The Cosmological Views of Democritus and Modern Physics

 

 

Danezis, E., Theodossiou, E., Manimanis, V., Stathopoulou, M.,Grammenos, Th.

Department of Astrophysics-Astronomy and Mechanics, School of Physics, University of Athens

 

 

Introduction

 

The modern scientific views

 

As it is known today, the scientific notion of space is closely connected with the natural properties of space. Their experimental verification supplies its form for the human senses and logic.

The description of space through its properties consists a topic of geometry, and the best known form of space is the one described by the Euclidean geometry, which is based on the well-known axioms of Euclid, propositions that cannot be proven mathematically, but instead we accept them as «logically self-proven».

What should be noted is that the notion of a geometry cannot be identified with the notion of space and the number of its dimensions. Geometry describes a set of properties of the space independently of the number of its dimensions. For example, a space, regardless of its dimensions, is Euclidean if it obeys the basic axioms of the Euclidean geometry.

Beyond the known, and immediately conceivable through the human senses, Euclidean space, the great mathematicians Lobatschewski and Riemann built two non-Euclidean geometries that describe the respective properties of two independent and different spaces, which bear their names.

These two spaces and their respective geometries were mere theoretical constructions, without any physical significance, until the moment that Einstein introduced the General Theory of Relativity, which presupposes and operates only inside the frame of a Riemannian space. In short, the space of the Universe that surrounds us and which we want to claim we measure, if we accept within its frame the validity of the General Theory of Relativity, is not Euclidean but Riemannian¹.

The Euclidean geometry can be applied with very good approximation to very small portions of a Lobatschewski space. However, its deviation from reality becomes noticeable in astronomical scales. This indicates that the Euclidean geometry consists a limiting case of Riemannian geometry.

But at this point start the paradoxes for the human «common sense», since, as we know today, our senses can record and specify shapes that take form only in spaces of up to three dimensions, described by Euclidean geometry. The shapes that take form in spaces described by non-Euclidean geometries, such as the Riemannian and the Lobatschewski geometry, are imperceivable by the human senses^* .

Therefore, since the geometry of the four-dimensional space of Einstein’s General Theory of Relativity is Riemannian, the Universe is not generally Euclidean. This means that the forms of our cosmic space should not be perceivable through our senses. The fact that we realize the shapes that surround us is a consequence of the property of our senses to record, by creating virtual divisions of the spacetime continuum of the cosmic space, small pieces of the surrounding non-Euclidean Riemannian space, which as we mentioned behave as Euclidean spaces, perceivable by our senses.

Thus what we essentially perceive is simply the projectional shadow of Riemannian forms and shapes in the three-dimensional Euclidean space, which is created by arbitrary divisions of the continuous and indivisible cosmic space perceived by our senses.

 

The arbitrary divisions of the senses

 

The virtual view of the events in the cosmic spacetime that we form through our senses can be also perceived through the classic theory of physics.

It is common knowledge that the human eye is an imperfect radiation collector. Its imperfection consists mainly in that it cannot perceive:

The same illusion is created by the sense of touch. We think we touch an object. In reality, however, the terminal structural components of our hand during the event we call «touch», stay at relatively large distances from the terminal structural components of the object we «think» we touch. What we perceive with our brain as touch are just the repulsive forces created between the fields that surround the structural components of our hand and of the object.

The previous facts are stressed in a characteristic way by Michael Talbot in his book Mysticism and Modern Science⁷. He writes: «According to the New Physics we can only dream of the real world. We dream that it exists mysteriously visible, omnipresent in space and constant in time. Nevertheless, we consciously assented to the fictitious creation of illogical, sparse and eternal breaks of its architecture, so that we may be able sometime to see how false is our initial frame».

The classical physical theory was structured based on this arbitrary division of the cosmic continuous four-dimensional Riemannian space. As the father of the General System Theory, Ludwig von Bertalanffy, writes⁶: «It seems that the only purpose of science was the analysis, i.e. the division of reality into much smaller units and the isolation of the individual chains of causes. Thus the physical reality was divided into point masses or in atoms, the living organism into cells, the behavior into reflexes, the perceptions into exact senses. Therefore, the causality was the necessary way.»

On the same topic D. Bohm and B. Hiley write in their article «On the Intuitive Understanding of Non-Locality as Implied by Quantum Theory»²:

 

«Our work shows intuitively exactly how and why a quantum many-body system cannot be analyzed into independent parts with constant and determinable dynamical relations among them. The parts appear rather to be in direct relation with each other. A connection on which depend their dynamical relations within the whole system. Moreover, within the framework of the wider systems in which they are incorporated, they finally extend in principle to the whole Universe. Thus we come to the new idea of the indivisible wholeness, which negates the classical idea of analyzing the world into separate and independent parts.»

 

In this new physical reality, what is «matter», a notion based up to now on the illusion of the human sensory organs, is described elegantly by Charles Muses³ in his book Consciousness and Reality:

 

«A tree, a table, a cloud, a stone. All these are dissolved by the science of the twentieth century into something consisting of the same material. This something is a medley of whirling particles that obey to the laws of quantum physics. This means that all the objects we can observe are three-dimensional images formed by by waves stationary or moving under the influence of electromagnetic and nuclear processes. All the objects of the world are three-dimensional images formed electromagnetically, images of a superhologram, if you wish.»

 

This of course is true for the limited space of our close environment. However, in the case we want to observe very large parts of the Universe, such as the ones studied by cosmology, the Euclidean geometry does not describe them, and the resulting shapes remain unconceivable by the human senses.

Thus, the human senses do not represent an infallible criterion of the truth of the forms and phenomena of the Universe, so that we can now say that: «through our senses, and through our instruments that amplify them, we do not perceive the Universe as it really is, but as our brain has the capability to perceive it through the very imperfect human senses. The real nature of the four-dimensional Riemannian Universe is imperceptible and can be described only through mathematical relations.»

