Introductory summary quote (abstracts).

This article was first published in the magazine «Ο Κήπος του Επίκουρου» ("The Garden of Epicurus") in September 2014.

Some of the main points are:

The presentation of the view of Epicurus (as expressed in the Επιστολή προς Ηρόδοτον, (Letter to Herodotus (Diogenes Laertios 47)), concerning the images and the transmitters of images and light, the κουφότατες ατόμους which now a days are called photons. This view is equivalent to the modern physical interpretation for light and its speed, which is the cornerstone of the Special Theory of Relativity.

Also of importance, is the treatment of the differences between the Epicurean and the Democritean natural philosophy. There are two main differences: on one hand, the question of randomness or causality and on the other, the question of the number of different types of particles (ατόμων).Epicurus, unlike Democritus, admits that there is a finite number of types of particles. The author of the article beyond quoting the justification given by Epicurus himself in the subject, gives his own justification supported by Bolzano-Weirstrass theorem and the equivalent Heine-Borel’s lemma.

A third point of interest that could be mentioned, is the phenomenon of “Brown’s Movement” described by Lucretius, exactly as described in modern physics textbooks.

Another point of interest is Epicurus view that bodies within vacuum, fall with the same speed, a view expressed 19 centuries before Galileo.

The article consists of excerpts of a broader study of the author in Epicurus physical theory.

THE EPICUREAN PHILOSOPHY FOR NATURE IN THE LIGHT OF MODERN PERCEPTION

«...ότι τα είδωλα ταις λεπτότησιν ανυπερβλήτοις κέχρηνται [ατόμοις], ουδέν αντιμαρτυρεί των φαινομένων· όθεν και τάχη ανυπέρβλητα έχει, πάντα πόρον σύμμετρον έχοντα …»

Letter to Herodotus, 47

PrologueAccording to Diogenes Laertios, Epicurus said that he first came into contact with the philosophy at the age of 14 years (according to Ariston at the age of 12. (Diogenes Laertios (DL) X, 14, line 7)). According to the Epicurean Apollodorus, Epicurus turned to philosophy disappointed by his teachers,1 because they could not explain chaos to him, as presented by Hesiod.Something similar happens with Ilya Prigogine 23 centuries later, when as a young scientist he asked, not ordinary schoolteachers as the young teenager Epicurus did, but prominent scientists of the modern era such as Pauli and Bohr to explain to him “What is Time”.

Texts of Epicurus about NatureAlthough the philosophy of Epicurus endured for seven centuries since he founded the Garden (Κήπος), in the end, thanks to the "contribution" of Christianity2, very little of what he wrote reached our days3. Of the 37 books written by Epicurus about Nature, nothing is saved. The same fate suffered: the "About atoms and vacuum", the "Compendium for physicists", the "Canon", and many other books on the same subject4. The "Canon" (which according to Ariston was written by Epicurus having as model the “Tripod” of Nausiphanes (DL X 14, line 5)), is supposed to be the logical tool for the management of Epicurus’ theories and philosophical ideas (equivalent to "Organon" of Aristotle). The only complete works about Nature that survived are: the letters to Herodotus and Pythokles. The other main source of Epicure’s natural philosophy is the “De Rerum Natura” (DRN) of Lucretius. In these three works and

1 From disdain to the schoolteachers (καταγνόντα των γραμματιστών) D. Laertius: “Life of Epicurus” X2.2 "The Epicurean materialist psychology and the denial of life after death were the main reasons for the violent attacks Epicureanism suffered, especially under the Christian centuries. Perhaps explaining why the Epicureans, although withstood the challenges of Christianity for four centuries, finally lost the battle: The immortality promised by Christianity was more alluring and comforting than the promise of an epicurean Mors ... immortalis (DRN III, 869) ... », a death, that when it comes, we are not here anymore. See De Rerum Natura, editions “Θύραθεν”, introduction by Martin Ferguson Smith, page 34.3 Hopefully, new data will be provided by the charred and ash converted Papyri of Herculaneum, which can now be read thanks to techniques and methods whose first theoretical foundations were established by the physical philosophers and Epicurus. You see Nature protected the Ancient Knowledge from the obscurant mania of the fanatic religious man in a paradoxical way, by earthquakes, by sinking and silt and even by pyroclastic waves of volcano eruptions such as Vesuvius’.4 From what Diogenes Laertius refers as writings of Epicurus, except the «Επιστολή προς Ηρόδοτον» and «Επιστολή προς Πυθοκλή», I guess from the titles that the works related to the nature and physiology are the following: «Περί Φύσεως» 37 books, «Περί ατόμων και κενού», «Επιτομή των προς τους φυσικούς», «Περί κριτηρίου ή Κανών», «Περί του οράν», «Περί της εν ατόμω γωνίας», «Περί αφής», «Περί παθών δόξαι προς Τιμοκράτην», «Περί ειδώλων», «Περί φαντασίας», «Περί νόσων δόξαι προς Μίθρην».

in the Inscription of Oenoanda5 one can find a comprehensive and not fragmental authentic presentation of the Epicurean theories about nature and the natural phenomena. Titus Lucretius Carus “does not claim ownership of the philosophical statements he deals with in his poem. His aim is to present poetically as closely as possible the Epicurean teaching"6. The poem of Lucretius is embellished with hymns and praise for Epicurus and the Epicurean teaching7. It does not add anything more to what was developed by Epicurus. "He follows his teacher faithfully but not slavishly. This does not mean that he is unorthodox”8, he simply shows the Epicurean philosophy, especially when it relates to nature, in a poem, with a single exception: Lucretius is stricter and more audacious in terms of religion and priesthood9.In my opinion it should not be forgotten that Epicurus, when he spoke about the gods, had to take into account the Diopeitheion psifisma10, the law which, inter alia, sentenced Socrates to death.For these reasons I regard “De Rerum Natura” of Lucretius (DRN), equivalent to the “Letter to Herodotus” (LtH), the“Letter to Pythokles” (LtP) and the “Inscription of Oenoanda” (IoO) as authentic sources of the Epicurean natural philosophy.The study you have in your hands refers mainly to these four sources.

Terminology: Modern and ancientBefore going into the main subject of this essay, which is a comparative presentation of the theories of Epicurus in relation to modern scientific views and perceptions of the physical and natural science, I think I should mention the importance of certain words used by him. «Πρώτον μεν ουν τα υποτεταγμένα τοις φθόγγοις, δει ειληφέναι…» (We should therefore first of all define the concepts corresponding to the words ...)11. Those words as definitions are the cornerstones for the Epicurean philosophical and naturalistic construction.But before I show you the keywords of the Epicurean philosophy I would like to dwell briefly on some definitions of modern science.

First of all, what is science and scientific theories?

By some definition:Science is a set of logical and empirical rules that allow for the systematic observation of empirical phenomena. This definition is in complete agreement; we could say it is identical, with the Epicurean method of research.

5 The inscription of Diogenes of Oenoanda, at Oenoanda in Asia Minor.6 Introduction by Martin Ferguson Smith in De Rerum Natura, εκδόσεις Θύραθεν, page 40 onwards.7 See: De Rerum Natura, I 62-79, II 1-61, III 1-30, V 1-54, VI 1-42, εκδόσεις Θύραθεν,.   8 DRN, p. 46.9 DRN, I, verses 80-135, pp. 64-67.10 The city life and democracy in Athens was inherent in the joyous worship of the twelve gods. Fear of democratic Athens (unfortunately confirmed by the historical evolution of the overthrow of democracy, not only from the "Thirty Tyrants" but by the descendants of Alexander and finally from Rome), was the one who pushed the Athens Demos to vote at 432 B.C. for the "blasphemy resolution" of Diopeithes, which sentenced some individuals, especially oligarchic, usually in exile and sometimes to death, among them the oligarchic Socrates of impiety to ancestral gods and introducing "new demons". See Georges Minua "History of Atheism" editions Narcissus, page 58 onwards11 Letter to Herodotus, 37

Modern scienceIn mathematics, a purely conceptual (non-empirical) discipline (the American scientists do not regard mathematics as science), the various theories admit as true certain a priori axioms (primary assumptions), considering the obvious truth without being able to demonstrate (prove) it. The axioms, together with the rules of logic, (which also have axiomatic status) and some definitions, are the core and the shell of each mathematical theory. From (and with) the axioms, the definitions and the rules of logic, various inferences like: theorems, lemmas and corollaries are produced, through procedures known as methods of proof. I repeat: The theorems, lemmas and corollaries can be proved and are derived from the definitions and mathematical and logical axioms (which we accept as true without being able to prove them). For each theory to be credible it must have certain properties, such as consistency (been not contradictory), completeness12 and closure. These properties ensure the consistent use and adequacy of axioms and definitions.

