Eternity by the Stars (1872)


I. The universe – The infinite

The universe is eternal in time and space – eternal, boundless and indivisible.1 All bodies, animate and inanimate, solid, liquid and gaseous, are linked by the very things that separate them. Everything holds together. Without the astral bodies [astres], only space would remain, absolutely empty no doubt, but retaining the three dimensions, length, width and depth –– indivisible and unlimited space.

Pascal once said, in his magnificent style: ‘The universe is a circle whose centre is everywhere and whose circumference is nowhere.’2 Could there be a more striking image of infinity? After him, let us say, a little more precisely: the universe is a sphere whose centre is everywhere and whose surface is nowhere.

The universe lies before us, open to observation and reasoning. Innumerable astral bodies shine within its depths. Let us imagine ourselves at the centre of one of these spheres, which are everywhere and whose surface is nowhere, and also assume for a moment the existence of this surface, which is therefore found at the limit of the world.

Will this limit be solid, liquid or gaseous? Whatever its nature, it immediately becomes the extension of what it demarcates or claims to demarcate. Let us assume that no solids, liquids, gases – not even ether – exist at this point. There is nothing but black and empty space. This space will still possess the three dimensions, however, and it will necessarily have as its limit –– which is to say, as its continuation –– a new portion of space of the same nature, and then another after that, then yet another still, and so on, indefinitely.

The infinite can only be presented to us through its appearance as indefinite. The one leads to the other through our manifest inability to find, or even to conceive of, a limitation to space. An infinite universe is certainly incomprehensible, but a limited universe is absurd. This absolute certainty of the infinity of the world, together with its incomprehensibility, constitutes one of the most irritating provocations that torments the human mind. No doubt somewhere, on some wandering world, there exist brains powerful enough to comprehend the enigma that remains impenetrable to our own. Our jealousy has to come to terms with this fact.

This enigma is just the same for the infinite in time as it is for the infinite in space. The eternity of the world seizes our intelligence even more vividly than its immensity. If one does not concede that the universe has boundaries, how can one accept the idea of its non-existence? Matter did not arise from nothingness. It will not return to nothingness. It is eternal, imperishable. Although it is undergoing constant transformation, it can neither diminish nor grow by one atom.

If matter is infinite in time, why would it not be so in extension or space? The two infinites are inseparable. The one implies the other, and to deny this is to invite contradiction and absurdity. Science has not yet discovered a law of interdependence between space and the globes that cross it. Heat, motion, light and electricity are necessary throughout the entirety of extension. Many capable men think that none of its parts could remain widowed from these great luminous spheres [foyers] which sustain worlds. Our opuscule rests entirely on this opinion; it assumes that the infinity of space is filled with the infinity of globes, leaving no corners of darkness, solitude or immobility anywhere.

II. The indefinite

Any idea of the infinite, even a weak and poor one, can only be taken from the indefinite. And yet even such a weak and poor idea still appears imposing and formidable. Sixty-two digits, a number that takes about 15 centimetres of a page to write, can measure a span of 20 octodecillion leagues or, in other words, billions and billions and billions and billions and billions of times the distance that separates the Sun from the Earth.

Then imagine a line of digits going from here to the Sun – that is to say, not one of 15 centimetres, but of 37 million leagues. Is not the expanse that this enumeration would cover frightening? Now take this expanse itself as a unit in the following number: the line of digits that it forms begins on Earth and ends at that star over there, the one whose light takes more than a thousand years to reach us, at a speed of 75,000 leagues per second. Think of the distance such a calculation would produce, assuming that language could even find the words and the time to express it!

One can thus prolong the indefinite as much as one wants without exceeding the limits of intelligence, but also without even beginning to convey infinity. If each word denoted the most frightening of distances, one would have to say one word per second for billions and billions of centuries in order to express no more than something insignificant when it comes to the infinite.

III. The prodigious distances of stars

The universe seems to unfold in all its immensity before our gaze. In reality we see little more than a tiny part of it. The Sun is one of the stars of the Milky Way, that great stellar gathering that sweeps across half of the sky, and whose constellations are nothing more than detached members, scattered across the vault of the night. Beyond it are a few imperceptible points, piercing the firmament, signalling the stars half-extinguished by distance; and further still, in the concealed depths, the telescope is able to make out the nebulae, small star clusters of pale dust, the background of the Milky Way.

The remoteness of these bodies is prodigious. It eludes all the calculations of the astronomers who have tried in vain to discover a parallax for some of the brightest among them: Sirius, Altair, Vega (of the Lyre). Their results have not attained any credence and remain very problematic. They are vague approximations, or rather estimations of minimal distances that put the closest stars at more than 7000 billion leagues away. The best observed among them, 61 Cygni, gave a distance of 23,000 billion leagues, 658,700 times the distance from the Earth to the Sun.

Travelling at 75,000 leagues per second, light will cover this distance in ten years and three months. The same journey by railway, travelling at ten leagues per hour, without stopping or slowing down, would last 250 million years. It would take 400 years to get to the Sun on the same train. The Earth, which travels 233 million leagues every year, would take one hundred thousand years to get to 61 Cygni.

The stars are suns similar to our own. Sirius is said to be one hundred and fifty times larger than ours. Although possible, this cannot be verified. The disparities in volume between these luminous spheres should certainly be extremely large. But for us the comparison is beyond our grasp in any case, and apparent differences in size and brightness can scarcely be understood as anything but questions of distance, or rather questions of doubt. For without sufficient data, any assessment would be foolhardy.

IV. The physical composition of stars

Nature is marvellously skilled in the art of adapting organisms to different environments without ever departing from the general plan that governs all its work. With simple modifications it is able to multiply its types to a seemingly impossible degree. It has been quite wrongly assumed that on other celestial bodies there might be situations and beings, both equally fantastical, that in no way resemble the inhabitants of our planet. No doubt a myriad of forms and mechanisms do exist. But the plan and the materials remain invariable. One can confidently affirm that, even at the opposite extremities of the universe, nerve centres are the base and electricity the principal agent of all forms of animal life. All other [organic] systems and apparatuses are subordinate to it, in the thousands of ways that might be in keeping with each environment. The same principle certainly applies in our own planetary group, which must contain innumerable series of differing forms of organisation. One need not even leave the Earth to see this almost limitless diversity.

We have always considered our globe to be the Queen of planets – a vanity that has often been humbled. We are mere intruders in the very group that our vainglory pretends to see bowing before its supremacy. It is density that determines the physical constitution of an astral body. And our density is not that of the solar system. It is nothing but a minuscule exception that almost puts us outside of the true family that is composed of the Sun and the large planets. With respect to the full cortège or sequence [cortège] of planets, Mercury, Venus, Earth and Mars together only make up, in terms of volume, 2 parts out of 2,417; if you include the Sun as well, then the small planets account only for 2 out of 1,281,684. In other words, we count for nothing!

Faced with such disparities, only a few years ago the field was still open to speculation regarding the structure of celestial bodies. The only thing that seemed beyond doubt was that they would in no way resemble ours. We were mistaken. Spectral analysis has since dispelled this error and shown, in spite of many appearances to the contrary, that there is an identity in the composition of the universe. The forms are innumerable, the elements remain the same. Here we come to the fundamental question, one that overshadows and pushes aside all others. It must therefore be considered in detail, proceeding from the known to the unknown.

As things stand, on our planet the only elements available to nature are the 64 simple bodies listed below. We say ‘as things stand’ because we knew of only 53 of these bodies a few years ago. Every now and then, their nomenclature is enriched by the discovery of some metal that through chemistry has been extracted with great difficulty from the stubborn bonds that link it to oxygen. It is likely that our 64 may eventually grow to reach around one hundred. But the key actors number not much more than 25. The rest play only minor parts. They are called simple bodies because until now they have been found to be irreducible. We shall arrange them here more or less in order of importance:

1. Hydrogen 2. Oxygen 3. Nitrogen 4. Carbon 5. Phosphorus 6. Sulphur 7. Calcium 8. Silicon 9. Potassium 10. Sodium 11. Aluminium 12. Chlorine 13. Iodine 14. Iron 15. Magnesium 16. Copper 17. Silver 18. Lead 19. Mercury 20. Antimony 21. Barium 22. Chromium 23. Bromine 24. Bismuth 25. Zinc 26. Arsenic 27. Platinum 28. Tin 29. Gold 30. Nickel 31. Beryllium [Glucinium] 32. Fluorine 34. Zirconium 35. Cobalt 36. Iridium 37. Boron 38. Strontium 39. Molybdenum 40. Palladium 41. Titanium 42. Cadmium 43. Selenium 44. Osmium 45. Rubidium 46. Lanthanum 47. Tellurium 48. Tungsten 49. Uranium 50. Tantalum 51. Lithium 52. Niobium 53. Rhodium 54. Didymium 55. Indium 56. Terbium 57. Thallium 58. Thorium 59. Vanadium 60. Ytterbium 61. Caesium 62. Ruthenium 63. Erbium 64. Cerium.

The first four – hydrogen, oxygen, nitrogen and carbon – are the great agents of nature. Their effects are so universal that it is hard to say which of them should be given precedence. Hydrogen nonetheless comes first because it is the light of all the stars. These four gases alone constitute almost all organic matter, flora and fauna, when combined with calcium, phosphorous, sulphur, sodium, potassium, and so on.

Hydrogen and oxygen form water, along with chlorine, sodium and iodine for the sea. Silicon, calcium, aluminium and magnesium, together with oxygen, carbon, etc., constitute the great mass of geological formations – the superimposed layers of the Earth’s crust. Precious metals matter more to mankind than they do in nature.

Even until recently, these elements were taken to be unique to our world. There used to be great controversies about the Sun, for example, regarding its composition, origin and the nature of its light! The great quarrel over emissions and undulations has only just come to an end; the recent rear-guard skirmishes still reverberate. The victorious supporters of undulations then went on to propose, on the basis of their success, the following, somewhat fantastic, theory: ‘The Sun –– an opaque simple body like any other planet –– is shrouded by two atmospheres: the first, which is similar to ours, serves as a parasol protecting the natives [indigènes] against the second, known as the photosphere, which is the eternal and inexhaustible source of light and heat.’

This universally accepted doctrine has reigned in science for a long time, in spite of all the analogies that suggest otherwise. The central fire that roars beneath our feet sufficiently attests to the fact that the Earth was once what the Sun is today, and the Earth has never been covered with an electrical photosphere graced with the gift of perennial existence.3

Spectral analysis has dispelled these errors. It is no longer a question of inexhaustible and perpetual electricity, but, quite simply, of hydrogen burning, here as elsewhere, in combination with oxygen. The sun’s pink protuberances are tremendous streams of this flaming gas, that extend beyond the halo which surrounds the moon during total solar eclipses. As for sunspots, they have been rightly represented as vast, open craters within the masses of gas. The flames of hydrogen that have been swept away by storms across these immense surfaces are what enable us to see the astral body’s nucleus –– not as a black opacity, but as something relatively dark – in either its liquid or its highly compressed gaseous state.

Gone are the chimeras, then. We have here two terrestrial elements that light up the whole universe, just as they light up the streets of Paris and London. Their combination is what gives off light and heat. It is the product of this combination, water, that creates and sustains organic life. Without water there is no atmosphere, no flora or fauna –– nothing but the cadaver of the moon.

There is an ocean of flames amongst the stars to vitalise, an ocean of water on the planets to organise; the association of hydrogen and oxygen is the government of matter, and sodium their inseparable companion in their two opposed forms: fire and water. In the solar spectrum, sodium shines in the front ranks; it is the main element in the salt of the seas.

These seas, so peaceful today despite their gentle ripples, were whipped up in completely different kinds of storms, back when they whirled around in devouring flames on the Earth’s lava. It is still the very same mass of hydrogen and oxygen, but what a metamorphosis! The evolution is complete. It will likewise be completed on the Sun. Its spots already show fleeting lacunae in the combustion of hydrogen that will, with time, continue to grow until they eventually become permanent. Although this time will no doubt be measured in millennia, it is on the downward slope.

The Sun is a star in its decline. A day will come when the product of the combination of hydrogen and oxygen, ceasing to decompose repeatedly so as to regenerate the two elements separately, will instead remain what it should be: water. This day will see the end of the reign of flames and the beginning of that of aqueous vapours, whose final stage is the sea. As the thick masses of these vapours shrouds the deposed star, our planetary world will fall into eternal night.

Humanity will have time to learn a great many things before this fateful end. Through spectrometry, it already knows that half of the 64 simple bodies that constitute our planet also form part of the Sun, the stars and their satellites. It knows that the entire universe gets light, heat and organic life from the combination of hydrogen and oxygen as either fire or water.