However, these views about the falsehood of the human senses and the imperceptible truth of the creation, although they seem novel, had not escaped the ancient greek positive thinking. In the contrary, they had been analyzed in length and depth enough that is interesting to be registered and connected with the modern physical theory, which, in addition to predicting, can probably expand mentally and theoretically.

After all these ruminations, let us examine a part of the views of Democritus along with the corresponding commentary, that makes clear the fact that Democritus and other presocratic philosophers knew the inability of our senses to perceive the real (non-sensed) nature of the Universe. They were referring to it as the «μη ον». Similarly, they had in full the feeling of the illusion of the sensed Creation, referring to it with the philosophical term «ον».

 

Information about Democritus is supplied by Diogenes Laertius (Diogenes Laertius, Φιλοσόφων βίων και δογμάτων συναγωγή, IX, 34), who reports:

 

«Democritus, son of Egesistratos or, according to other evidences, of Athenocritos or Damasippos, was from Avdera or, as some say, from Miletus... Later on he was acquainted with Leucippos and, according to some, with Anaxagoras... As he himself relates in his work «Mikros Diakosmos», he was young at Anaxagoras’ old age, being forty years younger than him. He says that «Mikros Diakosmos» was written 730 years after the capture of Troy. As Apollodorus writes in his «Chronika», he should have been born during the eightieth Olympiad (460-457 B.C.), while according to Thrasylos in his work with the title «The ones before reading the books by Democritus», he was born in the third year of the seventy-seventh Olympiad (470/69 B.C.), being (as he says) one year younger than Socrates.»

 

About the opus of Democritus, Diogenes Laertius [Diogenes Laertius, Φιλοσόφων βίων και δογμάτων συναγωγή, IX, 45-49 ], reports:

 

«Thrasybulus classified his writings according to tetralogies, exactly as he did with the works of Plato. His ethical works are... The natural philosophy ones are: The «Megalos Diakosmos», the «Cosmographia» and the «Peri Planeton»...»

 

Presocratic thought and modern physics

 

The terminology in the texts of Democritus

 

A serious problem faced by students of the ancient texts when they try to compare the views expressed therein with the modern scientific positions, is the meaning of the employed terms. These terms have different meanings in the texts of the various authors, while in most cases they do not have any relation with the meaning we assign to them today. For this reason it would be prudent to study the meaning of some terms used by Leucippos and Democritus, and to distinguish them from the meaning we assign to them nowadays. Let us consider the three following quotations:

 

1. [Simplicius, Υπόμνημα εις τον Αριστοτέλη, «Περί Ουρανού», 294, 33]: ...Democritus thought that the nature of the eternal things is an infinite number of small «ουσίες» (essences). And for them he supposes that there exists another place («τόπος») of infinite size, calling the τόπος with the names «κενόν» (void) and «ουδέν» (nothing) and «άπειρον», while the ουσίες with the names «δεν» (something) and «ναστόν»^* (solid, dense) and «ον».

2. [Aristotle, Μετά τα Φυσικά, Α4. 985β4.Λ.]: ...Leucippos and his follower Democritus maintain that «πλήρες» (full) and κενόν are elements, calling the one ον and the other μη ον, and of these the πλήρες and «στερεόν» (solid) is the ον, while the κενόν and «αραιόν» (diffuse) is the μη ον. Therefore they claim that the ον has no more real existence than the μη ον, because nor the void is less real than the body... These are the material causes of the beings.

3. [Simplicius, Υπόμνημα εις την Αριστοτέλους «Φυσική Ακρόαση», 28,4. Λ.]: ...Leucippos hypothesized that there is an infinite number of evermoving elements, the «άτομα» (atoms)... For, supposing that the essence of atoms is solid and compact, he said that this essence is the ον and that it moves in the void, called μη ον, and he alleged that its existence is no less real than the existence of the ον. Similarly, his follower Democritus from Avdera also posited as basis the πλήρες and the κενόν, calling the one ον and the other μη ον.

It appears that Democritus describes the «τόπος», i.e. what we call today «mathematical space», using the words κενόν, ουδέν or άπειρον. The void for him coincides with the notion of «μη ον». The «μη ον» according to Democritus (quotation 2) has an existence in no way inferior to that of the sensed «ον», since it also possesses a nature and substance of its own.

Similarly he calls the ον «πλήρες» or «στερεόν», identifying it with the notion of atoms, thus calling the ον «ναστόν» and «δεν».

At this point we must distinguish the notion of «μη ον» in Democritus from the notion given by Parmenides. According to Parmenides, the «μη ον» is a more general with respect to its nature cosmological constituent, having no relation with the material nature of the Universe and attributed to the sphere of the mental or the metaphysical. As D. Makriyannes¹⁰ writes in his work Cosmology and Ethics of Democritus (award of the Academy of Athens):

 

« [the «μη ον» = void] is not just the empty space (the one we mean today by this term) inside which the atoms move, but something more essential, extending as a substrate for the motion of atoms. Without it this motion would be physically impossible. So we can compare the void as a kind of screen upon which the atoms move, like the figures on the screen of the shadow theatre. The screen does not take part at the essence of the images showed, but without it the images would be impossible to appear. The same with the void according to the theory of Democritus: it is a cause of the existence of beings, not because it forms a part of their nature, but because it contributes as an invisible substrate to their appearance.»

 

The word «λόγος» acquires a different content than the modern one in the texts of presocratic philosophers. As Sextus relates:

 

[Sextus VII 126 (Heraclitus A 16)]: «...Heraclitus also believed that man employs two organs for learning the truth, the sense and the logos. Of these, he considered the sense deceptive, in accordance with the previous natural philosophers, while he accepts as a criterion the logos.»

[Sextus VII 122 (Empedocles B 1)]: «...There are two kinds of the right logos, the divine and the human. Of these, the divine is inexpressible, while the human is expressible.»

