Chinese politics was dominated by Mao Zedong from 1949 to 1976, and for more than a decade before that if we count the period from the Long March forward. Mao was effectively President for Life of China, though he wasn’t called that. However, he was called “The Red Emperor.” After the chaos of the Cultural Revolution some effort was made to regularize the political system after Mao’s death, and, to a certain extent, China managed to present itself to the world as a “normal” nation-state under the rule of law (not under military rule, or in the grip of a warlord or a strongman) and with a political succession that, while entirely internal to the communist party, seemed to follow certain rules. There was a semi-orderly succession process from Deng Xiaoping to Jiang Zemin to Hu Jintao to Xi Jinping.

This façade of orderly political succession occurred throughout a period a spectacular economic growth for China. Given that economic growth at this pace can result in extreme social dislocation, it reflected well on the Communist Party of China’s firm grasp on power that it was able to preside over this orderly succession of political power during economic and social conditions that would prove challenging even to a stable and well-established political system. In consequence, the CPC seemed to be a source of strength, stability, and order for China at a time when much else was in flux.

The apparent solidity of the CPC and its own internal mechanisms for orderly political succession have now been revealed to be illusory. It has been clear for some time that Xi Jinping has been the strongest political figure in China since Deng Xiaoping, but we now must see him as the strongest figure in China since Mao Zedong. This month, the CPC eliminated term limits for the president and vice president, re-appointing Xi Jinping as president with no term limit. What this means is that a sufficiently powerful individual can bend the CPC to his will, so that the power is vested in the individual rather than in the party or its offices. And given that the CPC is the political institution of China, that these institutions can bend to the will of one man points to the weakness of CPC institutions. In other words, China is much more vulnerable than it appears on the surface.

To a remarkable extent the western press have given Xi uncritical coverage during his rise to power. A few China specialists discuss how the elements of Shanghai clique were pushed aside in Xi’s rise to power, and some of the internal machinations of the state machinery, but much less than the issue deserves with China now the second largest economy in the world, and the largest nation-state on the planet in terms of population. Most notable of all is the uncritical coverage of Xi’s “anti-corruption” drive, which has given Xi the moral high ground in cleaning house and consolidating power. I have not read a single account in the western press that has observed that the anti-corruption efforts in China have left Xi’s inner circle entirely untouched. But who is going to take a stand in favor of corruption? Consolidating power by punishing rivals for corruption is a winning strategy.

Now that we know that China is a nation-state secondarily, and primarily the domain of a strongman, all that follows will depend on Xi himself. If Xi cares about the Chinese people and their welfare, he will use his power to strengthen the institutions of the country and will make it possible for an orderly political succession after he leaves power. But Xi could just as easily transform China into the largest kleptocracy on the planet, or into a tyranny, or any number of suboptimal outcomes. The stakes are high. The lives of more than a billion persons are in play. Much of the world’s manufacturing is sourced from China; rare is the supply chain that does not incorporate China at some point.

Even if Xi proves to be an honest and competent leader, China’s position in the world economic system is placed at risk merely by the revelation of the weakness of its institutions. China has put a lot of effort into trying to convince western businesses that China is a stable place to do business, where assets would not be arbitrarily expropriated and international legal norms would be respected. There is no reason to believe that this will suddenly change, but the weakness of the CPC is (or ought to be) a red flag for every business operating in China. The economy is stable at present, but that could change with a single executive decision on the part of Xi.

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quoted text



Ribera painted several imaginary portraits of ancient philosophers.

Protagoras of Abdera, by Jusepe de Ribera

In the spirit of my Extrapolating Plato’s Definition of Being, in which I took a short passage from Plato and extrapolated it beyond its originally intended scope, I would like to take a famous line from Protagoras and also extrapolate this beyond its originally intended scope. The passage from Protagoras I have in mind is his most famous bon mot:

“Man is the measure of all things, of the things that are, that they are, and of the things that are not, that they are not.”

