FROM THE HISTORY OF PHYSICS

THE PHYSICS OF LUCRETIUS*)

S. I. Vavilov

I. LUCRETIUS AND THE PRESENT DAY

Hardly any other poetic and scientific work of antiquity (even if we speak of the creations of Homer, Euripides, Euclid, Archimedes, Virgil, and Ovid) has carried down to our own day, across millennia, the same freshness and topicality as the unfading poem of Lucretius. Cicero and Virgil admired it; the fathers of the Church angrily attacked it, rightly discerning in Lucretius a terrible danger to themselves. This poem determined many features of the world-outlook of Newton and Lomonosov, delighted Herzen, deeply interested the young Marx, and served as the banner of the mechanical materialism of L. Büchner. Diels’s German translation of Lucretius’ poem appeared with a preface by Einstein. Lucretius was probably read by Turgenev’s Bazarov, and the hero of Anatole France did not part with the cherished little book at the most critical moments of his life.

Such two-thousand-year efficacy is an exceedingly rare case in the history of culture, one deserving special attention. Wherein lies Lucretius’ strength? Is it in his poetry—beautiful, but, in the opinion of connoisseurs and laymen alike, still inferior to Virgil, Ovid, and many others? Or is it in his world-outlook and science, in which he basically follows faithfully his own, deified teacher Epicurus?

The appeal of Lucretius lies neither in the one nor in the other taken separately. It is hidden, undoubtedly, in the astonishing fusion—unique in its effectiveness—of the poem’s eternally valid and broad philosophical content with its poetic form. Lucretius with full justification repeatedly says of himself:

“Through the trackless fields of the Pierides I go,
where no foot of any man has trodden before.”**

*) Report at the joint session of the Physico-Mathematical Division and the Division of History and Philosophy of the Academy of Sciences of the USSR in February 1946, on the occasion of the 2000th anniversary of the death of Lucretius.

**) For example, the beginning of Book IV. Quotations from Lucretius are given in the translation of F. A. Petrovsky; the Roman numeral designates the book, the Arabic numeral the line.

The didactic poem, condemned as a kind of poetry both in ancient and in modern times, became in Lucretius’s hands powerful, speaking in a living voice across centuries and millennia to the present day. There is no doubt that the great idea of atomism reached Galileo, Newton, and Lomonosov not through scattered fragments of Democritus and Epicurus, but through the hexameters of Lucretius’s poem.

No one either before or after Lucretius succeeded in doing anything similar, although many sought to follow in his footsteps, imitating him or attempting to counter his influence with various unsuccessful “Anti-Lucretiuses.”

In Lucretius’s lines the eternal materialist doctrine—admittedly still in its initial form—was expressed with unprecedented persuasiveness and poetic pathos. A cultured person of our time, a descendant of the forebears who created great natural science, who has the possibility of seeing atoms with his own eyes, counting them, destroying them, creating them, and releasing the energy hidden within them—such a person, reading Lucretius, often finds not an archaic primitive, but something that he still regards, or until quite recently regarded, as the foundation of his worldview. Lucretius belongs to the group of artists and poets for whom art was inseparably intertwined with science and philosophy. This group is extensive; it includes Leonardo, Dürer, Lomonosov, Goethe, Novalis, Browning, Blake, and others. But, apparently, it is indisputable that no one achieved such effectiveness in linking science and art as Lucretius.

2. THE PHYSICAL BASIS OF THE POEM

One should not, however, approach Lucretius’s poem from the standpoint of the concrete features and results of modern natural science. In this respect Lucretius-Epicurus inevitably made crude, and even very crude, errors. Their science was the result only of observation and reflection. The art of experiment was at its very earliest stage, and to observations there was added in large quantity “unverified information,” as we would now put it—for example, reports of the existence of centaurs, or that lions are unusually afraid of roosters. On the other hand, from the standpoint of modern science one should not overestimate Lucretius’s individual fortunate conjectures. In the fourth book of the poem, on the question of heredity, we read, for example, the following:

“Thus Venus, by the lots, produces children and the faces
Of ancestors, and the voice, and hair she revives in descendants,
For indeed this always arises from certain seeds,
Just as do our faces and bodies, and all our members.” *)

Here, as it were, the outlines of modern genetics seem to be sketched, even down to Mendelian statistical ratios, expressed by the word “lots” (Inde Venus varia producit sorte figuras). But, probably,

*) Lucretius, p. 134.

we read into Lucretius in this case more than he in fact knew and intended to say.

The significance and enduring influence of the poem lie not in its separate and accidental verses, but chiefly in its leitmotif, in the doctrine of “first principles,” of atoms.

