Tag: theory

Can a Movie Excite an Unexpected Intellectual Adventure?

Consider the political thriller The Eagle Has Landed. There’s a scene where Col. Radl discusses Jung’s concept of synchronicity. For example, a man checking out drops a coin near the register and searches for it momentarily before giving up. Years later, he is at the same store and finds a similar coin. He rationalizes this with a mundane story, not some cosmic notion of fairness.

…Jung was working, in collaboration with Pauli, on his treatise on Synchronicity: An Acausal Connecting Principle, which was published together with Pauli’s essay on Kepler in one volume. This was evidently meant as a symbolic act: one of the greatest physicists of the century joining forces with one of its greatest psychologists. The result was a stimulating exercise in unorthodox speculation, but at the same time sadly disappointing. It did not amount to a theory in the proper sense, but rather to a universal schema, both very bold and very vague.

Jung’s treatise hinges on his concept of “Synchronicity”. He defines it as “the simultaneous occurrence of two meaningfully but not causally connected events”;1 or alternatively as “a coincidence in time of two or more causally unrelated events which have the same or similar meaning2…equal in rank to causality as a principle of explanation”.3 This is an almost verbatim repetition of Kammerer’s definition of “Seriality” as “a recurrence of the same or similar things or events in time or space”—events which, as far as can be ascertained; “are not connected by the same acting cause”. The main difference appears to be that Kammerer emphasises serial happenings in time (though, of course, he includes contemporaneous coincidences in space), whereas Jung’s concept of synchronicity seems to refer only to simultaneous events—although he includes precognitive dreams which occurred sometimes several days before the events. He tried to get around the time paradox by saying that the unconscious mind functions outside of the physical framework of space-time; thus precognitive experiences are “evidently not synchronous but are synchronistic since they are experienced as psychic images in the present as though the objective event already existed”.4 One wonders why Jung created these unnecessary complications by coining a term which implies simultaneity, and then explaining that it does not mean what it means. But this kind of obscurity combined with verbosity runs through much of Jung’s writing.

Although Kammerer’s “Seriality” and Jung’s “Synchronicity” are as similar as a pair of gloves, each fits one hand only. Kammerer confined himself to analogies in naive physical terms, rejecting ESP and mentalistic explanations. Jung went to the opposite extreme and tried to explain all phenomena which could not be accounted for in terms of physical causality, as manifestations of the unconscious mind: “Synchronicity is a phenomenon that seems to be primarily connected with psychic conditions, that is to say with processes in the unconscious.”5 Its deepest strata, according to Jungian terminology, are formed by the “collective unconscious”, potentially shared by all members of the race. The “decisive factors” in the collective unconscious are the archetypes which “constitute its structure”.6 They are, as it were, the distilled memories of the human species, but cannot be represented in verbal terms, only in elusive symbols, shared by all mythologies. They also provide “patterns of behaviour”7 for all human beings in archetypal situations—confrontations with death, danger, love, conflict, etc. In such situations the unconscious archetypes invade consciousness, carrying strong emotions and—owing perhaps to the archetype’s indifference to physical space and time—facilitate the occurrence of “synchronistic” events. The appearance of the scarab while the patient was telling her archetypal dream is considered by Jung as an illustration of this nexus. The same applies to the detonations in Freud’s bookcase during Jung’s visit, indicating the explosive nature of their father-son relationship: “Meaningful coincidences which are to be distinguished from meaningless chance-groupings—therefore seem to rest on an archetypal foundation. At least all the cases in my experience and there is a large number of them—show this characteristic?”8

Elsewhere in the essay he writes:

Synchronistic events rest on the simultaneous occurrence of two different psychic states. One of them is the normal, probable state (i.e., the one that is causally explicable), and the other, the critical experience, is the one that cannot be derived causally from the first. In the case of sudden death, the critical experience cannot be recognised immediately as “extra-sensory perception” but can only be verified as such afterwards. …In all these cases, whether it is a question of spatial or of temporal ESP, we find a simultaneity of the normal or ordinary state with another state or experience which is not causally derivable from it, and whose objective existence can only be verified afterwards. …An unexpected [mental] content which is directly or indirectly connected with some objective external event coincides with the ordinary psychic state: this is what I call synchronicity.”9

  1. Jung (1960), p. 441 [ref]
  2. Jung (1960), p.551 [ref]
  3. Jung (1960), p. 435 [ref]
  4. Jung (1960), p. 445 [ref]
  5. Jung (1960), p. 511 [ref]
  6. Jung (1960), p. 436 [ref]
  7. Jung (1960), p. 438 [ref]
  8. Jung (1960), p. 440 [ref]
  9. Jung (1960), pp. 444-5 [ref]
Arthur Koestler, The Roots of Coincidence, Picador, 1974 (first published by Hutchinson & Co. Ltd., 1972), pgs. 94-97.