…and in the original Greek…

“πάντων χρημάτων μέτρον ἔστὶν ἄνθρωπος, τῶν δὲ μὲν οντῶν ὡς ἔστιν, τῶν δὲ οὐκ ὄντων ὠς οὐκ ἔστιν”

Presocratic scholarship has focused on the relativism of Protagoras’ μέτρον, especially in comparison to the strong realism of Plato, but I don’t take the two to be mutually exclusive. On the contrary, I think we can better understand Plato through Protagoras and Protagoras through Plato.

Firstly, the Protagorean dictum reveals at once both the inherent naturalism of Greek philosophy, which is the spirit that continues to motivate the western philosophical tradition (which Bertrand Russell once commented is all, essentially, Greek philosophy), and the ontologizing nature of Greek thought, which is another persistent theme of western philosophy, though less often noticed than the naturalistic theme. Plato, despite his otherworldly realism, is part of this inherent naturalism of Greek philosophy, which in our own day has become explicitly naturalistic. Indeed, Greek philosophy since ancient Greece might be characterized as the convergence upon a fully naturalistic conception of the world, though this has been a long and bumpy road.

The naturalism of Greek thought, in turn, points to the proto-scientific character of Greek philosophy. The closest approximation to modern scientific thought prior to the scientific revolution is to be found in works such as Archimedes’ Statics and Eratosthenes of Cyrene’s estimate of the diameter of the earth. If these examples are not already fully scientific inquiries, they are at least proto-science, from which a fully scientific method might have emerged under different historical conditions.

Plato and Protagoras were both guilty of a certain degree of mysticism, but strong traces of the scientific naturalism of Greek thought is expressed in their work. Protagoras’ μέτρον in particular can be understood as an early step in the direction of quantificational concepts. Quantification is central to scientific thought (in my podcast The Cosmic Archipelago, Part II, I offered a variation on the familiar Cartesian theme of cogito, ergo sum, suggesting that, from the perspective of science, we could say I measure, therefore I am), and when we think of quantification we think of measurement in the sense of gradations on a standard scale. However, the most fundamental form of quantification is revealed by counting, and counting is essentially the determination whether something exists or not. Thus the Protagorean μέτρον — specifically, the things that are, that they are, and the things that are not, that they are not — is a quantificational schema for determining existence relative to a human observer. Protagoras’ μέτρον is a postulate of counting, and without counting there would be no mathematicized natural science.

All scientific knowledge as we know it is human scientific knowledge, and all of it is therefore anthropocentric in a way that is not necessarily a distortion. For human beings to have knowledge of the world in which they find themselves, they must have knowledge that the human mind can assimilate. Our epistemic concepts are the framework we have erected in order to make sense of the world, and these concepts are human creations. That does not mean that they are wrong, even if they have been frequently misleading. The pyrrhonian skeptic exploits this human, all-too-human weakness in our knowledge, claiming that because our concepts are imperfect, no knowledge whatsoever is possible. This is a strawman argument. Knowledge is possible, but it is human knowledge. Protagoras made this explicit. (This is one of the themes of my Cosmic Archipelago series.)

Taking Plato and Protagoras together — that is, taking Plato’s definition of being and Protagoras’ doctrine of measure — we probably come closer to the originally intended meaning of both Plato and Protagoras than if we treat them in isolation, a fortiori if we treat them as antagonists. Plato’s definition of being — the power to affect or be affected — and Protagoras’ dictum — that man is the measure of all things, which we can take to mean that quantification begins with a human observer — naturally coincide when the power to affect or be affected is understood relative to the human power to affect or be affected.

Since human knowledge begins with a human observer and human experience, knowledge necessarily also follows from that which affects a human being or that which a human being can effect. The role of experimentation in science since the scientific revolution takes this ontological interaction of affecting and being affected, makes it systematic, and derives all natural knowledge from this principle. Human beings formulate scientific experiments, and in so doing affect the world in building an experimental apparatus and running the experiment. The experiment, in turn, affects human beings as the scientist observes the experiment running and records how it affects him, i.e., what he observers in the world as a result of his intervention in the course of events.