Lucretius’ work has not preserved a definite title. It is known that the title De rerum natura is arbitrary, and, for example, the latest Italian translation of 1944 is entitled “Il poema della natura”*). In one of the two surviving principal lists of the poem it is called: De physica rerum origine vel effecta (“On the physical origin or formation of things”**). This title, which may seem prosaic and cumbersome, nevertheless has great significance in substance. It draws attention to the physics of the poem as to its basic part. The first words of Aristotle in his Physics***) may serve as the best commentary on what should be understood by the physical origin or formation of things: “Since—as we think there—in all investigations which extend to first principles, causes, or elements, knowledge and science arise through their assimilation (for we are then confident in our knowledge of any thing when we know its first causes, its first principles, and decompose it down to the elements), it is clear that in the science of nature too one must attempt first of all to determine what pertains to the principles. The natural path to this leads from what is more known and evident to us to what is more evident and known by nature: for what is known to us and directly, in itself, is not the same thing. Therefore the necessary procedure must be precisely this: from what is less evident by nature, but more evident to us, toward what is more evident and known by nature.” From these arguments of Aristotle it is obvious that, despite the great differences in the understanding of the term “physics” in our time and among the ancients, both Lucretius himself and the copyists of his work who added the title understood, as we do, by physical phenomena chiefly the simplest forms of matter and motion, and not the doctrine of nature as a whole. This is borne out by the whole poem, which begins with an inquiry into “first principles.”

“Now do you strain your hearing and your discerning mind,”

Lucretius addresses Memmius,

“For of the essence of the highest heavens and gods I am preparing
to speak, and for you I explain the principles of things”****).

On the basis of these principles, all the complexity of phenomena is then “physically” explained. Physics constitutes the leitmotif of the poem. Marx in his doctoral

*) Il poema della natura. Testo latine versione italino di Pietro Parella. Bologna, 1944.

**) Lucretius, 1936, see note on p. 215.

***) Aristotle, Physics. Translation by V. I. Karpov. Moscow, 1937, p. 7.

****) Lucretius, I, 50 ff.

...wrote in his dissertation*): “In Lucretius, who, of all the ancients, is virtually the only one to comprehend Epicurean physics, we shall find a more profound exposition of it.” In passing from the simplest physical phenomena to more complex ones, Lucretius, often following Epicurus, confines himself to indicating the possibility in principle of an explanation, while at the same time offering various hypotheses about one and the same subject. Thus he sets forth the important question of the motions of the sun, the moon, and the stars. Describing various remarkable phenomena on the surface of the earth—the flooding of the Nile, sulphurous lakes, and so on—he observes:

“There are also things for which not one,
But many causes can be adduced, though only one is true.”**)

Hence it is clear that Lucretius is interested first and foremost in the physical essence of phenomena, and not in the phenomena themselves as such. From this point of view, Lucretius’ poem is the first ancient attempt that has come down to us to explain nature completely on the basis of physical principles.

3. BODIES, SPACE—VOID, AND TIME

Let us proceed to a brief analysis of Lucretius’ physics. Its initial axiom is the principle of the conservation of bodies***).

“As our basic position we shall take the following:
Nothing is created out of nothing by divine will...

. . . . . . . . . . . . . . . . . . . . . . . . .

Things by no means turn into nothing,
But all decompose back into the primary bodies...

. . . . . . . . . . . . . . . . . . . . . . . . .

In short, nothing perishes that seems wholly to perish,
Since nature always brings one thing back from another
And allows nothing to be born except through the death of another.”

What, then, are Lucretius’ “bodies”; how does he define them?

“...For what is the mark of a body?
To resist and not to let pass”

he writes*), and later further adds**)

“Only a body can act or be acted upon.”

This wholly correct definition is taken by Lucretius, evidently, from the properties of impenetrability and elasticity of objects. It coincides to a certain degree with Boscovich’s famous conception of elementary bodies as centers of forces, and hardly any other definition of body can be given unless one makes use of the more complex concepts of mass and energy, which were not yet known to Lucretius.

) K. Marx and F. Engels, Works, vol. 1, p. 29, 1938.
) Lucretius, VI, 703.
) Lucretius, I, 149, 248, 262, etc.
) Lucretius, I, 337.
***) Lucretius, I, 443.

The second principle of Lucretius’ world is empty space *)

“But if space, or places, which we call the void,
Did not exist at all, bodies could not be anywhere,
Nor could they move anywhere in various ways.”

Lucretius adduces various proofs of the existence of void, “the receptacle of bodies,” considering, contrary to the later Cartesian picture of the world, the complete filling of space to be entirely inconceivable, since in his opinion it would make motion impossible.

Bodies and space delimit, according to Lucretius, the fundamental principles or essences of the world.

“Besides, you could produce nothing of such a kind
As not to be either body, or void together with it,
And as might prove to be some third nature,”

he addresses Memmius **),

“For whatever we can name will turn out to be a property
Of these two principles, or an occurrence, as you will see” ***).

Such a property or occurrence of bodies and void in Lucretius, in agreement with Democritus and Epicurus, is time ****).

“Likewise time does not exist by itself, but things
Themselves lead us to the sensation of what has happened in the ages,
What is taking place now, and what will follow later;
And it must be acknowledged that no one can perceive
Time by itself, apart from the motion of bodies and rest.”

