevertheless you cannot because of them assert an infinite space. For if they are, individually, of a finite size, they must, all of them, be of a finite number. Otherwise, if they were of an infinite number, then, be they as small as you like, provided they are not infinitely so, they would be able to constitute one infinite [star] and thus there would be a body, of three dimensions, and nevertheless infinite, which implies a contradiction. For we call infinite what lacks limit and end, and therefore also dimension. Thus all number of things is actually finite for the very reason that it is a number; consequently a finite number of finite bodies does not imply an infinite space, as if engen­dered by the multiplication of a multitude of finite spaces. [p.45, my emphasis; English translation of Latin from Koyré, pp.85-86]

I find Kepler’s first argument truly astonishing: just because certain stars cannot be seen, because our telescopes are too weak, “they in no way concern astronomy”!? My first impression reading this sentence is that Kepler decided to go sit in Plato’s cave, so that he could observe the shadows.

The second argument is also astonishingly weak. Just because there are no stars between us and the stars that we can see, there cannot be any stars behind those that we can see!

As for the third argument, it is a bit more subtle. The way I understand it, it supposes that were there an infinite number of stars, and that these were homogeneously distributed, then they would effectively be seen as a single star, i.e., that the night sky would be uniformly lit. This is essentially Olber’s Paradox, named in honour of Heinrich Wilhelm Olbers (1758-1840).

Whether the universe is infinite or finite is one of the most fundamental questions in science. Having read the arguments put forward by Kepler against an infinite universe, notwithstanding the highest respect I have for him as a researcher, I find them to be utterly unpersuasive. Bruno’s ideas, for which he paid the highest price, are for me the most inspiring.

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1. Dorothea Waley Singer. Giordano Bruno: His Life and Thought. With Annotated Translation of His Work On The Infinite Universe and Worlds. New York: Henry Schuman, 1950.

2. Sir Arthur Eddington. The Nature of the Physical World. Ann Arbor Paperbacks, The University of Michigan Press, 1968. First published by Cambridge University Press in 1928.

3. Johannes Kepler. De Stella Nova in Pede Serpentarii, et ejus exortum de novo iniit, Trigono Egneo (1606). In Johannes Kepler, Gesammelte Werke, Band I, pp.149-487. Herausgegeben von Max Caspar. München: C.H.Beck’sche Verlagsbuchhandlung, 1938.

4. Alexandre Koyré. From the Closed World to the Infinite Universe. Johns Hopkins Press, 1957.

5. Johannes Kepler. Dioptrice (1611). In Johannes Kepler, Gesammelte Werke, Band IV, pp.326-414. Herausgegeben von Max Caspar und Franz Hammer. München: C.H.Beck’sche Verlagsbuchhandlung, 1941.

6. Galileo Galilei. The Sidereal Messenger and a Part of the Preface to Kepler’s Dioptrics. A Translation and Introduction by Edward Stafford Carlos. London: Rivingtons, 1880.

7. Johannes Kepler. Epitome Astronomiae Copernicae (1618-1621). In Johannes Kepler, Gesammelte Werke, Band VII, pp.7-537. Herausgegeben von Max Caspar. München: C.H.Beck’sche Verlagsbuchhandlung, 1991.