 

What should be stressed is that with the term «λόγος» is described the opposite of the product of senses, the non-discernible by the senses. With the previous meaning, logos is still used by the Christian theology in order to render the notion of God, considering God through this expression «non-discernible by the senses».

 

The delusion of the senses

 

As can be seen from the introduction, the modern scientific view accepts the idea that the objective world of the senses is an erroneous image, and a very small part of what really exists and evolves around us. This fact had not escaped the comprehension of the ancient greek philosophers.

The first allusion to the relativity of the truth of the events perceived through the human senses can be attributed to Xenophanes:

[Fragm. 34, Sextus, Προς Φυσικούς VII, 49 & 110 comp. Plutarch]: «No man knows, nor will ever learn, the truth about gods and about what I say, for even if someone happens to say the whole truth, he will not know it; for all matters there are only opinions.»

[Fragm. 35, Plutarch, Symposiaka Zetemata IX, 7, 746b]: «Let us consider that the matters resemble the truth.»

 

A second allusion is recorded in the words of Heraclitus, who is reputed to say:

[Fragm. 123, Themistios, Logoi 5, p. 69D]: «The true structure of things usually is hided.»

[Fragm. 54, Hippolytus, El. IX, 9, 5]: «The obscure link is stronger than the obvious.»

 

Moreover, Sextus Empiricus, referring to Heraclitus’ views, finally persuades us that the great positive philosopher had fully perceived the illusion of our sensory world:

[Sextus VII 126 (Heraclitus A 16)]: «...Heraclitus also believed that man employs two organs for learning the truth, the sense and the logos. Of these, he considered the sense deceptive, in accordance with the previous natural philosophers, while he accepts as a criterion the logos.»

 

But also Parmenides, as mentioned by Diogenes and by Simplicius, had a correct view about the illusion of the natural world as it is perceived through the human senses. Specifically about the views of Parmenides they report:

[Diogenes IX, 22 (Parmenides A 1, 22)]: «Parmenides said that philosophy is dual: Its one form agrees with truth, while the other guesses... ...and he defined the logos^* as a criterion, because the senses are not exact.»

[Simplicius Peri Ouranou 557, 20 (Parmenides B 1)]: «These men hypothesized two substances: The one of the mental real «ον», and the other of the becoming and sensed, which did not condescend to call simply «ον»^** , but they called it «νομιζόμενον ον»^*** . Therefore they say that truth relates to the real «ον», while for the changing ον (the physical things) there is only guess.»

 

These views of Parmenides are described in their entirety in his hexameter poem, large fragments of which were saved by Sextus Empiricus (the preamble) and by Simplicius. But according to Sextus Empiricus the idea of the false reality created by our senses had been formed also by Empedocles:

[Sextus VII 122 (Empedocles B 1)]: «Others were saying that according to Empedocles criterion of truth are not the senses but the right logos («ορθός λόγος»). There are two kinds of the right logos, the divine and the human. Of these, the divine logos is inexpressible, while the human is expressible.»

 

As can be understood by all the previous passages, the fact that the natural creation as perceived by the human senses is just a human «delusion», was a common realization of the presocratic positive philosophical thought. At the same time, the belief in an objectively real physical creation perceivable not through human senses but only through thought (through mathematical analysis and models, as we would say now), was deeply rooted.

These expressed views, predating Democritus, very probably consisted the necessary original material upon which he, but also Leucippos, was based in order to formulate some more integrated positions on the topic, and in turn to support their expressed atomic theory.

Let us now examine more closely the views of Democritus on the «truth» of the sensed Creation, as reported by Simplicius, Sextus, Galenos, Aetius and Aristotle, adding our respective comments.

 

1. (Sextus, Προς Φυσικούς, VII, 138) ...But in the Kanones he writes that there are two kinds of knowledge, the one through the senses and the other through the mind. Of these, the one acquired through the mind he calls genuine, attributing to it reliability for expressing correct judgement, whereas the one acquired through the senses he calls spurious, not acknowledging infallibility at the discernment of truth. He writes «there are two forms of knowledge, one genuine and one spurious. To the spurious one belong all of the following, the sight, the hearing, the smelling, the taste, the touch. The other form of knowledge is genuine and separate from the spurious.

It is interesting to observe that Democritus recognizes as spurious the knowledge resulting through the senses, referring to them by name. A second interesting point that should be stressed is that the majority of the presocratic philosophers, including Democritus, refer to the intellect proclaiming it as a sixth sense, through which we can perceive the non-sensible but existent and objective reality of the natural world. Therefore, it will no more seem strange that, rephrasing the view, if we want in the future centuries to perceive as objective reality the physical and universal structuring, as this is expressed by the modern physics and astrophysics, we must train our intellect, proclaiming it as a sixth super-sense.

 

2. (Democritus, fragm. 9, Sextus, Προς Φυσικούς VII, 135) ...In the cratynteria (proving elements), although [Democritus] had promised to assign to the senses the authority of certitude, on the contrary he finds himself condemning them, for he says: «But in reality we don’t conceive anything certain, only something that changes according to the condition of the body and to the things entering it and pressing it.»

 

3. (Sextus, Προς Φυσικούς, VII, 137) ...And again he says (fragm. 10) «So it became obvious in many ways that in reality we do not conceive truth, we don’t conceive how things are or are not.» And in Peri Ideon (fragm. 6) «Man must learn from this rule that he is separated from the reality.» And again (fragm. 7) «And also this argument shows that in reality we don’t know anything for any object, but for each one of us there is a recreated form of it, the belief.» And yet (fragm. 8) «However, it should be obvious that it is very difficult to learn how really is each object.»

 

4. (Sextus, Προς Φυσικούς, VII, 135) ...Democritus sometimes refutes those that seem to the senses and says that no one of them corresponds to the truth, only in the human imagination.