Plato and Protagoras taken together as establishing an initial ontological basis for quantification lay the metaphysical groundwork for scientific naturalism, even if neither philosopher was a scientific naturalist in the strict sense.

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I have previously discussed Protagoras’ μέτρον in Ontological Ruminations: Six Protagorean Propositions on the Nature of Man and the World and A Non-Constructive World.

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Biological Bias

3 March 2018


What does it mean to be a biological being? It means, among other things, that one sees the world from a biological perspective, thinks in terms of concepts amenable to a biological brain, understands oneself and one’s species in its biological context, which is the biosphere of our homeworld, and that one persists in a mode of being distinctive to biological beings (which mode of being we call life). To be a biological being is to be related to the world through one’s biology; one has biological desires, biological aversions, biological imperatives, biological expectations, and biological intentions. Human beings are biological beings, and so are subject to all of these conditions of biological being.

When we think in terms of human bias — and we are subject to many biases as human beings — we usually focus on exclusively human biases, our anthropocentrism, our anthropic bias, but we are also subject to biases that follow from the other ontological classes of beings of which we are members. We are human beings, but we are also cognitive beings (i.e., intelligent agents), linguistic beings, mammalian beings, biological beings, physical beings, Stelliferous Era beings, and so on. This litany may be endless; whether or not we are aware of it, we may belong to an infinitude of ontological classes in virtue of the kind of beings that we are.

Another example of a bias to which human beings are subject but which is not exclusively anthropic, is what I have called terrestrial bias. Some time ago in Terrestrial Bias: Thought Experiments I asked, “…is there, among human beings, any sense of identification with the life of Earth? Is there a terrestrial bias, or will there be a terrestrial bias when we are able to compare our response to terrestrial life to our response to extraterrestrial life?” As I write this it occurs to me that a distinction can be made between planetary bias, to which any being of planetary endemism would be subject, and terrestrial bias understood as a bias specific to Earth, to which only life on Earth would be subject. In making this distinction, we understand that terrestrial bias is a special case of planetary bias, which latter is the more comprehensive concept.

Similarly, anthropic bias is a special case of the more comprehensive concept of intelligent agent bias. Again, we can distinguish between intelligent agent bias and anthropic bias, with intelligent agent bias being the more comprehensive concept under which anthropic bias falls. However, intelligent agents could also include artificial agents, who would be peers of human intelligent agents in respect of intelligence, but which would not share our biological bias. The many biases, then, which attend and inform human cognition, are nested within more comprehensive biases, as well as overlapping with the biases of other agents that might potentially exist and which would share some of our biases but which would not fall under exactly the same more comprehensive concepts. In Wittgensteinian terms, there is a complicated network of biases that overlap and intersect (cf. Philosophical Investigations, sec. 66); these biases correspond to a complicated network of ontological classes that overlap and intersect.

Our biological biases overlap and intersect with our other biases, such as our biases as the result of being human (anthropic bias) or our biases in virtue of being composed of matter (material or physical bias). Biological bias occupies a point midway between these two ontological classes. Our anthropic bias is exclusive to human beings, but we share our biological bias with every living thing on Earth, and perhaps with living things elsewhere in the cosmos, while we share our material bias much more widely with dust and gas and stars, except that these latter beings, not being intelligent agents, cannot exercise judgment or act as agents, so that their bias can only be manifested passively. One might well characterize the Platonic definition of beingthe capacity to affect or be affected — as the passive exercise of bias, with each class of beings affecting and being affected by other beings of the same class as peers.