Lucretius does not further develop this remarkable assertion. Meanwhile it is extremely important for the whole physics and philosophy of Lucretius. It turns time into a property of body and deprives it of any content outside motion. It is noteworthy here that, establishing bodies and space as the fundamental principles of phenomena, Lucretius is silent about the motion of bodies, considering motion a necessary and inseparable property of bodies. The motion of bodies in the void is connected, according to Lucretius, with their heaviness *).

“For to press everything downward is a sign of body.”

We shall return later to this motion of bodies under the action of heaviness when considering the “first beginnings”—the atoms of Lucretius. For now let us note one more fundamental property of Lucretius’ physics.

Space is boundless, the universe is infinite **).

) Lucretius, I, 426.
) Lucretius, I, 430.
) Lucretius, I, 450.
) Lucretius, I, 459 ff.
) Lucretius, I, 352.
***) Lucretius, I, 964.

“It has no edges, and it has neither end nor limit.
And it makes no difference in what part of the universe you may be:
Wherever you may be, everywhere, from the place that you occupy,
It remains infinite in all directions.”

At the same time, matter too is infinite in space. Lucretius proceeds from the proposition that the structure of the universe is repeated *) like a crystal or like honeycombs:

“...Nature takes care that the aggregate of things should not be able
To set itself a limit: she makes void the boundary
Of body, and body she compels to bound void,
By this alternation causing everything to be.”

At first glance, the features just set forth of Lucretius’ picture of the world may seem to coincide with the well-known classical system of Newton. In reality there are very substantial differences. Newton’s absolute space is in no way connected with bodies, but may be boundlessly empty. Lucretius’ space—void—and bodies are mutually conditioned, according to the lines already cited once: “Nature... makes void... the boundary of body, and body she compels to bound void...”

On the other hand, we have seen that, unlike Newton’s absolute time, independent of matter, in Lucretius “there is no time by itself.” One might say, if it did not sound too modern, that for Lucretius time and space are determined by matter—by bodies. Another fundamental difference between Lucretius’ scheme and Newton’s scheme is that gravitation is an internal motive property of bodies, their “attribute,” and not the result of the action of other bodies. We shall have occasion to return to the question of gravitation in Lucretius.

4. “FIRST PRINCIPLES”—THE ATOMS OF LUCRETIUS

The triumphant advance of atomism in science during the last half-century and its astonishing practical results in recent times compel us to look with special wonder at the conjectures of Democritus—Epicurus—Lucretius concerning the “first principles” that make up bodies and possess many of the properties of modern atoms.

How could this subtle thought have arisen among the ancients, a thought whose correctness was doubted quite recently by entire modern schools? Lucretius unfolds before the reader of the poem many arguments, a considerable part of which are found, in their essence, already in Democritus and Epicurus.

Stars, people, trees, grains of sand are separate, as is clear even from the most superficial observation. They change, die, are born, transform one into another, while nevertheless composing a closed,

*) Lucretius, I, 1008 ff.

recurring circle. This also follows at once from everyday observation.

Lucretius, following Democritus and Epicurus, concludes on the basis of these phenomena of nature that there exist primary bodies, or simply first principles, the various combinations of which form all things.

Bodies are divisible, they are separated from one another by void, but if they were divided without limit, then nature would be full of infinitely different forms, and constancy or repetition in nature would be impossible*).

“... Why then could nature not have been able
To make men so that they might ford the sea,
Or with their hands tear down mighty mountains,
And surpass many generations of men with long life,
If not because to everything that is capable of being born,
At its birth there is given a precise portion of matter?”

Later**) Lucretius varies this argument:

“Since then, finally, firm limits are set
For each kind of thing, for its growth and life,
Since it is established what, according to the laws of nature,
They can produce and what they absolutely cannot,
Since there are no changes, but everything is unalterable,
So that even the birds, always in their variegated plumage,
Preserve on their bodies the markings proper to each breed,
It follows that all matter must remain unchanged
In the body of the separate breeds.”

Lucretius explains the idea of finite atoms of different kinds and of their combinations, again in the tradition of the ancient atomists, by comparison with letters and words***):

“Even in our verses, as you can constantly observe,
Many words consist of many homogeneous letters.
But both verses and words, as you will surely admit,
Differ from one another in meaning and also in sound.
You see how powerful letters are by a mere change of order.
As for the first principles, they have still more
Means whereby different things may arise from them.”

The arguments of Lucretius presented so far may be summarized as follows. Bodies are divisible; they undergo diverse transformations, but return again to the same forms. If bodies consisted of an infinite number of infinitely small or infinitely divisible parts, then the possible combinations would be boundlessly diverse, and the restoration of former forms would be completely improbable. It is precisely the fact of the unfailing return of former forms

) Lucretius, I, 200 ff. (italics ours).
) Lucretius, I, 584 ff.
**) Lucretius, I, 823 ff.