Can a movie trigger an unexpected intellectual adventure?

Usually, when considering this question, you might see a film on a specific subject, then perhaps read an article or try to find a book about it.

In his essay on Synchronicity (Jung’s term for meaningful coincidences of events separated in space and/or in time,1 Jung examined some of the beliefs surrounding apparently related incidents which seem to have no causal connection. These incidents could be, for example, the coinciding of a patient’s dream with an actual event corresponding to its occurring at the same time some distance away, it could be ESP phenomena—response to some event that does not become known through any sense; it could be a horoscope reading which corresponds to the observed character of the individual or his self-image, or an astrological prediction which seems to be borne out in subsequent events. The possibility of finding meaning in these correspondences had tantalized Jung for many years. The beginning of his serious study goes back to the days when Albert Einstein was developing his first theory of relativity. During this time he was a guest on several occasions for dinner in Jung’s home. In a letter on Einstein and synchronicity, Jung wrote: “It was Einstein who first started me off thinking about a possible relativity of time as well as space, and their psychic synchronicity.”2

  1. In The Structure and Dynamics of the Psyche, C. W. 8, pp. 417-531. [ref]
  2. Letter to Dr. Selig dated 25 February, 1953, in Spring, 1971, p. 127. [ref]
June Singer, Boundaries of the Soul: The Practice of Jung’s Psychology, Anchor Books edition, 1973, p. 398.

The Eagle Has Landed begins with newsreel footage depicting Mussolini’s rescue by the Germans during the Gran Sasso raid. This probably inspires the plot to abduct Churchill. Come to the present. Did the operation to capture Venezuelan president Nicolás Maduro and his wife, Cilia Flores, stem from this, or is there no causal connection? All of this is the intellectual adventure of Jung’s synchronicity.

We Are Finite. Does This Affect What We Can Know?

§2. What Can We Know?

The theme of this section is that We Are Finite: while our knowledge of the number 3 is intimately associated with experiences of some kind or other of triples of one or another sort, surely nothing like that is the case for our knowledge of the number ω or, for that matter, the number 10101010.

To avoid misunderstanding, let me emphasize that the issue being addressed is not “How can we have knowledge of mathematical objects despite their abstractness?” but rather “How can we have knowledge of infinite mathematical objects despite their huge size and consequent remoteness from experience?” Here is what I mean by remoteness: Not only do we not have experience of infinite mathematical objects, but we do not have any experience of anything suitably like them. The number 2 bears some relation to pairs of objects. The points and lines of Euclidean geometry bear some relation to pencil points and lines. But there does not seem to be anything suitable to play any analogous role for infinite mathematical objects.

Of course infinite mathematical objects are abstract. The issue of remoteness is an addition to that of abstractness. Both are apparent epistemological difficulties caused by the distance of mathematical objects from experience.

But if we divide the problem of the abstract into two parts, the problem of the finite and the problem of the infinite, it becomes clear that the two have quite distinct features.

The problem of the abstract, in Paul Benacerraf’s words, is this [Ben73, p. 409]: “the concept of mathematical truth, as explicated, must fit into an over-all account of knowledge in a way that makes it intelligible how we have the mathematical knowledge that we have. An acceptable semantics for mathematics must fit an acceptable epistemology?” For Benacerraf, an acceptable semantics is a Platonist one, and so his problem is that of the difficulties involved in giving an acceptable account of knowledge of abstract objects. Benacerraf concentrated on a weaker version of the problem: not on accounting for the mathematical knowledge that we have but on accounting for how we can have any mathematical knowledge whatever. “The minimal requirement, then, is that a satisfactory account of mathematical truth must be consistent with the possibility that some such truths be knowable” [Ben73, p. 409]. Philosophers have tended to concentrate on the minimal requirement and to offer up solutions to the problem of the finite to solve it.

Even those skeptical about the existence of any abstract mathematical objects at all want to endorse the truism ‘2 + 2 = 4’ in some way or other that acknowledges that it is better than ‘2 + 2 = 5’ even though they may not grant that it is true. Even without an abstract number 2, one is still faced with explaining the general fact that the members of two nonoverlapping pairs form a quadruple.

Whatever one’s views about mathematical objects, it is necessary to make sense of our counting, computing, and bookkeeping activities. Skepticism about small finite mathematical objects—in particular small natural numbers is just not doubt about the acceptability in some form or other of many of the putative facts about them. Moreover, there are many stories one could tell about a source for genuine knowledge concerning some finite mathematical objects, including, as the most trivial special case, knowledge of their existence. Take, for example, small natural numbers. Various explanations of our knowledge about them might invoke the experience of time, the experience of bunches of physical objects or of patterns exhibited by them, or the sequencing of words in sentences. Other explanations might rely on the exigencies of the construction of theories of the physical world. We are faced with too many ways of accounting for our knowledge of small finite mathematical objects, not too few. For example, Parsons [Par80] showed how to account for such knowledge on the basis of our linguistic capacities, while Maddy [Mad90] showed how to do it on the basis of experiences with medium-sized physical objects.

