Wednesday


Jane Austen’s novel Sense and Sensibility is not only a classic of English literature, but also a classic of moral psychology, investigating the contrast in temperaments between sense (in the person of Elinor Dashwood) and sensibility (in the person of Marianne Dashwood). This was one of the internal tensions of the Enlightenment, and Austen personalizes this tension in the lives of her memorable characters. The proneness to emotion (or, we might even say, emotionalism) represented by sensibility in the character of Marianne Dashwood was given philosophical expression in the the life and work of Jean-Jacques Rousseau, who pioneered the valorization of feeling even in the midst of the Enlightenment and its rationalism.

The more sober side of life, as represented by the self-sacrificing prudence of Elinor Dashwood, is a perennial tradition in western thought, most famously and anciently represented by Stoicism. The Enlightenment thinkers who distanced themselves from Rousseau’s emotionalism didn’t call themselves Stoics, but they were, after a fashion, Stoics by another name, and they were able to draw upon a deep philosophical well, including the great Stoic philosophers of classical antiquity. For example, Marcus Aurelius.

In his Meditations, Marcus Aurelius introduced what we would today call a thought experiment — a thought experiment that has subsequently come to be known as, “the view from above.” Here is the locus classicus from the Meditations:

Look round at the courses of the stars, as if thou wert going along with them; and constantly consider the changes of the elements into one another; for such thoughts purge away the filth of the terrene life.

This is a fine saying of Plato: That he who is discoursing about men should look also at earthly things as if he viewed them from some higher place; should look at them in their assemblies, armies, agricultural labours, marriages, treaties, births, deaths, noise of the courts of justice, desert places, various nations of barbarians, feasts, lamentations, markets, a mixture of all things and an orderly combination of contraries.

Consider the past; such great changes of political supremacies. Thou mayest foresee also the things which will be. For they will certainly be of like form, and it is not possible that they should deviate from the order of the things which take place now: accordingly to have contemplated human life for forty years is the same as to have contemplated it for ten thousand years. For what more wilt thou see?

That which has grown from the earth to the earth, But that which has sprung from heavenly seed, Back to the heavenly realms returns. This is either a dissolution of the mutual involution of the atoms, or a similar dispersion of the unsentient elements.

Marcus Aurelius, The Meditations, translated by George Long, Book Seven

This idea was taken over by Antony, Earl of Shaftesbury, who rendered the same idea in the more flowery English prose of his time:

“View the heavens. See the vast design, the mighty revolutions that are performed. Think, in the midst of this ocean of being, what the earth and a little part of its surface is; and what a few animals are, which there have being. Embrace, as it were, with thy imagination all those spacious orbs, and place thyself in the midst of the Divine architecture. Consider other orders of beings, other schemes, other designs, other executions, other faces of things, other respects, other proportions and harmony. Be deep in this imagination and feeling, so as to enter into what is done, so as to admire that grace and majesty of things so great and noble, and so as to accompany with thy mind that order, and those concurrent interests of things glorious and immense. For here, surely, if anywhere, there is majesty, beauty and glory. Bring thyself as oft as thou canst into this sense and apprehension; not like the children, admiring only what belongs to their play; but considering and admiring what is chiefly beautiful, splendid and great in things. And now, in this disposition, and in this situation of mind, see if for a cut-finger, or what is all one, for the distemper and ails of a few animals, thou canst accuse the universe.” 8

Antony Ashley-Cooper, the third Earl of Shaftesbury (1671-1713), The Philosophical Regimen, “Diety”

Here we have the Enlightenment mirror of a classic Stoic idea. I find it fascinating that this Stoic thought experiment is intended to communicate what is essentially a Copernican lesson — the smallness of human beings and their concerns in the “ocean of being” that is the universe. The view from above is a moral thought experiment rather than a cosmological or metaphysical thought experiment, and it draws upon Stoic cosmology and metaphysics in order to underline the central moral lesson. As a moral thought experiment, the view from above is to be compared to more familiar thought experiments of our time, the most obvious being the ability to imaginatively place oneself in the circumstances of another, and thereby by gain a visceral appreciation of the other’s moral experience. This latter idea is not only familiar to us in our ordinary day-to-day moral thought, but also forms the basis of John Rawl’s “veil of ignorance” thought experiment intended to define a just society.