(heredity, etc.) attests to the finite dimensions and finite diversity of the primordial elements. Under these conditions the probability of the restoration of former forms becomes finite.

If one reflects on these arguments of Lucretius, their great persuasiveness becomes clear. They deserve serious attention not only in historical perspective, and one must be surprised that they are forgotten in modern textbooks. Lucretius’ arguments are entirely modern and irrefutable.

Like Democritus, Lucretius tries to substantiate atomism also by abstract considerations on the basis of Zeno’s paradox of infinite division*). According to the teaching of the Eleatics, with such division of bodies of finite size one would obtain an infinite number of small, but not equal to zero, parts, which in sum would have to give infinity, in contradiction with the initial assumption. From this Zeno drew the conclusion that division in general is impossible, whereas Democritus drew the conclusion that there exists a finite limit of divisibility, i.e. atoms. Lucretius repeats this paradox in verse**).

“If, then, there will be nothing smallest, the smallest body
Will consist of infinite parts.
In the half there will always be found its half,
And for division nowhere will there be any limit at all.
How then will you distinguish the smallest thing from the universe?
By nothing, believe me, in any way. For, although
The universe has no end, yet even the smallest things
Will consist equally of infinite parts.
Sound reason, however, denies that one should believe this,
And it can remain in our mind and compel us inevitably to admit
The existence of that which is wholly indivisible, being
In essence the smallest.”

From these reasonings of Lucretius it is clear, in any case, how small he imagined the primordial elements to be.

“For far beyond the limits of sense lies
The whole nature of the first-beginnings”***).

Let us consider the other properties of Lucretius’ primordial elements. They are “absolutely” dense, or, more precisely, solid (solidi), approaching in this respect the elementary particles of modern physics. Lucretius attempts to prove this, proceeding from the very definition of body****).

“First of all, since here there is given to us the fundamental distinction
Between two things, according to their twofold nature,—
Namely body and place, in which everything happens,—
They must necessarily exist quite independently.
For wherever there is the space that we call empty,
There is no body; and everywhere where only body is found,
Empty space can in no way be present.
Therefore the first bodies are dense, and there is no void in them.”

*) Cf. S. Lur’e, Democritus, Moscow, 1937, p. 60.
**) Lucretius, I, 615 ff.
***) Lucretius, II, 312.
****) Lucretius, I, 503.

One cannot deny this proof its logic, but it compels one to reflect on the definition of density, or more precisely—of hardness. The modern concept of density is equally applicable both to a complex body (for example, a sponge, a crystal, a molecule) and to an elementary particle, for example, a proton or a neutron. In Lucretius, who does not make use of the concepts of mass and weight, density or “hardness” has a qualitative, specific character. “Absolute density” is the density of a body without void; what it is in magnitude is impossible to say. From the idea of the absolute density of the first-beginnings Lucretius then draws the further conclusion of their eternity and indestructibility.

“If, then, the first bodies are solid, if there is no void in them,
As I have taught, then they must necessarily be eternal”*).

Besides absolute density, the first-beginnings have form, differing from one another in it**):

“...That in general they are by no means like one another
Is not surprising: for since their number is so abundant,
Since they have no end, as I have shown, nor any sum,
Therefore, of course, they cannot all entirely
Have a uniform structure and be similar in figure.”

The difference concerns size and form.

“...Through the horn of a lantern there passes freely
Light, but not rain. Why? Because the primary bodies of light
Are smaller than those of which beneficent moisture consists***).

. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . Honey and milky moisture
Are felt by us as pleasant on the tongue and in the mouth;
On the contrary, wormwood, full of its bitterness, or centaury
Twist our mouths with a repulsive taste.
Thus it is easy to conclude that of smooth and round particles
Consists that which can affect our senses pleasantly;
On the contrary, that which appears to us bitter and tart
Is formed of hooked particles, tightly interwoven.”

Lucretius, however, cautiously limits the diversity of forms****):

“The first-beginnings of things . . . . . . . . . . . . . . . .
Are diverse in form only up to certain limits.”

and adduces proofs of this in the fact that the forms of natural formations are limited. In just the same way he also limits the possible combinations among the first-beginnings, as though anticipating modern chemistry:

“One must not think, however, that everything can combine
With everything in every way...”*****).

*) Lucretius, I, 538.
**) Lucretius, II, 337.
***) Lucretius, II, 388 ff.
****) Lucretius, II, 479.
*****) Lucretius, II, 701.

These reservations are needed to explain the constancy and recurrence of forms in nature. They are just as necessary for the teaching of the atomists as the assertion of the finiteness of the sizes of the primordia, and they show the profound thoughtfulness of the whole doctrine.

Lucretius attributes to the primordia only mechanical properties in the form of density, shape, and size; he denies that they possess color and other qualities*).

“But do not think, mind you, that bodies originally
Are only without color entirely: that there is no warmth in them whatsoever,
Nor likewise do they possess any cold, nor hot vapor,
And without sound they are, and without any taste,
Nor does any special smell issue from them either.”