Benacerraf’s minimal requirement can surely be met with an acceptable solution to the problem of the finite—though I make no claim to know what the actual solution is. That is a question whose answer involves detailed psychological information about how people typically actually acquire knowledge of small finite mathematical objects, and we do not yet have sufficiently detailed information to answer it. Acquisition of the number concept does, however, involve both linguistic components—learning to count aloud—and experience of medium-sized physical objects—counting them using the spoken number sequence. It is therefore likely that the actual solution involves components of both the one proposed by Parsons and the one proposed by Maddy—and probably other components as well.

In sharp contrast to the situation about ‘2 + 2 = 4’, many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice—not only its truth, but its acceptability in any form whatever. General facts about the infinite are not robust in the same way that the facts of counting, computing, and bookkeeping are. Moreover, it is not at all clear what we can fall back on as a source of mathematical knowledge concerning the infinite—what can play the role that bunches and sequences of moments, objects, or words seem so well suited to play for small finite mathematical objects. It is that lack that raises the problem posed by the remoteness of the infinite: it seems that we cannot have grounds to know what we find we actually do know about the infinite.

In Chapter VIII I shall show that as a matter of fact the combinatorial infinite is not remote—it has pretty much the same kinds of ties to experience as do small natural numbers. (That may be a bit misleading see Chapter VIII for a more careful formulation.) That solves the problem of the remoteness of the infinite philosophical problems concerning infinite mathematical objects become just like the familiar ones concerning finite mathematical objects. That is important because the problems concerning finite mathematical objects are not skeptical ones—the genuine doubts about the acceptability of our theory of the infinite are refuted. It also provides the essential missing ingredient for an explanation of the grounds on which mathematicians are entitled to make claims of self-evidence. But before presenting the solution, it is necessary to become clearer on the nature of the problem.

The two Benacerrafian problems—of the finite and the infinite—are both important, and every adequate philosophy of mathematics must be compatible with solutions to them. Nonetheless, the problem of the infinite deserves special emphasis because it is in danger of being lost as the result of the huge amount of attention being devoted to the Benacerrafian problem of the abstract in its simplified guise as the problem of the finite. That loss would be most unfortunate. The problem concerning the infinite was a primary concern of the philosophy of mathematics for many years—as may be seen in the work of Brouwer and that of several philosophers discussed by Benacerraf, such as Hilbert, Gödel, and Quine.

Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 162-165.

You do not doubt that ‘7 – 7 = 0’, but you cannot say ‘∞ – ∞ = 0’. In math lingo, the latter is indeterminate. Does this mean we are incapable of understanding the indeterminate, or is this just the nature of the universe? Consider Eugene Wigner’s lecture, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. He noted, “It is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.”

Still, complete understanding often seems to elude us.

“Fog Everywhere” Continued

[read the previous essay on this topic]

Consider mathematics and the aspect of fog. Nietzsche argued that the world is not knowable to us as a whole. This includes trying to express it with numbers. A recent example is Max Tegmark’s assertion that the universe is not something explained by mathematics; rather, it is itself mathematics. To contrast, Karl Jaspers, summarizing Nietzsche, wrote:

We cannot say what the world as a whole is. It is false to change all processes into a familiar world of our own, and then say: “All is will (everything wills); all is pleasure or pain (everything endures); all is motion (everything flows); all is tone (everything sounds); all is spirit (everything thinks); all is number (everything reckons).” Nietzsche warns us against all notions of the whole: “Let us guard against thinking that the world is a living being…or that the universe is a machine…Let us guard against saying that there are laws of nature…Let us guard against thinking that the world eternally creates novelties.” All these “shadows of God” darken actuality. We are within the world, and the whole of the world is, as a whole, not accessible to us.

Karl Jaspers, Nietzsche: An Introduction to the Understanding of His Philosophical Activity, Henry Regnery Company, 1966, p. 293

Notice in the paragraph quoted above that Nietzsche specifically excludes reducing everything to numbers, in opposition to Tegmark and the simulation hypothesis.

Robert Kanigel describes Srinivasa Ramanujan as “the man who knew infinity” in his biography of the same title, but mathematicians disagree on the ontological status and utility of infinity. The discussion of applying Ramanujan’s sum to arrive at -1/12 is very intricate and complex.

To make things even more puzzling, math students are confronted with the Gaussian integral, with its positive and negative infinities.