Not all the simple bodies appear in the solar spectrum, and the spectra of the Sun and the stars both reveal the existence of elements that remain unknown to us. But this science is still new and untested. It has barely uttered its first words and they have already been decisive. The elements that compose celestial bodies are everywhere identical. The future will only offer further proof of this identity. The differences in density –– which at first glance seemed to present an insurmountable obstacle to finding any similarity between the planets of our system – lose much of their distinguishing significance when one sees that the Sun, whose density is a quarter of ours, contains metals such as iron (which has a density of 7.80), nickel (8.67), copper (9.95), zinc (7.19), cobalt (7.81), cadmium (8.69) and chromium (5.90).

There is nothing more natural than the fact that simple bodies exist on different globes in unequal proportions, and thereby give rise to divergences in density. A nebula’s materials must, of course, be classified on each planet according to the laws of gravity. But this classification does not prevent the simple bodies from co-existing within the whole of the nebula, even if they are then divided up according to a certain order, in keeping with these laws. This is precisely the case in our own system, and seemingly also in that of other stellar groups. We will consider the conditions that arise from this fact later.

V. Observations on Laplace’s cosmogony –– The Comets 

Laplace derived his hypothesis from conclusions Herschel drew from his telescope.4 As a result of his mathematical background and approach, the illustrious geometer dealt mostly with the motion of astral bodies, and very little with their nature. He engaged with the physical questions only in passing and through simple affirmations, always seeking to return to his main concern – gravitational calculations. His theory is clearly wrestling with two fundamental issues: the origin and high temperatures of nebulae on the one hand, and comets on the other. Let us put the nebulae to one side for now and consider the comets. Unable to find any place for them in his system, in order to be rid of them the author sent them off to wander from star to star. Let us follow along after them, to see if we can have done away with them ourselves.

Everyone today has profound contempt for comets, these miserable playthings that the larger planets jostle around, tug and pull at in hundreds of different ways, inflate with the Sun’s flames, and finally discard in tatters. How the mighty have fallen! They were once so humbly respected, when they were hailed as messengers of death! But since they were found to be harmless there has been nothing but boos and jeers! Such is the way of mankind.

This impertinence is not expressed without a touch of concern, however. Oracles are not without contradictions. Thus Arago – after having repeatedly proclaimed the absolute nullity of comets, after having affirmed that the most perfect vacuum of a pneumatic machine is even denser than cometary substance – nevertheless admitted in a chapter of one of his works that ‘the transformation of the Earth into the satellite of a comet is not beyond the realm of possibility.’5

Even so careful and serious scholar as Laplace likewise outlines the arguments for and against such a question. He writes somewhere: ‘A comet’s collision with the Earth could not produce any noticeable effect. It is highly likely that comets have enveloped it several times without this even having been noticed…’6 But elsewhere: ‘It is easy to imagine the effects of the impact of a comet on the Earth: the axis and motion of rotation would change; the seas would abandon their former positions to rush towards the new equator; a great number of men and animals would drown in the universal deluge or be destroyed by the violent jolt transmitted to the Earth, entire species would be annihilated…’ etc.7

It is remarkable to see such a categorical yes and no in the writings of a mathematician. Gravitational attraction, that fundamental dogma of astronomy, is sometimes equally ill-treated, as we can see with respect to the question of zodiacal light.8

Several different explanations have already been given for this phenomenon. It was first attributed to the atmosphere of the sun – an idea that Laplace strongly opposed. According to him, ‘the solar atmosphere does not reach the halfway point of Mercury’s orbit. The zodiacal lights are the result of molecules that were too volatile to combine themselves with the planets during the period of their great initial formation, and that today circle around the central astral body. Their extreme tenuity poses no resistance to the course of celestial bodies, giving us this light that is permeable to stars.’9

Such a hypothesis is highly unlikely. Planetary molecules volatilised by high temperatures do not conserve their heat eternally. They would not, therefore, maintain their gaseous form in the icy deserts of the expanse. Moreover, and despite whatever Laplace might say about it, this matter (however tenuous we might suppose it to be) would still represent a significant obstacle to the movements of celestial bodies, and in time would lead to serious disturbances.

The same objection disproves a recent idea attributing zodiacal light to fragments of comets broken up in the storms of the perihelion. These remains, it is claimed, form a vast ocean that encompasses and even surpasses the orbits of Mercury, Venus and the Earth. To confuse the comets’ nullity with that of the ether, or even with emptiness itself, is to heighten disdain for comets further still. No, the planets would not easily make their way across these nebulosities, and in this scenario gravitation itself would soon come to grief.

It seems even less rational to look for the origin of the mysterious lights of the zodiacal region in a ring of meteors circling around the Sun –– meteors that, by their very nature, are not very permeable to starlight.

Perhaps if we go back a little further we might find the answer. Arago somewhere says: ‘Cometary matter has been able to enter into our atmosphere quite frequently. If it does so it does not pose any danger. We can pass through a comet’s tail without even noticing it…’ Laplace is no less explicit: ‘It is highly probable’, he writes, ‘that comets have enveloped the Earth several times without having been noticed…’

No doubt everyone can agree with this. But we might still ask the two astronomers to explain what became of these comets. Did they continue their journey? Is it possible for them to free themselves from the Earth’s grip and to continue on their course? Has gravitational attraction therefore ceased? What! This vague cometary effluence – whose nothingness language struggles to define – somehow defies the force that governs the universe!

One could understand how two massive globes, travelling at full speed, might pass each other at a tangent and then continue to speed along after a double jolt. But to suggest that some inane and wandering objects might merge into our atmosphere and then calmly detach themselves so as to continue on their own course is very far fetched. Why do these diffuse vapours not remain firmly attached to our planet by gravity?

‘Precisely because they weigh nothing at all!’, it will be claimed. ‘Their very lightness is what protects them. No mass, no attraction.’ This is flawed logic. If they break away from us to rejoin their own forces or army it is because these forces attract them and take them from us. On what grounds? The Earth is far superior to them in strength. Comets, as we know, do not disturb anyone; and yet everyone disturbs them because they are the humble slaves of attraction. How could they ever stop obeying attraction, particularly when our globe takes hold of them and cannot let go? The Sun is too far away to contest the power that binds them so tightly, and even if it managed to drag away the front line of one of these swarms of comets, the rear guard, broken off and dislocated, would still remain under the Earth’s control.

Many still speak, however, of comets that surround and then abandon our globe, as if it were that straightforward. No-one has yet made the slightest observation that might confirm this point. Is the rapid movement of these astral bodies enough for them to elude the effects of the Earth, and does the impulse they acquire as a result propel them along their own course?

Such an attack on the law of gravity is impossible, and this may help account for zodiacal light. The cometary detachments – taken prisoner in these sidereal encounters and driven back towards the equator through the Earth’s rotation – develop into the lenticular bulges that are illuminated by the Sun’s rays before daybreak and particularly after dusk. The heat of the day causes them to expand and makes their luminosity more noticeable than it is in the morning, after having cooled during the night.

These diaphanous masses, which appear to be entirely cometary and permeable to the light of the smallest stars, occupy an immense expanse going from the equator – their centre, and the point at which their altitude and brilliance rise to their highest – to far beyond the tropics and probably as far as the two poles, where they drop, contract and extinguish.

Until now, zodiacal light had always been lodged outside the Earth, and it was difficult to assign it either a place or a nature compatible with both its permanence and its variations. But it is the Earth itself that is its cause, since it is wound round its atmosphere, without the weight of the atmospheric column increasing by a single atom. This poor substance could not provide more conclusive proof of its own inanity or emptiness.

The comets, in their visits [to Earth], may well renew their imprisoned contingents more often than is thought. Moreover, these contingents could not exceed a certain height without being skimmed and plundered by centrifugal force, which carries its spoils away with it into space. The terrestrial atmosphere is thus lined with a cometary envelope that is more or less imponderable, and the centre and source of zodiacal light. This explanation is not only consistent with the diaphanous nature of the comets but it also takes account of the law of gravity, which prevents those detachments captured by planets from escaping.

Let us return to the history of these blaze-tailed nullities [nihilités chevelus]. If they evade Saturn they then fall prey to Jupiter, the policeman of the system. Standing guard in the shadows, it senses the comets even before one of the Sun’s rays makes them visible. It then overpowers them and drags them down into its perilous abyss. There, captured and monstrously dilated by the heat, they lose their form and grow longer. They are disaggregated and escape the terrible pass in a chaotic retreat. Leaving stragglers everywhere, they are only able to regain their unknown solitudes with great difficulty, protected by the extreme cold.

Only those comets that evade all the traps of the planetary zone escape. This is how, having avoided the fatal gorges, and leaving in the distance of the zodiacal plains its fat spiders to wander along the edge of their webs, the comet of 1811 swooped down from the polar heights to the ecliptic. It outflanked and rapidly turned around the Sun, before again rallying and reforming its immense columns that had been scattered by enemy fire. Only after the manoeuvre has been successfully executed does the comet deploy, before the eyes of stupefied onlookers, the splendour of its army, before majestically continuing its victorious retreat into the depths of space.

Such triumphs are rare. The poor comets arrive in their thousands, and are quickly lured into danger. Like moths, they carelessly rush from the depths of the night and pirouette around the flame that draws them in; they do not manage to slip away without leaving a mass of casualties and debris, strewn across the fields of the ecliptic. If some chroniclers of the heavens are to be believed, between the Sun and a zone beyond the terrestrial orb sprawls a vast cemetery of comets, with a mysterious glow that appears in the evenings and mornings of clear days. The deaths of these luminous phantoms are seen as they allow the light of the living stars to pass through them.

Or rather are they not more like supplicating captives, enchained for centuries to the gates of our atmosphere and vainly demanding either freedom or hospitality? From its first to its last ray, the inter-tropical sun reveals to us these pale Bohemians who are paying such a high price to atone for their indiscreet visit among more settled and established people.

Comets are truly fantastic beings. Since the beginning of the solar system, they have passed through the perihelion by the millions. Our world in particular abounds in them, and yet more than half escape our view, even with the use of a telescope. How many of these nomads have taken up residence with us?… Three… and even then it can still be said that they are only camping out.10 One of these days they will up stakes and disappear off to rejoin their innumerable tribes scattered across the spaces we can only imagine. In truth, it is of little importance whether they do so by way of ellipses, parabolas or hyperbolas.

After all, they are harmless and graceful creatures that often play the leading role on the most beautiful of starry nights. If they happen to get caught like fools in a trap, astronomy gets caught there with them – and it has a still harder time releasing itself. They are a veritable nightmare for science. What a contrast with the celestial bodies! These are the two extremes of an antagonism, of overwhelming masses and of imponderables; the excess of the gigantic and the excess of nothing.

And yet, when it comes to this nothing, Laplace speaks of condensation and vaporisation, as if what is at issue were a gas like any other. He affirms that eventually the comets completely dissipate in the heat of the perihelion. But what happens to them after this volatilisation? The author does not say, and he probably does not worry about this very much either. As soon as it is no longer a matter of geometry, he proceeds in summary fashion, with few scruples. However ethereal the sublimation of these blaze-tailed celestial bodies may be, it nonetheless still consists of matter. What will its fate be? No doubt the cold will lead it to readopt its original form. So be it. It is part of the essence of a comet to reproduce ambulatory, diaphanous bodies. But according to Laplace and other authors these diaphanous bodies are identical to fixed nebulae.

Wait! Hold on now, stop right there! We should pause to check the meaning of these words. ‘Nebula’ [nébuleuse] is suspicious. It is a name that is attributed too easily, for it has three different meanings. It can denote: 1) a pale light that powerful telescopes break down into innumerable, densely packed stars; 2) a similar-looking pale light, dotted with one or several small bright points, and that does not allow itself to be resolved into stars; 3) the comets.

A meticulous comparison of these three categories is essential. The first one, the clusters of small stars, poses no difficulty at all – everyone agrees on this. The dispute only concerns the other two. According to Laplace, when nebulosities so profusely scattered across the universe undergo their first stage of condensation they form either comets or the nebulae that possess bright points, that are irreducible to stars and that transform into solar systems. Laplace explains and describes this transformation in detail.

When it comes to comets, however, he simply presents them as small, wandering nebulae that he leaves undefined, making no attempt to differentiate them from those nebulae that are in the process of giving birth to a star. On the contrary, he insists on their close resemblance, which only allows them to be distinguished through the displacement of comets that have become visible in the light of the Sun’s rays. In a word, he takes irreducible nebulae from Herschel’s telescope and indiscriminately turns them either into planetary systems on the one hand or comets on the other. It is merely a question of orbits and of fixedness or irregularity in gravitation. Besides, since ‘the nebulae scattered across the universe’ all have the same origin they must therefore have the same constitution.