The contemporary moral thought experiment that is so familiar to us places us in the midst of the ocean of being; its ontological parallel might be taken to be an object-oriented ontology that insists upon a “democracy of objects.” The Stoic thought experiment is profoundly anti-modern in so far as it places us above the ocean of being, putting the thought experimenter not in the shoes of another, but transcending the other, and transcending everything of this world. (Nietzsche — the modernist’s anti-modernist — has several similar passages, especially when he writes about hyperboreanism.) The ontological parallel to the Stoic thought experiment may be taken to be the Great Chain of Being, which is a hierarchical conception — an aristocratic ontology, if you will. While Stoic moral thought may be considered a perennial touchstone in western philosophy, its tenets, as we have seen, are in many respects radically alien to the modern mind. The “view from above” is intended to inculcate an noble attitude to the world, but the idea of nobility as a virtue has almost disappeared from a world in which aristocracy (presumably the social class with the greatest nobility) is considered at best irrelevant and at worst an evil to be extirpated.

From space we have achieved the Stoic ‘view from above,’ but we don’t interpret it as the Stoics would have interpreted it.

The nobility of the “view from above” is, at the same time, an invocation of what we today call the overview effect, though an overview effect conceived before an actual visual overview of our homeworld was technically possible and, perhaps more importantly, conceptualized in terms of Stoic reserve and moral distance. Since the Greek scientists of classical antiquity proved that the Earth is a sphere, and that it is indeed a world among worlds (an idea that the ancients called the infinity of worlds), there has always been the possibility of conceptualizing the overview effect, though it was only with twentieth century industrial technology that it became possible to see the sphere of the Earth and its place in the cosmos with the same eyes that had, until then, only seen Earth from its surface.

If the civilization of classical antiquity had not faltered, but had remained more-or-less intact until it had produced a technology capable of achieving Earth orbit, the overview effect as experienced by individuals of that civilization would doubtless have been taken as scientific confirmation of Stoic moral ideals. This is not, today, how the overview effect has been received. While a perennial form of moral psychology, the particular form of ancient Stoicism was an intellectual expression of a particular era of human experience; the selection pressures that shaped Stoicism, while partly reflective of perennial features of the human condition, have nevertheless qualitatively changed since classical antiquity.

The overview effect would have had an impact upon any conscious being, and especially upon a reflexively self-conscious being, regardless of the social milieu of any such being. Had it been possible for our Paleolithic ancestors to experience the overview effect, or for the Greeks in the time of Pericles, or the Mongols in the time of Genghis Khan, or for the Victorians to experience the overview effect, that effect would have been profound, but, in each case, interpreted and understood within the context of the conceptual framework of the conscious being who attains a homeworld overview. I have here used examples from different times and places of terrestrial history, but the idea can be generalized to the experience of any conscious being and its conceptual framework. As we have all learned from recent philosophy of science, all observations are theory-laden, and so too with the overview effect: all experiences of the overview effect are theory-laden, and the theory with which they are informally laden is the conceptional framework of the society from which the observer is derived.

A gold doubloon from Quito was nailed to the mast of the Pequod in Moby Dick.

Long before it was asserted that all observation is theory-laden, Kant put it like this: “Concepts without percepts are empty, percepts without concepts are blind.” (“Gedanken ohne Inhalt sind leer, Anschauungen ohne Begriff sind blind” in the section “Von der Logik Überhaupt” KdRV) This, too, is a perennial idea of western civilization — i.e., the idea that our perceptions are shaped by our conceptions; that we are blind without our conceptual framework — and we find it in a famous passage from Moby Dick, in which Melville describes the response of the crew of the Pequod to the golden doubloon from Quito nailed to the mast:

Now those noble golden coins of South America are as medals of the sun and tropic token-pieces. Here palms, alpacas, and volcanoes; sun’s disks and stars, ecliptics, horns-of-plenty, and rich banners waving, are in luxuriant profusion stamped; so that the precious gold seems almost to derive an added preciousness and enhancing glories, by passing through those fancy mints, so Spanishly poetic.

It so chanced that the doubloon of the Pequod was a most wealthy example of these things. On its round border it bore the letters, REPUBLICA DEL ECUADOR: QUITO. So this bright coin came from a country planted in the middle of the world, and beneath the great equator, and named after it; and it had been cast midway up the Andes, in the unwaning clime that knows no autumn. Zoned by those letters you saw the likeness of three Andes’ summits; from one a flame; a tower on another; on the third a crowing cock; while arching over all was a segment of the partitioned zodiac, the signs all marked with their usual cabalistics, and the keystone sun entering the equinoctial point at Libra.

Before this equatorial coin, Ahab, not unobserved by others, was now pausing.