 

5. (Aristotle, Μετά τα Φυσικά, Γ5, 1009b7) ...Moreover, to many healthy animals the same things appear opposite than to us, but also a human does not feel always things in the same way. Thus it is unknown which of them is true and which is false, because the former are not more true than the latter, but equally. That’s why Democritus says that either nothing is true, or [if it is true] it is obscure to us.

 

6. (Galenos, Περί Ιατρικής Εμπειρίας, εκδ. Schone 1259,8. ) ...Oh wretched mind, after you took your certainties from us (i.e. the senses) you reject us? Our rejection is your collapse.

 

7. [Aetius, Αυτόθι, IV 9,8] ...Others say that the sensed are physical, but Leucippos and Democritus that we think them as such, from our personal opinion and our impressions. Nothing is true or perceivable, except from the first elements, the atoms and the void. For only these exist physically, and all the rest happen from differences in position, in class and in shape.

 

8. [Simplicius, Υπόμνημα εις την Αριστοτέλους «Φυσική Ακρόασιν» 28,4. Λ.] ...Leucippos hypothesized that there is an infinite number of evermoving elements, the atoms... For, supposing that the essence of atoms is solid and compact, he said that this essence is the being and that it moves in the void, called non-being, and he alleged that its existence is no less real than the existence of the being. Similarly, his follower Democritus from Avdera also posited as basis the full and the void, calling the one being and the other non-being.

At this point, an interesting observation should be made, which follows from all the previous passages. As mentioned, since the full and the void, that is the atoms and space, are true and objective realities according to the atomic philosophers (passage 7), they must be outside the field of human senses, because in their view the products of the senses consist mere illusions, separated from the truth and the objective reality. This thesis is confirmed by the following quotation 11, that claims the atoms are «naked of perceivable quality».

 

9. [Galenos, Περί των καθ’ Ιπποκράτην στοιχείων, I,2] ...By convention there is colour, by convention there is sweet or bitter; in reality, there are only the atoms and the void, says Democritus, believing that all sensed properties result from the engagement of the atoms and depend on us who sense these. In nature the white, the black, the yellow, the red, the sweet, the bitter, etc. do not exist. And the term «νόμω» means exactly that «we think that it is so», without this being the nature of things, which he calls again «ετεή» from the adjective «ετεόν», meaning true.

 

10. [Sextus, Προς Φυσικούς, VII 137] In the book «Peri Ideon» he writes: «man should know according to the rule that he is far away from the true reality».

 

11. [Sextus, Προς Φυσικούς, VII 6] The Platonic and the Democriteans understood that only the mentally conceived is true. But Democritus thinks so because no physical sensed thing exists, since the atoms composing all bodies are naked of perceivable quality, while Plato because the sensed change continually...

Here it should be noted that Democritus considered the atoms, i.e. the basic structural unit of what we call today matter, «naked of any notion of perceivable quality». In a few words, atoms, being real, consist imperceivable entities, hence mental. This idea agrees with the theories of modern physics, considering the elementary particles as a kind of whirl transmitted through the field (Relativity) or as an energy wave (Quantum Mechanics). That is, their nature is imperceivable by the human senses.

 

12. (Aetius, Συναγωγή των αρεσκόντων, IV 8, 10.Λ.) ...Leucippos, Democritus and Epicurus say that sensing and thinking are caused by images of external origin, neither sensing nor thinking occuring without the knocking of an image against the being that [then, after the stumbling has the feeling that...] senses or thinks.

As we realize from this passage, Democritus considers that the senses are just the result being caused when «images», radiations as we could say today, of external origin (from the field of the real world of thinking) stimulate the organs of our senses. The result of these stimuli (the senses) does not, according to Democritus, consist an objective reality. This view coincides with the modern scientific view^*.

An interesting view, however, is expressed in the following quote:

(Aristotle, Fys. A 3, 187 α1, DK29 a22) «...Some accepted both arguments, the argument that everything is one, if being (ον) means an object, stating that the non-being (μη ον) exists as a result of the bisection...»

Most probably, as the previous thesis evidences, Democritus had moreover understood that the field where our senses operate is but a subjective arbitrary division our senses create out of the empty space of «μη ον», in order to perceive as sensed beings some interpretations (projections) of the properties of the «μη όντα». This view is supported by the fact that Democritus believed, as we will see, that one (out of many) sensed world is created when in the total «void» space of the Universe (μη ον) is formed a partial «great void» (a section of a more general space of the Universe), within which many bodies concentrate (Leuc. A 10)^* .

 

This view apparently agrees with the modern scientific theories, as expressed in the words of the father of the General System Theory, Ludwig von Bertalanffy, reported previously^**. Another interesting point that deserves attention is the following view of Democritus:

[Diogenes Laertius, Φιλοσόφων βίων και δογμάτων συναγωγή, IX, 40] «...There is an infinite number of words being created and destroyed. Nothing is generated from the μη ον, neither is destroyed to become μη ον.»

This view, under the aspect of all things said about the μη ον, is extremely interesting, since it clearly supports that the μη ον, or else the void or the infinity, that is the non-sensed world by itself cannot generate worlds, as for this the contribution of the ον (the atoms) is needed. And the opposite, a world cannot be disintegrated and converted simply into μη ον (space); i.e. matter cannot be converted into void space, since in essence it includes not only void, but also atoms.

 

Some other interesting views

 

It is interesting to mention the Democritean view about «time»:

[Sextus, Προς Φυσικούς X 181] «...To the natural philosophers who were followers of Epicurus and Democritus they attribute this saying about time: time (the time measured by humans) is a ghost similar to the day and the night.»

This view is not contrary to the view of physics, because the notion of time as perceived by Democritus is identical with what we call today «Newtonian time» and is measured with our clocks and calendars. But the Newtonian time, as we now know, constitutes only the projection of the Riemannian relativistic dimension «time» inside and over a Euclidean space or a Minkowski space, i.e. a ghost of what is time in reality.