All the enumerated qualities are subjective; objectively, only the indicated mechanical properties of the primordia really exist.

5. THE MOTION OF THE PRIMORDIA

An inseparable mechanical property of the primordia is their motion. According to the teaching of Epicurus–Lucretius, motion is as innate in the primordia as their body and weight. It is precisely weight and the fall of bodies that determine, as will be seen below, the innateness and organic character of the motion of the primordia.

“But if you think that the primordia of things are able to stand motionless
And then give rise anew to motion in things,
You wander far astray from true reasoning,
For, being in the void and moving through it, inevitably
The primordia of things are carried along by their own weight or by the blows of others” **).

After this general assertion, Lucretius, as proof, with brilliant precision and accuracy draws a picture of the motion of dust motes in a sunbeam, sketching a quite correct theory of Brownian motion, anticipating by two millennia Smoluchowski, Einstein, and Perrin***).

“Now look: each time a sunbeam penetrates
Into our dwellings and cuts through the darkness with its rays,
You will see many little bodies in the void, flickering,
Rushing back and forth in the shining radiance of the light;
As though in eternal struggle they clash in battles and combats,
Suddenly they fling themselves into conflict by detachments, knowing no rest,
Now coming together, now scattering apart again without cease.
From this you may make clear to yourself how unceasingly
The primordia of things move in the vast void.
Thus, from small things one may form an understanding of great things,
Small things revealing the path to their comprehension.”

) Lucretius, II, 842 ff.
) Lucretius, II, 80 ff.
**) Lucretius, II, 114 ff.

Recalling the phenomenon itself, Lucretius proceeds to its deeper interpretation:

“Know, then, that from the first beginnings comes this universal wandering.
First the first-beginnings of things move by themselves;
Next after them bodies made from the smallest combinations of them,
Near, so to speak, in strength to the primary beginnings,
Hidden from them, receiving blows, begin to strive,
Themselves toward motion, then impelling larger bodies.
Thus, proceeding from the first beginnings, motion little by little
Touches our senses and becomes visible as well
To us in the motes, that they move in the sunlight,
Though imperceptible are the blows from which it arises.”

A physicist will at once recognize in these lines the chief propositions of the modern theory of Brownian motion. Lucretius’ error—if one is to be strict and captious—is only that the motion of motes in a sunbeam is in reality not purely Brownian: it is distorted by thermal vortices, the radiometric effect, and so forth. But it is hardly proper to subject the two-thousand-year-old patriarch of atomism to such a school examination.

Lucretius in no way limits the possible velocity in the void of his first-beginnings*).

“All the first-beginnings, then, which are simple and dense,
Through the void, following their own path, encountering no
External obstacles, being one whole with their own parts,
And rushing unswervingly thither where once they have hastened,
Clearly must possess a speed altogether boundless,
Flying incomparably faster than the light of the sun flies.”

The modern relativistic limitation of velocities was indeed not dreamed of by any sages, even such as Epicurus and Lucretius.

Very vividly and with complete clarity Lucretius explains why in large bodies we do not see the motion of the constituent first-beginnings. It is hard to refrain from quoting in full this passage of the poem, remarkable for its pictorial quality**).

“Here it should not arouse surprise in you that at a time
When all first-beginnings are in motion,
Their aggregate appears to us to remain in complete rest
(If one does not count that it moves with its own body),
For the whole nature of the beginnings lies far beyond the limits
Of our sense. Therefore, since they are inaccessible
To our sight, their motions too are hidden from us.
Even of things, indeed, that we are able to see, the movements are often concealed,
Often hiding their motions at a distance far from us:
Often on the slope of a hill thick-fleeced sheep are grazing,
Slowly going whither, on the rich pasture,
Fresh grass calls them, sparkling with diamond dew;
The well-fed lambs there leap and frolic, butting one another,

) Lucretius, II, 157 ff.
*) Lucretius, II, 308 ff.

All this seems to you to have merged together,
As though it were a white spot, motionless on a green slope.
Likewise, when the mighty legions, having run, swiftly
Course everywhere across the field, representing a mock battle,
The gleam from their arms rises to the sky, and everywhere
The earth around shines from the bronze, and from the heavy infantry’s trampling
A rumble is heard all around. The mountains, shaken by the cries,
Answer them loudly, and the noise is borne to the heavenly constellations;
Horsemen gallop around and, in a swift onrush, suddenly
Cross the fields, shaking them with their mighty tread,
Yet on the high mountains there is surely a place from which
It seems to be a spot, motionless, sparkling in the field.”

To explain his thesis, Lucretius, not yet knowing the microscope, employs a method no less convincing than the observation of the motion of invisible objects under a microscope. The picture of the state of motion of matter is so clear and convincing in Lucretius that one is compelled to wonder why it exerted comparatively little influence even on the few naturalists of former centuries.

6. GRAVITATION AND “CLINAMEN” IN LUCRETIUS

The most complex and obscure part of the physics of Epicurus–Lucretius is that which concerns gravitation and the collision of the first principles. Here the ancient atomistic doctrine is in decisive contradiction with the basic conceptions of Newtonian physics.