“There’s something ever egotistical in mountain-tops and towers, and all other grand and lofty things; look here, — three peaks as proud as Lucifer. The firm tower, that is Ahab; the volcano, that is Ahab; the courageous, the undaunted, and victorious fowl, that, too, is Ahab; all are Ahab; and this round gold is but the image of the rounder globe, which, like a magician’s glass, to each and every man in turn but mirrors back his own mysterious self. Great pains, small gains for those who ask the world to solve them; it cannot solve itself. Methinks now this coined sun wears a ruddy face; but see! aye, he enters the sign of storms, the equinox! and but six months before he wheeled out of a former equinox at Aries! From storm to storm! So be it, then. Born in throes, ‘t is fit that man should live in pains and die in pangs! So be it, then! Here’s stout stuff for woe to work on. So be it, then.”

Herman Melville, Moby-Dick; or, The Whale, Chapter 99 — The Doubloon

After Ahab’s “not unobserved” soliloquy on the Quito doubloon, Starbuck, Stubb, Flask, Manxman, and then Queequeg look into the doubloon and gave their own account of it, each distinctive of the man, thus confirming Ahab’s judgment of the doubloon as a microcosm reflecting the macrocosm. Melville’s account, then, of how perceptions are shaped by conceptions is based on the differences among individual men, but there are also differences based on particular peoples from different times and different regions of the world. Indeed, all of the harpooners of the Pequod — Queequeg, Tashtego, Daggoo, and Fedallah — are representatives of distinct civilizations, though all have, by chance, been brought together on the Pequod. Each has his distinctive conceptual framework that overlaps and intersects with that of his crew mates, but which perfectly coincides with none of the others.

We too, today, have our peculiar conceptual framework, and it pervasively shapes our view of the world. It needs to be understood that our peculiar conceptual framework determines how we experience the world, and, in the case of the overview effect, “the world” means the planet entire. The overview effect appeared at a particular moment in human history, and, as a consequence, the overview effect was and has been primarily interpreted in terms of human experience in the twentieth, and now the twenty-first, century. That the overview effect appeared at the historical moment in which it did appear — relatively early in the development of a technological civilization, and immediately upon the advent of spacefaring capacity — is significant.

We are closer in time to Marianne Dashwood than to Candide, or indeed closer to Werther in his blue coat and yellow breeches than to Rameau’s Nephew. That is to say, our worldview is more akin to romanticism than to the Enlightenment, owes more the Rousseau than to Locke, though romanticism, too, has passed into history and into dust, and has been replaced by newer ideas and ideologies. Nevertheless, the romantic ideal remains stamped on western civilization and the experience of individuals within that civilization (moreover, romanticism, like Stoicism, is a perennial expression of the human condition), and it is the romantic response of primarily an emotional character that marks responses to the overview effect. This may not be obvious at first, but it becomes more obvious in comparison to the Stoic idea of the overview effect in the view from above thought experiment.

Astronaut Edgar Mitchell has been the most forthcoming in describing his unique experiences while in space. Mitchell had a particularly compelling experience while returning from the moon during the Apollo 14 mission:

“Perhaps it was the disorienting, or reorienting, effect of a rotating environment, while the heavens and Earth tumbled alternately in and out of view in the small capsule window. Perhaps it was the air of safety and sanctuary after a two-day foray into an unforgiving environment. But I don’t think so. The sensation was altogether foreign. Somehow I felt tuned into something much larger than myself, something much larger than the planet in the window. Something incomprehensibly big…”

“Then, looking beyond the Earth itself to the magnificence of the larger scene, there was a startling recognition that the nature of the universe was not as I had been taught. My understanding of the separate distinctness and the relative independence of movement of those cosmic bodies was shattered. There was an upwelling of fresh insight coupled with a feeling of ubiquitous harmony—a sense of interconnectedness with the celestial bodies surrounding our spacecraft. Particular scientific facts about stellar evolution took on new significance.”

Edgar Mitchell, The Way of the Explorer, New York: Putnam, 1996, p. 57-58

Mitchell was driven by his experience to read widely about religious and mystical experiences, eventually commissioning a study on esoteric practices. Mitchell’s sponsored study converged upon the idea of savikalpa samadhi, as a traditional (at least, native to the Indian tradition of thought) expression of what he experienced as an astronaut.

Astronaut Russell L. Schweickart has also given a detailed account of his experiences in space. Frank White has cited Schweickart’s experiences in his exposition of the overview effect:

“The Earth is so small and so fragile and such a precious little spot in the universe that you can block it out with your thumb. And you realize on that small spot, that little blue and white thing, is everything that means anything to you — all of history and music and poetry and art and death and birth and love, tears, joy, games, all of it on that little spot out there that you can cover with your thumb. And you realize from that perspective that you’ve changed, that there’s something new there, that the relationship is no longer what it was.”