You can gain additional insight into infinity with:

Cauchy and Weierstrass had eliminated infinitely small and infinitely great numbers from analysis and replaced them by limits. But the theory of limits that thereby became so central required a clearer theory of the real line, that is to say, a theory of the irrational numbers. And that theory promptly reintroduced the infinite into analysis. The old infinity of infinitesimal and infinite numbers was simply replaced by the new infinity of infinitely large collections.12

In 1831 Carl Friedrich Gauss said [Kli72, p. 994], “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound.” But only 52 years later, we find this in Cantor’s Grundlagen [Can76, p. 75]: “The idea of considering the infinitely large not only in the form of the unlimitedly increasing magnitude and in the closely related form of convergent infinite series…but to also fix it mathematically by numbers in the definite form of the completed infinite was logically forced upon me, almost against my will since it was contrary to traditions which I had come to cherish in the course of many years of scientific effort and investigations.”

12 See Russell’s Principles of Mathematics [Rus03, p. 304] for a related sentiment.

Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 38-39

In 1961, the great Russian physicist George Gamow’s popular math and physics overview was republished to great acclaim among science and math aficionados. Intriguingly titled One, Two, Three…Infinity, the book gives you a hint that the relationship of numbers and integers to the concept of infinity is still intriguing even after the intricate analyses of Cauchy, Weierstrass et al.

Let us conclude by considering Zeno’s dichotomy paradox of motion, in which “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” As the goal is divided into halves, one must complete an infinite number of tasks, which Zeno maintains is an impossibility.

[read the previous essay on this topic]

Is There a Scheme of Things Underlying Everything?

In The Thibaults (the novel sequence for which Roger Martin du Gard won the 1937 Nobel Prize in Literature), a fundamental motif is the question of whether the universe is coherent. Roughly speaking, there are three competing schools of coherence—science, religion and art. Antoine Thibault discusses with the Abbé (French title for abbot):

Antoine did not seem to hear him. “Just think,” he exclaimed, “what it means to a youngster, when he’s turned loose, by gradual stages, on mathematics, physics, chemistry! Suddenly he discovers that he has all space, the universe, for his playground. And after that, religion strikes him as not only cramped, but false, illogical. Untrustworthy.”

Roger Martin du Gard, The Thibaults, translated by Philip Thody & Ellen Kennedy, Bantam Modern Classic Edition, Viking Press, 1968. page 762.

The climax of this debate appears when Antoine says:

“…I talked just now about Universal Order and a Scheme of Things; but that was merely to talk like everyone else. Actually it seems to me that we’ve as many reasons to question the existence of a Scheme of Things as to take it for granted. From his actual viewpoint the human animal I am observes an immense tangle of conflicting forces. But do these forces obey a universal law outside themselves, distinct from them? Or do they, rather, obey—so to speak—internal laws, each atom being a law unto itself, that compels it to work out a kind of ‘personal’ destiny? I see these forces obeying laws which do not control them from outside, but join up with them, which do nothing more than in some way stimulate them.…And anyhow, what a jumble it is, the course of natural phenomena! I’d just as soon believe that causes spring from each other ad infinitum, each cause being the effect of another cause, and each effect the cause of other effects. Why should one want to assume at all costs a Scheme of Things?…”

Roger Martin du Gard, The Thibaults, translated by Philip Thody & Ellen Kennedy, Bantam Modern Classic Edition, Viking Press, 1968. page 768.

The topic of an underlying scheme of things is close to the central question of Western civilization. In Plato’s Republic, we have the allegory of the dark cave occupied by humanity. It looks at shadows dancing on the wall, projected by a fire. Liberating humanity requires leaving the cave and climbing to the surface of the earth, glimpsing the sun for the first time. From here, with the help of philosophy, humanity flies off and encounters the Logos and the Eidos. Mathematical truth crowns this journey.

Aristotle, Plato’s star pupil and later rival, takes this quest and focuses on the biological. The Athenian tradition invents theory, a pillar of Western tradition, culminating in modern science. Jerusalem’s competing tradition, the Judeo-Christian worldview, derives its scheme of things from divinity before biology and mathematics. Thus, the novel’s debate is ultimately the struggle between Athens and Jerusalem.

Monomania and the West

There have been all kinds of “voices” in the history of Western civilization. Perhaps the loudest voice is that of monomaniacs, who always claim that behind the appearance of the many is the one. If we illustrate the West, and at its roots, the intersection of Athens and Jerusalem, we see the origins of this monomania. Plato’s realm of ideas was supposed to explain everything encountered in our daily lives. His main student and rival, Aristotle, has his own competing explanation, based in biology instead of mathematics.

These monomanias in their modern counterpart in ideologies. In communism, the key to have everything is class and the resulting class struggles. Nazism revolves around race and racial conflict.

In our own era, the era of scientism, we have the idea of god replaced with Stephen Hawking’s “mind of god,” Leon Lederman’s The God Particle and KAKU Michio’s The God Equation. In the 2009 film, Angels & Demons, there’s a senior Vatican official, played by Ewan McGregor, who is absolutely outraged by the blasphemous phrase, “the god particle.”