How can such a great physicist conflate these glacial and empty glowings of borrowed light with the immense jets of ardent vapour that will one day become suns? If the comets were made of hydrogen, then this might make sense. One might then imagine that large masses of this gas, remaining outside of the star-nebulae, could float freely across the expanses where they act out gravity’s little play. These would still be made up of cold and dark gas, whereas the stellar-planetary cradles are in fact incandescent, so much so that the conflation of these two sorts of nebulae would still remain impossible. But even this provisional hypothesis is flawed. Compared with comets, hydrogen is like granite. There can be nothing in common between the nebulous matter of stellar systems and that of comets. One is force, light, weight and heat; the other is nullity and ice, empty and dark.

Laplace says the two kinds of nebulae are so similar that one can barely distinguish them. What! Volatilised nebulae are immeasurable distances apart; comets are almost within arm’s reach of each other. And yet he concludes from a false resemblance between two such profoundly different bodies that their composition is identical! But the comet is something infinitely small, and the nebulae is almost a universe. Any comparison between such things is absurd.

Let us repeat once again that if a mass of hydrogen evaded both gravitational attraction and combustion during the volatile phase of a nebulae and thereby escaped into free space and became comets, then these new celestial bodies would enter into the general composition of the universe. Moreover, they would play a formidable role. Powerless as a mass in a planetary collision, yet set ablaze by an encounter with air and contact with its oxygen, they would burn all organic bodies to death, both plants and animals. However everyone agrees that hydrogen is to cometary substance what a block of marble would be to hydrogen itself.

Let us now imagine fragments of stellar clouds, wandering from system to system, like comets. These volatile clusters, when at the highest of temperatures, would pass around us not as thin fog, lifeless and motionless, but rather as a terrifying torrent of light and heat, one that would have soon cut short our polemics about them. The uncertainty about comets drags on. Debate and conjecture settle nothing. Certain points do appear to have been clarified, however. The unity of cometary matter is now beyond doubt. It is a simple body that has never shown any variation in any of its already numerous appearances. One constantly discovers the same elastic tenuousness, dilatable to the point of emptiness, and this absolute translucency that in no way hampers the faintest of lights from passing through it.

Comets are not composed of ether, gas, liquid, solid, or anything like that which makes up the celestial bodies. Rather, they are formed from an indefinable substance that appears to share none of the properties of known matter and does not exist separately from the solar rays that momentarily pull them out of nothingness, only to let them fall back into it. There is a fundamental separation between this sidereal enigma and the stellar systems that constitute the universe. They are two isolated modes of existence, two totally distinct categories of matter, with no other link than a disordered, indeed almost crazed, gravitation. The description of the world need not take them into account. They are nothing, they do nothing, and they have only one role – that of an enigma.

With its excessive dilatations at the perihelion and its icy contractions at the aphelion, this meteoric astral body represents a certain giant from the One Thousand and One Nights that was bottled up by Solomon. When the chance arises, it slowly spreads forth from its prison in an immense cloud to take on a human form, before returning back to vapour and going back down the neck of the bottle, where it disappears once again. A comet is an ounce of fog that first expands to fill a billion cubic leagues, then shrinks to the size of a carafe.

Let us move on from playing these games, for they do not resolve the question: are all the nebulae composed of clusters of adult stars, or do they contain the foetuses of stars in some of them, whether these be single or multiple? Only two judges can pronounce on this question: the telescope and spectral analysis. We demand of them strict impartiality, above all to guard against the occult influence of great scientific names. Indeed, it seems that spectrometry is tending towards results that agree with Laplace’s theory.

There is even less need to be lenient with regard to the illustrious mathematician’s possible errors, now that his theory can draw a strength from our current understanding of the solar system that even allows it to keep pace with the telescope and spectral analysis, which is no small thing. It is the only rational and reasonable explanation of planetary mechanics, and it will certainly only succumb to the irresistible arguments…

VI. The origin of worlds

This theory does have a weakness, however, the same one as before – the question of origins, which is only evaded here through reticence. Unfortunately, to omit a question is not to resolve it. Laplace has skilfully sidestepped the problem, leaving it for others to solve, and by doing so he was able to develop his hypothesis, having cleared its path of this stumbling block.

Gravitation only partially explains the universe. The motion of celestial bodies obeys two forces: centripetal or gravitational force, which makes them fall or attracts them to each other; and centrifugal force, which pushes them forward in a straight line. The combination of these two forces results in the astral bodies’ more or less elliptical motion. If there were no centrifugal force, the Earth would fall into the Sun. If there were no centripetal force, it would break out of its orbit by following its tangent and would escape, continuing straight ahead.

The source of centripetal force is known: attraction, or gravitation. The origin of centrifugal force remains a mystery. Laplace left this difficulty to one side. According to his theory, the translatory motion – in other words, centrifugal force – originates in the rotation of the nebula. This hypothesis is no doubt correct, since it would be impossible to provide a more satisfactory account of the phenomena that take place in our planetary group. Nonetheless, we are still entitled to ask the illustrious geometer: What led the nebula to rotate? What was the source of the heat that first volatilised this gigantic mass and later condensed it into a sun surrounded by planets?

Heat! It seems that in space it is everywhere available for the taking. Yes, there is still heat at 270 degrees below zero. Is this what Laplace is alluding to when he says that ‘because of excessive heat, the Sun’s atmosphere originally stretched out beyond the orbits of all the planets’? Following Herschel, he notes the existence of a large number of nebulosities that are at first so diffuse that they are barely visible, and that, through a series of condensations, then turn into stars. And these stars are gigantic globes in full incandescence like the Sun, which would suggest a considerable amount of heat. Imagine what their temperature must have been when, having been reduced entirely to vapours, these enormous masses were then dilated to such a degree of volatilisation that they became a barely perceptible nebulosity!

These are the very nebulosities that Laplace presents as spread in profusion across the universe, and as giving birth to comets and stellar systems. This is an unacceptable assertion, as we have shown for cometary substance, which has nothing in common with that of nebulae-stars. If these substances were similar, then comets would always and everywhere be mixed with stellar matter to the point that they would simply become part of it. They would not then constantly follow their own course, separate from that of the other astral bodies, on account of their inconsistency, and of their vagabond habits, and of the absolute unity of substance that characterises them.

Laplace is perfectly right to say: ‘Thus, the progressive condensation of nebulous matter leads us to consider the possibility that a vast atmosphere once surrounded the Sun, and as we have seen we are also led to consider this possibility through examination of the phenomena of the solar system. Such a remarkable coincidence lends the idea that the Sun previously existed in this state a near certain probability.’11

On the other hand, there is nothing more mistaken than to conflate comets – these imponderable, icy futilities – with the stellar nebulae that are massive parts of nature, brought by volatilisation to maximum levels of temperature and brightness. That comets are an enigma is certainly disheartening, for so long as they remain inexplicable while everything else can be explained, they become an almost insurmountable obstacle to our understanding of the universe. But obstacles are not overcome with absurdities. We would do better to cut our losses and accord these impalpable things a special existence outside of matter proper, which can certainly act upon them through gravity, but without mixing with them or being subject to their influence. Although transient, unstable and short-lived, we know them to be a simple, single, invariable substance that is incapable of any form of modification, yet that can divide, reunite, form masses or be torn apart without ever changing. They therefore play no part in nature’s perpetual development or becoming [devenir]. We can take consolation in the inconsequential role played by this logogriph.

The question of origins is much more serious. Laplace diminishes its importance – or, rather, he takes no account of it; he does not even deign or dare to address it. With his telescope, Hershel recorded numerous clusters of nebulous matter in space at varying degrees of diffusion –– clusters that, through progressive cooling, end up as stars. The illustrious geometer describes and explains these transformations very well, but he has hardly a word to say about the origin of these nebulosities. Naturally, one therefore wonders: Where do these nebulae –– that relative cold turns into suns and planets –– come from?

According to certain theories, there may be chaotic matter in the open expanses of space that would, with the help of heat and attraction, agglomerate together to form planetary nebulae. But why, and since when, has this chaotic matter existed? And this extraordinary heat that facilitates such agglomeration, where does it come from? There are many questions that no-one asks, which exempts us from answering them.

There is no need to point out that the chaotic matter that constitutes modern stars also constituted the ancient ones, from which it follows that the universe does not date back any further than the oldest stars existing today. We readily accord immense life spans to these astral bodies, but we know nothing of their beginning except for the agglomeration of chaotic matter. As for their end – silence. What is farcical about all these theories is that they presuppose the existence of a sort of factory in imaginary space producing unlimited heat in order to provide indefinite volatilisation to all the nebulae and every possible chaotic material.

Although Laplace is a very scrupulous geometer, he is not a particularly rigorous physicist. He claims that matter vaporises simply by virtue of excessive heat. Once one accepts the existence of a condensing nebulae, one then admiringly follows his account of the successive birth of planets and of their satellites as a result of progressive stages of cooling. But this nebulous matter that comes from nowhere, attracted in every direction for reasons and by means that we cannot explain, also serves to cool our enthusiasm. It is hardly an acceptable way to treat one’s readers, by obliging them to rely on a hypothesis posited in the absence of any justification, and then to abandon them to it.

Heat and light do not accumulate in space at all – they dissipate there. Their source is eventually exhausted. All celestial bodies cool down through radiance. The stars, which begin as a tremendous incandescence, end up as a black congealment. Our seas were once oceans of flames; they are now nothing but water. When the Sun is extinguished, they will turn into a block of ice. Those cosmogonies that claim the world was created only yesterday may believe that the astral bodies have only just begun to burn. Even so, what next? The millions of stars that illuminate our nights have only a limited existence. They began in a blaze of fire; they will end in cold and darkness.

Can one simply say: ‘this will at least endure longer than us’? ‘Let us take it as it is. Carpe diem. What does it matter what came before! What does it matter what will follow? Avant et après nous le déluge! [Before and after us, the Flood!].’ No. The enigma of the universe continuously confronts our every thought. The human mind seeks to decipher it at all costs. Laplace was on the right track when he wrote the following words: ‘Viewed from the Sun, the Moon appears to follow a series of epicycloids whose centres lie on the circumference of the terrestrial orbit. Similarly, the Earth follows a series of epicycloids whose centres lie on the curve the Sun follows around the centre of gravity of the group of stars to which it belongs. Finally, the Sun itself follows a series of epicycloids whose centres lie on the curve followed by the centre of the group around that of the universe.’12

‘Of the universe’! That is going a bit far. This so-called centre of the universe and the immense cortège that gravitates around it is no more than an imperceptible point in the expanse of space. Laplace was nonetheless on the path that led to the truth. Indeed, he almost touched upon the key to the whole enigma. But this phrase, ‘of the universe’, proves that he had touched upon it without seeing it – or without looking at it, at least. He was an ultra-mathematician. He believed to his very core in an unalterable harmony and solidity of celestial mechanics. It may be solid, very solid in fact. Yet one must distinguish between the universe and a clock.

When a clock goes off time, one resets it. When it breaks, one fixes it. When it no longer works, one replaces it. But who can repair or replace celestial bodies? Do these flaming globes, these truly splendid representatives of matter, enjoy the privilege of perennial existence? No. Matter is eternal only in its elements and as a whole. All of its forms, whether they be humble or sublime, are transitory and perishable. Astral bodies are born, they shine, and they die. After lingering for perhaps thousands of centuries in their vanished splendour, they leave nothing but floating tombs to the laws of gravity. How many billions of these icy cadavers must be crawling along like this in the darkness of space, awaiting the hour of destruction, which will also be that of resurrection!

For all deceased forms of matter come back to life, whatever their condition. If the night of the grave is long for these finite astral bodies, there eventually comes a moment when their flame lights up again like lightning. On the surface of planets, beneath solar rays, a form that dies quickly disintegrates in order to reconstruct its elements into a new form. The metamorphoses follow one another without interruption. But when a sun dies out and turns to ice, who will provide it heat and light once again? It can only be reborn as a sun. It gives life to a myriad of diverse beings. It can only hand it down to its sons through marriage. Under what guise could the nuptials and births of these luminous giants take place?

When, after millions of centuries, one of these immense whirlpools of stars –– stars that were born, revolved and died together –– grows to cover the regions of space that lie open before it, its frontiers collide with other extinguished whirlpools coming its way. A furious melee then begins that will last for countless years on a battlefield that stretches across billions and billions of leagues. This part of the universe is then reduced to little more than a vast atmosphere of flames, relentlessly crossed by the cataclysm’s lightning bolts that instantly volatilise both stars and planets.