In physics things are somewhat different: Beyond the mathematic and logical axioms and definitions used, there are some assumptions that are called natural laws or principles. These assumptions are considered to be apparently true and the obviousness of their inherent truth is controlled by experience and observation through the senses. In physics, the developed theories try, within their given axiomatic frame, invoking the natural law, to describe the physical reality that is perceived through the senses by observation and experiment. If a theory cannot describe and explain some aspects of physical reality then another new theory is sought that explains the additional unexplained phenomena.But there is also the possibility of coexistence for two or more theories that explain each in its own way the same phenomenon. A typical example of modern physics is the wave-particle duality composed of two theories that describe the photon, the first as a wave and the other as a particle13. There is the question whether the wave-particle duality is itself an ambivalent phenomenon or if scientists without knowing yet the deep nature of this phenomenon describe it with two alternative ways.

Another example of how to interpret in a pluralistic way is the interpretation of classical mechanics by the different ways mentioned in footnote 17.

12 See, however, the theorems of Gödel on incompleteness and hence non-consistency and ultimately non closure of certain axiomatic systems.

13    Epicurus said: «Μήτε ομοίαν κατά πάντα την θεωρίαν έχειν…», ΕπΠ 86, also in the same: «…αλλά ταύτα γε πλεοναχήν έχει και της γενέσεως αιτίαν και της ουσίας ταις αισθήσεσι σύμφωνον κατηγορίαν,…». Also in ΕπΗ 79 «πλείους αιτίας ευρίσκομεν τροπών και δύσεων και ανατολών και εκλείψεων …», also in ΕπΠ 87 «…ενδέχεται πλεοναχως γίνεσθαι. ». Also in: ΕπΠ 91, 92, 93 etc. Epicurus in these cases use the terms: may be, probable, it may not be impossible, etc and raises the question of the impossible interpretation of all phenomena from a general theory that explains everything, a "Theory of Everything" as it is called by modern physicists to pursue. This diversity of interpretations involves the Epistemological pluralism, a term used in philosophy of sciences referring to different ways of acquiring knowledge and different epistemological methodologies to achieve a complete description of a particular sector. In the philosophy of science, the epistemological pluralism is resulting from opposition to reductionism, to express the opposite view, that at least some natural phenomena can not be fully explained by a single theory or fully investigated using a single approach. Epicurus is the first to speak in detail about the pluralistic explanations of phenomena and for this reason could be regarded as father of epistemological pluralism.

The physics and science in general, in contrast to religious doctrines and transcendent beliefs are susceptible to changes. The changes are indeed presupposed to allow science to evolve and give an increasingly successful description of physical reality. For this reason physical theories accept completion, partial or even total substitution. This is observed and is considered obvious in the world of physics, chemistry, biology and related sciences.An example of evolution is the transition from the Aristotelian, let's call it natural science, to classical physics and from that to relativistic physics: For Aristotle it was obvious that for the existence of movement a driving force was necessary (τι το κινούν, the impetus of scholastics)14, a force that constantly pushes the moving body.What was obviously "true" for Aristotle was wrong for Newton. By now the obvious truth was the principle of inertia that is: a body tends to maintain its kinetic state, i.e. moving as initially swung, in such a way that the force presupposed by Aristotle to maintain the movement of the movable, for Newton was required only to change the movement of the movable (cf. the αντικοπήν and the αποπαλμόν of Epicurus). Newton's laws postulated, relying of course on a number of other obvious truths based on observation (bodies are attracted to each other etc.) and form, along with some principles, such as the laws of Electromagnetism, the Wave Theory and the Thermodynamics, the so called Classical Physics.One of the obvious "truths" of Classical Physics was that: the interactions between bodies and the light signals are transmitted instantaneously, at infinite speed. This was accepted and postulated by the ancient philosophers and physicists except Epicurus (as we will see below). This obviousness was tested and proved to be wrong after some observations and experiments. The speed of light not only was not infinite but finite, (measured to be about 300,000 kilometres per second), but apart from that, was the same in any direction it was measured. Whether we move towards the light source or away from it, either transversely or in any direction relative to the source, the velocity (or more accurately the scalar part of the velocity i.e. the speed) is always the same (designed by the letter c, derived from celeritas the Latin word for speed). The carriers of the light, i.e. the photons, all and always move with the same speed c (in vacuum). In other words, the speed of light has nothing to do with our speed relative to the speed of the source that emitted it. It was relatively easy to accept that what we thought obviously true before, namely that the light had infinite speed, was not the case. What was difficult was to accept that the finite velocity of light does not add to the finite velocities of the emitting sources. If we add or remove something from an infinite quantity the result is infinite. But here we have something finite: the speed c 300.000 kilometres per second. From our experience we know that if you throw a stone from a moving vehicle towards the driving direction, the stone, for an observer standing still, moves faster than if you had thrown it while the vehicle was stationary. The speed of the stone is added to the speed of the vehicle. This is not the case with light. This was true in Classical Physics, not in Relativistic Physics.However, now in relativistic physics the true principle (law of nature) is not so obvious. It states that light has always the same speed (c) relatively to the sources that emit it and relatively to the observers, irrespective of their movement. It also states that the speed of light is the largest permissible speed in our natural world.

14 This wrong view was not shared by Epicurus

This factum, which is the cornerstone of the Special Theory of Relativity was accepted and formulated by Epicurus 22 centuries before the modern formulation.

Here is the relevant text in the ancient original:Letter to Herodotus, 47: «ειθ’ ότι τα είδωλα ταις λεπτότησιν ανυπερβλήτοις κέχρηνται [ατόμοις], ουδέν αντιμαρτυρεί των φαινομένων· όθεν και τάχη ανυπέρβλητα έχει, πάντα πόρον σύμμετρον έχοντα …» And in translation:“Also none of the phenomena disproves (no observation contradicts) that the images use (are composed of) the finest particles (photons) and therefore have insuperable speeds, and obey symmetry with respect to the space of origin and transmission (regardless of where they come from and pass through, their insurmountable speed is the same15)”.He also says explicitly that the particles which make up the images, move in space all at the same speed, with the same insurmountable speed (τάχος in ΕπΗ 43, 61, 62, etc.).

In the above formulation Epicurus formulates the fundamental principles of the Theory of Special Relativity just as they were formulated 22 centuries later, since the erroneous notion of Ether was abandoned and discarded, and the correct physical interpretation of the phenomenon was given by Einstein.

Macro theories and micro theoriesIn terms of examination of the world, scientific theories are divided into macro theories and micro theories, depending on whether the macrocosm or the microcosm is examined. The duo also constitutes a pluralistic pair of observation, for the understanding, interpretation and description of nature. Many of the theories of Epicurus have micro theoretic character. The atoms exist in the microcosm.The micro theories cooperate with and complement the macro theories.A good example of correlation and cooperation between macro theoretical and micro theoretical sciences is the Evolutionary Theory of Darwin - Wallace, Mendel’s Theory of Inheritance (Laws of Mendel) and Modern Genetic (Molecular) Biology. The triptych is part of the so-called New Synthesis (socio-biology) in the science of biology16 and is another example of the Epicurean «πλεοναχώς γίγνεσθαι».There is a parallel counterpart to the biological triptych in physics: Classical Physics17, Relativistic Physics and Quantum Physics. Quantum physics is the micro theory while Relativistic and Classical Physics are macro theories. There are some

15 Epicurus talks about passing through the empty space, which is everywhere homogeneous and homotropic. To reiterate the point I mention elsewhere: When light moves through matter that is transparent materials e.g. crystals, there is no homogeneity and/or homotropy. In this case the speed is a rate of c and is often different in various directions. This is because even if crystals are homogeneous (chemically pure) they are usually not homotropic because the fundamental crystal cell which recurring constructs the crystal, exhibiting asymmetries. This is the reason for the different indices of refraction of light presented by crystals. For further information, see e.g.: Alonso - Finn, Fundamental University Physics II, Fields and waves, versions Gleerups - Addison - Wesley, p. 792, ff see especially the section: Fresnel’s Ellipsoid. Also: P. Lorrain - D. Corson, Electromagnetic Fields and Waves, second edition, Publications CBS, pp. 467 ff and 508 et seq16 See Edward Wilson, Sociobiology, The New Synthesis, εκδόσεις Σύναλμα17 As stated in equivalent ways by Newton - Leibniz - D 'Alembert - Lagrange - Hamilton and others

incompatibilities between relativistic physics and quantum physics that the Relativistic Quantum Mechanics attempts to remove.