 

Let us examine the topic more specifically. According to Einstein the three-dimensional space and the dimension «time» consist two inseparably interconnected entities and construct a unified reality of the Universe, the reality of spacetime. From this unity we cannot separate time facing it independently from the other three (spatial) dimensions, because the dimension «time» loses its identity and also the system of the independent entities «space, time» cannot describe the reality of the Universe any more.

But even if we could separate time from the structure of spacetime, in order to comprehend it through our senses the four-dimensional spacetime of the Universe should be describable through Euclidean geometry, while it is expressed through Riemannian geometry. This means that we cannot perceive with our senses the real essence of the time dimension.

Our senses, however, can perceive infinitesimal parts of the Universe, that with good approximation can be described by Euclidean geometry. Inside these small parts of the Universe we perceive what humans call Newtonian time and they measure it with their clocks and calendars. As it is evident, this time has no relation with the dimension «time»⁹.

 

Another question answered by Democritus, but proved with the use of scientific instruments many centuries later, was the problem of the structure of our Galaxy. As Democritus believed [Achilles Tatios, Των Αράτου φαινομένων προς εισαγωγήν εκ των Αχιλλέως περί του παντός, 24, εκδ. Maas, 55,24. Περί γαλαξίου): «...Others say that the Galaxy consists of very small and dense stars, that to us appear united due to the large distance from heaven to Earth, as an object powdered with many grains of salt...»

The first scientific verification of these views of Democritus about the nature of Galaxy was obtained by Galileo circa 1610 A.D. when, turning his small telescope towards it, he realized that, as he reports in his book Nuntius Sidereus, «...[the Galaxy] consists of a mass of innumerable stars, being placed one close to the other by swarms...»⁹.

 

The cosmology of Democritus

 

Although everyone today considers Democritus along with Leucippos the fathers of the Atomic Theory, not many know that the two atomic philosophers are the forefathers of a cosmological proposition, which has not been analyzed in depth, as it should, nor it has been placed under the judgement of the modern scientific knowledge, as it happened in the case of their views about atoms.

In what follows, we try to concisely comment and study these cosmological views, under the light of the observations and comments stated earlier. Let us see what Diogenes Laertius writes about the views of Leucippos, that had been also accepted by Democritus.

 

[Diogenes Laertius, Φιλοσόφων βίων και δογμάτων συναγωγή, IX, 30-33] ...Leucippos believed that... ...the worlds are created when bodies fall in some void and engage with each other, and from their motion and accumulation the nature of stars comes into being... (31) And the worlds are created as follows. Many bodies, with a great variety of shapes, are being detached from the infinity and brought to a great void where, being accumulated, form a whirl. Colliding and twirling due to this whirl, they become separated according to their shape. When they come to an equilibrium due to their large number and cannot whirl any more, the thin [bodies] advance towards the external void, as if being hurled, while the rest become entangled and approaching to each other form initially a spheroidal subsystem. (32) From this, a membrane is detached containing various bodies inside it. As they whirl due to the centrifugal force, the membrane becomes thin, because the elements being close accumulate always towards the center entangled in the whirl. This way the earth (= the sensed matter) was created, when all that was accumulated at the center united. Now this external membrane grew due to the accumulation of bodies coming from outside, because as it is carried away by the whirl it encorporates the bodies with which it comes into contact. From these, some get entangled and form initially a system very wet and muddy. After they dry and follow the general whirl, they are heated and constitute the nature of stars...

With this quotation as a basis, the main steps of the cosmic creation, according to Leucippos and Democritus were the following.

 

1. In the beginning there was the full and the void

 

Prior to the events described in the previous quotation, as already has been mentioned, initially there was the total creation (μη ον = void = infinity), inside which were floating the atoms (ον). The system ον + μη ον was beyond the perceptual capabilities of the human senses, since (as already has been mentioned) the atomic philosophers were supposing that «the full and the void, i.e. the atoms and space, are true and objective realities outside of the field of the human senses».

As can be seen, with the unified system full + void (= atoms + space) Democritus replaces a previous system, that of the Orphic Chaos and Erebos, without of course suggesting the identification of the respective partial components of the system.

 

2. Creation of the «great voids»

 

[Diogenes Laertius, Φιλοσόφων βίων και δογμάτων συναγωγή, IX, 31] ...The worlds are created as follows. Many bodies are being detached from the infinity (the void) and brought to the «great void».

In this phase, in the frame of the total original space of the Universe (μη ον = void = infinity) many partial «great voids» (μεγάλα κενά), i.e. smaller sub-spaces of the total space, are created. This could be expressed in the modern scientific terminology as creation (inside the total non-perceivable and non-Euclidean space of the Universe) of partial sub-spaces with different density and curvature, a fact that also caused different geometries of the created sub-spaces.

This cosmological procedure described by Democritus constitutes, as we shall see, the basic principle of the quantum cosmological theory of Andrei Linde, that predicts and tries to explain the creation of these voids, which calls bubbles, via the inflation field.

It is an interesting fact that Democritus seems to be especially intrigued about the «cause» (the great voids) that, as we shall see, forced the atoms to accumulate into small regions, and not about the cause that created the great voids themselves. For this reason he fashions the notion of the partial voids-spaces as the cause for the subsequent accumulation of the atoms, but without explaining the physical process of their formation.

 

3. Local collapse of «atoms» in the «great voids», formation of the «whirl»

 

In this phase, non-perceivable parts of the ον (atoms), originated from the total non-perceivable creation of the Universe (infinity + atoms = void + full = μη ον + ον), tend to occupy the created «great voids», generating for each one of them a corresponding «whirl» («δίνη»)^*. With the entry of atoms inside the sub-spaces of the «great voids» are created the perceivable through the senses «worlds», perhaps infinite in number and contained in the total non-perceivable set «ον + μη ον» (atoms + void = Universe).