I have sought to exhibit and disentangle and overlapping and intersecting of biological baises in a number of posts related to biophilia and biophobia, including:

Biocentrism and Biophilia

The Biocentric Thesis

The Scope of Biophilia

Not all biases are catastrophic distortions of reasoning. In Less than Cognitive Bias I made a distinction between anthropic biases that characterize the human condition without necessarily adversely affecting rational judgment, and anthropic biases that do undermine our ability to reason rationally. And in The Human Overview I sketched out the complexity of ordinary human communication, which is dense in subtle biases, some of which compromise our rationality, but many of which are crucial to our ability to rapidly reason about our circumstances — a skill with high survival value, and a skill at which human beings excel and which will not soon by modeled by artificial intelligence on account of its subtlety. A tripartite distinction can be made, then, among biases that compromise our reason, biases that are neutral in regard to out ability to reason, and biases that augment our ability to reason.

Our biological biases coincide to a large extent with our evolutionary psychology, and, in so far as our evolutionary psychology enabled us to survive in our environment of evolutionary adaptedness, our biological biases augment our ability to reason cogently and to act effectively in biological contexts — though only in what might be called peer biological contexts, as far as our particular scale of biological individuality allows us to identify with other biological individuals as peers. Our peer biological biases do not allow us to interact effectively at the level of the microbiome or at the level of the biosphere, with the result that considerable scientific effort has been required for us to understand and to interact effectively at these biological scales.

A similar applicability of bias may be true more widely of our other biases, which help us in some circumstances while hurting us in other circumstances. Certainly our anthropic biases have helped us to survive, and that is why we possess them in such robust forms, though they have helped us to survive as a species of planetary endemism. In the event of humanity breaking out of our homeworld as a spacefaring civilization, our anthropic, homeworld, and planetary endemism biases may not serve us as well in cosmological contexts. however, we know what to do about this. The cultivation of science and rigorous reasoning has allowed us to transcend many of our biases without actually losing our biases. Instead of viewing this as a human, all-too-human failure, we should think of this as a human strength: we can, when we apply ourselves, selectively transcend our biases, but when we need them, they are there for us, and they will be there for us until we actually alter ourselves biologically. Thus there is a biological “way out” from biological biases, but we might want to think twice before pursuing this way out, as our biological biases may well prove to be an asset (and perhaps an asset in unexpected, instinctive ways) when we eventually explore other biospheres and encounter another form of biology.

What Carl Sagan called the “deprovincialization” of biology may also take place at the level of human evolutionary psychology. If so, we shouldn’t desire to transcend or eliminate our biological biases as we should desire to augment and expand them in order to overcome what will be eventually learn about our terrestrial and homeworld biases from the biology of other worlds.

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Grand Strategy Annex

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Herodotus, the Father of History

In Rational Reconstructions of Time I described a series of intellectual developments in historiography in which big history appeared in the penultimate position as a recent historiographical innovation. There is another sense, however, in which there have always been big histories — that is to say, histories that take us from the origins of our world through the present and into the future — and we can identify a big history that represents many of the major stages through which western thought has passed. In what follows I will focus on western history, in so far as any regional focus is relevant, as “history” is a peculiarly western idea, originating in classical antiquity among the Greeks, and with its later innovations all emerging from western thought.

Saint Augustine, author of City of God

Shortly after Christianity emerged, a Christian big history was formulated across many works by many different authors, but I will focus on Saint Augustine’s City of God. Christianity takes up the mythological material of the earlier seriation of western civilization and codifies it in the light of the new faith. Augustine presented an over-arching vision of human history that corresponded to the salvation history of humanity according to Christian thought. Some scholars have argued that western Christianity is distinctive in its insistence upon the historicity of its salvation history. If this is true, then Augustine’s City of God is Exhibit “A” in the development of this idea, tracing the dual histories of the City of God and the City of Man, each of which punctuates the other in actual moments of historical time when the two worlds are inseparable for all their differences. Here, the world behind the world is always vividly present, and in a Platonic way (for Augustine was a Christian Platonist) was more real than the world we take for the real world.