Ancient terminology in modern light

The Atoms (αι άτομοι)The ancient philosophers Leucippus, Democritus, Epicurus and others, designate by the term “η άτομος” the individual, something that cannot be further sectioned. During the Renaissance and the Enlightenment modern chemists and physicists encountered the atomic theory of the ancient Greeks and called atoms the chemical elements contained in the table of Mendeleyev18. But later discoveries showed that these individual elements consisted of subatomic particles and thus could be sectioned into them. Subatomic particles other than the photon (which is considered to have no mass and belongs to the group of particles called bosons or energy carriers) are leptons, mesons and baryons (the last two groups have the common name hadrons). It was later discovered that the fundamental subatomic particles mesons and baryons i.e. hadrons were composed of more fundamental particles indistinguishable from each other: the quarks. Lucretius predicted (DRN 599-610) the existence of indivisible subatomic particles that cannot exist in isolation, just as quarks, which are inseparably united forever and form larger particles (our hadrons). Nowadays, research deals with "strings" (called even "hairs") and "membranes" as the most fundamental individual entities.The physical-philosophic «άτομος» ("atom") of the ancient Greek philosophers was on occasion: 1) our own atom (chemical element), 2) subatomic particles (including the photon), 3) quarks and 4) until today, "strings" or "membranes".

Even in its details the theory of atoms as described by Epicurus agrees with the modern concept of the structure and function of matter and light. The atoms do not coalesce into the body to which they are bound but have a vacuum between them (actually a large amount of vacuum); otherwise their movement and movement in general would not be possible. The atoms, when bound to the material grid19 of the body surrounded by vacuum, can move at πάλσιν and περίπαλσιν i.e. oscillate in vibrating and rotating modes.Nowadays modern chemistry recording the oscillations and rotations of atoms within the molecules (and subatomic particles within atoms) may "photograph" each molecular species and distinguish it from the others20.

18 It seems that the first chemists and physicists of our time were directly influenced by the teachings of Epicurus, as relayed through Pierre Gassendi. They thus expressed: the principle of indestructibility of matter (Lavoisier), the atomic theory in chemistry, the principle of conservation of energy, etc. It seems that we have not rediscovered what Epicurus had said but we received it as a legacy by Epicurus himself through Gassendi. It is crucial to know all the details of the contribution of Gassendi in conveying the theories of Epicurus in the modern world. If the prevalence of the atomic theory in the minds of the chemists and the physicists of the new world is due to Gassendi, then the modern scientific views are based directly on the teachings of Epicurus and are successors of the «προλήψεις» and «δόξας» of this teaching, and the similarity with them is not due to simple coincidence, but to didactic continuity.19 See Letter to Herodotus, 43, 44 and 50

20 See the topics: Ultraviolet absorption spectroscopy, Infrared spectroscopy or Raman absorption spectroscopy, Nuclear Magnetic Resonance and Mass Spectrometry. E.g. in "Modern principles of organic chemistry" of John Kice - Elliot Marvell, editions Collier Macmillan, pages 147, 154, 151, 168 and 160

According to Epicurus (unlike Democritus) the different kinds of compounds (substances) constitute a finite set because the different kinds of atoms themselves forming the compounds constitute a finite set. However each type of compound may be innumerable (infinite) because each type of atom represents an infinite number of similar atoms21.Modern Chemistry presents a finite number of chemical elements and compounds, but every kind of compound can represent an infinite number and consequently the molecules representing each compound can be innumerable (since the atoms which make up the compound are in unlimited number in the infinite universe).The same thing happens at a lower level: the kinds of subatomic particles are finite in number, but any kind represents innumerable particles in the universe (if the universe is infinite). Accordingly the kinds of chemical elements (atoms with all isotopes) are not infinite in number, in the table of Mendeleyev they were 103, in the laboratory some more were synthesized, but disintegrated shortly after their creation because of their large size. More types of elements cannot be "made".But there may be countless atoms of every kind, provided that the universe is infinite. Let's look at the logic that underpins these views of Epicurus.There are four cases:1st: infinite universe - infinite number of atoms2nd: infinite universe - finite number of atoms3rd: finite universe - infinite number of atoms4th: finite universe - finite number of atomsOf these four possibilities Epicurus accepts the first:If the universe is infinite then the number of atoms should also be infinite, because according to Epicurus if it was a finite number of atoms in the infinite universe, then the atoms in an infinite dilution would be at infinite distances apart from each other and we would not have a structured universe with interacting parts, but individual, isolated non-interacting atoms. But, I repeat, the number of species of atoms is finite. If on the other side, according to Epicurus, the universe was finite and the number of atoms was infinite we would have the undesirable situation of compact coexistence of atoms with no space between them. As mentioned in another passage, this prohibits the movement and therefore any functionality. The fourth possibility: that of the finite universe and the finite number of atoms, for reasons that I will negotiate elsewhere, is rejected as well by Epicurus.

The diversion (η παρέγκλισις) The diversion (deviation, deflection, perturbation, swerve) (παρέγκλισις22 <paregklisis> in Epicurus, clinamen, declinatio and inclinatio in Lucretius23) is the deviation or diversion from destination. As such it is not deterministic and it is a random event.For his theory of paregklisis, Epicurus received the taunts of Cicero24. In modern times, Marx, neo-Hegelian at his youth, accepted in his doctoral thesis25 the random 21 See letter to Herodotus, 42.22 Diogenes of Oenoanda (Inscription of Oenoanda) quote 54 verses 2 and 323 De Rerum Natura II 216 - 224 and 251-293, editions Θύραθεν, pages 139 and 141- 143.24 “Cicero (De Finibus 1.6.19) says the whole thing is a monstrous conception and adds that the theory except of been childish is arbitrary.” De Rerum Natura, editions Θύραθεν, Introduction Page 31 and onwards.25 K. Marx "The difference between the Democritean and the Epicurean natural philosophy", translation Panayiotis Kondylis, publishing "Γνώση ".

παρέγκλισις view of Epicurus versus the deterministic causality view of Democritus, although Marx was a dialectical determinist, he sent the taunts of Cicero where they deserve to be, to the wastebasket.In modern times the first scientist who discovered the problem of irreversibility of the arrow of time, (the paradox of time) directly related to individual random events in the microcosm or successive random events in the macrocosm, was Ludwig Boltzman. He received, as Epicurus, criticism and was accused of "lack of logic in his work." However, Epicurus and Boltzman were right...The concept of randomness of events occupied almost all modern scientists of whom I choose to mention the great French mathematician Henry Poincaré. It was he who accused Boltzman of lack of logic in his work. And yet Poincaré later defined the concept of declination named after him. On the subject, apart from the Poincaré declinations, there are the Poincaré resonances and the Poincaré reappearance (or reoccurrence). To avoid obscure definitions and descriptions I will give two simple examples: Imagine that you have a glass of water and a drop of ink falling into it. What will happen is that the drop will soon be dissolved and will "disappear" in the water. Whenever ink molecules collide with water molecules and change position dispersibly (in a dispersible manner), a random event happens. There is no natural deterministic law that prevents the drop to reappear in the water of the glass. The reappearance of the drop is prevented by the randomness of the sequence of the dissolution events. It is very, very unlikely, that reversible events occur with some reversing sequence, so that the drop reappears. It is the lack of possibility to reverse the course of random events, which determines the direction of time from the past to the future and not vice versa. The other example has to do with the Poincaré reappearance: Imagine that you throw a dice which has six faces with six numbers written on each face, from 1 up to 6. The dice is a system (a universe if you like) consisting of six elements. Every time you throw the dice, one of the six numbers may come up (random event). Presume you wait for number three. If the dice is not "falsified" after a few throws and over some time, the dice will display the number three and later would display it again. If we increase the number to two dices, throw them together and expect the occurrence of the threes, the waiting time for the reappearance of threes will be longer, because the possible combinations with two dices are more. Each time you increase the number of dices or the elements of a system, the time it takes to wait for reappearance is longer. If the number of elements of a universe is finite, finite time for the reappearance of any arrangement of these elements is required. This is called Poincaré reappearance time. One can understand that for our universe, if it is finite and consists of a finite but huge amount of elements (which is not accepted by Epicurus), the reappearance time will also be huge but still finite. If the universe is infinite and the number of elements is infinite (as accepted by Epicurus) the reappearance time will also be infinite, in other words there will be no reappearance. This establishes the direction of the arrow of time from the past to the future. To the issue of the Epicurean παρέγκλισις I will return later in the text, because in addition to being a fundamental physical - philosophic concept it is connected with the ethical issue of the human free will.