Frank White, The Overview Effect: Space Exploration and Human Evolution, Third Edition, Reston, VA: AIAA, 2014, pp. 36-37; Part III of The Overview Effect consists of statements by and interviews with astronauts and cosmonauts, all of which are relevant here. An account of Schweickert’s experiences also can be read in No Frames, No Boundaries: Connecting with the whole planet — from space by Russell Schweickart.

As Plato quoted by Marcus Aurelius gives a litany of the familiar things of this world — assemblies, armies, agricultural labours, marriages, treaties, births, deaths, noise of the courts of justice, desert places, various nations of barbarians, feasts, lamentations, markets — so, too, Schweickart gives a litany of the familiar things of this world — history and music and poetry and art and death and birth and love, tears, joy, games — but the implied meaning and value of this terrestrial litany is different in each case. There is a difference between seeing these familiar things from a terrestrial perspective, and seeing them viewed from above, but what exactly is this difference?

Astronaut Ron Garan references the overview effect, but also formulated his experiences in space in terms of the “orbital perspective” and even “elevated empathy”:

“In addition to the overview effect, however, there is another element to the orbital perspective, which I call elevated empathy… For the fifty-plus years that humans have been flying in space, astronauts and cosmonauts have commented on how beautiful, tranquil, peaceful, and fragile our planet looks from space. These are not trite clichés; it truly is moving to see our planet from space. But looking down and seeing a border between India and Pakistan, recognizing the undeniable and sobering contradiction between the staggering beauty of our planet and the unfortunate realities of life on our planet for many of its inhabitants, also inspires empathy for the struggles that all people face.”

“This elevated empathy is an important aspect of the orbital perspective. Elevated empathy helps us realize that we are all riding through the universe together on this spaceship we call Earth, that we are all interconnected, that we are all one human family. This scar on the otherwise beautiful landscape was a compelling call to focus on the need for global collaboration to overcome the world’s problems, to recognize that, in spite of our disagreements, we should behave like a family, should communicate, support, stand by, and care for each other.”

Ronald J. Garan, Jr., The Orbital Perspective: Lessons in Seeing the Big Picture from a Journey of Seventy-One Million Miles, Oakland, CA: Berrett-Koehler, 2015, pp. 64-65

All of these accounts are experiences of connectedness and of integration, not of establishing a distance from which the petty concerns of the world seem as nothing. The ordinary business of life on Earth — death and birth and love, tears, joy, games — takes on a greater significance; rather than being diminished by the experience of the overview effect, they are magnified by it.

The overview effect has changed and is changing human perception of our homeworld.

Let me return to one of the opening thoughts of Frank White’s The Overview Effect in order to refocus on the difference between the Stoic “view from above” and the overview effect as it has been experienced by human beings as a consequence of space travel. Here is a passage I have quoted many times previously:

“…mental processes and views of life cannot be separated from physical location. Our ‘worldview’ as a conceptual framework depends quite literally on our view of the world from a physical place in the universe.”

Frank White, The Overview Effect: Space Exploration and Human Evolution, Third Edition, Reston, VA: AIAA, 2014, p. 1

As we have seen above, an observer not only has a physical location in space, but also observes from the point of view of a particular conceptual framework, which we might call the observer’s “location” in what Wittgenstein called logical space. While Wittgenstein did not develop his conception of logical space in any detail, Donald Davidson formulated a conception of logical geography that entails locatedness in logical space:

“…to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by.”

Donald Davidson, Essays on Actions and Events, “Criticism, Comment, and Defence”, p. 140

Since we’re talking about the overview effect, “logical space” is more appropriate than the essentially terrestrial (if not geocentric — a conceptual geocentrism, i.e., geocentrism in an extended sense) idea of “logical geography,” but the terminology doesn’t really matter. What does matter is the idea of the relation of ideas to other ideas, which is a function of a conceptual framework. I would go further than Davidson and add to his account of logical geography the particular logic employed, because relations of entailment are relative to the logic used to derive what is entailed by what.

Davidson’s formulation is strongly linguistic, which may be understood as an artifact of the high-water mark of linguistic philosophy; the same point could be given a somewhat more traditional formulation by substituting “proposition” for “sentence.” In any case, an observer’s conceptual framework could be described as a location in logical space or logical geography, and this location involves the relationship of each idea within the conceptual framework to other ideas within the conceptual framework, as well as the relationship of the conceptual framework entire (in so far as it can be understood as a whole) to other conceptual frameworks or to ideas that lie outside the framework.