Immanuel Kant, author of Universal Natural History and Theory of the Heavens

The Christian vision of history we find in Saint Augustine passed through many modifications but in its essentials remained largely intact until the Enlightenment, when the combined force of the scientific revolution and political turmoil began to dissolve the institutional structures of agricultural civilization. Here we have the remarkable work of Kant, better known for his three critiques, but who also wrote his Universal Natural History and Theory of the Heavens. The idea of a universal natural history extends the idea of natural history to the whole of the cosmos, and to human endeavor as well, and more or less coincides with the contemporary conception of big history, at least in so far as the scope and character of big history is concerned. Kant deserves a place in intellectual history for this if for nothing else. In other words, despite his idealist philosophy (formulated decades after his Universal Natural History), Kant laid the foundations of a naturalistic historiography for the whole of natural history. Since then, we have only been filling in the blanks.

Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet, author of Sketch for a Historical Picture of the Progress of the Human Spirit

The Marquis de Condorcet took this naturalistic conception of universal history and interpreted it within the philosophical context of the Encyclopédistes and the French Philosophes (being far more empiricist and materialist than Kant), in writing his Esquisse d’un tableau historique des progrès de l’esprit humain (Sketch for a Historical Picture of the Progress of the Human Mind), in ten books, the tenth book of which explicitly concerns itself with the future progress of the human mind. I may be wrong about this, but I believe this to be the first sustained effort at historiographical futurism in western thought. And Condorcet wrote this work while on the run from French revolutionary forces, having been branded a traitor by the revolution he had served. That Condorcet wrote his big history of progress and optimism while hiding from the law is a remarkable testimony to both the man and the idea to which he bore witness.

Johann Gottfried von Herder, author of Reflections on the Philosophy of History of Mankind

After the rationalism of the Enlightenment, European intellectual history took a sharp turn in another direction, and it was romanticism that was the order of the day. Kant’s younger contemporary, Johann Gottfried Herder, wrote his Ideen zur Philosophie der Geschichte der Menschheit (Ideas upon Philosophy and the History of Mankind, or Reflections on the Philosophy of History of Mankind, or any of the other translations of the title), as well as several essays on related themes (cf. the essays, “How Philosophy Can Become More Universal and Useful for the Benefit of the People” and “This Too a Philosophy of History for the Formation of Humanity”), at this time. In some ways, Herder’s romantic big history closely resembles the big histories of today, as he begins with what was known of the universe — the best science of the time, as it were — though he continues on in a way to justify regional nationalistic histories, which is in stark contrast to the big history of our time. We could learn from Herder on this point, if only we could be truly scientific in our objectivity and set aside the ideological conflicts that have arisen from nationalistic conceptions of history, which still today inform perspectives in historiography.

Otto Neurath, author of Foundations of the Social Sciences

In a paragraph that I have previously quoted in Scientific Metaphysics and Big History there is a plan for a positivist big history as conceived by Otto Neurath:

“…we may look at all sciences as dovetailed to such a degree that we may regard them as parts of one science which deals with stars, Milky Ways, earth, plants, animals, human beings, forests, natural regions, tribes, and nations — in short, a comprehensive cosmic history would be the result of such an agglomeration… Cosmic history would, as far as we are using a Universal Jargon throughout all branches of research, contain the same statements as our unified science. The language of our Encyclopedia may, therefore, be regarded as a typical language of history. There is no conflict between physicalism and this program of cosmic history.”

Otto Neurath, Foundations of the Social Sciences, Chicago and London: The University of Chicago Press, 1970 (originally published 1944), p. 9

To my knowledge, no one wrote this positivist big history, but it could have been written, and perhaps it should have been written. I can imagine an ambitious but eccentric scholar completely immersing himself or herself in the intellectual milieu of early twentieth century logical positivism and logical empiricism, and eventually coming to write, ex post facto, the positivist big history imagined by Neurath but not at that time executed. One might think of such an effort as a truly Quixotic quest, or as the fulfillment of a tradition of writing big histories on the basis of current philosophical thought.