At no point does this pandemonium disobey the laws of nature. The successive impacts reduce the solid masses to a vaporous state that is immediately seized by gravitation, which groups them into nebulae that are spinning on themselves as a result of the impact, and hurls them onto a regular orbit around new centres. Through their telescopes, distant observers are then able to catch a glimpse of the theatre of these great revolutions, which appear as a pale glimmer mixed with more luminous points. The glimmer is nothing more than a spot; but this spot is a mass of globes coming back to life.

To begin with, each of these newborn stars will live its infancy in isolation, as a thick, tumultuous cloud. Becoming calmer with time, the young astral body will gradually release from its womb a large family that will soon cool off though isolation and will thereafter only survive through paternal warmth. The new sun will be the sole representative of such warmth for each world, which will know it alone, never catching sight of its other children. Such is our planetary system. And the planet we inhabit is one the youngest daughters, followed by only one sister, Venus, and by a much younger brother, Mercury, the last to have hatched from the nest.

Are worlds really reborn in this way? I do not know. The dead legions that collide in order to come back to life are perhaps less numerous, the field of resurrection perhaps less vast. But it is certainly only a question of numbers and distances, not of the means or the process itself. As things stand we do not understand these encounters well enough to determine whether they take place simply between two stellar groups; or whether they occur between two systems where each star, along with its cortège of satellites, already only plays the role of a planet; or whether the collision is between two centres where the encounter is with nothing more than a modest satellite; or finally whether it is between two spheres [foyers] that represent a whole corner of the universe. The only legitimate assertion is as follows.

Matter cannot diminish or increase by so much as a single atom. The stars are nothing more than ephemeral flames. Thus, once extinguished, if they were not re-ignited, night and death would take hold of the whole universe in due course. And how could they re-ignite and light up again, if not through motion converted into heat in huge proportions – that is, through a collision with other extinguished stars that volatises them and lends them a new existence? One should not object that, motion’s conversion into heat would annihilate it, thereby immobilising the globes. Motion is nothing more than the result of attraction, and attraction, as the permanent property of all bodies, is imperishable. Indeed, motion would suddenly be reborn as a result of the shock itself. It may go off in new directions, but it will still have same cause: gravity.

Would you say that these upheavals were an attack on the laws of gravitation? You have no idea, and nor do I. Our only option is to rely on what we can know by analogy. And analogy replies: ‘For centuries, meteorites have fallen upon our globe by the millions and, without a doubt, upon the planets of all the stellar systems. This would represent a grave breach of the law of attraction, as you understand it. In fact, it is a form of attraction that you are unfamiliar with – or rather one that you disdain, because it applies to asteroids but not to astral bodies. After orbiting their planet for thousands of years in accordance with all its laws, one fine day they penetrated into its atmosphere in violation of the law [of gravity], converting motion into heat through their fusion or their volatilisation, as they encounter friction in the air. What happens to what is small can and must happen to what is large. Bring gravitation before the tribunal of the Observatory, on charges of having maliciously and illegitimately allowed to fall down to Earth those aerolites whose travels through empty space it was meant to sustain.’

Yes, gravitation has allowed them to fall, and allows them and will continue to allow them to fall, just as it has knocked, does knock and will knock old planets and old stars against one another, even those old defunct stars making their lugubrious way through their old cemetery. The deceased then explode like fireworks, and new torches shine forth to illuminate the world. If you disagree with this interpretation, find a better one. But be careful. The stars last only so long, and together with their planets they comprise all matter. If you do not revive them one way or another, the universe is finished. In any case, we will carry out our demonstration in every key, major and minor, without fear of repeating ourselves. The subject is worth the effort. Whether or not we understand how the universe is sustained is not a matter of indifference.

Until proven otherwise, let us say then that the astral bodies are extinguished as a result of old age, and ignite again through some sort of impact. Such is the method by which sidereal entities convert matter. By what other process could they both obey the law common to all change and escape eternal immobilisation? Laplace says that: ‘In space there are dark bodies that are as considerable, and perhaps just as numerous, as the stars.’13 These bodies are simply extinguished stars. Are they condemned to a cadaverous perpetuity? Will all the living ones, without exception, join them forever? How can these vacancies be filled?14

The rather vague origin Laplace himself assigns to stellar nebulae seems somewhat unlikely. It would be an aggregation of nebulosities, of volatised, cosmic clouds – an aggregation incessantly formed in space. But how? Space is everywhere just as we see it: cold and dark. The stellar systems are enormous masses of material. Where do they come from? From nothing? The existence of such improvised nebulosities is too hard to swallow.

Likewise, the notion of chaotic matter should not have reappeared in the nineteenth century. There has never been and there never will be a shadow of chaos anywhere. The organisation of the universe is eternal. It has never varied by even a hair’s breadth, nor has it taken a second’s respite. There is no chaos, not even on the battlefields where billions of stars collide with one another and blaze for centuries upon centuries in order to refashion living systems from dead ones. The law of attraction presides over these radical transformations just as rigorously as it does over the most peaceful movements of the moon.

Such cataclysms are rare in all the cantons of the universe, since the number of births cannot exceed the number of deaths in the civil registry of infinity, and its inhabitants enjoy very long lives. The open expanse before them is more than enough for their existence, and the hour of their death comes well before they have traversed the whole of it. The infinite is certainly rich in both time and space. It distributes a just and large proportion of both to its people. We do not know exactly how much time is granted, but we can get some idea of the space by measuring the distance of the stars, our neighbours.

The minimum distance separating us is around ten thousand billion leagues – a veritable abyss. Is that not a magnificent stretch, and spacious enough to allow us to advance in complete safety? Our sun’s flanks are covered. Its sphere of influence must no doubt extend to that of the nearest attractions. There are no neutral fields where gravitation is concerned. On this point we lack sufficient data. We are familiar with our own surroundings. It would be interesting to establish those of these luminous spheres whose zones of attraction are adjoining ours, and to arrange them around it, just as one stacks a cannon ball amongst other cannon balls. Our domain within the universe could then be surveyed and registered. This is impossible, however, otherwise it would have already been done. Unfortunately we are in no position to go measure parallaxes from Jupiter or Saturn.

Our Sun is advancing; its rotational movement proves this beyond doubt. It circulates in concert with thousands, perhaps millions of stars that surround us and belong to our army. It has been travelling for centuries, though we do not know either its past, present or future itinerary. The history of humanity already dates back six thousand years. Even during those remote times astronomical observations were already being carried out in Egypt. Apart from a movement in the zodiacal constellations as a result of the precession of equinoxes, there has been no recorded change in the appearance of the skies. In six thousand years, our system might have been able to advance in one direction or another.

Even for a mediocre walker like our globe, six thousand years is one fifth of the way to Sirius. Yet there is no indication whatsoever that it has moved. Any rapprochement with the constellation of Hercules remains a mere hypothesis. We are frozen in place, and so are the stars. And yet, we are travelling with them towards the same end. They are our contemporaries, our fellow travellers, hence their apparent immobility; we are advancing together. The road will be long, and it will take a long time to reach old age, death, and finally resurrection. But from the perspective of the infinite even this road is but a tiny point, and this time amounts to not even one thousandth of a second. Eternity does not distinguish between a star and something ephemeral. What are these billions of suns that follow upon one another across time and space? A shower of sparks. This rain fertilises the universe.

This is why the renewal of worlds through the collision and the volatilisation of deceased stars takes place every minute across the fields of infinity. These gigantic conflagrations are both innumerable and rare, depending on whether we consider the whole universe or only one of its regions. What other process could replace them, that might preserve the general life of the universe? The nebulae-comets are ghosts; the stellar nebulosities, brought together in some unknown way, are chimeras. There is nothing in the expanse except astral bodies small and large, infant, adult and dead, and their entire existence unfolds before us. The infants are volatilised nebulae; the adults are the stars and their planets; the dead are their dark cadavers.

Heat, light and movement are forces of matter, and not matter itself. Attraction, which launches so many billions of globes off into their incessant race, cannot add a single atom to it. Nevertheless it is the great, fecund force, the inexhaustible force that no prodigality can impoverish, since it is the permanent and common property of bodies. Attraction is what casts the whole celestial machinery into motion and sets the worlds off on their endless peregrinations. It is rich enough to provide the revitalisation of astral bodies with the motion that is converted into heat through a collision.

These encounters between sidereal cadavers which collide with one another until they result in a resurrection may be seen as a disturbance to the established order. A disturbance! But what would happen if the old, dead suns, with their string of defunct planets, were to continue their mortal procession indefinitely, extending it every night with new funerals? All these sources of light and life shining in the firmament would be extinguished one after the other, like lanterns in an illumination. Eternal night would descend upon the universe.

The initial high temperatures of matter can have no other source than motion – the permanent force from which all others derive. The lighting up of a sun, that sublime undertaking, is solely the work of this reigning force. It can have no other possible origin. Gravitation alone renews the worlds, just as it directs and maintains them through motion. This is a truth that we can grasp almost as much from instinct as from reasoning and experience.

Experience unfolds before our eyes every day; it is up to us to observe and to draw conclusions. What is an aerolite that ignites, volatilises and vanishes as it cuts through the air, if not the miniature image of a sun’s creation through motion that is converted into heat? Is this corpuscle, which has been diverted from its regular course to sweep through the atmosphere, not also a form of disorder? What was normal about that? And when these clouds of asteroids are moving at planetary speeds along their orbit’s track, why is only one of them diverted, and not all of them? Where is the good order in all of this?

At every point discord incessantly shatters this supposed harmony – a harmony that would otherwise stagnate and, soon after, decompose. The laws of gravity have millions of unexpected consequences; they produce a shooting star here, a sun-star there. Why banish them from the general harmony? These accidents displease, and yet we are born from them! They are the antagonists of death, the always-open sources of universal life. It is only through a permanent failing of its good order that gravitation is able to reconstruct and repopulate the globes. On its own, the good order that we vaunt would let them disappear into nothingness.

The universe is eternal, but the astral bodies are perishable. And since they constitute all matter, each one of them has already passed through billions of existences. Through the resurrecting collisions that it sets in motion, gravitation incessantly divides, combines and shapes them to the point that every one of them is a compound of the dust of all the others. Every inch of the ground we walk upon has been a part of the entire universe. But it is nothing more than a silent witness, who never speaks of what it has seen in Eternity.

In revealing the presence of a certain number of simple bodies in the stars, spectral analysis has only told part of the truth. It will gradually tell the rest through advances in experimentation. Two important remarks should be made here. The densities of our planets are different. But that of the Sun is the precise proportional encapsulation of these densities, and because of this it remains the faithful representative of the primitive nebula. This phenomenon is no doubt the same in all star systems. When the astral bodies are volatilised through a sidereal encounter, all of the substances merge together into a gaseous mass that arises from the impact. The nebula’s process of organisation then slowly separates them out from one another, according to the laws of gravity.

In each stellar system, the densities must therefore be layered or spread out in intervals according to the same order, such that all the planets are alike – not as if they actually belong to the same sun, but in such a way that their differences of rank apply across all groups. Indeed, as a result they possess identical conditions of heat, light and density. As for the stars, their composition is certainly similar, for they reproduce, billions of times over, the combinations that are produced by the impacts and volatilisations. The planets, by contrast, result from the processes of sorting and selection that are carried out according to the difference and classification of densities. Needless to say, the mixture of stellar and planetary elements thus prepared by infinity is far more comprehensive and fundamental than that of the most carefully prepared drugs, ground to the finest powder by generations of pharmacists, for a hundred years.

But I hear voices crying out: ‘On what basis can one presuppose the existence of this perpetual torment, which consumes the astral bodies on the pretext of recasting them, and which offers such a strange refutation of gravitation’s regularity? Where is the proof of these collisions and their resurrectionary conflagrations? Men have always admired the imposing majesty of celestial movements, and yet we now want to replace such a beautiful order with permanent disorder! Who has ever seen, anywhere, the slightest symptom of such disarray?

Astronomers are unanimous in proclaiming the invariability of the phenomena of attraction. Everyone agrees that it is an absolute guarantee of stability and security, but here comes another theory that seeks to establish it as an instrument of cataclysms. Centuries of experience and universal testimony vigorously reject such hallucinations.

Almost all the changes in the stars that have been observed until now are nothing more than periodic irregularities, and they therefore exclude the idea of catastrophe. The star in the Cassiopeia constellation in 1572, like that of Kepler in 1604, shone only as temporary flashes of light. This is incompatible with the volatilisation hypothesis. The universe appears to be very tranquil, quietly following its path. Humanity has been observing the spectacle of the sky for five to six thousand years. It has not noted any serious tumult there. The comets have only ever caused fear, not harm. Six thousand years is a considerable length of time! The telescope’s range is quite considerable, too. Neither the expanses of time or space have revealed anything. Such gigantic upheavals are nothing but dreams.’

