Revealing the Foundations of the Universe: The Presocratics Establish Modern Physics

Who were the Presocratics? They were a group of philosophers who did most of their work between 600 B.C. and 400 B.C., give or take a few decades. They did not all live in the same place; they were separated by hundreds of miles, at a time when travel and communication were much slower than they are now.

They did not all know each other, and they certainly did not all agree on many topics. They are divided into a number of different subgroups.

Yet they are all categorized together, and for good reasons. Yes, it’s true that they all — or most of them — did their work prior to the famous career of Socrates. But there is a better reason for lumping them all together. It’s the way they thought — the way they reasoned. Even when they came to different conclusions, they were using similar methods.

Donald Palmer explains that “the thinkers who were active in Greece between” 600 B.C. and 350 B.C. “are known today as the pre-Socratic philosophers, even though the last group so designated were actually contemporaries of Socrates.” Those dates are, of course, approximate, because these kinds of trends fade into, and out of, existence in a gradual way.

While the beginning and ending of a construct like the Presocratic era is fuzzy, the life of Socrates had definite beginning and ending points. Socrates was born in 469 B.C. and died in 399 B.C.

Donald Palmer explains some common threads among the diverse group: “What all the pre-Socratic philosophers have in common is their attempt to create general theories of the cosmos (kosmos is the Greek term for “world”) not simply by repeating the tales of” what happened, but rather explaining why and how it happened.

The Presocratics thought that myths — even when they are true — are not sufficient explanations. A myth is an explanation by means of narrative. A myth can be true or false. In slang and casual speech, ‘myth’ is sometimes used to refer to a falsehood, but that is not its meaning in philosophical discourse. The Presocratics pointed out that, if a conceptual explanation was given in addition to a myth, then the net amount of knowledge and understanding would be greater.

For example: a person might ask about how the first men arrived on the moon and walked around on it. A mythological answer would talk about Wernher von Braun and Neil Armstrong and the Apollo spacecraft, etc.. That myth would be true as far as it went, but it lacks some information.

A conceptual answer would talk about the forces of gravity, how much acceleration a spacecraft needs to reach a certain speed, what the escape velocity is for earth orbit, etc.

The Presocratics wanted to explain physical phenomena, not by giving a narrative, “but by using observation and reason to construct general theories that would explain to the” rational “and curious mind the secrets behind the appearances in the world.” A conceptual answer articulates principles which can be applied beyond the case in question. A mythological answer, even when it’s true, is usually limited to a concrete and specific instance.

Another commonality was that all the pre-Socratic philosophers stemmed from the outlying borders of the Greek world: islands in the Ionian Sea or Greek colonies in Italy or along the coast of Persia (in today’s Turkey).

Some scholars speculate that social life on the edges of the Greek Empire was more interesting than life back home on the Greek mainland, and that this circumstance occasioned the birth of philosophy. This is an interesting hypothesis, with plausible arguments both for and against it.

In any case, “knowledge of these thinkers is tremendously important not only for understanding the Greek world of their time, but” for gaining insights into modern physics, modern mathematics, and modern philosophy. Of course, one must also define when the modern era begins.

One of the reasons that the study of the Presocratics is good “for grasping the origins of” most subsequent “philosophy and science” is that they developed a concept of matter. One might look at different objects: a tree, an iceberg, a distant planet.

Those objects seem dissimilar to one another, but the Presocratics saw that they were all physical objects, and that there is some underlying commonality shared by all physical objects. They are all composed of matter. This is an abstraction. Abstraction is important in philosophy, in physics, and in all rational thought.

The Latin words from which the word ‘abstract’ arises mean to “pull away” or to “take off.” In abstraction, the thinker “pulls away” a concept or a principle from the specific instance in which she or he finds it. Having separated the concept from the context, she or he can then apply that concept elsewhere — or everywhere.

The Presocratics developed a way of understanding the universe which was systematic and unified. Their understanding revealed an underlying structure to reality which made modern physics possible. This understanding included that reality is intelligible, i.e., that it can be understood; that some laws of nature are universal, i.e., they apply everywhere and everywhen; and that certain elements of logic and mathematics are the foundations of the universe.

Topics in Early Greek Philosophy: The Presocratics Explore New Disciplines

Before Siddhartha formulated his thoughts in India, and before Confucius in China, the first philosophers lived and worked in Greek territories and colonies. Thales, who is reasonably cited as the world’s first philosopher, did his work around 600 B.C.