Infinite (Άπειρον)You should keep in mind the original meaning of the word. Originally άπειρον is what we cannot have experience of. With this original meaning, infinite is a definition of anything which we cannot perceive with our senses. It can be infinite because e.g. it is

"infinitely far" or it is "infinitely small" which arises after countless cuttings. The "infinitely small" is also called infinitesimal. The infinitely far was replaced by the word for non-experience (άπειρον) which changed its primary meaning. Today, when we say Infinite, we mean the boundless (which has no bound), the unlimited (which has no limit, which is beyond all limits). Epicurus uses the word άπειρον with both meanings: the original (non giving experience) and the secondary (unlimited in size, at unlimited distance, in unlimited numbers, etc.) and therefore we must analyse texts attributed to it with caution.

The Bulk matter (Οι Στερέμνιοι) The στερέμνιοι or στερέμνια (Letter to Herodotus 10.46) is the tangible, the material bodies of the macrocosm. In English terminology for physics they are called physical objects or bulk matter.According to Epicurus bulk matter is composed of atoms when they lose their freedom and get bound (today we would say by chemical bonds, although they are not the only binding bonds) in the matrix of the body (crystalline or amorphous), which is the στερέμνιο. This is fully in line with the modern concept for the composition of material bodies (solid-, liquid- and gas-bodies) from atoms. The στερέμνια are not necessarily solid, e.g. a lake's surface sends every moment its image είδωλο (idol) (see the section below) to the environment, and for that reason is a στερέμνιο. The clouds, sending at any moment their images to the environment, are στερέμνια. We can say that the operational definition of στερέμνιο is: something which at any time (when illuminated and gleaming) sends images to the environment.

The images (Τα είδωλα)The images are pictures of the bulk matter. They are types of the same shape26 with στερέμνια flowing (being radiated) from them27. The images are composed of the most delicate, the most weightless (κουφότατες) atoms surpassing in speed all other particles, moving all at the same speed (ισοταχώς). (They have all the qualities of our photon without missing or surplus any). The images reaching our eyes28, give us the opportunity to understand the στερέμνια constituting the material world. This description is in full agreement with the modern photon theory (Wave-particle duality) and the Special Theory of Relativity.

26 Note: The images are conformal with the physical objects of bulk matter, but our brain perceives them as plane. The three-dimensional objects are perceived as such by the binocular vision and not by the time difference of arrival of photons coming from different parts of the objects, because this difference is extremely small. For example, two photons emitted at the same time from two sources that one is three meters behind the other will come to us with a time lag of about 10 nanoseconds, which is extremely short time to be managed and exploited by the instruments of our vision and brain which have not the resolution capacity to distinguish such small time differences.27 Letter to Herodotus, 4628 Epicurus thought rightly that the images of physical objects arriving from the objects to our eyes are composed of ultra fine atoms (photons) and give us the sense of sight. Other ancients believed that our eyes send a kind of "radiation" to the objects reflected by them so we can see. They believed in a vision of "radar-type". The vision of radar-type, or sonar-type vision, is not unknown in nature; although it is substantially ultrasonic hearing. For example bats "see" in this particular way, using ultrasound although they are equipped even with conventional eyes. Also the whales talk and probably "see" each other by sending ultrasound. In closing I have to say that with regard to actual vision Epicurus was right.

But why are images moving at the same speed carried by the lightest particles i.e. photons «ταις λεπτότησιν ανυπερβλήτοις κέχρηνται [ατόμοις], τάχη ανυπέρβλητα έχει, πάντα πόρον σύμμετρον έχοντα …»?Why are photons moving at the same maximum speed, in all directions, permissible in the world?The answer has an implicit teleological logic:As I explain in the chapter "The logic of Epicurus", if this were not so, the world would be invisible, preposterous and incoherent.

I repeat in a comparative table the Epicurean view for “the atoms of the images” in line with the modern view for the photons:

Comparison table for the transmitters of images:According to modern science According EpicurusThe transmitters of images are the finest particles (thinner than leptons) and are called photons

They are the finest άτομοι (atoms) of all atoms

They have no mass(and for this reason they cannot be "perceived" by gravitational fields29)

They have no weight (actually Epicurus argues that they are κουφότατες i.e. they possess the least lightweight) Comment of the author: The weight corresponds to the mass of a body as it is "perceived" and attracted by a gravitational field. The force of attraction suffered by the mass at this point of the gravitational field is the weight of the mass there.

They move with the highest speed allowed in nature

They surpass in speed all other atoms and bodies

They move with the speed c in vacuum

They move with the same speed in vacuum30

Their speed c is approximately equal to 300,000 kilometres per second

Their speed is not known, but it is not infinite, it is approximately equal to the speed of thought (see the text below the table)

Photons have integral spin, hence Well, Epicurus did not know this fact! 29 It seems that photons have some minimum mass and for this reason they get "perceived" and "captured" by the powerful gravitational fields of black holes, called black just because they capture the photons and do not let them go through so we can see them. Black holes are not holes but highly concentrated celestial bodies causing immense gravitational fields. Modern scientists had to change their view for photons with no mass and from now on talk of "κουφότατα" photons, i.e. photons having a minimal mass, following necessarily Epicurus.30   Here exists an ostensible ambiguity. Although Epicurus says that αι κουφόταται άτομοι (those who have minimum mass, i.e. our photons) move ισοταχώς i.e. at the same speed in a vacuum, says also that atoms with mass move ισοταχώς (… του κενού την είξιν ομοίαν παρεχομένου και τη κουφοτάτη και τη βαρυτάτη) Letter to Herodotus, 43. ( ... because the vacuum gives the same possibility of moving through it, both to the lightest and heaviest atom). He also refers elsewhere on the ισοταχώς movement of bodies under the influence of Earth's gravity. Here Epicurus refers to two different phenomena: first the speed of light and the other in bodies falling with the same speed under the acceleration of the gravitational field of the Earth.

they are bosons and obey Bose - Einstein statistics

Although he knew περίπαλσιν, i.e. rotation around itself, i.e. the spin, he did not know that this spin is integral for the photon and that for this reason the photons obey Bose - Einstein statistics31

How fast are images moving?The answer of Epicurus:Άμα νοήματι! As fast as thought!As I said, we now know that massless particles like photons move in vacuum at the speed of light c 300.000 kilometres per second, and always only at this speed (in vacuum). Those particles that have mass cannot reach this speed, and can move at different speeds, but always less than the c.As we said in the question: How fast do images and the smallest of all particles (the κουφόταται of ατόμων - read photons) constituents of the images move? Epicurus answered: "with the highest speed that exists in nature, ισοταχώς - all at this same speed". He i.e. said 22 centuries ago, something which was confirmed by the Michelson - Morley experiment, leading to the final version of the Special Theory of Relativity.When Epicurus is asked about the size of this speed, he does not make the mistake of answering with one of the following: instantly, instantaneously or promptly. Instead he responds: Άμα νοήματι! As fast as thought! Leaving the issue of determining the size of the speed of light open, because he did not have the instruments (interferometer) to measure this speed. The consequences of this formulation of Epicurus are huge. For the first time the speed of the images (of the photons as carriers of the light) is presented as an universal constant, which we were able to measure in modern times and to which we assigned the magnitude of about 300,000 kilometres per second, symbolized by the letter c.