Currently, the monomania impetus continues full-force. For example, Professor Seth Lloyd of MIT tells us that reality is the cosmos and not chaos, because all of reality together is a computer. His MIT colleague, Max Tegmark, argues in his books that the world is not explained by mathematics, but rather is mathematics. Perhaps the climax of this kind of thinking is given to us by the essay “Everything Is Computation” by Joscha Bach:

These days we see a tremendous number of significant scientific news stories, and it’s hard to say which has the highest significance. Climate models indicate that we are past crucial tipping points and irrevocably headed for a new, difficult age for our civilization. Mark van Raamsdonk expands on the work of Brian Swingle and Juan Maldacena and demonstrates how we can abolish the idea of spacetime in favor of a discrete tensor network, thus opening the way for a unified theory of physics. Bruce Conklin, George Church, and others have given us CRISPR/Cas9, a technology that holds promise for simple and ubiquitous gene editing. “Deep learning” starts to tell us how hierarchies of interconnected feature detectors can autonomously form a model of the world, learn to solve problems, and recognize speech, images, and video.

It is perhaps equally important to notice where we lack progress: Sociology fails to teach us how societies work; philosophy seems to have become infertile; the economic sciences seem ill-equipped to inform our economic and fiscal policies; psychology does not encompass the logic of our psyche; and neuroscience tells us where things happen in the brain but largely not what they are.

In my view, the 20th century’s most important addition to understanding the world is not positivist science, computer technology, spaceflight, or the foundational theories of physics.

It is the notion of computation. Computation, at its core, and as informally described as possible, is simple: Every observation yields a set of discernible differences.

These we call information. If the observation corresponds to a system that can change its state, we can describe those state changes. If we identify regularity in those state changes, we are looking at a computational system. If the regularity is completely described, we call this system an algorithm. Once a system can perform conditional state transitions and revisit earlier states, it becomes almost impossible to stop it from performing arbitrary computation. In the infinite case that is, if we allow it to make an unbounded number of state transitions and use unbounded storage for the states—it becomes a Turing machine, or a Lambda calculus, or a Post machine, or one of the many other mutually equivalent formalisms that capture universal computation.

Computational terms rephrase the idea of “causality,” something that philosophers have struggled with for centuries. Causality is the transition from one state in a computational system to the next. They also replace the concept of “mechanism” in mechanistic, or naturalistic, philosophy. Computationalism is the new mechanism, and unlike its predecessor, it is not fraught with misleading intuitions of moving parts.

Computation is different from mathematics. Mathematics turns out to be the domain of formal languages and is mostly undecidable, which is just another word for saying “uncomputable” (since decision making and proving are alternative words for computation, too). All our explorations into mathematics are computational ones, though. To compute means to actually do all the work, to move from one state to the next.

Computation changes our idea of knowledge: Instead of justified true belief, knowledge describes a local minimum in capturing regularities between observables. Knowledge is almost never static but progresses on a gradient through a state space of possible worldviews. We will no longer aspire to teach our children the truth, because, like us, they will never stop changing their minds. We will teach them how to productively change their minds, how to explore the never-ending land of insight.

A growing number of physicists understands that the universe is not mathematical but computational, and physics is in the business of finding an algorithm that can reproduce our observations. The switch from uncomputable mathematical notions (such as continuous space) makes progress possible. Climate science, molecular genetics, and AI are computational sciences. Sociology, psychology, and neuroscience are not: They still seem confused by the apparent dichotomy between mechanism (rigid moving parts) and the objects of their study. They are looking for social, behavioral, chemical, neural regularities, where they should be looking for computational ones.

Everything is computation.

Know This: Today’s Most Interesting and Important Scientific Ideas, Discoveries, and Developments, John Brockman (editor), Harper Perennial, 2017, pages 228-230.

Friedrich Nietzsche rebelled against this type of thinking the most profoundly. If scientism represents the modern, then Nietzsche was the prophet of postmodernism. Nietzsche’s famous phrase, “God is dead.” is not about a creator or divinity, but rather finality itself. There is no final explanation.

Realms and Domains: Levels and Confusion

Are we governed by words or numbers? Martin Heidegger’s star pupil, Hans-Georg Gadamer, points a penetrating flashlight at this question of words vs. numbers when he writes, “It is obvious that not mathematics but the linguistic nature of people is the basis of human civilization.”