 

 

The cosmological whirl

 

A first reference to the notion of whirl is made in the Orphic Cosmology. The primaeval cosmological egg, the natural creation and composition of which is remarkably and scientifically related by Democritus, generates a whirlwind, described by the atomic philosophers as a secondary whirl and by the Orphic texts as «Ερως»:

 

[Aristophanes Ornithes 693] ...the black-winged Night begets first a windbeaten egg; from where, when the time came, flaming Eros came out, golden wings glittering on his back, the like of a whirlwind...

 

The notions of whirl and whirlwind occurs also in the cosmological view of Empedocles:

 

[Simplicius, Peri Ouranou 529, 1 (verses 1-15), in Fysika 32, 13 (verses 3-17)] ...When the dispute arrived in the depths of the whirl and the amity came in the midst of the whirlwind, all these began to come together and become one...

[Aristotle, Peri Ouranou B 13, 259^α 29] ...Besides, it is strange that [Empedocles] did not realize that, if initially the molecules of earth accumulated towards the center due to the whirl, he should explain why all things carrying weight tend now to go towards the center. Because the whirl cannot be what brings them close to us...

[Aetius II, 6, 3 (DK 31a 49)] ...Empedocles suggests that the first to separate was the aether, second came the fire and next the earth (matter). From the earth being intensely tighten round due to the force of rotation came out the water...

 

However, to the notion of «whirl» is assigned a specific physical meaning by Democritus, that assumes today a special cosmological interest. Initially, the Democritean «whirl» forms within the framework of the original non-perceivable system «void + non-void» (ον + μη ον = atoms + space = Riemannian space of the Universe). As Diogenes Laertius describes:

 

[Diogenes, Φιλοσόφων βίων και δογμάτων συναγωγή, IX 30-33] ...And the worlds are created as follows. Many bodies, of various shape, detach from the infinity and are brought to a great void...

 

In a second phase the «whirl» evolves inside a small region of the «great voids» (Euclidean sub-spaces).

[Diogenes IX 30 (Leuc. A 1)] ... are brought to a great void forming a whirl ...

 

That the whirl initially occupies a small part of a great void is evident from the fact that:

[Diogenes IX 30 (Leuc. A 1)] ...When [the bodies] come to an equilibrium due to their large number and cannot whirl any more, the thin [bodies] advance towards the external void, as if being hurled, while the rest become entangled and approaching to each other form initially a spheroidal subsystem...

 

This means that the whirl was initially occupying a small part of the great void, since it could advance towards the exterior.

But returning to the notion of the whirl, as described by Leucippos and Democritus, the question of how it evolves is open. Where is placed its funnel and where its «cord». It is difficult to answer, because the presocratics acknowledged two kinds of whirls. The first appeared in the case of liquids, e.g. in rivers, lakes and the sea, when through whirls the water disappears in underground cesspools. In this case the material falling in the whirl is directed from the funnel to the cord (vortices). In the second case, e.g. in the phenomenon of the whirlwind or the tornado, materials from the surface of the earth, where the base of the whirl, are directed through the cord towards the funnel of the whirl, being elevated from the earth. In the case of Democritean Cosmology the material should be lead from the funnel to the edge of the cord, since as we shall see the final result of the whirl is a sphere of limited dimensions.

All the previous thoughts, as in the Cosmology of Alkman⁴, lead us to the conclusion that, if we want to describe using modern scientific terminology the views of Leucippos and Democritus in respect to what existed before the perceivable Universe was created and to how we were led to the starting point of the cosmic creation, we come to the conclusion that the atomic philosophers, in addition to Alkman, describe the creation of the Universe through a white hole. The difference between the cosmological system of Alkman and the one of Leucippos / Democritus is that the atomic philosophers, being experts on the scientific knowledge of their time, expose in greater detail their views attaching to them a series of scientific (for their era) explanations. The notion of whirl in particular renders the cord of Alkman easier to understand, while the spherical condensation of «not thin» materials makes more concrete the notion of the Alkmanian «τέκμωρ».

The coincidence of the views of Leucippos and Democritus about the creation of the Universe with those of Alkman leads to questions, such as whether the atomic philosophers knew the Alkmanian Cosmology and, moreover, whether their views consist the lost or destroyed continuation of the text of Alkman, wherein he continued the exposition of his cosmological proposal.

 

The infinite worlds and the «great voids»

 

In the context of Democritean Cosmology appears, with a physical etiology, the idea of the existence of many perceivable worlds like ours within the frames of the created «great voids». The idea of the existence of many «worlds» inside successive «heavens» consists an older presocratic view. As reported by Simplicius and St.Augustine, Anaximander was stating the same view:

 

[Simplicius, in Fysika 24, 17] ...[Anaximander believed that]...some other substance is the infinity, from which all heavens were made, and the worlds existing in them...

[Augustine, De civ.Dei VIII, 2] ... [Anaximander] believed that these origins of the partial things are infinite, and that they produce innumerable worlds, and all that appear inside them, and the worlds themselves, as he believed, get destructed and reborn from time to time...

 

The view of Anaxagoras was also similar:

 

[Simplicius, in Fysika 157, 9] ...That he[Anaxagoras] hints at another world besides ours, is evident from the phrase «exactly as we», that he uses many times. And that he does not consider this other world a perceivable world that preceded ours is evident from the phrase «from which they gather the best in his houses and use them». For he didn’t say «used» but «use»...