Aristotle and other philosophers have made the mistake to believe that light motion and the spread of interaction and information can be made with infinite speed, instantaneously. Those philosophers bequeathed their misconception, through Christianity and scholasticism, to classical physics.

It needed the Michelson - Morley observation experiment, that measured the speed of light, and the Special Theory of Relativity based on it, to reverse the erroneous perception of instantaneous interaction prevailing in classical physics.

The logic of EpicurusThe unsurpassed tool of Epicurus is his irrefutable and consistent logic. He comes to all his correct conclusions by his pure rationalism.Initially he uses the iterative, carefully circumstantial observation of the phenomenon. He ascertains that the observed phenomenon is attested (επιμαρτυρείται, confirmed) several times and not contradicted (αντιμαρτυρείται, refuted) at all. Then he proceeds to scientific conception (πρόληψιν) and finally,

31 See Federick Reif: "Fundamentals of Statistical and Thermal Physics" Editions Mc Graw-Hill Kogakusha, page 331 and subsequent. Chapter 9: Quantum statistics of ideal gases. Especially see pp 332, 334, 337 and 342, and 345-349 subsections: 9.5 Photon statistics - 9.6 Bose - Einstein statistics.

combining scientific conceptions, formulates a scientific view i.e. a scientific theory (δόξα). The remarkable success of Epicurus, in the formulation of his theories is that they are compatible with modern scientific theories. This happens mainly due to the consistent use of Logic. Unfortunately we do not have a short extract from his "Κανών", which would shed light on the issue. However, the substrate for his right views is his correct reasoning.Let us look at some examples:For Epicurus the world consists of bodies and vacuum (Diogenes Laertius 39-40, DRN 419-448), both are logical conditions. There is the matter, but there is also vacuum between matter32 (τας ατόμους), because if there was no matter, there would not be a material-physical world, and if there was no vacuum between matter, it could not be possible for the matter to move and therefore the natural world would be static and could not evolve. Of course behind these concepts that are intertwined with that reasoning, there are deeper meanings: the existence, the movement and the evolution with their opposites.

32 If we take the simplest chemical element, hydrogen, consisting of one proton and one electron that is "orbiting" around the proton, and "zoom in" so that the proton reach orange size, the electron will take the size of a pinhead and the radius of its orbit around the proton will have the length of the distance Stockholm - Athens, so vast is the void space between them.

The natural world is moving and evolving, otherwise we would not be here to observe it. Here emerges the Anthropic Principle33, a theory extremely endearing in leading contemporary scientists.In Epicurus: Matter and the Void (vacuum) are imperishable entities. The existence of Matter and Void has as logical consequence (and presupposition) their incorruptibility. They are not made from non-being, nor can result in non-being. Note that according to Epicurus, even the void, being real, does not come from nothing and he feels obliged to declare its incorruptibility. The status of the void, as a real entity, was according to Aristotle, also accepted by Leucippus and Democritus (see Aristotle's Metaphysics I [985β 4-19] and the reference 39 in this text).

The universe, chaotic in the beginning, becomes adorned by the physical laws; it becomes Κόσμος i.e. well ordered World. Today we accept that physical laws when applied to the entire Universe convert it from chaotic entity to Cosmos. But who has dictated these laws. According to Anaxagoras and Plato Cosmos was adorned by a Mind (Νους), «Πάντα χρήματα ην ομού. είτα ο νους ελθών αυτά διεκόσμησε» (all things were mixed up and then came the mind and settled them). In Epicurus (and modern physicists), this mind is not a divine mind, but the mind of Nature itself, (because, according to Epicurus, the gods, living eternally blessed in Μετακόσμιο (somewhere apart from the world) get not involved in the mundane). In Euripides, who raises the issue of recycling of composite matter, it is the mind of the Earth, 33 According to Anthropic Principle, man appeared in the Universe to observe it. In other words, in the self-development process, the Universe itself, in a quasi "Darwinian" evolutionary way, produced the human being to acquire self-consciousness through self observation, since man is a part of it. In astrophysics and cosmology, the Anthropic Principle is a philosophical view implying that the physical world must be compatible with the life form which can observe it. According to Stephen Hawking, "we see the universe to be as it is, because if it were different we would not be on earth to observe it". Some supporters of the Anthropic Principle believe that it explains why the universe has the age and the fundamental physical constants needed to accommodate life that is aware of its existence. Therefore, they consider surprising coincidence the fact that the fundamental constants of the universe happens to fall into a narrow range that is compatible with life. Outside this narrow range, the life (and especially intelligent life) would be impossible.

There are three versions of Anthropic Principle: the Weak, the Strong, and the Final.

According to the Strong Anthropic Principle, there are many different universes or many different regions of the Universe itself, each with its own initial configuration and, perhaps, with its own set of laws. In most of these universes the conditions for the development of complex organisms are incorrect (not proper). Only in few universes like ours would intelligent beings develop and ask the question: “Why is the Universe as we see it?” The answer, as mentioned above, is very simple: “if it was different, we would not be here!”

The Universe must have those properties which allow life to develop within it at some point in history, because a) there must be a potential universe designed to create and maintain "observers" or b) observers are indispensable for the existence of a universe (equity universe), or c) a set of other different universes is necessary for the existence of our Universe. (See the relevant literature, e.g.: Stephen Hawking: “A brief history of Time-From the Big Bang to Black Holes”. Notes of James Schombert, Department of Physics, University of Oregon, USA. The Anthropic Cosmological Principle (Oxford Paperbacks), John D. Barrow, Frank J. Tipler, John A. Wheeler), etc.

which gives rise to everything to take it back again «Άπαντα τίκτει χθών πάλιν τε και λαμβάνειν».But the meaning of the adorned Universe, i.e. the Cosmos (the World), has as a logical consequence the existence of function and structure (λειτουργίας και δομής). Function that obeys the laws mentioned above and structure having an inherent system defined by laws. Furthermore, the word structure (δομή in Greek) contains inherently the systematic correlation of the building materials “δομικών υλικών”. There is the ancient saying for building structures: «Λίθοι τε και πλίνθοι και ξύλα και κέραμοι ατάκτως εριμμένα ουδέν χρήσιμα εισίν» "Stones and bricks and wood and tiles randomly thrown are useful to nothing" which exactly expresses the need for operational correlation.

The theory of Epicurus that the number of species of atoms is finite has also logical requirements, not only because of the prohibition imposed on the infinity of species by the theorem of Bolzano-Weierstrass mentioned in the relevant section but also because with infinite kinds of atoms a Cosmos i.e. an adorned Universe cannot be systematically built, because if the species of atoms were innumerable then the categorisation of atoms and consequently the adornment of the universe would not be possible, nor would it allow their systematic study, which also contravenes the Anthropic Principle. Each kind of atom, in an innumerable set of species of atoms, would have at least one characteristic in addition; this would make the systematic knowledge of them impossible. As an indicative analogy I mention the difference between alphabetic and ideogrammic languages: An alphabetical language with 24-25 letters can easily and comprehensibly synthesize the multitude of words and expressions contained in it. This is not the case with ideogrammic languages, which for each word use a separate and distinct ideogram. The difficulty in ideogrammic languages arises although they have on the one hand some classification rules, and on the other, a finite multitude of words. Imagine how insurmountably difficult the things would be, if every one of the innumerable kinds of atoms (accepted by Democritus and rejected by Epicurus) would have its own structural regulations. Then these rules would be innumerable and we could not talk about laws that govern the universe. Modern physics has discovered composition rules for the finite number of species of atoms and subatomic particles, such as Bohr’s Orbital Electron Layers, Pauli’s Exclusion Principle, and many others, that actually confirm beyond any doubt the theory of Epicurus.