According to Gadamer, our primary way of being is interpretative rather than computative. Our fundamental function is to cope, not to theorize. He argues, we can never finally step outside the traditions and practices of our culture. As one critic stated, “the metaphysical aid of a view from nowhere is seen by Gadamer as a questionable illusion that can have damaging consequences for a culture. It is not that scientific methods are mistaken—he thinks that science is involved an unstoppable dynamic which cannot be halted by philosophical or other objections…Gadamer gives a central role to art in questioning the dominance of the methods of the natural sciences. The artwork is not something to be determined by concepts, but something which ‘happens’ via its reception in real social contexts…”

Think about the interaction between words and numbers in the opening of Vladimir Nabokov’s memoir, Speak, Memory:

The cradle rocks above an abyss, and common sense tells us that our existence is but a brief crack of light between two eternities of darkness. Although the two are identical twins, man, as a rule, views the prenatal abyss with more calm than the one he is heading for (at some forty-five hundred heartbeats an hour).

Vladimir Nabokov, Speak, Memory, Vintage Books, 1989, page 19.

Note how Nabokov describes our existence above. Think about the word “eternities”? It brings to mind infinity. For example, in algebra, 1/x goes to infinity as 1 approaches zero. Nabokov also states that man is doing all this infinity-watching which he describes in heartbeats per hour.

Another issue in this realm and domain confusion is provided by Gabriel Marcel, when he writes, “We must carefully avoid all confusion between the mysterious and the unknowable.” Marcel continues:

A problem is something which I meet, which I find complete before me, but which I can therefore lay siege to and reduce. But a mystery is something in which I myself am involved, and it can therefore only be thought of as “a sphere where the distinction between what is in me and what is before me loses its meaning and its initial validity”. A genuine problem is subject to an appropriate technique by the exercise of which it is defined; whereas a mystery, by definition, transcends every conceivable technique. It is, no doubt, always possible (logically and psychologically) to degrade a mystery so as to turn it into a problem. But this is a fundamentally vicious proceeding, whose springs might perhaps be discovered in a kind of corruption of the intelligence. The problem of evil, as the philosophers have called it, supplies us with a particularly instructive example of this degradation.

Just because it is the essence of mystery to be recognized or capable of recognition, it may also be ignored and actively denied. It then becomes reduced to something I have “heard talked about” but which I refuse as only “being for other people”; and that in virtue of an illusion which these “others” are deceived by, but which I myself claim to have detected.

We must carefully avoid all confusion between the mysterious and the unknowable. The unknowable is in fact only the limiting case of the problematic, which cannot be actualized without contradiction. The recognition of mystery, on the contrary, is an essentially positive act of the mind, the supremely positive act in virtue of which all positivity may perhaps be strictly defined. In this sphere everything seems to go on as if I found myself acting on an intuition which I possess without immediately knowing myself to possess it— an intuition which cannot be, strictly speaking, self-conscious and which can grasp itself only through the modes of experience in which its image is reflected, and which it lights up by being thus reflected in them.

Gabriel Marcel, The Mystery of Being, Vol. 1: Reflection & Mystery, Harper Torchbooks, 1965, page 260-261.

A final profound confusion is the body as a physical item vs. a means of expression. Picture Fred Astaire dancing opposite Ginger Rogers. You have both the movements of his dance and what he conveys through body language. In order to dance, you have the biochemical fuel (food) to enable the biomechanical movement of the dance. The courtship expressed through his movements is something different. Marcel describes it thus:

We should recall, at this point, what we said in an earlier lecture about the body; the latter is not merely an instrument, it presents us with a kind of reality which is quite different from the reality of any sort of apparatus, in so far as it, my body, is also my way of being in the world.

Gabriel Marcel, page 257.

See also “Existence and the Problem of Separability”, “Is It Good to Be a Detached Observer?” and “Arguments Without End: A Few Simple Examples” which also reference Marcel.

Education and the Triple Helix underneath It

We want to restate the basic instinct and intuitions of this education or re-education project.

To get at the “schema” it will help you if you digress for a second and absorb this writeup of Professor Richard Lewontin’s (Harvard biology) 2002 masterpiece, The Triple Helix: Gene, Organism and Environment.

The blurb from Harvard University Press tells us:

“One of our most brilliant evolutionary biologists, Richard Lewontin has also been a leading critic of those—scientists and non-scientists alike—who would misuse the science to which he has contributed so much. In The Triple Helix, Lewontin the scientist and Lewontin the critic come together to provide a concise, accessible account of what his work has taught him about biology and about its relevance to human affairs. In the process, he exposes some of the common and troubling misconceptions that misdirect and stall our understanding of biology and evolution.

The central message of this book is that we will never fully understand living things if we continue to think of genes, organisms, and environments as separate entities, each with its distinct role to play in the history and operation of organic processes. Here Lewontin shows that an organism is a unique consequence of both genes and environment, of both internal and external features. Rejecting the notion that genes determine the organism, which then adapts to the environment, he explains that organisms, influenced in their development by their circumstances, in turn create, modify, and choose the environment in which they live.

The Triple Helix is vintage Lewontin: brilliant, eloquent, passionate and deeply critical. But it is neither a manifesto for a radical new methodology nor a brief for a new theory. It is instead a primer on the complexity of biological processes, a reminder to all of us that living things are never as simple as they may seem.”