In Newton, the world is conceivable even without gravitation. The law of gravitation is not the fourth law of mechanics, but the same sort of particular law of force interactions as, for example, Coulomb’s laws. In Lucretius, on the contrary, a body is unthinkable without gravitation:

“For that everything presses downward is a sign of body.” *)

And motion itself is the result of gravitation. However, the fall of bodies by no means follows solely from the properties of the body itself; for this another body is needed—the earth:

“Do you not see how the torches of the night sky
Leave a fiery trail behind them on the vault of heaven,
Flying in the direction where nature has shown them the path?
Or how the shining stars fall downward to the earth?
Likewise the sun from the height of heaven pours its heat everywhere,
Sprinkling both fields and meadows with its rays:
Thus, too, the sun’s heat likewise gravitates toward the earth.
Obliquely, you see, through the rain the lightning flashes from above,
And, bursting from the clouds, now there, now here continually
The fires run about, and their flame falls to the earth.” **)

With astonishing perspicacity, from purely speculative conceptions, Lucretius, following Epicurus and anticipating Galileo by millennia, asserts that bodies in a void must fall with equal

) Lucretius, I, 362.
*) Lucretius, II, 206 ff.

speed, independently of weight. Lucretius correctly observes that a body in water or air

“Must fall more quickly in accordance with its own weight
Only because water or the subtle essence of air
Is not able to put equal obstacles before things,
But yields more readily to those having greater heaviness.
On the contrary, never and in no way is empty space capable
Of detaining a thing and appearing as some sort of support,
Since by its nature it constantly yields to everything.
Therefore all things, passing through the void without obstacles,
Must have equal speed despite the difference in weight” *).

The doctrine of Epicurus rises resolutely against the assertion of the sphericity of the earth and the existence of antipodes.

“Here beware of one thing and do not believe the assertion, Memmius,
That everything strives toward some universal center;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
As though the earthly heavy things all strive toward it from below
And abide upon it, turned upward with their feet
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
As though the sun and moon beneath us, while the night luminaries
We behold: and we mutually exchange with them
The change of times, and their days correspond to our nights” **).

Lucretius regards this as an impossible thing and does not stint on harshness:

“But it is permissible to prove this only to arrogant fools,
Whose mind is always inclined to the distortion of truth.”

Lucretius’ extreme indignation at the theory of the antipodes apparently derives from purely principled “Copernican” aspirations. Epicurus and Lucretius in no way wish to recognize a center of the universe. True, their notions of the universe are still very unclear and confused. In Lucretius the earth is in essence an infinite half-space bounded by a plane, if it is permissible to use mathematical concepts that are utterly alien to Lucretius. His physics is entirely qualitative and is completely devoid of a mathematical skeleton.

In the fifth book of the poem, where Lucretius turns to concrete astronomical questions, one can find obvious contradictions in the scheme set forth. The author knows this, and it does not trouble him: as soon as he passes from physical principles to more particular and special problems, he considers it sufficient to confine himself to indicating one possible explanation.

“It is difficult, perhaps, to decide what cause acts in this
World, but what is possible and what occurs
In the various worlds of the universe, created on different principles,
I explain and set forth a series of causes by which

) Lucretius, II, 231 ff.
*) Lucretius, I, 1053 ff.

Perhaps the motion of the luminaries takes place in the space of the universe.
Yet of these causes, one must necessarily impel
The stars to motion here as well; but which one—to prescribe this
Is not at all the duty of him who investigates everything gradually*).

Setting forth two possible explanations of the phases of the moon, Lucretius, in keeping with this same position, observes, for example:

“Moreover, as though one could not admit that both are possible,
Or that that teaching is not in the least worse than this”**).

The conception of the earth as an infinite half-space bounded by a plane leads to the conclusion that the first-bodies, moved by gravity, would have to move in the void in a parallel vertical stream with the same velocity. In this case the possibility of collisions of the first-bodies with one another, necessary for the formation of things, would be completely excluded.

This difficulty is resolved in Epicurus–Lucretius, from our point of view, in an extraordinarily surprising and unexpected way: spontaneous deviations of the first-bodies are introduced. Addressing Memmius, Lucretius writes:

“I would wish that you be informed here in just the same way,
That, borne through the void in the downward vertical direction,
By their own weight the bodies primordial at some time
In a place unknown to us begin to swerve slightly,
So much that one may call it a change of motion.
But if, like raindrops, they continued to fall downward,
Not deviating at all on their path through the measureless void,
Then no meetings, no impacts among the first-beginnings would arise,
And nature could never have brought anything forth”***).