What constitutes philosophy? What was it that the Greeks did to qualify as the inventors of philosophy? Donald Palmer writes that “early Greek philosophers reframed the perennial puzzles about reality in such a way as to emphasize the workings of nature rather than the” dramatic explanatory power of a narrative. In other words, the Greek found a new way to explain things. In addition to myth, the Greeks began to formulate conceptual explanations.

Mythical explanations are narratives; in this sense of ‘myth,’ it’s important to remember that there are “true myths.” This is in contrast to the colloquial or informal use of ‘myth’ as a synonym for ‘falsehood.’

So the birth of philosophy among Greeks is, in part, about the “how” of explanations — aside from whether those explanations are true or accurate.

Not only did the Greeks arguably invent philosophy, they also created many of the various subtopics within philosophy. Donald Palmer identifies some of these specific subdisciplines:

This new direction represents the beginnings of a way of thinking that the Greeks would soon call “philosophy” — the love of wisdom. We can discern in these early efforts what we now take to be the main fields of the discipline that we too call philosophy: ontology (theory of being); epistemology (theory of knowledge); axiology (theory of value), which includes ethics, or moral philosophy (theory of right behavior), and aesthetics (theory of beauty, or theory of art); and logic (theory of correct inference).

One particular subtopic, cosmology, fascinated many of the earliest philosophers, including Thales, Anaximander, and Anaximenes. Cosmology asks about the foundational principles of the universe: What constitutes the universe? What keeps the universe in existence? What are the underlying essential components of the universe?

Donald Palmer remarks about these earliest philosophers:

They tended to demote cosmogony (theories about the origins of the world) and promote cosmology (theories about the nature of the world).

In addition to getting credit for inventing philosophy, the Greeks can plausibly get credit for inventing the natural sciences. To be sure, early Babylonians, Egyptians, and Persians made some interesting astronomical observations. In order to give the Greeks the honor of inventing the natural sciences, a clear boundary between the mere collection of observational data and scientific reasoning would be necessary.

“In fact, the theories put forth in ancient Greece could be called the origins of” modern science and mathematics “with as much justification as they can be called the origins of” philosophy “even though at that early period no such distinctions could be made.” Among ancient thinkers, there was no sharp separation between philosophy and the natural sciences.

Even today, there are ambiguous areas of overlap between mathematics, philosophy, and physics.

Among the Presocratics, thinkers like Zeno of Elea are still cited today in university departments of physics and mathematics. Zeno wrestled with concepts of time, space, and infinity — and wrestled with them in a way which kept his musings relevant for 2,000 years.

Other presocratics, primarily the Milesians, worked out a relationship between density, heat, and motion — anticipating the physicist Robert Brown by two millennia. The Milesians were the philosophers who lived in or near the city of Miletus: Thales, Anaximander, and Anaximenes.

Roughly, I would say that science deals with problems that can be addressed experimentally by subsuming the observable events that puzzle us under the dominion of natural laws and by showing how these laws are related causally to those events. Philosophy, on the other hand, deals with problems that require a speculative rather than an experimental approach. Such problems often require conceptual analysis (the logical scrutiny of general ideas) rather than observation or data gathering.

Before the birth of Socrates, around 470 B.C., these earliest philosophers had invented philosophy, invented most of its subdisciplines, and laid the foundations of modern physics and modern mathematics.

Greek Beginnings: The Origin of the Word ‘Philosophy’

While debatable, it is convenient to take the Ionian philosophers on the west coast of Turkey, formerly known as Asia Minor or Anatolia, as the first philosophers. Certainly, the Greeks dominated philosophy for its first few centuries: There was little philosophical activity outside of the Greek lands, so philosophy was not only predominantly Greek during these years, but exclusively so.

So it was that the word ‘philosophy’ arose out of the Greek language. ‘Sophia’ is a Greek word for wisdom, and ‘Philo’ is a Greek word for love. Philosophy is etymologically the love of wisdom, as Donald Palmer writes:

The Greek word “Logos” is the source of the English word “logic” as well as all the “logies” in terms like “biology,” “sociology,” and “psychology,” where “logos” means the theory, or study, or rationalization of something. “Logos” also means “word” in Greek.

Reasoning is impossible without words. “Logos” can mean “word,” but it can also mean reasoning or any ongoing interactive linguistic activity, “so it involves the act of” writing, “or setting forth an idea in a clear manner.” Philosophy is impossible without language, and without writing, only simplistic reasoning is possible. Complex trains of thought require writing.