Another point of the Epicurean teaching which I am going to mention here, deals with the speeds of “the most weightless (κουφότατες) atoms” of images, i.e. the photons. The view of Epicurus, as we said, is that the images move ισοταχώς i.e. equivelocitally with the same greatest speed in nature. Here again, behind this view lies the logical reasoning:   1. Regarding the equivelocity of photons: If photons were not equivelocital, if for example the photons that reach our eyes from a house, come at different speeds, then the image (το είδωλο) of the house would be so vague and diffuse that the house would literally be invisible. Then our vision would have the ambiguity of smell34 in 34 The sense of smell occurs when some volatile substances (some volumes according Epicurus, DL I 53) from the odorous object, drifted by streams travelling with different speeds, reach the surface of the olfactory organ and stimulate the nerves ending there, causing the stimulus (το αισθητήριον κινείν) which at the end of the process is carried to the brain. The olfactory detection of odorous sources can not be done by a mechanism corresponding to binocular vision. The detection is accomplished by following the stream of volatile substances with maximum density. Regarding the

determining the position and appearance of the objects. For hearing, concerning the determination of the position and form of the source of the sound, things are better than for smelling... (See DL I 52, 53).

2. Concerning the maximum speed in nature held by photons, which indeed is not additive to velocities of material bodies: If it was not so, and material bodies had velocities with speeds greater than photon speeds, which could moreover be added to the vector speeds i.e. velocities of photons, then the following would happen: Material objects moving away from us could never be visible for us, it would be like they do not exist in our universe or they would be considered dark. If instead they approached us faster than the images (photons), unexpected "meetings" would occur and we would live in a preposterous world i.e. a world that is dominated by visual-material inverse priority.

Epicurus and mathematicsIt has been said by his taunts that he did not know mathematics.But first of all the way he refers to the infinite and infinitesimal shows that he has a deep knowledge of the limit or accumulation point as a mathematical concept. The limit, together with the continuity, is the key concept for the Infinitesimal-, the Integral- and generally the Differential Calculus (the Mathematical Analysis). Epicurus speaks about the infinite and the infinitesimal (e.g. LtH 42) and contrasts those concepts to the indivisible entities of atoms (LtH 40, 41 etc.).We must always keep in mind that the way Epicurus imagines nature is quantum theoretic (LtH 56, 57, etc.). The material objects cannot be divided indefinitely because then we would end up in non-being. They possess body (δέμας) however small it may be. So Epicurus abandons the continuity which is a fundamental concept for the Classical Physics and the mathematics describing it. The bodies, either composed of crystalline or amorphous or mixed structures, do not consist of innumerable point scale parts, but of some quantum like (δεματικής υπόστασης) indivisible particles. If we take a typical representative crystalline cell which builds up the total lattice of a crystal with its periodic repetition, we see that it consists of some atoms that vibrate holding some positions. The difference of the amorphous material versus the crystalline is that unlike what happens in the crystalline, in the amorphous neither the atoms nor their positions are at a uniform periodicity in the body, but are constellations of atoms apart from each other without periodicity.The crystalline cell of NaCl (table salt) for examble is of the type FCC (Face Centered Cubic). Similar things happen with other crystalline forms. Such a crystal cube differs from its geometric (stereometric) counterpart in that it does not consist of an infinite number of points, but only of some atoms possessing some positions and vacuum, a lot of vacuum35. This quantum structure is a prerequisite for the stability of matter and the world around us. This was proclaimed by Epicurus, Democritus and other

hearing, its mechanism is relevant to the mechanism of vision. For this reason we have a stereophonic hearing using two ears apart from its other, as we have stereoscopic binocular vision using two eyes also apart from its other, while our nostrils been very close to each other terminate in a common tube See DL I 52, 53.35 The reason I use the expression "holding some positions" rather than the expression "located in certain positions," is that in quantum physics, unlike what is accepted in classic physics, an atom can not be located exactly in a position (point) but there is probability for it to be there.

  

Atomic Philosophers. It was one of the truths concealed by Christian obscurantism and it took 22 centuries to reclaim it.

Schematic representation of the structure of a crystalline cell of table salt NaCl

Photography of Titanic Strontium crystal surface magnified by electron microscope, showing the atomic structure of the Titanic Strontium (SrTiO3). The brightest are

atoms of Strontium and the darker of titanium, oxygen atoms are not shown.

Schematic crystal structure of Titanic Strontium (SrTiO3) showing as red beads oxygen anions (O2-), which because of their small size do not appear in the image of microscope. The blue beads are titanium cations (Ti4 +) and green strontium cations

(Sr2+)

As stated in the relevant section, the reasoning Epicurus employs to confirm his view that there is a finite number of types of atoms, and also a finite number of atoms in a finitely extended body, penetrates deep into the concepts of Mathematical Analysis, namely, two fundamental theorems: the Bolzano-Weirstrass theorem and the equivalent to this Heine-Borel’s lemma36, which are cornerstones in Infinitesimal and Differential Calculus.So much for those who believe that Epicurus did not possess mathematical skills!Epicurus touches these concepts, which are fundamental for establishing the status of continuity of functions examined by Mathematical Analysis, because continuity constitutes a prerequisite for the differentiability and inerrability of the functions. But, I repeat, Epicurus is not interested in the continuity, because the object of his research: the atoms and the multitude of them in the bodies or the number of their species are not innumerable. He refers to the concept of continuity to validate the non continuous quantum structure of the atoms and the material bodies composed of them.

36 See Murray R. Spiegel, Advanced Calculus, Schaum Publishing Co, New York, pp. 5, 11-12, 42-43, 50, and 102. The subject is taught in depth at PhD courses in mathematics. See e.g. Walter Rudin, Principles of Mathematical Analysis, and McGraw-Hill. Mats Neymark, Analysens grunder, Studentlitteratur, Lund 1970.

He uses the concepts that describe continuity to consolidate the opposite of it, the discontinuity (discreteness) and quantum structure of matter. Incidentally I would like to mention that these mathematics were invented and used by classical physicists (Newton, Leibniz and others)37, who supported in their reasoning the wrong assumption of infinitesimal structure and continuity of matter in contrast to quantum reality underlying matter and nature. I do not claim that mathematical analysis is not useful for quantum physics; on the contrary, is not only useful but necessary. For example, Hamilton’s operator, the Hermitian operator, or the tensors of Absolute Differential Calculus and many others, are ideal mathematical tools for quantum physics.

Epicurus and DemocritusThe mockers of Epicurus (Cicero, etc.), said that he stole the theories of Democritus but he did not understand the stolen material and destroyed it.Let's look if these taunts are accurate and have not become a boomerang for the mockers.In principle, to accept a theory and extend it, is entirely legitimate, this way science evolves and develops.Epicurus admits that Democritus is a correct thinking philosopher (Diogenes Oenoanda excerpt 6 verse 2) and accepts his atomic theory. But he expresses some views that differ from those of Democritus. Concerning the view of Democritus that atoms "are infinite in size and number"38, he has objections, sound objections, resulting from his clear, consistent logic. He accepts that atoms are infinite in number (innumerable), but claims that the atoms can not be infinite (innumerable) with respect to size. According to Epicurus atoms have three properties: shape, weight (mass) and size (volume) characterizing by their combinations, all the kinds of atoms. Also Epicurus states that complex substances have completely different properties from the atoms (elements) composing them. Aristotle says that according to Democritus, the atoms had three differentiating properties: they were different in shape, location and order (class)39.

37 Newton and Leibniz, in their efforts to describe natural phenomena in mathematical terms, simultaneously and independently of each other, invented Differential Calculus. These efforts are reflected in the title of the work of Newton, “Philosophiae Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy)38 D. Laertius Βίος Δημόκριτου Θ κεφ. ζ 4439 Aristotle, in his second reference on the subject , (Metaphysics VIII [1042 β 11-15]) makes the following statement: “Δημόκριτος μεν ουν τρεις διαφοράς έοικεν οιομένω είναι το μεν γαρ υποκείμενον σώμα, την ύλην, εν και ταυτόν, διαφέρειν δε ή ρυσμώ, ο εστί σχήμα, ή τροπή, ο εστί θέσις, ή διαθιγή, ο εστί τάξις”. In the translation of Perseus: “Now Democritus4 apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement”. My translation: “Now Democritus states that there are three differences, the bodies and the material being the same thing, (the bodies are expressions of matter) and the bodies under consideration are different either in ρυσμώ, that is shape, or in τροπή, that is position, or in διαθιγή, that is order of attachment.