Borrow from Lewontin the idea of a “triple helix” and apply it to the ultimate wide-angle view of this process of understanding. The educational triple helix includes and always tries to coordinate:

  1. The student and their life (i.e., every student is first of all a person who is playing the role of a student). Every person is born, lives, and dies.
  2. The student and their field are related to the rest of the campus. (William James: all knowledge is relational.)
  3. The student and the world. (Container ships from Kaohsiung, Taiwan are bringing Lenovo and Acer computers to Bakersfield, California in a world of techno-commerce, exchange rates, insurance, customs, contractual arrangements, etc. In other words, always with some sense of the global political economy.)

The student keeps the triple helix “running” in the back of the mind and tries to create a “notebook of composite sketches” of the world and its workings and oneself and this develops through a life as a kind of portable “homemade” university which stays alive and current and vibrant long after one has forgotten the mean value theorem and the names and sequence for the six wives of Henry VIII).

The reader should think of Emerson’s point from his Journals of Ralph Waldo Emerson: 1824–1832—“The things taught in schools and colleges are not an education, but the means to an education.”

Education and Circular Causation: Everything Causes Everything Else

The student will have seen in these educational essays the notion of “Husserl’s rhomboid”:

The great philosopher, Edmund Husserl, who died in 1938, would bring a matchbox to class and show his students they see parts and some surface area of the matchbox (a kind of rhomboid, hence the name “Husserl’s rhomboid”) but never all of it at the same time. Students can walk around the matchbox and see facets. They can twirl the matchbox but whatever they do, the students cannot “espy” or glimpse all of it except in their imaginations, once they have been exposed to all of it, side by side, facet by facet.

Gunnar Myrdal, the Swedish economist who won the Nobel Prize in 1974, has something a bit analogous when he speaks of “circular cumulative causation”:

Circular cumulative causation is a theory developed by Swedish economist Gunnar Myrdal in 1956. It is a multi-causal approach where the core variables and their linkages are delineated. The idea behind it is that a change in one form of an institution will lead to successive changes in other institutions. These changes are circular in that they continue in a cycle, many times in a negative way, in which there is no end, and cumulative in that they persist in each round. The change does not occur all at once, which would lead to chaos, rather the changes occur gradually.

Gunnar Myrdal developed the concept from Knut Wicksell and developed it with Nicholas Kaldor when they worked together at the United Nations Economic Commission for Europe.

In the characteristics relevant to an economy’s development process, Myrdal mentioned the availability of natural resources, the historical traditions of production activity, national cohesion, religions and ideologies, and economic, social and political leadership.

He writes:

“The notion of stable equilibrium is normally a false analogy to choose when constructing a theory to explain the changes in a social system.

What is wrong with the stable equilibrium assumption as applied to social reality is the very idea that a social process follows a direction—though it might move towards it in a circuitous way—towards a position which in some sense or other can be described as a state of equilibrium between forces. Behind this idea is another and still more basic assumption, namely that a change will regularly call forth a reaction in the system in the form of changes which on the whole go in the opposite direction to the first change. The idea I want to expound in this book is that, on the contrary, in the normal case there is no such a tendency towards automatic self-stabilisation in the social system. The system is by itself not moving towards any sort of balance between forces, but is constantly on the move away from such a situation. In the normal case a change does not call forth countervailing changes but, instead, supporting changes, which move the system in the same direction as the first change but much further. Because of such circular causation as a social process tends to become cumulative and often gather speed at an accelerating rate…”

(Gunnar Myrdal, Economic Theory and Underdeveloped Regions, Gerald Duckworth, 1957, pp. 12–13)

Myrdal developed further the circular cumulative causation concept and stated that it makes different assumptions from that of stable equilibrium on what can be considered the most important forces guiding the evolution of social processes. These forces characterize the dynamics of these processes in two diverse ways.

These essays that you are reading here are examples encouraging students to put causes in a kind of circle: history exists because economics exists because psychology exists because society exists because history exists. Everything is causing everything else. There isn’t a simple “linear parade.”

By way of contrast, in a person’s private life, he/she went to the dentist before buying the batteries and after having lunch. There’s a timeline of events.

In history, there are such linear timelines also: John Kennedy was assassinated before Donald Trump became president. You had breakfast before dinner. You slept before you got up in the morning.

However, processes (industrialism, migration, urbanization, inflation, etc.) are not analyzable as events like meals and one-time occurrences but are more like getting old or learning a language.

Multi-causal interpretations and circular causes get the student out of simple, “this happened and that happened” in favor of “this and that caused each other, going both ways and interacting with other pressures too.” Everything is causing and altering everything else in all directions.

Education and Pre-Understanding

To embark on an education in any field, physics, say, is enervating because the student (in high school) say, enters a strange ocean with “zillions” of names and laws, units of measurement (amps, ohms, coulombs, faradays, etc.) which are very intricate and confusing.