But there are complications to this simple story about how the word ‘philosophy’ came to be. The Greek language has at least four words that can be translated into English as ‘love.’ Why was ‘philo’ chosen, instead of another similar word? The Greek language reflected the awareness that there are different types of love. A person might love ice cream, and parents love their children. The same word ‘love’ is used to refer to two different relationships.

Likewise, the word ‘gnosis,’ from which the English word ‘cognition’ arises, could have been used instead of ‘sophia.’

So the simple story about the origins of the word ‘philosophy’ is not so simple after all.

“Logos,” therefore, designates a certain kind of thinking about the world, a kind of logical analysis that places things in the context of reason and explains them with the pure force of thought. Such an intellectual exercise was supposed to lead to wisdom (Sophia) and those who dedicated themselves to Logos were thought of as lovers of wisdom (love = philo), hence as philosophers.

Greek philosophy began around 600 B.C., plus or minus a decade, and Greek philosophers were active until sometime after 100 A.D. There were quiet periods during those centuries when philosophy was inactive, and other periods when it was prolific.

It was in this context that the word “Logos” was applied to Jesus, and to the Hebrew concept of God which Jesus made accessible to larger audiences.

“What was there before philosophy, before Logos? There was Mythos — a certain way of” explaining things by means of narrative, i.e., by telling a story. Used in this way, the word ‘myth’ doesn’t necessarily mean falsehood. Contrary to everyday usage of the word, in philosophy, one can speak of a true myth. Myths tell of “events that caused the world to be as it is now.”

It’s understandable that philosophers would like to get rid of false myths. People like to think that they’re correct, and that what they believe is true.

But if some myths are true, why would philosophers still want to investigate the matter and find another, Logos-based, explanation?

Philosophy was, in part, a drive to develop concept-based explanations, which not only explained why things are the way they are, but explained it in a way which used reason instead of narrative, which used abstractions instead of concrete details.

In some situations, it is possible for myth-based and logos-based explanations to coexist. A true myth can give a specific and historical narrative to explain a certain state of affairs, while philosophy can explain the same state of affairs conceptually.

What Existentialism Might Be: From Kierkegaard to Sartre

The word ‘existentialism’ appears often in writings of the twentieth and twenty-first century. The frequency of its use is one of several reasons for its ambiguity. The word began to be used regularly in the 1920s and 1930s, and its appearances multiplied even more in the postwar decades.

While each author who uses the word seems to be confident about what it means, the kaleidoscope of usages does not allow for a clear meaning. A near-infinite collection of quotations about which authors are, or are not, existentialists would yield a mass of contradictions.

Alasdair MacIntyre writes:

Existentialism is not easily definable. Its protagonists have traced it back to Pascal, to St. Augustine, even to Socrates. It has been alleged in our time to be the doctrine of writers as various as Miguel de Unamuno and Norman Mailer. At first sight, characteristics of the doctrine are almost as various. That two writers both claim to be existentialists does not seem to entail their agreement on any one cardinal point. Consequently, to define existentialism by means of a set of philosophical formulas could be very misleading. Any formula sufficiently broad to embrace all the major existentialist tendencies would necessarily be so general and so vague as to be vacuous, for if we refer to a common emphasis upon, for example, the concreteness of individual human existence, we shall discover that in the case of different philosophers this emphasis is placed in contexts so dissimilar that it is put to quite different and incompatible uses. How then is existentialism to be defined?

Yet MacIntyre bravely ventures forth to attempt some semblance of a definition. Voluntarism is a common theme among those who are frequently labeled as existentialists.

If any single thesis could be said to constitute the doctrine of existentialism, it would be that the possibility of choice is the central fact of human nature. Even the thesis that existence precedes essence often means no more than that people do not have fixed natures that limit or determine their choices, but rather it is their choices that bring whatever nature they have into being. As existentialists develop this thesis, they are involved in at least three separate contentions.

The theme of voluntarism runs through, and loosely connects, the writings of thinkers like Kierkegaard, Dostoyevsky, Ibsen, and Dickens. In each, individuals are seen as making choices, or exhorted to make choices, with the awareness that the choices of individuals are significant.