An observer, then, has a particular location in physical space as well as a particular location in logical space. These locations are not independent, but rather each informs the other: the observer’s location in physical space shapes his location in logical space, and his location in logical space shapes his location in physical space. The second part of this sentence may sound a bit odd. Think of it as a form of emergent complexity: the observer’s location in logical space does not physically create or physically shape the observer’s physical space, but it does transform this physical space through making it the space of an observer, and hence a vantage point from which to observe, describe, and understand the world. A standpoint comes into being, as it were, by being the vantage point of an observer; before that it is merely a coordinate in space, but it is not a standpoint, so that the existence of an observer brings a standpoint as a standpoint into existence. That is to say, a standpoint is an emergent complexity from space simpliciter.

When a Stoic assumes the standpoint of the view from above, he sees the world brought into existence by his standpoint, and when a contemporary astronaut sees the overview of the planet from space, he too sees the world brought into existence by his standpoint. From a purely formal point of view, these experiences are symmetrical. These standpoints are distinct in so far as they do not perfectly coincide (like the harpooners on the Pequod), but they overlap and intersect. The harpooners on the Pequod lived in close quarters and hunted whales together, so they had much in common. And we have much in common with them, as we do with the Stoic emperor Marcus Aurelius or the Stoic slave Epictetus, and more yet in common with the astronauts on the ISS. But there are aspects of experience that are narrower, and are thus shared by fewer individuals than the way in which all human beings share their experience of the human condition.

If humanity is able to project itself beyond its homeworld and to build a spacefaring civilization, the overview effect will be experienced from as many different standpoints as what was seen by the sailors of the Pequod when they looked into the Quito doubloon. Over time, the overview effect will be not one, but many. Our history has already supplied us with an example of this: if an astronaut came back from space and asserted that the overview effect made him wish to purge away the filth of the terrestrial life, this account would not be well received; it belongs to a different age and to a different conceptual framework. And if human beings use their advanced technology to change themselves (technology derived from the same industrial infrastructure that makes space travel possible), the human condition itself may change, and then the overlap of our experiences with those of our ancestors will be diminished. We will have less in common, and what we see when we look into the Quito doubloon will evolve over time, and humanity will be not one, but many.

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Overview Effects

The Epistemic Overview Effect

The Overview Effect as Perspective Taking

Hegel and the Overview Effect

The Overview Effect in Formal Thought

Brief Addendum on the Overview Effect in Formal Thought

A Further Addendum on the Overview Effect in Formal Thought, in the Way of Providing a Measure of Disambiguation in Regard to the Role of Temporality

Our Knowledge of the Internal World

Personal Experience and Empirical Knowledge

The Overview Effect over the longue durée

Cognitive Astrobiology and the Overview Effect

The Scientific Imperative of Human Spaceflight

Planetary Endemism and the Overview Effect

The Overview Effect and Intuitive Tractability

Stoicism, Sensibility, and the Overview Effect

Homeworld Effects

The Homeworld Effect and the Hunter-Gatherer Weltanschauung

The Martian Standpoint

Addendum on the Martian Standpoint

Hunter-Gatherers in Outer Space

What will it be like to be a Martian?

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Grand Strategy Annex

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Friday


The thesis that epistemic space is primarily shaped and structured by geometrical intuition may be equated with Bergson’s exposition of the spatialization of the intellect. Bergson devoted much of his philosophical career to a critique of the same. Bergson’s exposition of spatialization is presented in terms of a sweeping generality as the spatialization of time, but a narrower conception of spatialization in terms of the spatialization of consciousness or of human thought follows from and constitutes a special case of spatialization.

One might well ask, in response to Bergson, how we might think of things in non-spatial terms, and the answer to this question is quite long indeed, and would take us quite far afield. Now, there is nothing wrong with going quite far afield, especially in philosophy, and much can be learned from the excursion.

There is a famous passage in Wittgenstein’s Tractatus Logico-Philosophicus about “logical space,” at once penetrating and obscure (like much in the Tractatus), and much has been read into this by other philosophers (again, like much in the Tractatus). Here is section 1.13:

“The facts in logical space are the world.”

And here is section 3.42:

“Although a proposition may only determine one place in logical space, the whole logical space must already be given by it. (Otherwise denial, the logical sum, the logical product, etc., would always introduce new elements — in co-ordination.) (The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)”

I will not attempt an exposition of these passages; I quote them here only to give the reader of flavor of Wittgenstein’s . Clearly the early Wittgenstein of the Tractatus approached the world synchronically, and a synchronic perspective easily yields itself to spatial expression, which Wittgenstein makes explicit in his formulations in terms of logical space. And here is one more quote from Wittgenstein’s Tractatus, from section 2.013:

“Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.”

I find this particularly interesting because it is, essentially, a Kantian argument. I discussed just this argument of Kant’s in Kantian Non-Constructivism. It was a vertiginous leap of non-constructive thought for the proto-constructivist Kant to argue that he could imagine empty space, but not spatial objects without the space, and it is equally non-constructive for Wittgenstein to make the same assertion. But it gives us some insight into Wittgenstein’s thinking.