Now it is true that we have not seen anything, but this only because we cannot see anything. Although they occur frequently across the expanse of space, nowhere are such scenes performed in front of an audience. The observations carried out on the luminous astral bodies concern only the stars of our own celestial province, the contemporaries and companions of our Sun, and therefore that share its same destiny. One cannot infer from the prevailing calm of our surroundings that there is monotonous tranquillity across the rest of the universe. There are no witnesses to the renewing conflagrations. If they are ever glimpsed, it is only at the end of a telescope, where they appear as an almost imperceptible faint light. Telescopes reveal thousands of them in this way. The day that our province itself becomes the theatre for such dramas once again, its inhabitants will have long since moved elsewhere.

The incidents of Cassiopeia in 1572 and Kepler’s star in 1604 are merely secondary phenomena. One could certainly attribute them to an eruption of hydrogen or to the fall of a comet, which might have crashed into the star like a glass of oil or of alcohol in a furnace, causing an ephemeral burst of flames. The latter case would imply that the comets are made of a combustible gas. But who could possibly know this, and what does it matter? Newton thought that they nourished and sustained the Sun. Should we generalise this hypothesis, and consider these wandering wisps [perruques vagabondes] as the regular nourishment of the stars? What meagre, ordinary fare! It is surely incapable of igniting or relighting these torches of the world.

The problem still remains, then, of how the luminous astral bodies are born and die. Who could have set them alight? And who replaces them once them they cease to shine? Not one atom of matter can be created, and if the deceased stars do not relight then the universe dies out. I defy anyone to find a way round this alternative: ‘Either the resurrection of the stars, or universal death…’ This is the third time I have repeated the point. The sidereal world is alive, very much alive, and since within life as a whole the lifespan of each star lasts no longer than a flash of lightning, all the astral bodies have already ended and begun anew billions and billions of times. I have already explained how. And yet the idea of collisions between globes travelling back and forth across space with thunderous violence is considered quite extraordinary. There is nothing extraordinary here other than this very incredulity, for these globes rush straight at one another, and only narrowly avoid colliding with each other. But they cannot always dodge each other. Those who seek, find.

On the basis of the preceding assumptions, we are entitled to conclude that there is a unity in the composition of the universe, which is not to say that there is a ‘unity in its substance’. The sixty-four (or let us estimate one hundred) kinds of simple body that make up our Earth likewise form the basis of all the globes without distinction –– except the comets, which remain an indecipherable and unimportant myth, and which are not globes in any case. Nature therefore has very little variety in its materials. It certainly knows how to put them to good use. Indeed, to see it take two simple bodies, hydrogen and oxygen, and alternately make fire, water and ice, is truly astounding. Chemistry is far from knowing everything, but it knows a great deal about this. Despite so much power, however, one hundred elements are not a lot to work with in the workshop of infinity. We are coming now to the crucial point.

All celestial bodies, without exception, have the same origin: the blaze caused by impacts. Each star is a solar system resulting from a nebula that has been volatilised in a collision. It is the centre of a group of planets that are already formed or in the process of forming. The role of the star is simple: it is sphere and source of light and heat that ignites, shines, and then goes out. Consolidated and strengthened through cooling, the planets alone have the privilege of organic life, which takes its source from the heat and light of their star and dies with it. The composition and mechanism of all the astral bodies is identical. Only the volume, form and density vary. The entire universe is set up, operates and lives according to this plan [plan]. Nothing could be more uniform.

VII. Analysis and synthesis of the universe

We are authorised at this point to make use of obscure language, since here the question itself becomes obscure. The infinite cannot be grasped though words. We are thereby entitled to go over these ideas several times. The necessity of doing so justifies the repetitions.

The first problem is that we find ourselves confronted with arithmetic that is certainly rich, indeed very rich in names for numbers, but whose richness is unfortunately quite ridiculous in its forms. Words such as trillion, quadrillion, sextillion, etc., are ludicrous. Moreover, to the majority of readers they mean little more than a more common and familiar word, and which is the expression par excellence for large quantities: billion. For astronomy, however, it has very little significance, and certainly in terms of the infinite it denotes next to nothing. Unfortunately, it is precisely when it comes to the infinite that it springs most imperiously to mind – but use of it is deceptive when going beyond the realms of the possible, and it remains deceptive even when it is simply a matter of the indefinite. In the following pages, numbers –– which provide the only language available to us –– are all either inaccurate or devoid of meaning. This is neither their fault nor mine; it is the fault of the topic. Arithmetic is not suited to the task of describing it.

Nature thus has one hundred simple bodies at hand with which to forge all of its works and cast them in a uniform mould: ‘the stellar-planetary system’. It has nothing but stellar systems to make, and one hundred simple bodies must provide all the materials – which is a lot of work and very few tools. Indeed, with such a monotonous plan and such unvarying elements, it is not easy to generate the quantity of different combinations required to populate the infinite. Resorting to repetitions becomes necessary.

It is claimed that nature never repeats itself, and that no two men or two leaves are identical. This may be so with the men on this Earth, where the total number, which is quite restricted, is distributed and shared out among several races. But there are thousands of oak leaves and billions of grains of sand that are exactly alike.

Of course, the hundred simple bodies can indeed produce a staggering number of different stellar-planetary combinations. Xs and Ys can be derived, however laboriously, from this sort of calculation. In short, this number is not even indefinite; it is finite. It has a fixed limit. And once this has been reached, [if repetitions are forbidden then] the process cannot go any further. This limit then becomes that of the universe itself, which, consequently, would not be infinite. Despite their incredible multitude, the celestial bodies would each occupy only one point in space. But can we accept this? Matter is eternal. We cannot imagine any situation in which it has not been formed into regular globes in keeping with the laws of gravitation – and we are supposed to treat these formations as a few isolated and exceptional sketches scattered amidst the void! A mere hovel in the infinite! It is absurd. We posit as a principle, then, the infinity of the universe as a consequence of the infinity of space.

Now nature is not obliged to undertake the impossible. The uniformity of its method, which is everywhere visible, refutes the hypothesis of an infinite number of creations that are each thoroughly original. Their number is limited by the strictly finite quantity of simple bodies. The distinct forms constitute so many typical combinations, or combination-types, so to speak, whose endless repetitions fill the expanse of space. ‘Different’, ‘differentiated’, ‘distinct’, ‘primordial’, ‘original’, ‘special’ – all of these words, in expressing the same idea, are for us synonymous with what we shall call ‘combination-types’. Determining their number would be a matter for algebra if this kind of problem were not rendered indeterminate (or in other words, insoluble) by the lack of data. This indetermination, however, cannot be understood as equivalent with or approximate to the infinite itself. Since the simple bodies alone comprise all matter, the amount of every one of them is certainly an infinite quantity. What is not infinite, however, is the variety of these elements themselves, whose number does not exceed one hundred. Even if there were a thousand of them, which there are not, the number of combination-types would certainly grow to fabulous heights – but, unable to reach the infinite, this number would still remain insignificant by comparison with it. This proves, then, their incapacity to populate space solely with original types.

We have thus established that the organic unit of the universe is the stellar-planetary group or more simply the stellar, or planetary, or solar group – four names that are equally suitable and that have the same meaning. The entire universe is made up of an infinite series of these systems, which themselves all come from a volatilised nebula that then condensed into a sun and planets. These latter bodies, having successively cooled, circulate around the central sphere, which is kept ablaze by its enormous volume. They must therefore move within the limit of their sun’s attraction and, moreover, must not exceed the circumference of the primitive nebula that gave birth to them. Their number is thus severely restricted, and depends on the original size of the nebula. There are nine of them in our system: Mercury, Venus, Earth, Mars (the aborted planet, consisting only of remnants), Jupiter, Saturn, Uranus and Neptune. Perhaps there might be as many as a dozen, if we include three still-unknown ones. Their distance increases to such an extent in this progression that it becomes difficult to extend the limits of our group any further.

The other stellar systems no doubt vary in size, but they do so according to proportions that are strictly circumscribed by the laws of equilibrium. Sirius is thought to be one hundred and fifty times larger than our sun. What do we know about it? All we have to go on, at present, are problematic parallaxes of little or no value. Moreover, since telescopes do not enlarge the stars, only the human eye can size them up, and it is limited to assessing the way certain aspects appear, which are themselves dependent on various causes. Thus we do not accept that observers are entitled to assign to the stars these various sizes – or indeed any size at all. They are suns, that is all we can say. If ours governs a maximum of twelve astral bodies, then why should its colleagues have far larger kingdoms? –– ‘Why not?’, one might respond. Indeed such a question merits such a response.

But let us accept this for the sake of argument. The causes of diversity still remain fairly weak. What are they? The primary cause stems from disparities between the volumes of the nebulae, which lead to corresponding disparities in the size and number of planets that they make. Then there are the disparities in impacts that modify the speed of rotation and translation, the flattening of the poles, the inclination of the axis on the ecliptic, etc., etc.

We should also refer to the causes of similarity. First there is identity of formation and mechanism: a star, the condensation of a nebula and the centre of several planetary orbits, which are spread out at certain intervals – such is the foundation common to every system. Moreover, spectral analysis has revealed the unity in the composition of celestial bodies. The same basic elements are found everywhere. The universe is nothing but a collection of families that are, in a certain way, united by flesh and blood. Everywhere we find the same matter, classified and organised by the same method, according to the same order. Its foundations and its government are identical. This above all is what appears to limit dissimilarities and open the door to the Menaechmi twins.15 Let us repeat, nonetheless: this system can indeed produce unimaginably large numbers of different combinations of planetary systems. But are these numbers infinite? No, because they are all formed from one hundred simple bodies, a minute and insignificant number.

Infinity is a matter of geometry and has nothing to do with algebra. Algebra is sometimes a game; geometry never is. Algebra gropes along in the dark, like a mole. Only after all this fumbling around does it find a result – often this is a fine formula, sometimes it is a mystification. Geometry never ventures into the darkness; it keeps our eyes fixed on the three dimensions, which allow no room for sophisms and sleights of hand. It tells us: look at these thousands of globes, this tiny corner of the universe, and remember their history. A conflagration tore them from the clutches of death and threw them into space [to form] immense nebulae, the origin of a new Milky Way. By understanding one, we shall reveal the destiny of all.

The resurrecting shock fused the nebulae’s simple bodies through volatilisation. Condensation separated them again before classifying them, in each planet and in the group as a whole, according to the laws of gravity. The lighter parts dominate the distant planets; the dense parts the central ones. Hence, as regards the proportions of simple bodies, and even as regards the total number of globes, there is a necessary tendency towards similarity between planets of the same rank, across all stellar systems; hence too the progressive changes in magnitude and lightness, from the capital or centre of each system to its frontiers – and for the same reason planets become more and more dense, and shrink in size, as we move from the frontiers back to the capital. One can now anticipate the conclusion. Already, the uniformity in astral bodies’ mode of creation and their shared elements means that the resemblances between them must be more than fraternal. These growing parities in their constitution must obviously result in frequent cases of identity. The Menaechmi brothers become doubles or twins [sosies].

Such is the initial basis upon which we affirm the limitation of matter’s differentiated combinations and, consequently, their inability to sow the expansive fields of space with celestial bodies. In spite of their vast numbers, these combinations have a limit and an endpoint. They must therefore be repeated in order to attain the infinite. Nature prints billions of copies of each of its works. When it comes to the texture of the astral bodies, similarity and repetition are the rule, dissimilarity and variety the exception.

As we grapple with these ideas of number [ces idées de nombre], how can they be formulated if not with numerals [des chiffres], their only possible interpreters? But here these necessary interpreters are either unfaithful or powerless: unfaithful and inaccurate when it is a question of matter’s combination-types, which are limited; powerless and empty as soon as one speaks of infinite repetitions of these combinations. In the first case, that of the original combinations or types, the figures will be arbitrary, vague, randomly chosen, and without even an approximate value. One thousand, one hundred thousand, one million, one trillion, and so on and so forth – they are all errors, just errors of varying degree. Conversely, in the second case, that of infinite repetitions, any figure becomes absolutely nonsensical, since it attempts to express that which is inexpressible.

In truth, it cannot be a question of real numbers: for us they are nothing more than a manner of speaking. Two elements alone confront each other: the finite and the infinite. Our thesis claims that the one hundred simple bodies are unable to generate an infinite number of original combinations. Therefore the only tension, in the end, is between the finite, represented by indeterminate numerals [chiffres], and the infinite, represented by a conventional numeral.

Celestial bodies are thus classified as either originals or copies. The originals are the set of globes that together form a distinct or special type. The copies are repetitions, duplicates or proofs [épreuves] of this type. The number of original types is limited, that of the copies or repetitions, infinite. The infinite constitutes itself through the latter. Each distinct type has behind it an unlimited army of doubles.