This aspect of existentialism can perhaps be highlighted by contrasting it with those thinkers who oppose it. In the writings of Marx, Freud, Darwin, and sometimes Nietzsche, there is a certain mechanism or determinism which either denies choice to the individual, or minimizes its significance.

Maybe one could attempt to define existentialism by what it opposes. Marx argues that the individual human is the passive object which the grand forces of history and economics toss about like a cork on the ocean’s waves. Freud hypothesized that an individual’s thoughts and emotions were determined by experiences. Darwin constructed a system which saw choices as issuing from being who is the product of the impersonal forces of chemistry and physics.

Existentialism could be seen as a response to, or reaction against, Marx, Freund, Darwin, and similar thinkers. On the other hand, Kierkegaard, often cited as the father of existentialism, largely predated them.

By contrast, the existentialists would argue that human beings make numerous choices. Even when these choices seem to be dictated by a relatively rigid value system, that value system itself was chosen by the individual. These choices are not determined in any calculable way; therefore, any analogy to chemistry or physics is rejected.

This emphasis on choice is accompanied by a fondness, among at least some existentialist writers, for the words “free” and “freedom.”

Alasdair MacIntyre explains:

The first is that choice is ubiquitous. All my actions imply choices. Even when I do not choose explicitly, as I may not do in the majority of cases, my action bears witness to an implicit choice. The second contention is that although in many of my actions my choices are governed by criteria, the criteria which I employ are themselves chosen, and there are no rational grounds for such choices. The third is that no causal explanation of my actions can be given.

These partial hints about what existentialism might be, or about how the word ‘existentialism’ might be defined, notwithstanding, it remains difficult to answer questions like “Is Martin Heidegger an existentialist?” or “What does existentialism say about the afterlife?”

Existentialism is a construct, not a primary source. As such, it is of secondard concern relative to the actual texts of individual thinkers. Jean-Paul Sartre once famously remarked, “Existentialism? I don't know what that is. My philosophy is a philosophy of existence.”

The best and wisest route for scholarship is to treat each thinker as an individual, and to examine each thinker by means of the close reading of that philosopher’s texts.

Logical Positivism: The Influential if Unloved Innovations of the Vienna Circle

During the first half of the twentieth century, several major philosophical trends shaped the era’s significant thought. One of those movements is known by at least three names: Logical Positivism, Logical Empiricism, the Vienna Circle. These three names are almost synonymous, with only slight differences between them.

The Vienna Circle was a group of philosophers and other thinkers who met on a regular basis, discussing and publishing, in the city of Vienna during the 1920s and 1930s. While Vienna was the location of the earliest and most influential developments within this movement, Berlin and other cities were also important locations for the development of Logical Empiricism.

Movements are by nature ambiguous at their boundaries, and Logical Positivism is no exception. It is impossible to identify precise starting and ending points in time for this movement. It is not always clear which philosophers were part of the movement, and which ones were merely similar to, or associated with, the movement. Despite this vagueness, and despite the fact that movements are always constructs and not specific data points, it is nonetheless meaningful and useful to speak of Logical Positivism.

What is Logical Positivism? A definition or description of the movement would include these points: It is heavily empirical; it is anti-metaphysical; it takes physics and mathematics as paradigmatic for knowledge; it seeks to clarify philosophical questions by analysis of the words and propositions used to formulate those questions; its understanding of language is encapsulated in the slogan “The meaning of a word or sentence is the method of its verification.”

Each point in that definition requires considerable expansion.

Writing in 1969, Herbert Feigl explains:

Logical positivism began to form a fairly definite outlook in philosophy about forty years ago. As is well known, it was primarily the influence of Ludwig Wittgenstein and Rudolf Carnap that initiated the early phase of this — then new and radical — departure from the traditional ways of philosophizing. To be sure, some aspects of logical positivism are derived historically from Hume and Comte; but, in contrast, especially to Mill’s positivism, a new conception of logic (having its origins in Leibniz, Frege, and Russell) was united with the empiricism of Hume, Mach, and the early Einstein.

When Logical Positivism is described as heavily empirical, it means that the movement took observation to be the foundation of most knowledge.

As an anti-metaphysical movement, it considered words and sentences which refer to nonobservable things to be not wrong, but nonsensical. Thus the movement would consider a discussion of the mind, as separate from the brain, to be nonsense.

Because it takes physics and mathematics as paradigmatic for knowledge, it tends to favor what is quantifiable and measurable in observation. It looks to mathematics, and mathematical logic, to provide a framework in which observations can be organized.