Understanding the space of atomic facts as logical space, we can see that logical space is driven by logical necessity to relentlessly expand until it becomes a kind of Parmenidean sphere of logical totality. This vision of logical space realizes virtually every concern Bergson had for the falsification of experience given the spatialization of the intellect. The early Wittgenstein represents the logical intellect at its furthest reach, and Wittgenstein does not disappoint on this score.

While Wittgenstein abandoned this kind of static logical totality in this later thought, others were there to pick up the torch and carry it in their own directions. An interesting example of this is Donald Davidson’s exposition of logical geography:

“…I am happy to admit that much of the interest in logical form comes from an interest in logical geography: to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by. The location must be given relative to a specific deductive theory; so logical form itself is relative to a theory.”

Donald Davidson, Essays on Actions and Events, pp. 139-140

In a more thorough exposition (someday, perhaps), I would also discuss Frege’s exposition of concepts in terms of spatial areas, and investigate the relationship between Frege and Wittgenstein in the light of their shared equation of logic and space. (I might even call this the principle of spatial-logical equivalence, which principle would be the key that would unlock the relationship between epistemic space and geometrical intuition.)

Certainly the language of spatiality is well-suited to an exposition of human thought — whether it is uniquely suited is an essentialist question. But we must ask at this point if human thought is specially suited to a spatial exposition, or if a spatial exposition is especially suited for an exposition of human thought. It is a question of priority — which came first, the amenability of spatiality to the mind, or the amenability of the mind to spatiality? Which came first, the chicken or the egg? Is the mind essentially spatial, or is space essentially intellectual? (The latter position might be assimilated to Kantianism.)

From the perspective of natural history, recent thought on human origins has shifted from the idea of a “smart ape” to the idea of a “bipedal ape,” the latter with hands now free to grasp and to manipulate the environment. Before this, before human beings were human, our ancestors lived in trees where spatial depth perception was crucial to survival, hence our binocular vision from two eyes placed side by side in the front of the face. Color vision additional made it possible to identify the ripeness of fruit hanging in the trees. In other words, we are a visual species from way back, predating even our minds in their present form.

With this observation it becomes obvious that the human mind emerged and evolved under strongly visual selection pressure. Moreover, visual selection pressure means spatial selection pressure, so it is no wonder that the categories native to the human mind are intrinsically spatial. Those primates with the keenest ability to process spatial information in the form of visual stimuli would have had a differential survival and reproductive advantage. This is not accidental, but follows from our natural history.

But now I have mentioned “natural history” again, and I pause. Temporal selection pressure has been no less prevasive than spatial selection pressure. All life is a race against time to survive as long as possible while producing as many viable offspring as possible. Here we come back to Bergson again. Why does the intellect spatialize, when time is as pervasive and as inescapable as space in human experience?

With this question ringing in our ears, and the notable examples of philosophical logical-spatial equivalence mentioned above, why should we not have (parallel to Wittgenstein’s exposition of logical space) logical time and (parallel to Davidson’s exposition of logical geography) logical history?

To think through the idea of logical history is so foreign that is sounds strange even to say it: logical time? Logical history? These are not phrases with intuitive self-evidence. At least, they have very little intuitive self-evidence for the spatializing intellect. But in fact a re-formulation of Davidson’s logical geography in temporal-historical terms works quite well:

…the logical form of a sentence is to give its logical position in the elapsed sequence of sentences, to describe it in a way that explicitly determines what are following sentences it entails and what previous sentences it is entailed by…

Perhaps I ought to make the effort to think things through temporally in the same way that I have previously described how I make the effort to think things through selectively when I catch myself thinking in teleological terms.

In the meantime, it seems that our geometrical intuition is a faculty of mind refined by the same forces that have selected us for our remarkable physical performance. And as with our physical performance, which is rendered instinctive, second nature, and unconscious simply through our ordinary interaction with the world (all the things we must do anyway in order to survive), our geometrical intuition is often so subtle and so unconsciously sophisticated that we do not even notice it until we are presented with some Gordian knot that forces us to think explicitly in spatial terms. Faced with such a problem, we create sciences like topology, but before we have created such a science we already have an intellect strangely suited to the formulation of such a science. And, as I have written elsewhere, we have no science of time. We have science-like measurements of time, and time as a concept in scientific theories, but no scientific theory of time as such.