From this thought experiment in the ex post facto writing of a history not written in its own time we can make an additional leap. I have noted elsewhere (The Cosmic Archipelago, Part III: Reconstructing the History of the Observable Universe) that scientific historiography has reconstructed the histories of peoples who did not write their own histories. This could be done in a systematic way. An exhaustive scientific research program in historiography could take the form of writing the history of every time and place from the perspective of every other time and place. We would have the functional equivalent of this research program if we had a big history written from the perspective of every time and place for which a distinctive perspective can be identified, because each big history from each identifiable perspective would be a history of the world entire, and thus would subsume under it all regional and parochial histories.

I previously proposed an idea of a similarly exhaustive historiography of the kind that could only be written once the end was known. In my Who will read the Encyclopedia Galactica? I suggested that Freeman Dyson’s eternal intelligences could busy themselves as historiographers through the coming trillions of years when the civilizations of the Stelliferous Era are no more, and there can be no more civilizations of this kind because there are no longer planets being warmed by stellar insolation, hence no more civilizations of planetary endemism.

It is a commonplace of historiographical thought that each generation must write and re-write the past for its own purposes and from its own point of view. Gibbon’s Enlightenment history of the later Roman Empire is distinct in temperament and outlook from George Ostrogorsky’s History of the Byzantine State. While an advanced intelligence in the post-Stelliferous Era would want to bring its own perspective to the histories of the civilizations of the Stelliferous Era, it would also want a complete “internal” account of these civilizations, in the spirit of thought experiments in writing histories that could have or should have been written during particular periods, but which, for one reason or another, never were written. If we imagine eternal intelligences (at least while sufficient energy remains in the universe) capable of running detailed simulations of the past, this could be a source of the immersive scholarship that would make it possible to write the unwritten big histories of ages that produced a distinctive philosophical perspective, but which did not produce a historian (or the idea of a big history) that could execute the idea in historical form.

There is a sense in which these potentially vast unwritten histories, the unactualized rivals to Gibbon’s Decline and Fall of the Roman Empire, are like the great unbuilt buildings, conceived and sketched by architects, but for which there was neither the interest nor the wherewithal to build. I am thinking, above all, of Étienne-Louis Boullée’s Cenotaph for Isaac Newton, but I could just as well cite the unbuilt cities of Antonio Sant’Elia, the skyscraper designed by Antonio Gaudí, or Frank Lloyd Wright’s mile high skyscraper (cf. Planners and their Cities, in which I discuss other great unbuilt projects, such as Le Corbusier’s Voisin Plan for Paris and Wright’s Broadacre City). Just as I have here imagined unwritten histories eventually written, so too I have imagined these great unbuilt buildings someday built. Specifically, I have suggested that a future human civilization might retain its connection to the terrestrial past without duplicating the past by building structures proposed for Earth but never built on Earth.

History is an architecture of the past. We construct a history for ourselves, and then we inhabit it. If we don’t construct our own history, someone else will construct our history for us, and then we live in the intellectual equivalent of The Projects, trying to make a home for ourselves in someone else’s vision of our past. It is not likely that we will feel entirely comfortable within a past conceived by another who does not share our philosophical presuppositions.

From the perspective of big history, and from the perspective of what I call formal historiography, history is also an architecture of the future, which we inhabit with our hopes and fears and expectations and intentions of the future. And indeed we might think of big history as a particular kind of architecture — a bridge that we build between the past and the future. In this way, we can understand why and how most ages have written big histories for themselves out of the need to bridge past and future, between which the present is suspended.