The group sought to resolve philosophical paradoxes — longstanding questions, riddles, mysteries — by analyzing the words and sentences which formulated them. The Logical Positivists thought that many problems which had puzzled philosophers for years were the result of poorly-phrased propositions.

The method by which the Logical Positivists hoped to clear up philosophical misunderstandings — or what they took to be misunderstandings — was called “verificationism.” This method looked at a sentence — a proposition — and asked: by which procedure would it be determined whether this sentence is true or false? If such a method were found, then the Logical Positivists asserted that the method is the meaning: The meaning of a sentence is the method of its verification.

Herbert Feigl was a member of the Vienna Circle, and recalls:

The Vienna Circle consisted mainly of scientifically trained philosophers and philosophically interested mathematicians and scientists. Most of the members were tough-minded thinkers, Weltzugewandt (as Hans Hahn put it), ‘this-worldly’ rather than ‘other-worldly.’ They were radically opposed to metaphysical speculation, especially of the a priori and transcendent types. Since the development of the Vienna Circle is by now a familiar chapter in the history of recent philosophy, I propose, after dealing with some of the antimetaphysical doctrines of logical positivism, to concentrate on some of the aspects that are not as well known. I shall refer particularly to the work of Moritz Schlick, the founder and leader of the Vienna Circle. Schlick’s early work anticipated a good deal of what in more precise formulations was later developed by Carnap, Reichenbach, and others. In his Allgemeine Erkenntnislehre (first edition, 1918; second edition, 1925) there were also anticipations of some of the central tenets of Wittgenstein’s Tractatus Logico-Philosophicus. I think it was Schlick’s extremely unassuming character, his great modesty and kindliness, and his deep personal devotion to Wittgenstein that made him forget or suppress the great extent to which his views, independently developed and quite differently stated, already contained very important arguments and conclusions regarding the nature of logical and analytic validity; the semantic explication of the concept of truth; the difference between pure experience (Erleben), acquaintance (Kennen), and genuine knowledge (Erkennen), etc. Indeed, so deeply impressed was Schlick with Wittgenstein’s genius that he attributed to him profound philosophical insights which he had formulated much more lucidly long before he succumbed to Wittgenstein’s almost hypnotic spell.

The methods and assertions of Logical Positivism arose, in part, as reactions against some overly metaphysical trends among other groups of philosophers, like the British Idealists and other neo-Hegelian and post-Hegelian schools of thought. Logical Positivism may have served as a corrective and as a challenge to such idealism.

While there was value in not letting idealism go uninspected, it is also the case that, after the movement’s heyday in the late 1930s, there are few self-proclaimed Logical Positivists among the philosophers of the early twenty-first century.

Categorizing the Pre-Socratics

For a century or two, beginning with the work of Thales, Greek philosophy flourished, and flourished mainly outside of Greece, for philosophy was born primarily in the colonies belonging to Greece, and not in Greece itself. Thales began his work around 600 B.C.; it is impossible to specify a more precise date.

Thales was the first of a large group of pre-Socratic philosophers, scattered across the Mediterranean world and across many decades. This group contained a broad range of methods and views, and influenced nearly all subsequent philosophizing.

It is understandable and predictable that scholars would hope to organize these foundational thinkers into groupings. In the conflict between psychology and philosophy, the human mind naturally tends to look for patterns and categories, even when there might be none.

In the face of any proposed taxonomy of pre-Socratic philosophers, one must ask whether such a classification is valid, and what the evidence for it might be.

Examining what was, at one time, the standard classification of these thinkers, Eduard Zeller explores it and finds it wanting. This accepted classification divided the pre-Socratic philosophers into four groups, the Ionian, the Pythagorean, the Eleatic, and the Sophic. The Ionian and Eleatic groups were named geographically after Ionia and Elea; the Pythagorean group was named after the philosopher Pythagoras; the Sophic group’s name is derived from the Greek word for wisdom.

Man pflegte früher in der vorsokratischen Zeit vier Schulen zu unterscheiden: die ionische, die pythagoreische, die eleatische und die sophistische. Den Charakter und das innere Verhältnis dieser Schulen bestimmte man teils nach dem Umfang, teils nach dem Geist ihrer Untersuchungen.

This commonly-accepted taxonomy of the pre-Socratics grouped them partially with reference to the scope and range of their philosophical topics, and partially with reference to their spirit and way of thinking.