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Fractals and Geometrical Intuition

1. Benoît Mandelbrot, R.I.P.

2. A Question for Philosophically Inclined Mathematicians

3. Fractals and the Banach-Tarski Paradox

4. A visceral feeling for epsilon zero

5. Adventures in Geometrical Intuition

6. A Note on Fractals and Banach-Tarski Extraction

7. Geometrical Intuition and Epistemic Space

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Epistemic Space

19 February 2009


Wittgenstein, on the left, wrote one of the masterpieces of twentieth century philosophy, the Tractatus Logico-Philosophicus

Wittgenstein, on the left, wrote one of the masterpieces of twentieth century philosophy, the Tractatus Logico-Philosophicus

Ludwig Wittgenstein, in his Tractatus Logico-Philosophicus, introduced the concept of logical space. This does not play a large role in the Tractatus, but a few other philosophers have found it to be of interest and have fleshed out the concept. Donald Davidson formulated an analogous conception of logical geography: “to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by.” (Essays on Actions and Events, “Criticism, Comment, and Defence”, p. 140)

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Ultimately, all space is logical space, and all geography is logical geography, or, rather, these categories of logical space and logical geography are the most formal and abstract formulations of space as it is conceived by the intellect as an ideal form of order. Wittgenstein and Davidson present to us the most idealized and refined formulations of concepts that we employ daily in our ordinary lives in a less refined and less ideal form. But if we are to come to a theoretical understanding of space, we must master the abstract and formal conceptions. Geopolitics is ultimately incomprehensible without logical geography.

Foucault sought to map the spaces of knowledge, and called his chair that of "History of systems of thought"

Foucault sought to map the spaces of knowledge, and called his chair that of "History of systems of thought"

Our knowledge is laid out in epistemic space, so that our epistēmē (as Foucault called it; ἐπιστήμη in the original Greek) governs not only how we see and understand the world, but also how we move through it and how we construct our lives within the world, for the world is a world in space defined epistemically, that is to say, defined in terms of our knowledge.

The Tabula Peutingeriana

The Tabula Peutingeriana: this is a lesson in how differently ancient and modern peoples see (and construct) the space in which they live.

On 27 November 2007, in celebration of its inclusion in UNESCO’s Memory of the World Register, the Tabula Peutingeriana was displayed in Vienna. I should have liked to have seen this. It is a medieval copy of an ancient Roman road map. The copy is quite large, like many medieval maps, though quite long and thin, about seven meters by thirty-four centimeters. The Mediterranean Sea is stretched out like a river in this elongated space. The original is thought to date from some time in the fifth century AD.

The map mosaic at Madaba, Jordan.

The map mosaic at Madaba, Jordan.

One of the few maps to date from antiquity is perhaps a hundred or so years later than the original for the Tabula Peutingeriana, and this is the map mosaic at Mādabā, Jordan. While damaged, it survives in part because of the robust character of mosaics. Colored stone and glass set in concrete survives the centuries much better than parchment or papyrus. This map mosaic, like the Tabula Peutingeriana, and indeed as with all maps, there is a surprising combination of practical detail and ideological schematism. A map is a practice of political ideology.

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A detail from the Tabula Peutingeriana, showing the city of Rome as an Emperor, with globe and sceptre, seated on a throne.

As strange as the Tabula Peutingeriana looks to modern eyes, stranger still is the map of the world by Mahmud al-Kashgari. The Tabula Peutingeriana seems stretched and distorted, but it is still recognizably a map. The map of al-Kashgari might not be recognized as a map by the modern, western eye. Its schematism of a circle within a square contrasts with the schematism of “T in O” maps mentioned below, but perhaps as intriguingly, mirror the structure of Hagia Sophia, the great church built under the rule of Justinian, but which became the model of mosques the world over after Constantinople was taken by the Turks.

A map of the world by Mahmud al-Kashgari from his Diwan Lugat at-Turk, believed to date from 1072 AD.

A map of the world by Mahmud al-Kashgari from his Diwan Lugat at-Turk, believed to date from 1072 AD.

As with most maps of late antiquity and later, Jerusalem is shown at the center of the world in the Mādabā map, a Christian-era map, whereas the focus of the Roman map was Rome itself, represented by a crowned man sitting on a throne (on the far right of the larger section of the Tabula Peutingeriana pictured above, and shown in detail immediately above). And, as we know, all roads lead to Rome. The Via Appia Antiqua is shown radiating from Rome at about 4 o’clock. That the Roman map was a road map is a sign of the role that communications networks played in Roman administration.

A medieval "T" map, also called a "T-O" map or a "T and O" map or a "T in O" map.

A medieval "T" map, also called a "T-O" map or a "T and O" map or a "T in O" map.