In his first reference, Aristotle (Metaphysics I [985β 4-19]) expresses the following: “Λεύκιππος δε και ο εταίρος αυτού Δημόκριτος στοιχεία μεν το πλήρες και το κενόν είναι φασί, λέγοντες το μεν ον το δε μη ον, τούτων δε το μεν πλήρες και στερεόν το ον, το δε κενόν το μη ον (διό και ουθέν μάλλον το ον του μη όντος είναι φασιν, ότι ουδέ του κενού το σώμα), αίτια δε των όντων ταύτα ως ύλην. και καθάπερ οι εν ποιούντες την υποκειμένην ουσίαν τ’ άλλα τοις πάθεσιν αυτής γεννώσι, το μανόν και το πυκνόν αρχάς τιθέμενοι των παθημάτων, τον αυτόν τρόπον και ούτοι τας διαφοράς αιτίας των άλλων είναι φασιν. ταύτας μέντοι τρεις είναι λέγουσι, σχήμα τε και τάξιν και θέσιν: διαφέρειν γάρ φασι το ον ρυσμώ και διαθιγή και τροπή μόνον: τούτων δε ο μεν ρυσμός σχήμα εστίν η δε διαθιγή τάξις η δε τροπή θέσις: διαφέρει γαρ το μεν Α του Ν σχήματι το

In modern theory, atoms and subatomic particles apart from shape, mass and volume have many other properties that characterize matter in atomic and particle form. It is also well (trivially) known in modern chemistry that "the reaction products have different properties from the reagents" and that "the macroscopic properties of composite substances have no relation to the properties of the atoms who make them up" in full compliance with Epicurus (LtH 54-57).When Democritus states that "the atoms are innumerable with respect to size", he becomes unable to defend his own theory by setting limits for a maximum and a minimum size, as opposed to Epicurus who cares to do so and can do so (LtH 39, but mainly at 55, 56 and forward).We could literally take the statement of Democritus and accept infinitesimally small atoms, which contradicts the very definition of the atoms. We could also accept infinitely large atoms, such as to be equal in size to the universe itself (κοσμιαίες, big as Cosmos, as Stobaeus notes)40 in which, by a priori assumption, they are deemed to be included. We could also, by literally following Democritus, accept the existence of atoms of such magnitude, between zero and infinity, to be visible to us, something that does not seems to happen, as Epicurus says, criticizing Democritus: «…έδει και προς ημάς ορατάς ατόμους, ο ου θεωρείται γινόμενον, ουθ όπως αν γένοιτο ορατή άτομος εστίν επινοήσαι» (LtH 56). “In such case we accept visible atoms, something that does not happen, and it is not possible to invent visible atoms in our minds”.But even if Democritus restricted the innumerable sizes of atoms in a limited (bounded) region of small, invisible to the naked eye sizes, again he would have had a problem. Because then, he would have had the case of a bounded infinite set of sizes (bounded infinite set) which by the theorem of Bolzano-Weirstrass has at least one limit point, that is a point of accumulation (accumulation or cluster point). At this point (more accurately: in the vicinity of this point) innumerable sizes (types) of atoms would be accumulated, and would not be distinct from each other, and the atom theory which requires distinctiveness, again would collapse.

δε ΑΝ του ΝΑ τάξει το δε Ζ του Η θέσει. περί δε κινήσεως, όθεν ή πώς υπάρξει τοις ούσι”. In the translation of Perseus: Leucippus, 3 however, and his disciple Democritus4 hold that the elements are the Full and the Void—calling the one "what is" and the other "what is not". Of these they identify the full or solid with "what is," and the void or rare with "what is not" (hence they hold that what is not is no less real than what is,5 because Void is as real as Body); and they say that these are the material causes of things. And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the "differences"6 are the causes of everything else. These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination.7 (Of these: contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from H8 in position. As for motion, whence and how it arises in things, [20] they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

From this report of Aristotle seems that while the A and N are atoms with the modern sense, the AN and AN are compositions of atoms, i.e. molecules, and indeed isomers. Democritus in other words, has introduced the concept of Chemical Isomerism, but not only this, he also presented the first clue to the meaning of Biochemical Coding: because if we expand the number of digits in four and replace the A and N with A, G, C and T that is the initials of the bases Adenine, Guanine, Cytosine and Thymine, then we can with iterative selection of the pairs AT or TA and GC or CG in a codifying way, manufacture the double helix of DNA. Epicurus, who certainly knew this correct view of Leucippus and Democritus, probably accepted it, since there are not known to us some objections from him.

40 Johannes Stobaeus: Εκλογαί φυσικαί. K. Marx "The difference of Democritean and Epicurean natural philosophy", publisher «Γνώση», page 99.

On the contrary, Epicurus solves the problem, by accepting a finite number of sizes (species) of atoms. In fact in his proof, he uses reasoning that its similarity or rather its reverse correlation with the reasoning of the Bolzano-Weirstrass theorem, and the equivalent to that, Heine-Borel's lemma, is really astonishing. (LtH 58, 59 and 60).I repeat that Epicurus, for the removal of all inconsistencies and unreasonable conclusions, in order to ensure the distinctness and the quantum status of atoms, accepts finite number of types of atoms, a view that has been triumphantly confirmed today by Chemistry and Particle Physics.

Another issue on which Epicurus disagrees with Democritus (Diogenes of Oenoanda excerpt 54 verses 2 and 3) is the subject «τυχαία παρέγκλισις» of random swerve, a "δόξα" i.e. an opinion of Epicurus that is also triumphantly confirmed by Quantum Physics and Theory of Chaos.

Epicurus and dialecticEpicurus deplores the dialectic and insists that for the physicists in order to proceed in their research, it is sufficient to accurately define things (DL Life of Epicurus 31).We must not forget that dialectic, namely finding the "truth" through dialogue, was at the time of Epicurus, a method of the sophists and somehow was identified to sophistry. The sophists were the lawyers of the time and speculated as such. The "ability" of the sophists, to turn white into black through dialectic, was known to all. In his dialogues Plato uses the dialectic method, "He is the first in fact who establishes the term, with the adjective dialectical. (Cratylus 390c), and the expressions "dialectical process", "dialectical method", "dialectical reason" (Πολιτεία (State) 532b, 533c, 534b), and considers the dialectic overriding lesson of all the courses ("ώσπερ θριγκός τοις μαθήμασιν η διαλεκτική" State 334e). At the same time Plato accuses the Sophists by giving them the adjective "contentious" wanting to show that they were using arguments in bad faith. The adjective is established and used in the same sense from Aristotle onwards, and always states the "incorrigible sophist" who distorts the truth41. Though Socrates, explicitly asserted his hostility to the Sophists, used their dialectical method. The Socratic paradox «Εν οίδα ότι ουδέν οίδα» "I know one thing that I know nothing" which received the mocking criticism of Epicureans, is a product of dialectics.The method of Epicurus did not allow dialectical tricks and games. Epicurus used thorough and careful observation as well as logical consistency to interpret the phenomena of the natural world, without arbitrary obsessions and conjuring sophisms, and without the non existing divine intervention, just as modern scientists do. Finally I must mention that the dialectic of the Sophists and Socrates is not the dialectic of Hegel and Marx, which tries to interpret the evolution by following the path: statement – counter statement – composition of statements (thesis

41 Aristotle mentions the pre-Socratic (Eleatic) Philosopher Zeno as "finder of dialectic", while admitting that the teacher of Zeno, Parmenides, was not "inexperienced", i.e. unrelated to the dialectics (Aristotle, Quotes, Sophist). Source: Magazine "UTOPIA", September-October 2005, Article written by Kiki Alatzoglou-Themelis

– antithesis – synthesis). The dialectic of the Sophists, rejected by Epicurus, reminiscences, as I previously said, of greek lawyers’ tricks for the distortion of the truth. Anyone who wants to experience its modern version has only to attend oral arguments of greek lawyers lying in the courts.