For the first class or category, that of the types, the various numbers that might quantify it are more or less arbitrarily chosen, and they cannot and will not be accurate; they all simply signify a lot. For the second class, that is, the copies, repetitions, duplicates and proofs (words that are all synonymous), we will use the term billion alone, but always in order to mean infinite.

It is conceivable that the astral bodies might be infinite in number and yet all reproduce a single and same type. Let us assume for a moment that all the stellar systems, both in materials and in personnel, are an exact copy of our own, planet by planet, without an iota of difference. This collection of copies would here constitute the infinite all by itself. There would then be only one type for the universe as a whole. This is not the case, of course. Although finite, the number of combination-types is incalculably large.

On the basis of the facts and arguments outlined above, our thesis claims that matter would be unable to reach an infinite number of sidereal combinations if it relied on their diversity alone. Oh! If only the elements it had at its disposal were themselves infinite in their variety; if one could convince oneself that the composition of the remote astral bodies is nothing like that of our Earth, that everywhere nature works with the unknown – then one could concede anything and everything to the infinite. As far back as thirty years ago I had already begun to suspect that our planet must exist in thousands of copies, because of the infinity of celestial bodies. Yet this opinion remained simply a matter of instinct and intuition, one based solely on the fact of the infinite. Spectral analysis has completely changed the situation, and opened the doors to an understanding of the reality that has come rushing in.

Our old illusions regarding fantastic structures have dissolved. There are no other materials anywhere beyond the hundred or so simple bodies, two-thirds of which are visible before our eyes. The universe must be constantly made and remade from this meagre set. Monsieur Haussmann had just as many to rebuild Paris. Indeed, he had the exact same ones. His buildings are not notable for their variety, however. Nature, which also demolishes in order to rebuild, is somewhat more successful with its constructions. It is able to turn its poverty of means to such rich advantage that one hesitates before assigning a limit to the originality of its works.

Let us examine the problem more closely. Let us suppose that all the stellar systems have the same life span – say one thousand billions years or so, for example. Let us also hypothesise that they begin and end together, at the very same minute. We know that all these groups –– which share the same blood, flesh and bone structure, as it were – also develop in the same way. In the various systems, the planets line up in symmetrical lines according to how closely they resemble one another, and these similarities push them to become identical. Each of the one hundred simple bodies is a unique material that is part of a fundamentally unified set. Will they be capable of providing a different and special combination for each globe – that is to say, an infinite number of distinct originals? No, certainly not, since the diversity within any species that alters the combinations depends on a entirely restricted number: one hundred. The number of differentiated or typical astral bodies is therefore reduced to a limited amount, and the infinity of globes can only arise from the infinity of repetitions.

The series of original combinations is thus exhausted before it can reach the infinite. Myriads of different stellar-planetary systems circulate in any one province of space, and are limited to populating that one province. But will matter remain there, and resign itself to appearing as a mere point in the sky? Or will it be content with one thousand, ten thousand, one hundred thousand such points that would extend its meagre estate by an insignificant amount? No. Its vocation, its law, is the infinite. It will not allow itself to be overcome by emptiness. Space will not become its dungeon. It will invade and overrun space in order to give life to it. In any case, why would the infinite not be a universal prerogative, the property of the blade of grass and the mite as much as that of the great Whole?

Such is indeed the truth that emerges from these vast questions. Let us now rule out the hypothesis that prompted this demonstration. We quite agree that all the planetary systems do not follow the same course at the same time. Far from it – their ages are entangled and intertwined in every direction and at every instant, from the blazing birth of the nebulae through to the passing away of the star, and all the way to the shock that resuscitates it.

Let us set aside the original stellar systems for a moment, so as to focus on the Earth. Later we will link it to one system in particular, our solar system, to which it belongs and which determines its destiny. It is understood that, according to our thesis, mankind is no more entitled to an infinite duration than are animals or things. Considered as an entity in its own right, mankind is merely ephemeral. It is the globe from which he springs that authorises man to share in its status as infinite in both time and space. Each of our doubles is the son of an earth, which is itself the double of our present Earth. We are part of what is thus copied or duplicated. The Earth-double [Terre-sosie] reproduces exactly what is found on our own Earth, including, therefore, every individual, along with their family, their house (if they have one), and every event of their life. It is a duplicate of our globe, both as container and as a set of contents. Nothing is missing.

The stellar systems arrange their planets around their sun, in an order that is determined by the laws of gravity. These laws thereby assign a symmetrical place to the analogous creations in each group. The Earth is the third planet from our Sun, and this rank no doubt derives from certain particular conditions of size, density, atmosphere, and so on. Millions of stellar systems are certainly close to ours as regards the number and the arrangement of their astral bodies, for their procession is strictly arranged according to the laws of gravitation. In all of the groups containing eight to twelve planets, there is a strong chance the third will resemble the Earth –– first and foremost, because the distance from the Sun is an essential condition that provides the same amount of light and heat. The volume, the mass and the inclination of the axis on the ecliptic can vary. Again, if the nebula was more or less equivalent to ours, then there is every reason to suppose that its development would follow the same path, step by step.

Nevertheless, let us assume the existence of some differences that serve to reduce this similarity to one of simple analogy. One would go through billions of such earths before coming across one that completely resembles our own. As with ours, all these globes will have terraced fields, flora, fauna, seas, an atmosphere and humans. But the duration of geological periods, the distribution of water, continents, islands, animal and human races will offer innumerable varieties. Let us move on.

Then an earth is finally born with our humanity, whose history unfolds with its different races, its migrations, its struggles, its empires, its catastrophes. All of these events will change its destiny, sending it down paths very different to those of our globe. Every minute, every second, thousands of different directions are open to this human species. It chooses one of them, and forever abandons the others. How such swerves to the right and left alter individuals, and alter history! These versions of Earth do not yet include the path of our own past. Let us set aside these confused copies. They will continue to make their own path and will be worlds of their own.

But eventually we arrive [at our culmination]. Here now is a complete copy, of both things and people. There is no stone, tree or stream, no animal, man or incident that has not found its place and moment in this duplicate of our world. It is a genuine twin-Earth or Earth-double… up until today at least. For tomorrow, on each planet the events and the people will follow their own course. Henceforth everything is unknown for us. The future of our Earth, like its past, will change course millions of times. The past is a fait accompli, and it is ours. The future will come to end only when the globe itself dies. Until then, each second will bring its bifurcation: the path we will take, and the one that could have been taken. Whichever one it is, the path that will run to the end of this planet’s particular existence, until its final day, has already been travelled billions of times. Even this path will be nothing but a copy, printed in advance over the ages.

It is not the events alone that create human variants. What man has not at times found himself confronted with a choice of two possible paths or careers [carrières]? The one he rejects would indeed change his life, while not altering his individuality. One leads to poverty, shame and servitude. The other leads to glory and freedom. Here, a charming wife and happiness; there, a shrew and desolation. I speak for both sexes. One can take either option by chance or by choice, it matters little – one cannot escape fatality. But fatality has no place in the infinite, which knows nothing of alternatives and has room for everything. An earth exists where a man follows the path disdained by his double in another. His existence splits in two, with a globe for each course; it then bifurcates a second time, a third time, thousands of times. He thus possesses perfect doubles as well as innumerable variations on doubles who multiply and who always represent his person, yet who only retain scraps of his destiny. Everything that you could have been in this world, you actually are somewhere else. In addition to the whole course that one lives, from birth to death, on a great number of earths, one’s life also unfolds, on other planets, in many thousands of different editions.

The great events of our globe have their counterparts, particularly when fatality has played a role in it. Perhaps the English have lost the Battle of Waterloo many times over, on those globes where their adversary did not commit Grouchy’s blunder. The outcome depended on very little. On the other hand, elsewhere Bonaparte is not always victorious at Marengo, which on our planet was won by a stroke of good luck.

I can already hear the clamours: ‘This is pure folly straight from Bedlam! What? Billions of copies of analogous earths! Billions of others for those that had similar beginnings! Hundreds of millions for the follies and crimes of humanity! Then thousands of millions for all the individual whims! Every one of our good or bad moods will have its own special sample of the globe at its disposal! Everywhere the skies are cluttered with our doubles!’

No, no. There are no crowds of these doubles to be found anywhere. They are even very rare, despite numbering in the billions – which is to say that their number exceeds the scope of actual numbers. Our telescopes, which have quite a sizeable field to cover, would be unable to find in it one single copy of our planet, even if it were visible. A thousand or a hundred thousand times this amount of space would have to be crossed before even one such encounter might be possible. In a universe that stretches across thousands of millions of stellar systems, who can say if we would be able to come across a single reproduction of our group or one of its members? Nevertheless, an infinite number of them exist all the same. As we said at the beginning: ‘If each word denoted the most frightening of distances, one would have to say one word per second for billions and billions of centuries in order to express no more than something insignificant when it comes to the infinite.’

It is here and now that this thought finds its point of application. As special types, considered simply as one of a kind, the myriads of earths that possess every possible difference would still amount to nothing more than a mere point in space. Each of them must be infinitely repeated before they count for anything at all. From the day of its birth to the day of its death and then of its resurrection, an earth that is the exact double of our own will exist in billions of copies for every second of its duration. This is its destiny as a repetition of an original combination, and all the repetitions of other original types share it.

To suggest that there is a duplicate of our terrestrial residence, complete with all of its inhabitants, from the grains of sand to the Emperor of Germany, may seem somewhat fantastic in its boldness, particularly when it concerns duplicates generated or printed out by the billion. The author of these lines, needless to say, considers his reasoning to be excellent, since he has repeated it already five or six times, without posing any threat to the future. He finds it difficult to imagine that nature, carrying out the same work with the same materials and according to the same pattern, would not often be forced to cast its iron in the same mould. Indeed, the contrary would be more surprising.

As for the profligate print run, one need not worry about the infinite; it is abundant. No matter how insatiable one might be, it can cover more than every need, more than every dream. Moreover, this shower of proofs [épreuves] is not concentrated over one locality. It is spread across incommensurable fields. It does not matter much to us whether or not our doubles are our actual neighbours – even if they lived on the moon the conversation would not be any simpler to arrange, or the acquaintance any easier to make. It is in fact rather flattering to know that one is out there, a long way away, at the back of beyond, reading the newspaper in one’s slippers, or witnessing the battle of Valmy, which at this moment is being waged in thousands of French Republics.

Do you think that, at the other end of the infinite, on some congenial version of earth, the royal prince, in arriving at Sadowa too late, might allow the unfortunate Benedek to win his battle?16… But here comes Pompey, who has just lost at Pharsalus. The poor man! He is leaving to find consolation in Alexandria, in the company of his good friend, King Ptolemy… How Caesar will laugh… Ah! Not quite – he is being stabbed in the middle of the Senate… Well! Such is his daily ration since the non-beginning of the world, and he stockpiles such experiences with an imperturbable calm. It is true that his doubles do not sound the alarm for him. That is what is so terrible! No-one can be forewarned. If one were allowed to pass along the story of one’s life, together with some sound pieces of advice, to the doubles one has in space, then one could certainly spare them a great deal of folly and sorrow.

Joking aside, this is all, in fact, very serious. It is not a question of imagining fanciful creatures like anti-lions, or anti-tigers, or a pair of eyes at the end of a tail; it is a matter of mathematics and attested facts. I defy nature not to manufacture these billions of solar systems, these servile copies of our own, with the same materials, equipment and personnel, on a daily basis ever since the world was the world. I will allow it to run through the calculation of each and every probability, without exception. Once it has exhausted the full range of possibilities, I will force it back upon the inexhaustible resources of the infinite, and I will command it to act in compliance with them – that is, to make an unending series of duplicate copies. I must be sure not to propose the beauty of the samples as my motive, on the grounds that it would be a great shame not to multiply them in abundance. On the contrary, I find it distasteful and barbarous to poison space with a heap of fetid countries.

Such observations are useless, in any case. Nature knows nothing of morality, and does not act in keeping with it. What is does, it does unintentionally. It works blindfolded – destroying, creating, transforming. It disregards everything else. With its eyes shut, it applies the arithmetic of probabilities better than any mathematician could explain it with his eyes open. Not one variation eludes it; it draws every lot, and not one random chance is left over in the urn. It calls out every number. When there is nothing left at the bottom of the bag, it opens the box of repetitions. Similarly, this bottomless jar is never empty – indeed it is the exact opposite of the Danaids’ jar, which could never be filled.