Even more schematic, and nearly devoid of practical detail, is the medieval “T in O” map: the very name describes its structure. In many of these maps Jerusalem in prominently in the center with Asia on top, Europe to the lower left of the “T” and Africa to the lower right of the “T”. Such a construction of the world is purely about expressing the relation of the major divisions of the world to its center, positioning the human world within the divine cosmos — marking one’s place within the totality, to borrow a term of the Davidson quote above.

The Thomas Digges chart of a Copernican solar system from 1576.

The Thomas Digges chart of a Copernican solar system from 1576.

Even as maps became more scientifically sophisticated after the scientific revolution, they remain highly schematic and their purpose is often to show the interrelation of major epistemic divisions so that man can know his place in the world. The Thomas Digges Copernican solar system (shown above) is more sophisticated than a medieval “T in O” map, but similarly schematic in conception. A map orders the world for us, and in so ordering our world, orders our lives.

Scientific realism has produced its own abstract and schematic maps, not unlike the dramatic poster art of so-called socialist realism.

Scientific realism has produced its own abstract and schematic maps, with striking color contrasts and bold graphic motifs not unlike the dramatic poster art of so-called socialist realism.

Some of the most advanced scientific maps of our time continue to be as schematic as maps of the past, highly specialized depictions of the state of our knowledge, and such that can only be meaningfully interpreted and understood by an adept of the culture so formulated. One of the most famous scientific images of our time is that of the cosmic microwave background radiation, which showed very subtle differences in the background radiation. This slight departure from a purely homogeneous background radiation is the oldest evidence we have of the natural history of the universe. Here time is shown unfolded across deep space, mapped, as it were. The order mapped in space overflows into an order in time.

Maps of the Roman Empire are inherently problematic, as almost all have been formulated according to a paradigm derived from the territorial nation-state.

Maps of the Roman Empire are inherently problematic, as almost all have been formulated according to a paradigm derived from the territorial nation-state: at the heart of the empire is not a particular territory, but the Mediterranean Sea.

The maps we draw of the migration and distribution of species, with their long, sinuous lines demarcating broad swathes of territory, are redolent of the maps historians attempt to draw for past political entities, with their long, curving lines across deserts, steppe, and forest where the territorial sovereignty of any political entity would be questionable, especially before the age of the territorially defined nation-state.

Attempts to map bird populations and migrations always remind me of attempts to map pre-nation-state political entities: both the world of the past and the avian world are alien to us.

Attempts to map bird populations and migrations always remind me of attempts to map pre-nation-state political entities: both the world of the past and the avian world are alien to us.

A map represents a special kind of knowledge, and indeed a special approach to knowledge — a bird’s eye view of knowledge in which epistemic space is plotted out in a scheme that is both abstract and synthetic, at once intuitive and non-constructive. We are all familiar with the saying that, “The map is not the territory” (credited to Alfred Korzybski), which emphasizes the abstract and schematic character of maps. Like Magritte’s picture of a pipe, which is self-evidently not a pipe and yet recognizably a pipe, a map represents, and as a representation it assumes and presupposes certain principles of representation. Maps, thus, are texts inscribed in a symbolic language.

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In our bureaucratized industrial society, we live by flow charts, which are transparently maps of epistemic space. In this way we see at a glance our life mapped out, the paths we will take, the choices we must make, and even the choices that lead to other choices leave us within the well-worn schema of life reduced to an algorithm.

Medieval maps were often highly "realistic" in their use of projection and perspective, yet highly "realistic" in the one-to-one correspondence observed between objects and their representation.

Medieval maps were often highly "unrealistic" in their use of projection and perspective, yet highly "realistic" in the one-to-one correspondence observed between objects and their representation.

Today one commonly hears others say “It’s just semantics” as though semantics don’t matter, and one could equally well imagine someone saying, in the same dismissive vein, “It’s just syntactics” as though it doesn’t matter what language you happen to be speaking. But it does matter. A perspicuous symbolism can be the difference between getting your meaning across or failing to do so. In Principia Mathematica Russell and Whitehead wrote, “The terseness of the symbolism enables a whole proposition to be represented to the eyesight as one whole, or at most in two or three parts divided where the natural breaks, represented in the symbolism, occur.” (Whitehead and Russell, Principia Mathematica to *56, London and New York: Cambridge University Press, 1978, p. 2) And this was the same sort of thing that Wittgenstein was trying to do in his Tractatus, and in doing so found himself explicitly formulating a doctrine of logical space.

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The Forma Urbis Romae was a map of ancient Rome carved into marble slabs and on display in the Templum Pacis.

The Forma Urbis Romae was a map of ancient Rome carved into marble slabs, affixed to a wall, and (in antiquity) permanently on display in the Templum Pacis.

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