The criteria of Truth according EpicurusThe Epicurean criteria of truth are the following:1) The senses (αισθήσεις) that provide experience2) The concepts (προλήψεις), constituting confirmed (scientific) knowledge through rational criticism and processing of experiences by the mind. But apart from the concepts, their existence is owed to the senses, with some help and critical reasoning of the mind, the emotions (επαισθήματα) and conclusive reasoning (επίνοιες) (DL Life Epicurus 32, 33)3) Passions or experiences (πάθη) are the third criterion of truth. Epicurus separates passions into two categories: the unpleasant and pleasant, we could also call them painful and calming or afflictive and hedonistic (DL Life of Epicurus 34). Through the passions, man and animals, by their choice (αίρεσιν) or avoidance (φυγήν), manage to improve and lengthen their life, contributing to the conservation of the species. Passions guide the actions we should do or omit as living beings for better and longer life42. Under this reasoning, passions are critical experiential unforgettable truths (α-λήθειες), essentially utilitarian criteria of truth, which if were not experienced or forgotten i.e. if they were not an-oblivious (α-ληθή), our existence would have difficulties or could not be possible.

Confirmation of the existence of atomsThose who have been in a dark room, in which strong light shines through a split , will have noticed that the airborne particles are illuminated and can be seen. They perform a random motion with frequent changes of direction. This is described by Lucretius as a confirmation of the existence of atoms, which like small invisible spheres (billiard balls) move at different speeds in various directions, hitting (αντικόπτουν) the much larger than themselves visible particles, randomly changing their direction. According to Lucretius (who refers to the description of Epicurus), this is a presumption for the existence of the invisible atoms to the naked eye 43. Indeed this phenomenon is the only evidence for the existence of atoms, entities of microcosm, which can be done with the naked eye without experimental instruments.You can find this description in most of the modern physics school textbooks under the title “Brawn Movement”. I ask, perhaps out of respect to the first who described it, should it not be called “Epicurus - Lucretius Movement”?

42 See relevant sections for the functional significance of pain. See also relevant to the topic pertinent footnotes in the doctoral thesis of Marx.43 DRN, book II, 112-124

Example of Brown’s motion (random walk) in two dimensions.

Equivelocital movement of bodies in empty space.Epicurus stated that the bodies fall in vacuum equivelocitaly (ισοταχώς) irrespectively of their weight44. Despite of the fact that he had not formed a theoretical view of the Earth's gravitational field, he made this proposal from having personal experience of this field, as we all have. The same proposal was made by Galileo 19 centuries later. It is even said that Galileo did his experiments on the Leaning Tower of Pisa to prove it experimentally. Today few know that the first who pointed this out was Epicurus and not Galileo.I must add a comment to the above :In the text of the previous paragraph I avoided to talk about natural law and said that "stated or made the proposal." The reason is that when we talk about objects falling on Earth or attracted by the Earth, such as those examined by Epicurus and Galileo, we should bear in mind two restrictions: 1st that the falling objects should be considered at the same place, and 2nd that the mass of the objects is very small compared to the mass of the Earth and further that there is not a huge difference between their masses. The first restriction is because the Earth's gravitational field is not homogeneous but changes from place to place according to the latitude and the second because a body which is too heavy will "add" its gravitational field to the Earth's own gravitational field, e.g. we can not do the experiment by "throwing" the Moon from the top of the Tower of Pisa, because only the fact that we bring it close to Earth, its gravity will turn everything into Earth Midian.The law of Universal Gravitational Attraction exists and states: Every body with mass generates gravitational field proportional to the size of the mass, the field weakens as we travel away from the body proportional to the square of the distance from the body's center of mass . The configuration of the global gravitational field at a given time depends on the distribution of mass in the universe. This is valid taking into account the theory of classical physics in which by instantaneous interaction, one end of the universe knows what mass distribution is at the other end. But because there is no instantaneous interaction, classical physics can not be true. Instead the theory of special or general relativistic physics is valid, where the special takes account of the slowness of interaction and the general the bending of space-time, by dramatically changing the world and the view we could have for it.But what is a field?Consider for example what happens with gravity. We said that every mass exerts around it, the effect to attract any other mass. We also said that the attraction exerted is proportional to the size of the mass, and inversely proportional to the square of the distance separating the mass which exerts attraction on the mass pulled. It is obvious

44 LtH 43 (…του κενού την είξιν ομοίαν παρεχομένου και τη κουφοτάτη και τη βαρυτάτη) the void allows the same propagation to the lightest and to the heaviest atom , and in 61, although there, the reference of Epicurus to the lightest atoms of idols i.e. the photons, but also to atoms who make up the bodies and have mass, causes confusion.

that the pulled mass do the same. We can consider the attraction as a force exerted every moment of time in each space point (we can unify the one-dimensional time and three-dimensional space to "fix" the four-dimensional space-time and talk about points in the four-dimensional space-time). If you represent the force of attraction at each such point with an arrow whose direction and length will represent the direction and the magnitude of the pulling force, we can say that the picture created represents the gravitational field created by the concrete mass under consideration. Such arrows in the language of mathematics are called vectors and the set of points in space-time that these vectors form, is called vector field. The gravitational field is such a vector field. Another vector field is the electric field. In analogy with the attraction between the masses, the electrical charges attract or repel each other (here there is a difference) . If they have different polarity they are attracted, if they have the same polarity they repel each other. The interaction between charges evolves into a vector field, the electric field. Matter, having mass and charge, causes with its distribution in space-time two fields the gravitational and the electric. (Actually electromagnetic field because moving charges generate magnetic field).The fields for the same type of interaction (interaction between identical physical quantities) can be added vectorially and give a composite common field. But if in the same space-time, interactions of different type are acting , they can coexist in the same region of space-time, without directly affecting and altering each other45. Consequently the fields expressing them coexist without being added to one another. But the fields indirectly affect each other through matter; because matter, having mass and charge, with its distribution in space-time, interacts and affects both fields simultaneously. We can extend our reasoning beyond the gravitational and electromagnetic to the rest of interactions, i.e. the strong, the weak, the super strong and super weak interaction.Physicists seek a deeper, more fundamental interaction, were all known interactions are its different manifestations. This search for the unification of all four (or six) known interactions and corresponding fields, has taken the pompous name Grand Unifying Theory. Some overall consolidation has not happened so far.

Lightning consist of pure electricity for which the ancients had no developed theory

Electric field lines around two charged particles.In the left figure the particles have the same charge, in the right they have opposite

charge.

45 In this property, that is the coexistence of fields in the same region of space-time with no direct influence between them but only through matter, was based the Millikan experiment which first established the fundamental electric charge, i.e. the charge of the electron

The ancient Greeks knew that all bodies are pulled downwards. They knew in other words the gravitational attraction of Earth. But they did not know however, that this attraction is a global interaction, which keeps the Earth in orbit around the Sun, the Moon around the Earth and so on. They did not know that all celestial bodies (the meteors) are held in their orbits due to the interaction of gravity, and serious philosophers like Plato and Aristotle thought that they were moved by divine powers. They did not know Newton's law of Universal Gravitation. However Epicurus did not cease to tout, that there are no gods behind the movement of meteors and that this movement, like any function in the universe, is due to the Laws of Nature.

The heliocentric system of Aristarchus and the modern viewThe force of gravity keeps the planets in orbit around the sun.

(The picture is not to scale)

The ancient Greeks of the four (or six) interactions, knew only the interaction of gravity, and that only in a limited area on the Earth's surface or slightly above the Earth. The observations they have made for the discharging of electrified fish and the attraction or repulsion of amber and magnets, were isolated observations, they did not manage to integrate them into a wider physical philosophic context. They did not manage to develop a theory46 for the electromagnetic interaction and the relationship it has with light.Note: Although our senses operate all under the rules of the electromagnetic interaction, although everything we feel: see, hear, touch, taste and smell is perceived by electromagnetic signals coming into the brain, although even the sense of balance (the top and bottom) associated with gravity, is perceived by the brain via electromagnetic signals, and although even pain and pleasure are felt electromagnetically, the theory of electromagnetism was developed relatively recently with the work of J.C.F. Gauss, M. Faraday, A.M. Ampère and others, to be summarized by J.C. Maxwell in four equations, magnificent in their simplicity, which even though formulated before the Theory of Relativity, are fully compatible with it.

46 The Greeks did not have time to develop electromagnetic theory for the same reason they did not managed to develop technology, though they were on the verge of doing so. The reason for that was the stop of the continuation of their civilisation: the Roman conquest and the subsequent obscurantist storm of Christianity which eventually destroyed most of this civilization and brought the Dark Ages.