Such is the peculiarity of the motion of the first-bodies. In itself, if one passes to modern physics, it could naturally be compared with the deviation of bodies in force fields, gravitational or electromagnetic, caused by other first-bodies. However, Lucretius’ thought and intention go considerably further. The negligibly small deviation—clinamen according to Epicurus–Lucretius—is spontaneous, arbitrary, and, at the limit, is compared with man’s free will. Lucretius reasons thus****):

“If all motions form one continuous chain
And arise one from another in a definite order,
And if the first-beginnings by deviation cannot
Call forth other motions, destroying the laws of fate,
So that cause should not follow cause from the beginning of time,—
Whence in living creatures on earth, not subject to fate,
Whence, tell me, has free will appeared,
Which permits each to go where desire draws him,”

) Lucretius, V, 526 ff.
) Lucretius, V, 728.
) Lucretius, II, 216 ff.
**) Lucretius, II, 251 ff.

And permits it to change direction not in a known place
And not at a fixed time, but according to the awakening of the mind,
For there is no doubt that in all this for each thing the will
Serves as the initial impulse and carries it through the limbs into motion.”

In order to explain these complex but indubitable phenomena:

“A slight deviation of the first principles is what serves this end,
But not at a fixed time and not at all in a known place.”

(Nec regione loci certa nec tempore certo) *).

The first principles, then, are endowed with an infinitesimally small mechanical property, which in complex systems composed of an enormous multitude of first principles may lead to the emergence of consciousness and freedom of will.

K. Marx’s youthful doctoral dissertation, “The Difference Between the Democritean and Epicurean Philosophy of Nature,” contains a profound analysis of the Epicurean-Lucretian doctrine of the deviation of the first principles, and it runs counter to what had been written on this subject for millennia. Marx recalls the endless witticisms on this theme in ancient and modern times and says that Cicero reproached Epicurus for deviation without cause; he cites Cicero’s words that “nothing more shameful can happen to a physicist” ). However, from a very general principled dialectical-philosophical point of view, Marx takes the side of Epicurus-Lucretius. He proceeds from the clearly expressed tendency of both—to avoid, at the very foundation of the doctrine of atoms, iron necessity, fatalism. Objecting to Cicero apropos the words just cited, Marx writes: “But, first, the physical cause demanded by Cicero would again have relegated the deviation of the atom to the sphere of determinism, from which it was precisely meant to protect it. Then, the atom is by no means yet complete until the determination of deviation has been placed in it.** To ask for the cause of this determination is the same as asking for the cause which turns the atom into a principle—a question obviously devoid of meaning for one for whom the atom is the cause of everything and therefore itself has no cause.” Mentioning the reproaches of Bayle, who incriminated Epicurus with having devised spontaneous deviation in atoms instead of a spiritualistic principle, Marx observes: “With the soul of the atom only a word would have been acquired, whereas in deviation the actual soul of the atom is represented, the concept of abstract singularity.”

V. I. Lenin, in his conspectus of Hegel’s lectures on the history of philosophy, polemicizing with Hegel, also takes the side of Epicurus ), noting, among other things: “Epicurus on the *soul: finer (NB) atoms, more rapid (NB) motion of them, connection (NB) of them, etc. etc. with the body

) Lucretius, II, 292.
) K. Marx and F. Engels, Works, vol. I, OGIZ, 1938, p. 30 (emphasis ours).
) V. I. Lenin, Philosophical Notebooks, 1934, pp. 299 and 500.

(Diogenes Laertius, X, § 66; 63–4) — very naïve and good! — while Hegel is angry, scolding: “chatter,” “empty words,” “absence of thought.”

It is, of course, beyond doubt that the concrete picture in Epicurus–Lucretius of falling or freely moving primordial particles is erroneous. In particular, the well-known eighteenth-century physicist Lesage, author of an interesting hypothesis on the nature of gravitation, was right when, in his memoir “Newtonized Lucretius”*), he attacked the Epicureans: “If the first Epicureans had possessed information about cosmography, even as sound as that of their contemporaries whom they did not wish to listen to, and about geometry at least a part of the knowledge which was then common, they would, very probably, without difficulty have discovered the law of universal gravitation and its mechanical cause.”

Lesage meant by this that if the Epicureans had accepted the sphericity of the earth, then the falling primordial particles would initially have been directed toward the center of the earth. To explain collisions between particles there would have been no need for spontaneous deviations. “At the same time, if one were to introduce the hypothesis of a certain absorption of primordial particles in matter, then the gravitation, for example, of the earth toward the sun would be explained simply mechanically, both from the qualitative and from the quantitative side.” “I have not added to the atoms sung by Lucretius,” Lesage observes, “any new definition having the aim of explaining the great laws discovered by contemporaries. On the contrary, I limited myself to removing from their motion the arbitrary restriction (almost perfect parallelism) by means of which Epicurus disfigured the atom of Democritus (homogeneity in all directions)”**).

It is more correct to think, however, that it was not an erroneous cosmography, i.e. the conception of a flat earth, that led Epicurus and Lucretius to the idea of spontaneous deviation; on the contrary, the need to introduce spontaneity into the doctrine of primordial particles entailed the picture of a parallel stream of primordial particles moving with the same velocity.