 

But the complete physical etiology and description of a Universe including an infinite number of perceivable worlds was given by the atomic philosophers and in particular Democritus. D. Makriyannes¹⁰ writes in his 1999 book Cosmology and Ethics of Democritus (award of the Academy of Athens) about the structure of this Democritean Universe:

 

« ...Since there are infinite worlds, there are infinite empty spaces. So we can simulate the Democritean Universe with a sponge. The material of the sponge corresponds to the compact more or less structuring of the atoms comprising the medium that includes, while the spheroidal voids in the volume of the sponge are the spaces where the worlds are created and evolve. The cosmological sponge model is not static, neither with respect to the structure of the including medium, nor with respect to the shape and size of the voids. As inside the voids take place continuous reactions among the atoms, similarly the total including medium undergoes continuous mutations, the principal among them being the emission from it of all kinds of bodies to the interior of the voids, and the reabsorption of the bodies resulting from the destruction of the worlds.»

 

Thus Democritus documents logically in a natural way the possibility of the simultaneous existence of many perceivable worlds, which may nevertheless be imperceivable by us, since between them and our world intervenes the non-perceivable unified system of «ον» + «μη ον» (atoms + void)⁹.

As reported by Hippolytos:

 

[Ippolitus, Σύνταγμα κατά Αιρέσεων, Ι, 13, 2] ...Democritus supports the same as Leucippos, that there is an infinite number of worlds with different sizes. In some of them there is no Sun, nor Moon, in others these two celestial objects are larger than in our world, and in others more numerous. The distances among the worlds are unequal, in some regions there are more worlds and in others fewer; some worlds are developing, some are in the apex of their development and some are declining.In other places worlds are forming and in other disintegrate. Their destruction is caused by their mutual collisions.

 

In this passage, as in several previous ones, one can clearly discern the view that the natural laws can be different in the various worlds and hence totally different events can be generated. Even after Democritus, this same idea about many worlds is repeated by Diogenes Apolloniates:

 

[Pseudoplutarch, Stromateis 12] ...Diogenes Apolloniates hypothesizes that air is the element and that everything moves and the worlds are infinite in number...

 

But let us see what the modern cosmological theories have to say about the existence of many worlds⁹. According to the quantum cosmological proposal of Linde, in the original non-Euclidean, hence non-perceivable, Universe there were two known scalar fields: The «inflation field» and the «Higgs field». The inflation field and the associated phenomena are the reason for the expansion of space (void, μη ον), while the Higgs field is responsible for the kind of natural laws establishing themselves inside the expanding space. These two fields, as it has been proved, exist everywhere in the Universe, and their presence is betrayed from their influence on the elementary particles.

However, the scalar fields are not constant and, as proved by quantum physics, undergo unexpected fluctuations and variations. If the fluctuations cause a large increase in the intensity of the inflation field, then in this region the Universe begins to expand much faster, creating a bubble (generation of a great void). This effect can be produced continuously in different regions of the original non-perceivable Universe (creation of an infinite number of great voids). This implies that if we conceive the Universe as a homogeneous bubble, every new perturbation in it will create a new bubble of the universe (great void). In this way A. Linde answered the question that Leucippos and Democritus could not answer: how the great voids are created^*.

The bubble spaces are initially limited by irregular limits that continually smooth down, and tend to expand with velocities approaching the speed of light. Later on, the limits of the bubbles can possibly shrink with much lower velocities. On this basis, the Big Bang Theory describes the creation of just one bubble, inside which we find ourselves, and not of the total Universe of the infinite bubbles.

It should be noted that, if in the original non-perceivable Universe there was a set of specific natural laws, the Higgs field would have changed it in the produced bubbles (great voids). This means that every bubble (great void) will eventually have its own set of natural laws, i.e. exactly what Leucippos and Democritos had already said.

It should be mentioned that A. Linde’s model consists an elaboration of the inflation theory (A.H. Guth 1981), which predicts the existence of a Universe with many bubbles in spacetime, perhaps ruled by different natural laws. In 1982 American researchers Albrecht and Steinhardt announced similar results. The entire cosmological model of A. Linde we believe that does not need any further comments in order to be identified with the views of the atomic philosophers Leucippos and Democritus.

As it can be seen, the thoughts of the philosophers of the past can probably consist a source of inspiration for the formulation of modern theories in physics⁹.

 

4. Formation of spheroidal system of perceivable matter with simultaneous ejection of material in the external void

 

Due to the rotating «whirl», there is first a separation of the «similar» from the «dissimilar». Next the rotation ceases and a system is created consisting of «thin bodies» (not small in dimensions, nor atoms) that advance towards the external void (space) as if being hurled, while the rest, the «non-thin» (thick = hadra), remain united and becoming entangled approach each other and form initially a spheroidal system.

It is interesting to note that the new term «thin bodies» is used in order to set these bodies apart from all the others that have already been mentioned.

With a superficial reading of the corresponding text one could find apparent coincidences between the views of the atomic philosophers and the modern cosmological theory of Big Bang. The spherical condensation could superficially be thought as Lemaitre’s primaeval atom and the described explosion as the Big Bang. However, things are not that simple.

The hurling and the expansion of the «thin» material according to Leucippos and Democritus is not a result of the explosion of the spheroidal system formed by the «non-thin» materials, but instead they occur together with the creation of the spherical condensation, as a result of events taking place at the edge of the «whirl», since there the «similar» have separated from the «dissimilar» and equilibrated, and the bodies cannot rotate anymore.

In a few words, Leucippos and Democritus support that from a mixture of «thin» and «non-thin» bodies that is in equilibrium and does not rotate, the hurling of the thin ones towards the exterior creates an opposite motion, a contraction, of the «non-thin» ones, that tend to form a small but dense spheroidal structure of matter.