Eduard Zeller argues that identifying certain groups with particular themes — the Ionians with physics, the Pythagoreans with ethics, the Eleatics with dialectics, and the Sophists with the decline of these narrow specialties and rise of a more comprehensive systematic approach — is problematic. It represents a retrojection of the three branches of classical Greek philosophy — ethics, physics, and dialectic — onto an earlier, pre-classical era. An additional anachronism is this interpretation’s reading into the Sophists a desire for a unified systematic philosophy.

Was den Umfang betrifft, so wurde als die unterscheidende Eigentümlichkeit der vorsokratischen Periode die Vereinzelung der drei Zweige bezeichnet, die später in der griechischen Philosophie verknüpft sind: von den Ioniern‚ sagte man, sei die Physik einseitig ausgebildet worden, von den Pythagoreern die Ethik, von den Eleaten die Dialektik, in der Sophistik sehen wir die Entartung und den Untergang dieser einseitigen Richtungen, die mittelbare Vorbereitung einer umfassenderen Wissenschaft.

Although Zeller doesn’t state this explicitly, it is likely that he also discounted the received interpretation of the pre-Socratics into four schools because it relied in part on the accident of geography. To assume that merely being colocated in Ionia meant that the Ionian philosophers together formed a school, or that the same was true of those who happened to be in or near Elea, is a priori questionable. The entire project of organizing groups of philosophers into “schools” smacks rather of the Hellenistic Era, and would therefore constitute a retrojection when applied to the Archaic or Pre-Classical Era.

Zeller further identifies a weakness in the standard taxonomy of the pre-Socratics by noting that not only is the accident of geography taken as the foundation for common approach to philosophy among those who happen to be spatially near each other, but rather also a sort of ethnic identity is given to these schools, inasmuch as the conventional taxonomy termed the Ionian philosophy to be “realistic” and the Dorian philosophy to “idealistic.”

Dieser Unterschied der Richtungen wurde dann weiter mit dem Stammesunterschiede des Ionischen und des Dorischen in Verbindung gebracht; andere legten den letztern ihrer ganzen Betrachtung der älteren Philosophie zugrunde, indem sie aus den Eigentümlichkeiten des ionischen und des dorischen Charakters den philosophischen Gegensatz einer realistischen und einer idealistischen Weltanschauung ableiteten.

In this context, Dorian is taken to refer both to parts of mainland Greece as well as the colonies located in Italy and on the islands near Italy, whereas Ionia refers to the western coast of Turkey (i.e., Asia Minor or Anatolia).

As used here, the words ‘idealistic’ and ‘realistic’ refer to varying emphases. In this sense, ‘idealistic’ philosophy emphasizes thoughts, patterns, and principles, which ‘realistic’ philosophy would emphasize concrete objects and events.

In any case, Zeller is rightly skeptical of a too-tidy pigeonholing of pre-Socratic philosophers into various schools. Such categorizing hides the individual creativity and inventiveness of each of these clever and perceptive thinkers.

Boltzmann on Time: Directionality and Entropic States

The intuitive world of phenomena is generally, if not always, perceived as four-dimensional. The dimension of time differs from the three dimensions of space in that it is directional. One can travel between two spatial points in either order: from A to B, or from B to A.

But between two temporal points, one can, and usually must, travel only in one direction: from earlier to later, and never from later to earlier. How is this distinctive feature of time to be understood?

Ludwig Boltzmann looks to the second law of thermodynamics to understand time’s directionality. He argues that the move from order to disorder does not occur with time, but rather that this move is time, or rather, that it determines the direction of time.

Boltzmann further asks about the implications of time’s directionality. If one can travel through time in only one direction, then is the set of possible events limited or conditioned by this fact? In his words,

Is the apparent irreversibility of all known natural processes consistent with the idea that all natural events are possible without restriction? Is the apparent unidirectionality of time consistent with the infinite extent or cyclic nature of time? He who tries to answer these questions in the affirmative sense must use as a model of the world a system whose temporal variation is determined by equations in which the positive and negative directions of time are equivalent, and by means of which the appearance of irreversibility over long periods of time is explicable by some special assumption. But this is precisely what happens in the atomic view of the world.

The universe, which according Boltzmann is on average in equilibrium, can contain local regions which, apparently spontaneously, move themselves into a state of disequilibrium. His view of the universe is, in part, his gas theories writ large. His conception of the universe could be understood as vaguely analogous to Brownian motion: galaxies vibrating rather randomly and spontaneously.