We must return once again to the leitmotif of the poem, to the physical explanation, with the aid of primordial particles, of all phenomena of nature without exception. Absolutely dense primordial particles, falling in the void and possessing no other properties whatever, were not in a position to explain the facts of consciousness and freedom of will. To preserve the scheme it was necessary, for this purpose, to endow the primordial particles with certain inseparable organic spontaneous properties which are not at all like the consciousness and will of a complex organism, but which, when primordial particles are combined, and with special forms of organized matter, can lead to sensation, consciousness, and thought.

With such a general posing of the question one cannot pass over in silence the striking coincidence of the principal content of Epicurus–Lucretius’ idea—

*) Lesage, Lucrece Neutonien, Histoire de l’Academie Royale des Sciences.

**) Lesage, loc. cit., p. 425.

solution about spontaneous deviation with the so-called “uncertainty relation” of modern physics. Its essence consists in the fact that it is impossible by any means to determine simultaneously, with absolute precision, the position and velocity of an elementary particle. This impossibility is determined by the fact that the product of the coordinate and the momentum of a particle is a finite quantity, of the order of the quantum constant. In modern physics, a change in the motion of particles occurs, beginning from certain space-time limits, “not at the appointed time and not quite at the known place,” as in Lucretius. According to our present-day knowledge, many fundamental phenomena—for example, the emission of light by an atom or the radioactive decay of an atomic nucleus—therefore occur quite spontaneously.

It would be a gross error to see in Epicurus and Lucretius predecessors of quantum mechanics; however, one cannot regard a certain coincidence between the ancient idea and the modern one as wholly accidental. The quantization of atomic states and energies is undoubtedly connected by deep roots with the discontinuous character of the elementary particles themselves.

The quantum nature of these particles themselves, the initial principle of contemporary physics, probably also allows us to hope for the creation in the future of a quantum theory of elementary particles. Only from the point of view of such, as yet unattained, perspectives can one discern in the very idea of finite atoms the rudiments of modern quantum conceptions, including the uncertainty relation.

There is, however, the most profound difference between Lucretius’ doctrine of spontaneous deviation and the conclusions of certain modern physicists and philosophers who incline toward idealism and are carried away by an indeterministic form of the experimental uncertainty relation. For the Epicureans the clinamen was the basis of a strictly materialistic doctrine of consciousness and freedom of will. The consciousness of a complex organism differs from the spontaneous deviations of primordial particles just as much as these primordial particles differ from the organism as a whole:

“…The first-beginnings of things have no feeling of their own:
Yet if the first-beginnings could create living beings with feeling,
Merely because their first-beginnings must be credited with feeling,
What then would the first-beginnings be like in the human race?
Surely they would be able to burst into ringing laughter,
And to bedew both face and cheeks abundantly with tears,
And to speak with understanding about the structure of things,
And finally to reason about their own first-beginnings?”*)

For modern idealists, who try to rely on the experimental uncertainty relation, on the contrary, it becomes the basis of idealism and even a proof of the existence of God.**)

) Lucretius, II, 973 ff.
) Cf., for example, A. Compton, The Freedom of Man*.

In the doctrine of the clinamen, Epicurus and Lucretius for the first time linked the concepts of chance and necessity, of freedom and determinism. The Epicurean deviation of the atom, in Marx’s words,* “therefore changed the whole construction of the world of atoms by ... realizing the contradiction inherent in the concept of the atom.”

For philosophers and physicists who are frightened by the uncertainty relation as a road to indeterminism, or, conversely, who look upon it with hope as a support for idealism and mysticism, it is equally useful to reread the poem of Lucretius. Through the archaic character of ancient concrete images and knowledge, some may clearly read the end of their fears, others—the end of their hopes.

The doctrine of the spontaneous deviation of the first beginnings completes the basic propositions of Lucretius’ physics. The remaining four books of the poem are the application of the physical foundation to the explanation of more complex natural phenomena: the soul, sensations, astronomical phenomena, meteors, the development of the earth, life, society, and so on. Here one encounters lines relating to the domain of physics in the modern sense (the theory of images IV, the viscosity of liquids III, 186 ff., magnetism VI, 1090 ff., etc.), but in Lucretius they have rather an illustrative significance. The center of the physical poem is, undoubtedly, in the first two books.

Comparing the physics of our own day with the physics of Lucretius, and abstracting, as we should, from details, comparing only what is fundamental in the most abstract form, we indisputably recognize much in common, and in what is most important.

The great human thought of the Greco-Latin genius, reflecting and concentrating the external world, seems to have foreseen the line of growth and development of science, experience, and theory for millennia ahead.

Remembering and restoring now the words and thoughts of the ancient sage, scholar, and Epicurean poet, we—people who have at last seen, and not merely guessed at, atoms and are mastering them—cannot but bow our heads with deep reverence before the memory of a true classic of science, a great materialist and remarkable poet.

* K. Marx and F. Engels, loc. cit., p. 34.