As is evident from the respective quotation, at the end of the whirl, where it meets the great void, there is a limited in space, momentarily non-rotating and in equilibrium, spherical condensation of «non-thin» (not small in dimensions, nor atoms) material. The sphere occupies a very small space of the «great void», because how else could be the described «thin» material hurled into the external space if this space were occupied by the initial sphere? It is interesting that at the limits of the whirl, towards the region of the «great void», and before the formation of the spherical condensation, the material of the non-perceivable Universe (space + atoms) consists of an «exotic» for our senses «matter», indescribable by the atomic philosophers, that later on it separates into two constituents, the «thin» and the «non-thin» (thick = hadra), which in a later phase were to form the «matter» that is known today to our senses, according to the atomic philosophers.

In relation to the previous, it should be mentioned that in accordance with the modern cosmological views we can discern two cosmological periods, the Planck era and the inflationary expansion era. These precede the hypothetical creation of the initial spheroidal condensation of matter, the primaeval atom of Lemaitre, from which the Big Bang began. The matter under the extreme conditions prevailing during these periods was truly «exotic» for the modern scientific reality. During the inflationary expansion in particular, the conditions were such that they favored the creation of successive bubbles (great voids) and most probably the creation of «exotic» Higgs particles (Higgs bosons) that consist the hypothetical mediators assigning to the particles the property of their mass after the Big Bang.

Similarly, after the moment of the Big Bang modern cosmology adopts the view that there were two phases, during which two respective kinds of subatomic particles were formed, the hadrons (thick, non-thin) and the leptons (thin). As «hadrons» are classified the protons, the neutrons, the hyperons and the mesons. The «leptons» include the electrons and the neutrinos. The respective cosmological phases of creation were given the name of the particles being created. The correlation of the names of these elementary particle classes with the terminology of the atomic philosophers is characteristic.

 

5. Formation of a thin membrane. Onset of a rotational motion of the Universe

 

At this stage, from the central spheroidal condensation of «non-thin» material detaches a membrane, i.e. a thin shell of «non-thin» matter. This membrane starts rotating, while material from it is carried towards the central spheroidal condensation «due to the whirl». But which whirl? The original «whirl» was carrying material from the non-perceivable Universe of the «ον» + «μη ον» to the world of the «great void», that is the spherical accumulation of «non-thin» material we mentioned. On the contrary, the whirl referred here leads from the «world» of the «great void» to the original spherical accumulation of «non-thin». This means that the whirl mentioned here is of opposite direction in respect to the first. In other words, the atomic philosophers propose a cosmological system of two whirls of opposite polarity (+ and -). The first evolves outside the world of the «great void» and the second inside.* But both lead to a common region, which forms the beginning and the end of the world of the «great void».

 

Conclusions

 

If we summarize the views of Leucippos and Democritus about the structuring of the Universe using the corresponding modern scientific terminology, we can generally discern two periods:

 

1. The process before the creation of the spherical condensation and of the great voids, when the Universe (ον + μη ον = void + atoms) consisted a non-perceivable entity (logos), a situation Hesiod describes as Chaos and Erevos. This process can be compared with the process of the creation of the Universe through a white hole, which in turn is analogous to the processes described in Alkman’s cosmology.

 

 

_____________________________________________________________________________

* That is, the Universe evolves on the surface of a pseudosphere, on which the hyperbolic geometry is applied (negative curvature.

 

1. The process after the creation of the great voids and of the spherical condensation, which is interesting to analyze by phases:

1. A.D. Aleksandrov: «Μη Ευκλείδειες Γεωμετρίες», Εκδόσεις της Ελληνικής Μαθηματικής Εταιρείας, Μαθηματική Επιθεώρηση, Ιούλιος-Αύγουστος-Σεπτέμβριος 1976.
2. Bohm, D. and Hiley, B.: On the Intuitive Understanding of Non-Locality as Implied by Quantum Theory, Gordon and Breach, London February 1974.
3. Charles Muses and Arthur M. Young: Consciousness and Reality, Outerbridge and Lazard, N.Y., 1972.
4. Danezis, E., Theodossiou, E., Stathopoulou, M., and Grammenos, Th.: «A Presocratic Cosmological proposal». History and Heritage of Astronomy, 2(2):125-130.1999.
5. G.S. Kirk, J.E. Raven and M. Schofield: «Οι προσωκρατικοί Φιλόσοφοι», εκδόσεις του Μορφωτικού Ιδρύματος της Εθνικής Τράπεζας, Αθήνα 1990.
6. Ludwig von Bertalanffy: General System Theory, George Braziller, N.Y., 1968.
7. Michael Talbot
8. Βελισσαρόπουλος, Δ.: «Η Ιστορία της Ινδικής Φιλοσοφίας»,Εκδόσεις Δωδώνη, Αθήνα 1975.
9. M. Δανέζη και Σ. Θεοδοσίου: «Το Σύμπαν που αγάπησα - Εισαγωγή στην Αστροφυσική», Diavlos publ. Αθήνα 1999.
10. Δ. Μακρυγιάννη: «Κοσμολογία και Ηθική του Δημόκριτου», Εκδόσεις Γεωργιάδη, Αθήνα 1999.
11. Λεύκιππος-Δημόκριτος: «Η Ατομική Θεωρία». Εκδόσεις Εξάντας, από την σειρά Αρχαίοι Συγγραφείς, Αθήνα 1995.

1. G.S. Kirk, J.E. Raven and M. Schofield: «Οι προσωκρατικοί Φιλόσοφοι», εκδόσεις του Μορφωτικού Ιδρύματος της Εθνικής Τράπεζας, Αθήνα 1990.
2. Δ. Μακρυγιάννη: «Κοσμολογία και Ηθική του Δημόκριτου», Εκδόσεις Γεωργιάδη, Αθήνα 1999.

ΑΤΤΕΝΤΙΟΝ

As for as the work of SEXTUS EMPIRICUS, in which the above writers reffered, exists only the book «ΠΡΟΣ ΦΥΣΙΚΟΥΣ» (Against the Phycistes) and not «ΠΡΟΣ ΜΑΘΗΜΑΤΙΚΟΥΣ» (Against the Mathematicians).