This is how matter has always proceeded, ever since it is has been matter, which is not something that began yesterday. Following its uniform plan, with only a hundred forms of simple body to work with, and a total mass that never decreases or increases by a single atom, it can only endlessly repeat a certain quantity of different combinations, which in this sense are called primordial, original and so on. The only things that emerge from matter’s workshop are stellar systems.

The fact that any astral body exists proves that it has always existed, and that it will always exist – not in its present form or personality, which is temporary and perishable, but in an infinite series of similar personalities that are reproduced across the ages. Each astral body belongs to one of the original combinations that were made feasible by the various possible arrangements of the one hundred simple bodies. Because it is identical to its preceding incarnations, if it is placed in the same conditions it lives and will live exactly the same life, both in general and in detail, as that of its previous avatars.

All of the astral bodies are repetitions of an original combination or type. No new types are created. The number of types has been necessarily exhausted since the origin of all things – even though things have never had an origin. This means that a fixed number of original combinations exists for all eternity, and is no more likely to increase or decrease than matter itself. This is the way that it is, and the way it shall remain, until the end of all things – which can no more end than they can begin. There is an eternity of present types in the past as in the future, and not one astral body that is not a type infinitely repeated in time and space. Such is reality.

Our Earth, just like all other celestial bodies, is the repetition of a primordial combination that replicates itself, and which exists simultaneously in billions of identical copies. Each copy is born, lives and dies in turn. They are born and die by the billions with every passing second. On each copy all the material things, all the organised beings, follow one another in the same order, in the same place, at the same minute as they do on the other earths, its doubles. Therefore, all the events that have taken place or that are yet to take place on our globe, before it dies, take place in exactly the same way on its billions of duplicates. And since this is the case for all the stellar systems, the entire universe is an endless, permanent reproduction of an ever renewed and ever identical stock of materials, equipment and personnel.

Does the identity of two planets require the identity of their solar systems? That of the two suns is, without a doubt, an absolute necessity. They would otherwise be forced to change their conditions of existence, which would lead the two astral bodies towards different destinies in spite of their original identity, which is somewhat unlikely. But within these two stellar clusters, is complete similarity also de rigueur between all the globes that correspond to each other, according to their position in the system’s order? Must there be a double Mercury, a double Mars, a double Neptune, and so on? The lack of data makes the question insoluble.

These bodies no doubt undergo reciprocal influences, and the absence of Jupiter, for example, or its reduction in size by nine tenths, would bring about a noticeable change for its neighbours. However, distance attenuates these causes and can even cancel them out. Moreover, as the source of light and heat, the Sun reigns alone. And when one considers that its mass, in proportion to its retinue of planets, is 741 to 1, then it seems that this enormous power of attraction should annihilate any rivalry. Yet this is not the case. It is widely recognised that the other planets do have an effect on the Earth.

In any event this question is unimportant and does not affect our thesis. If it is possible for two earths to be identical, without their also being reproduced in the same position between other corresponding planets, then this possibility existed from the outset, for nature does not overlook any combination. In the contrary case it is of little importance. Should twin earths require twin solar systems as their condition sine qua non then so be it. The consequence is simply that there are millions of stellar clusters in which our globe possesses, instead of exact likenesses, varying degrees of Menaechmi – original combinations, infinitely repeated – just like all the others.

Moreover, solar systems that are perfectly identical and infinite in number easily meet the demands of the programme that needs to be carried out. They each constitute an original type. All of the planets in the corresponding echelons are perfectly identical. Mercury is there the double of our Mercury, Venus of Venus, Earth of Earth, and so on. Billions of these systems are scattered across space, as repetitions of a type.

Amongst the differentiated combinations, are there any whose differences appeared on globes that were initially identical at birth? Here a distinction must be made. These mutations can hardly be seen as the spontaneous work of matter itself. The first initial moments of an astral body determine the entire series of its material transformations. All natural laws are inflexible and immutable. So long as they govern alone, everything follows a course that is fixed and fated. But variations do begin to occur with animate beings that are endowed with will – or, in other words, caprice. Above all, as soon as human beings intervene, fantasy intervenes along with them. They are certainly unable to make much of an impact on the planet itself. Even their greatest efforts would hardly move a molehill, although this does not stop them from posing as conquerors and swooning in ecstasy before their own genius and power. Matter quickly sweeps aside the works of these Myrmidons, as soon as they stop defending them against it. Go and seek out the celebrated cities of Nineveh, Babylon, Thebes, Memphis, Persepolis and Palmyra, which were once teeming with millions of inhabitants and all their feverish activity. What remains of them? Not even rubble. Grass and sand cover their tombs. If human works are neglected for so much as an instant, nature peacefully begins to demolish them; and if we are slow to react, we find nature re-established and flourishing on the debris.

Although men may disturb matter very little, they do disturb one another a great deal. The turbulence they create never seriously disrupts the natural course of physical phenomena, but it does disrupt humanity. We must therefore take into account this subversive influence that changes the course of individual destinies, destroys or alters animal races, tears nations apart and topples empires. To be sure, these brutalities take place without even grazing the earth’s skin. If the trouble-makers disappeared they would not leave a trace of their so-called sovereign presence, and this alone would be enough to return nature to its virgin state, almost untouched.

It is amongst themselves that men create victims and bring about immense changes. When carried away by passion and competing interests, their species gets stirred up with a violence that is greater than that of an ocean whipped up by a storm. What differences in the paths taken by these humanities –– humanities that nevertheless set off on their journey with the same personnel, owing to the identity in the material conditions of their planets! If one considers the mobility of individuals and the thousands of upheavals that continuously come to knock them off course, one will easily arrive at the sextillions and sextillions of variants of mankind. But through successive repetitions, a single original combination of matter, that of our planetary system, generates billions of earths that each provide doubles for the sextillions of diverse humanities that emerge from the agitations of mankind. The first year of the journey may only produce ten variants; the second, ten thousand; the third, millions, and so on, with a crescendo proportional to the progress that, as we know, emerges through such extraordinary processes.

These different human groups have only one thing in common: their lifespan. Since they are born from copies of the same original type, each of them writes their own story in their own way. The number of these distinct histories, however large it might be, is always a finite number, and we know that the primordial combination produces an infinite number of repetitions. Each distinct history, representing one and the same collective group, has a circulation of billions of identical proofs. Each individual, as an integral part of this collective, therefore has billions of doubles. We know that every person can appear simultaneously under several variants as a result of changes in the paths followed by their doubles on their respective earths – changes that split the life in two, without affecting the individual personality.

To summarise: forced to build only nebulae that are later transformed into stellar-planetary groups, matter is unable, despite its fecundity, to exceed a certain number of special combinations. Each of these types is a stellar system that is endlessly repeated –– this is the only possible way to populate the expanse of space. Our Sun and its retinue of planets is one of the original combinations, and like all the others, millions of copies of it have been printed. Each of these proofs naturally includes an earth that is identical to ours, a double-earth as far as its material constitution is concerned, which therefore engenders the same vegetable and animal species as those born on our earth’s surface.

All identical at the outset of their journey, each of the Humanities follow, on their own planet, the road traced by the passions, and individuals contribute to changes in this road through their own particular influence. As a result, in spite of the consistent identity of its beginning, Humanity does not have the same personnel on all similar globes. Indeed, each of these globes has its own specific Humanity, so to speak, that emerged from the same source and began at the same point, but that was diverted along the way by a thousand alternations in the route, to culminate, in the end, in a different life and a different history.

But the restricted number of inhabitants of each earth still does not allow these variants of Humanity to exceed a fixed number. Thus, no matter how prodigious it may be, the number of particular human collectives remains finite. It is therefore nothing compared to the infinite quantity of identical earths, the full domain of the solar combination’s type. And although they were continually modified later, they originally all had parallel nascent Humanities. It follows that each earth, containing one of the particular human collectives that result from the incessant alterations, must be repeated billions of times in order to meet the requirements of the infinite. Hence the existence of billions of earths that are absolute doubles in matter and personnel, without a hair’s difference in either time or space – neither by a thousandth of a second nor by a single spider’s thread. These terrestrial variants or human collectives are arranged in the same way as the original stellar systems. Their overall quantity is limited because it draws on a finite number of elements, i.e. the number of people on an earth, just as the original stellar systems each have a finite number of elements, i.e. the one hundred simple bodies. But each variant produces its proofs [épreuves] by the billions.

Such is the common destiny of our planets – Mercury, Venus, Earth, and so on – and of the planets of all the primordial or typical stellar systems. We should add that amongst these systems, there are millions that resemble ours without being duplicates; they have innumerable earths that are no longer identical to the one we live on but that nonetheless share every possible degree of resemblance or analogy with it.

All these systems, all these variants and their repetitions make up innumerable series of partial infinites that rush towards the great infinite like rivers into the ocean. Readers should not object to this outpouring of globes that stream from my pen in their billions. The question one should ask here is not: where shall we find space for so many people and so many worlds? But rather: where shall we find enough worlds for so much space? One can multiply by the billions without scruples when it comes to the infinite; it will always ask for more

The scientific doctrines, which can be as quick to mock as they are to lament, may perhaps scoff at our partial infinities, while congratulating us for making so much money with forged coin. Indeed, those who refuse to treat the expanse of space as a single infinity will consider it shameless to grant it this status millions of times over. Nothing could be simpler, however. Since space is without limits, one can ascribe to it any and all possible figures, precisely because it does not itself have one. Presented until recently as a sphere, now it takes the guise of a cylinder.

Take a cylindrical block of wood; nine cuts of a saw can divide it into ten planks perpendicular to its axis. Now imagine, in the domain of thought, that the circular perimeter of each of these planks is infinitely extended. Thought also allows us to separate them from each other by septillions and septillions of leagues. There you are, you now have ten irreproachable partial infinities, albeit rather thin ones. According to our calculations, all the astral bodies, along with their respective domains, would fit comfortably within any one of these compartments. Moreover, there is nothing that might prevent others from being set alongside them, thereby adding as much more of the infinite as one might like.

Needless to say these astral bodies do not remain enclosed in their separate categories according to their different identities. The renewing conflagrations continually fuse and merge them together. A solar system is not born again out of its own combustion, like a phoenix. On the contrary, this combustion itself contributes to the formation of different combinations. The old system is avenged elsewhere, for it is reborn through other volatilisations. Since the materials are everywhere the same one hundred simple bodies, and since what is given is infinite, the probabilities level out. The result is the invariable permanence of the whole through the perpetual transformation of its parts.

If some quibbler, insisting on the nature of the Indefinite, were to pick a pointless quarrel with us in an attempt to get us to comprehend the Infinite and then explain it to them, we would refer them to the Jovians, who are no doubt endowed with larger brains than us.17 No, it is widely known that we cannot exceed the indefinite. We thus only try to conceive of the Infinite in this form. It is through adding space to space that thought quickly comes to the conclusion that it is without limits. Admittedly, across a myriad of centuries many calculated that the total amount would always remain a finite number. But what does that prove? First, the infinite itself through the impossibility of its attainment, and also the weakness of our brains.

Indeed, after having thrown around enough figures to be met with a few laughs and dismissed with a few shrugs, one is left breathless from the very first steps on the road to the infinite. The infinite is, however, as clear as it is impenetrable, and can be summarised with marvellous ease in a couple of words: space, filled with celestial bodies, forever, without end. It is really quite simple, if incomprehensible.

Our analysis of the universe has put the spotlight on the planets, the only theatre of organic life. The stars themselves have remained in the background. This is because with the latter there are no changing forms, and no metamorphoses. There is nothing but the tumult of the colossal blaze, that source of heat and light, then its progressive decline, and finally the frozen darkness. A star is nothing less than the vital source and epicentre of the groups that are constituted through the condensation of the nebulae. A star is what classifies and regulates the system of which it forms the centre. Its size and movements are different for each combination-type. It remains immutable for all the repetitions of this type, including the planetary variants that are created by humanity.

Indeed, it would be wrong to think that globes are reproduced like this just to please the doubles that inhabit them. The prejudice born of self-centredness and education that refers everything back to us is very foolish. Nature is not concerned with us. It makes stellar groups with the materials available to it. Some are originals, others are duplicates, produced by the billion. There are not even any proper originals – that is, any that were actually formed first – but various types, which serve to group the stellar systems.

Whether or not the planets in these groups produce people is not nature’s concern. Nature has no concerns at all; it simply does its job without worrying about the consequences. It applies 998 thousandths of matter to the stars, where neither a blade of grass nor a mite grow; and the rest – ‘two thousandths!’ – to the planets, of which at least half, if not more, do not attempt to accommodate and nourish the kind of bipeds found in our own familiar sphere [module]. Overall, however, nature does things rather well, and we have no grounds for complaint. Were it more modest, the lamp that lights up our world and warms us would soon abandon us to eternal night – or rather, we would never have entered into the light at all.