A student does start swimming in this ocean via school “coercion” (i.e., how one will be punished for “failing.”)

There’s a much deeper and useful and practical way to create a pathway into fields: looking for a pre-understanding of what the field is like by taking one particular question or “head-scratcher” and start to delve into it, welcoming any initial sense of not-being-sure, as part of the fun of it, the enchantment.

Consider this article from 2001 in Scientific American:

“Can somebody finally settle this question: Does water flowing down a drain spin in different directions depending on which hemisphere you’re in? And if so, why?” [Archived PDF]

If you start to worry about the water swirling down your kitchen sink or bathtub, you are inevitably faced with the puzzling discussions of something called Coriolis forces, named after the French scientist of this name:

“In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.”

The Coriolis force is called a pseudo-force or fictitious force which is already quite puzzling. It seems to push an ant walking across a 78 RPM record in motion on the turntable in unexpected ways and affects the swirling motions of storm phenomena (hurricanes, cyclones, etc.).

The student would immediately sense that at the heart of physics—using this Coriolis force as an indicator—there’s an unbelievable intricacy—but also the sense that these explanations (i.e., forces versus pseudo-forces) that are not entirely convincing and might well be overturned or re-done by someone with a deeper grasp of the problem, in the future. There’s an “ad hoc-ness” (i.e., the explanations and units and theories and proofs seem somehow “circular” or “tautological” in a way that eludes us, as we wait for a clearer theory).

A person walking across a moving merry-go-round or carousel and the complexity of the pushes and pulls experiences “shoves” that are unfamiliar and the water going down the drain in the bathtub awaits a better theory. There is a subfield called “turbulent flow” and that would need to be brought into it. Weather phenomena like tsunamis, cyclones, etc. are turbulences that are complex and our theories are both unbelievably intricate but perhaps subject to revision.

All of this might be an enchanting “gateway” into physics and would give the student a pre-understanding of physics’s “style of thinking and explaining.” In other words, to “parachute” into a field you need the parachute of some particular puzzling example which you use as a “private gateway” into the way people in that field think and act.

Just to go through the years of high school and college in an endless and mindless “slog” with the “failure gun” of coercion pointed at you, is a tremendously soul-destroying way to educate oneself. You have to “go underground” and find your own pre-understanding and its twin brother or clone, enchantment.

Science and Its Discontents: The Case of Natsume Sōseki (夏目 漱石) in Japan

Natsume Sōseki (夏目 漱石) is and was the most prestigious and respected novelist in modern Japan and every student has to engage with such novels of his as Botchan (坊っちゃん, “Young Master”) and Kokoro (こゝろ, or in post-war orthography こころ, “Heart”). Sōseki died in 1916.

Sōseki’s feeling that the modern world is some kind of runaway train with no brakes is expressed clearly in his 1913 novel, Kōjin (行人 , “The Wayfarer”).

One of Sōseki’s dialogues in the novel is about the current science and technology world, which was quite visible already then, and has a very nerve-racking or frightening tempo of a turbulent tsunami.

One character says:

“Now what you call insecurity is the insecurity of the entire human race, and it isn’t peculiar to you alone. Constant motion and flow is our very fate.

“Man’s insecurity stems from the advance of science. Never once has science, which never ceases to move forward, allowed us to pause. From walking to ricksha, from ricksha to carriage, from carriage to train, from train to automobile, from there on to the dirigible, further on to the airplane, and further on and on, no matter how far we may go, it won’t let us take a breath. How far it will sweep us along, nobody knows for sure. It is really frightening.”

Yes, it is frightening, indeed, I agreed.

“It is frightening because the fate that the whole of humanity will reach in several centuries, I must go through—in my own lifetime—and at that all alone. That’s why it is frightening. In short, I gather within myself the whole insecurity of the human race, and distill that insecurity down into every moment, that is the fright that I am experiencing.”

(Natsume Sōseki, Kōjin [行人], Charles E. Tuttle Company, 1991, 9th printing, page 285)

Comment: There’s no need to dismiss these feelings as Luddite. They represent a reaction to the vertiginous or dizzying pace of the modern techno-protean change machine with no pause button.

Notice that Sōseki’s life (1867-1916) is basically congruent with Globalization I (i.e., the period of 1870-1913) discussed in the previous essay on Arthur Lewis’s classic Growth and Fluctuations, 1870-1913.

Sōseki has been, like his spokesmen in the citation above, swept up into a change-storm which led to a globalization backlash from 1914-1945, the era of deglobalization. WWI is the beginning bookend of all this.

Notice that the micro world of feelings and moods in the novel are resonant with the macro world though people at a certain time, such as the Sōseki protagonists, are not rigorous or prophetic theoreticians but rather groping in the dark.