From this notion of the universe, Boltzmann sees the directionality of time, and perhaps time itself, as arising from pockets of disequilibrium. Time, and its direction, is the flow from a state of more disequilibrium to a state of less disequilibrium.

Boltzmann is, in effect, reversing the priority of the second law of thermodynamics: It is not the case, according to him, that a system moves within time, or through time, from a state of less entropy to a state of more entropy; rather, he seems to be saying that it is the move from one state to another which gives directionality to time, and perhaps even gives rise to time itself.

One can think of the world as a mechanical system of an enormously large number of constituents, and of an immensely long period of time, so that the dimensions of that part containing our own “fixed stars” are minute compared to the extension of the universe; and times that we call eons are likewise minute compared to such a period. Then in the universe, which is in thermal equilibrium throughout and therefore dead, there will occur here and there relatively small regions of the same size as our galaxy (we call them single worlds) which, during the relative short time of eons, fluctuate noticeably from thermal equilibrium, and indeed the state probability in such cases will be equally likely to increase or decrease. For the universe, the two directions of time are indistinguishable, just as in space there is no up or down. However, just as at a particular place on the earth’s surface we call “down” the direction toward the center of the earth, so will a living being in a particular time interval of such a single world distinguish the direction of time toward the less probable state from the opposite direction (the former toward the past, the latter toward the future). By virtue of this terminology, such small isolated regions of the universe will always find themselves “initially” in an improbable state. This method seems to me to be the only way in which one can understand the second law — the heat death of each single world — without a unidirectional change of the entire universe from a definite initial state to a final state.

Boltzmann argues that the direction of time is relative: to call a particular movement through time “forward” is merely a matter of perspective; another observer might call it “backward.” The direction of time is an indexical: to move “toward the future” or “toward the past” is like moving “to the right” or “to the left” — one observer’s “right” is another observer’s “left.”

As Lawrence Sklar has pointed out, Boltzmann even leaves room for the scenario in which different local pockets of disequilibrium might have their own times running in opposite directions. This would be within the larger framework of the universe as a whole, which Boltzmann seems to view as literally timeless, having no time because it is in a state of equilibrium.

Time, then, according to Boltzmann, is secondary, and contingent upon the primary appearance of local pockets of disequilibrium. Boltzmann has some explaining to do: how and why would these local pockets of disequilibrium randomly and spontaneously appear?

Obviously no one would consider such speculations as important discoveries or even — as did the ancient philosophers — as the highest purpose of science. However it is doubtful that one should despise them as completely idle. Who knows whether they may not broaden the horizon of our circle of ideas, and by stimulating thought, advance the understanding of the facts of experience?

On Boltzmann’s account, it could be that a pocket of disequilibrium would appear in the midst of a universe in equilibrium: this would constitute time moving backward, as it were. If that pocket of disequilibrium, in its process of moving toward equilibrium, would halt, that would amount to time standing still. If that process of moving toward equilibrium were subject to occasional relapses in which there was a temporary movement back to disequilibrium, this would amount to time repeatedly changing its direction.

Further, Boltzmann’s view might entail that within the one universe there could be various disparate pockets of disequilibrium, and these sundry pockets could have times which are moving in different directions. Simply put, in one part of the universe, time could move in a direction opposite to the way it’s moving in another part of the universe.

That in nature the transition from a probable to an improbable state does not take place as often as the converse, can be explained by assuming a very improbable initial state of the entire universe surrounding us, in consequence of which an arbitrary system of interacting bodies will in general find itself initially in an improbable state. However, one may object that here and there a transition from a probable to an improbable state must occur and occasionally be observed. To this the cosmological considerations just presented give an answer. From the numerical data on the inconceivably great rareness of transition from a probable to a less probable state in observable dimensions during an observable time, we see that such a process within what we have called an individual world — in particular, our individual world — is so unlikely that its observability is excluded.

Boltzmann’s notion that time is not merely the framework within which the second law of thermodynamics plays out, but rather that the very movement from disequilibrium to equilibrium is itself time, and sets the direction of time, is thought-provoking and worth consideration.

His claim, however, that pockets of disequilibrium might suddenly, spontaneously, and randomly appear within a universe which is in equilibrium is a bold claim, for which he offers no argumentation, the vague analogy to Brownian motion, and other phenomena within physical chemistry notwithstanding.