Only the stars might be entitled to complain, but they do not. The poor stars! Their splendid role involves only sacrifice. Creators and servants of the productive power of the planets, they do not possess any power of their own, and must resign themselves to their thankless and monotonous function as torches. They shine with brilliance but without enjoyment; the living realities are hidden away behind them, invisible. These enslaved queens are made of the same stuff as their cheerful subjects, however. The hundred simple bodies provide all that is needed. But the stars will only recover fecundity by shedding grandeur. Dazzling flames now, they will one day turn to darkness and ice, and will only be able to come back to life as planets, after the collision that will volatilise both the queen and its retinue into a nebula.

While awaiting the happiness that this deposition will bring, without knowing what they are doing the sovereigns govern their kingdoms by means of kindness. They prepare the harvests but never reap their fruits. They bear all of the burdens, and enjoy none of the benefits. The only masters of real force, they use it only to bring succour to the weak. Dear stars! You have few imitators.

Finally, we can conclude that immanence characterises the smallest particles of matter. Even if they endure only for a second, their rebirth has no limits. The infinite in time and space is not the exclusive prerogative of the universe as a whole. It also belongs to all the forms of matter, even to infusoria and to grains of sand.

Thus, by the grace of his planet, every man has an endless number of doubles across the expanse of space, living his life exactly as he lives it himself. Every man is infinite and eternal in the person of other versions of himself, not only at his current age, but at all his ages. At every second, he simultaneously has billions of doubles who are being born, others who are dying, others whose ages are spread, second by second, across the span that runs from his birth to his death.

Whenever someone examines the celestial regions in order to discover their secret, billions of doubles simultaneously lift their eyes, with the same question in mind, and every such gaze passes by the others, invisibly. And this silent questioning does not travel across space just once; it does so forever. Each second of eternity has seen and will see the situation of today – that is to say, billions of doubles of our earth, each carrying our own personal doubles.

Thus every one of us has lived, lives and will live endlessly, in the form of billions of alter egos. Whatever one has become, at every second of one’s life, so one is engraved in billions of stereotyped prints over the course of eternity. We share the destiny of the planets, our nourishing mothers, in whose bosom this inexhaustible existence is played out. The stellar systems carry us along with them in their perennial existence. As the sole organisation of matter, they share both its fixedness and its mobility. Each one of them is no more than a flash, but these flashes illuminate space eternally.

The universe is infinite as a whole and in each one of its parts, be it a star or a speck of dust. The way that it is at this very instant, such it was, such it will always be, without one atom or second of variation. There is nothing new under the sun. Everything that is done has been done, and will be done. And yet, although the same, the universe of a moment ago is no longer that of the present, and that of the present will not be like the one that follows it; for it is never immutable and immobile. On the contrary, it is constantly changing. All of its parts are in continuous movement. When they are destroyed here, they are simultaneously reproduced elsewhere as new individualities.

The stellar systems end, and then begin again with similar elements that are combined through other forms of union – an indefatigable reproduction of similar copies drawn from different remnants. It is an alternation, a perpetual exchange of rebirths that proceed through transformation.

The universe is at once life and death, destruction and creation, change and stability, tumult and repose. It is endlessly made and unmade, forever the same, with beings that are forever renewed. In spite of its perpetual development or becoming [devenir], its engravings are cast in bronze and incessantly print out the same page. Both as a whole and in detail, it is eternally transformation and immanence.

Humanity is one of these details. It shares the mobility and permanence of the great Whole. There is not a single human being who has not appeared on billions of globes, which have long since returned to the crucible in which they are recast. However far back upstream we might go, against the current of the ages, we would never find a moment when we had not lived. For the universe has no beginning, and so neither does humanity. It would be impossible to go back to a time when all the astral bodies – and so us too as their inhabitants –– have not already been destroyed and replaced. And in the future there will never be a moment when billions of other versions of ourselves are not in the midst of being born, of living and of dying. Humanity, just like the universe, is the enigma of the infinite and eternity, and so is a grain of sand, just like humanity.

VIII. Summary

The entire universe is composed of stellar systems. In order to create them, nature has only one hundred simple bodies at its disposal. Although it is able to make prodigious use of these resources, and despite the incalculable number of combinations contribute to its fecundity, the result is necessarily a finite number, like that of the elements themselves. So in order to fill the expanse, nature must infinitely repeat each of its original combinations or types.

An infinite number of every astral body, whatever it might be, therefore exist in both time and space, not only under one of its aspects, but as it is at every second of its life, from its birth to its death. All the beings that are spread out over its surface –– great or small, living or inanimate – share the privilege of this perennial existence.

The Earth is one of these astral bodies. All human beings are thus eternal at every second of their existence. What I write at this moment in the dungeons of the Fort du Taureau I have written and I will write for eternity, at a table, with a pen, in these clothes, in much the same circumstances. And so it goes, for everyone.

All of these earths sink, one after the other, into the rejuvenating flames, only to be reborn and then to fall back into them once again – the monotonous flow of an hourglass that eternally empties itself out and turns itself over. It is a matter of something new that is always old, and something old that is always new.

Meanwhile those who are curious about extraterrestrial life may smile at a mathematical conclusion that grants them not only immortality, but eternity. The number of our doubles is infinite in time and space. In all honesty one could hardly ask for more than this. These are doubles in flesh and blood, indeed in trousers and vest, in crinoline and chignon. These are no ghosts, they are actuality made eternal [l’actualité éternisée].

Nevertheless, there is a major drawback: there is no progress. Alas! No, these are all ordinary reprints, repetitions. So are the copies of past worlds, and so are those of future worlds. Only the chapter of bifurcations remains open to hope or expectation [espérance]. Let us not forget that all that we might have been in this world, we are somewhere else.

Progress in this world is only for our descendants. They are more fortunate than us. All the beautiful things that our globe will see, our future descendants have already seen, are seeing now and will always see – albeit only in the form, of course, of the doubles that have preceded them and will follow them. As sons of a better humanity, they have already scoffed and jeered at us on old dead earths, as they pass through them after us. They continue to denounce us on those living earths from which we have disappeared, and they will forever hound us with their contempt upon earths that are yet to be born.

Both they and we, and all the residents of our planet, return as prisoners of the moment and the place that our destinies assign us in the series of its avatars. Our perennial existence is an appendix of our planet’s own. We are merely partial phenomena of its many resurrections. Men of the nineteenth century, the hour of our appearances is forever fixed and will always return us as the same, with, at most, the prospect of happier variants. There is not much here that might quench any thirst for the best [of all things]. What can one do? I have sought the truth, and not my pleasure. One finds neither revelation nor prophecy here, but a simple deduction from spectral analysis and Laplace’s cosmogony. These two discoveries make us eternal. Is this a stroke of good fortune? If so, let us take advantage of it. Is it a joke at our expense? If so, let us resign ourselves to it.

But is it not a consolation to know oneself to be constantly, on billions of earths, in the company of loved ones who are for us today no more than a memory? And is it not yet another consolation, on the other hand, to think that one has savoured and one will savour this happiness eternally, in the figure of a double, indeed of billions of doubles? They are us, after all. For many small-minded people, the prospect of such happiness through substitution is not particularly thrilling. They would rather have three or four extra years as part of the current edition of our world than all the duplicates of the infinite. We grimly cling to what remains to us, in our century of disillusions and scepticism.

At bottom, humanity’s eternity by the stars is melancholic; sadder still is this imprisonment of brother-worlds by the inexorable barrier of space. So many identical populations that pass each other by without having ever suspected their mutual existence! Until now, at least. It has finally been discovered in the nineteenth century. But who will want to believe it?

Moreover, until now, for us the past represented barbarism, and the future meant progress, science, happiness. This is an illusion! On all of our twin- or double-globes, this past has seen the most brilliant civilisations disappear without leaving a trace, and they will disappear yet again without leaving any more of a trace. On billions of earths the future will once again see the same ignorance, the same foolishness, the same cruelty of our previous ages!

At present, the entire life of our planet, from its birth to its death, with all its crimes and misfortunes, unfolds bit by bit, day by day, on myriads of brother-planets. What we call progress is shut away on each earth and disappears with it. Always and everywhere, in the terrestrial camp there is the same drama, the same set on the same narrow stage, played by a noisy humanity, infatuated with its own grandeur, believing itself to be the universe and living in its prison as if it were a vast immensity – only to sink all too soon along with globe that has borne the burden of its pride with the most profound contempt. There is the same monotony, the same immobility on all foreign planets. The universe endlessly repeats itself, and paws the ground without moving. Unperturbed, eternity acts out the same scenes across the infinite.

  1.  Source: L’Éternité par les Astres: Hypothèse astronomique (Librairie Germer Baillière: Paris, 1872), and reprinted in MF, 318-382. Blanqui wrote his speculative ‘astronomical hypothesis’ in conditions of more or less total isolation while in prison at the Château de Taureau, off the coast of Brittany, in 1871. It was published in early 1872. We have benefited from consulting the two previous English translations of this text, Matthew H. Anderson’s ‘Eternity According to the Stars’, New Centennial Review, Vol. 9, No. 3 (Winter 2009), pp. 3–60, and Frank Chouraqui’s edition of Eternity by the Stars (New York: Contra Mundum Press, 2013), which includes a substantial set of endnotes and an introduction that relates Blanqui’s conception of eternal return to those of Nietzsche, Benjamin and Borges (for another interpretation see Hallward, ‘Blanqui’s Bifurcations’ (2014)). Although the terms often overlap, Blanqui distinguishes between les astres in general, which include planets like our Earth, and les étoiles in particular; like Anderson we have usually rendered the former as ‘astral bodies’ (with no theosophic connotations intended), and the latter as ‘stars’. We have most often translated the generic word foyer as ‘sphere’, though it also evokes connotations of home, hearth, centre and source. Blanqui uses the term étendu (extension or area) to mean the expanse of space, or simply space. We have given literal equivalents for the semi-technical terms like nébulosité, volatilisation, lumière zodiacale, and so on, which recur throughout the text. Where they seem redundant we have removed Blanqui’s recurring use of italics from terms like corps simples, répétitions, combinaisons originales, l’infini, etc.
  2.  Cf. Blaise Pascal, Pensées, ed. and trans. Roger Ariew (Indianapolis: Hackett, 2004), 58.
  3.  We follow Anderson’s elegant formulation here.
  4.  Blanqui’s rather eccentric and enthusiastic speculations about the nature of comets in the following pages should be read in context (and alongside his somewhat comparable conception of the relation between material reality and thought). As one survey notes, ‘the nineteenth century maintained an erratically dualistic attitude toward comets and meteors’; traditionally associated with obscure omens and portents of doom, many amateur astronomers remained fascinated by comets’ apparently unpredictable orbits, their uncertain physical composition, and the mysterious nature of their combustion, despite the accumulation of less fanciful scientific knowledge over the course of the century (Roberta J. M. Olson and Jay M. Pasachoff, Fire in the Sky: Comets and Meteors, the Decisive Centuries, in British Art and Science (Cambridge: Cambridge University Press, 1999), 180).
  5.  François Arago, Astronomie populaire (1855), II, 475. (Reference adopted from Chouraqui’s edition of Eternity by the Stars, 158n.10).
  6.  Pierre-Simon Laplace, Exposition du système du monde, in Laplace, Oeuvres complètes (Paris: Bachelier, 1835, 6ème édition), VI, 140; cf. Laplace, The System of the World, trans. Henry Harte (Dublin: Longman et al., 1830, 2 vols.), I, 205. For some details regarding Blanqui’s references to Laplace, see Chouraqui’s edition of Eternity, 158-9.
  7.  Laplace, Exposition, 234; cf. System, II, 49.
  8.  ‘Zodiacal light: a faint elongated ellipse of light extending along the zodiac on each side of the sun, visible (in the north temperate zone) chiefly after sunset in late winter and early spring, and before sunrise in autumn.’ (OED).
  9.  Partial citation of Laplace, Exposition, 294; cf. System, II, 137-8.
  10.  We have followed Anderson’s rendering here.
  11.  Laplace, Exposition, 482; cf. System, II, 336-7.
  12.  Laplace, Exposition, 483; cf. System, II, 338.
  13.  Chouraqui notes that this is an approximate citation from the second edition of Laplace’s Exposition (1798), 347-8, and that the passage does not appear in subsequent editions (Chouraqui, ed. cit., 159n.22).
  14.  We adopt Chouraqui’s concise rendering here.
  15.  A reference to Plautus’ play The Menaechmi, a source for Shakespeare’s Comedy of Errors.
  16.  A reference to Austria’s defeat at the battle of Königgrätz, in 1866.
  17.  We have benefitted from Anderson’s rendering here.