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Studies in Grand Historiography

1. The Science of Time

2. Addendum on Big History as the Science of Time

3. The Epistemic Overview Effect

4. 2014 IBHA Conference Day 1

5. 2014 IBHA Conference Day 2

6. 2014 IBHA Conference Day 3

7. Big History and Historiography

8. Big History and Scientific Historiography

9. Philosophy for Industrial-Technological Civilization

10. Is it possible to specialize in the big picture?

11. Rational Reconstructions of Time

12. History in an Extended Sense

13. Scientific Metaphysics and Big History

14. Copernican Historiography

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Grand Strategy Annex

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The Snapshot Effect

22 January 2018


Images will always be with us, but the age of the snapshot understood in its cultural and technological context, now belongs to the past. Or, if not to the past, it belongs to antiquarians and enthusiasts who will keep the technology of the snapshot alive even as it passes out of the popular mind. The snapshot inhabited that era that intervened between the age of cameras as large, bulky, specialized equipment that required a certain expertise to operate, and today’s universal presence of cameras and consequent universal availability of images — images often made available on the same electronic device that captured the image. The snapshot — presumably named for the onomatopoeic mechanical sound of the camera shutter that went “Snap!” as one took the “shot” — is, then, predicated upon a particular degree of finitude, of images more common and more spontaneous than a daguerreotype, but also less common and of more value than a smartphone selfie.

The most famous photographers of the snapshot era — for example, Henri Cartier-Bresson — become known for their candid and spontaneous images of ordinary life, sort of the still life version of cinéma vérité. Never before had so much of ordinary life been captured and preserved. Painters had always been interested in genre scenes, and the early photographers who lugged around their heavy and complex gear often followed the interest and example of these painters, but these images were relatively rare. In the age of the snapshot, images of ordinary people engaged in ordinary pursuits became as ordinary as the people and the pursuits themselves.

Part of what we mean, then, when we refer casually to a “snapshot,” is this sense of an image that spontaneously captures an ordinary moment of history, without formality or pretense, but with a documentarian’s fidelity. And once the moment is past, it remains only in the snapshot, almost a random moment fixed in time, while the persons and the events and the circumstances that once came together in the confluence of the snapshot, are now gone or changed beyond recognition.

It is partly this meaning that I want to tap into when I use the term “snapshot effect” to convey a particular idea about the human relationship to time and to history. Human life is long compared to the life of a mayfly, but it is quite short compared to the life of a redwood, and shorter still when measured against evolutionary, geological, or cosmological scales of time. What the individual human being experiences — what the individual sees, hears, feels, and so on — is as a snapshot in comparison to the world of which it is a fleeting image. A snapshot may or may not be representative of what it purports to represent; it may be a good likeness or a poor likeness. Because a snapshot is a moment snatched out of a continuum, we can only judge its fidelity if we compare it to a sufficient number of comparable moments taken from the same continuum. But the image often has the impact that it has precisely because it is a moment snatched out of time and stripped of all context. Often we resist a survey that would reveal the representativeness of the snapshot because to do so would be to deprive ourselves of the power of the isolated image.

I am going to use the term “snapshot effect,” then, to refer to the temporally narrow nature (and perhaps also the fragmentary nature) of human perception. We see not the world, but a snapshot of the world. We see not the object, but the side of the face that happens to be turned toward us when we glance in its direction. We hear not the narrative of a life, but a snippet of conversation that relates only a fragment of a single experience. We taste not the crop of strawberries, but the single strawberry that dissolves on our tongue, and judge the quality of the year’s produce by this experience. Even the grandest of grand views of the world are snapshots: to look into the night sky is to experience a snapshot of cosmology, and to recognize a geological formation is a snapshot of deep time. These snapshots reveal more than a casual glance, especially if they are attended by understanding, but they still exclude far more than they include.

Any rational individual, and any individual trained in the sciences, learns to control for the limited evidence available to us, but as carefully as we set our trap for limited evidence by rigorously controlling the conditions of our observations — observations that will count toward scientific knowledge, whereas our ordinary observations do not count because they are not so controlled — so too we also grant ourselves license to derive generalities from these observations. Ordinary experience is but a snapshot of the world; scientific experience derived from controlled conditions is an even more fragmentary snapshot of the world.

Because of the snapshot effect, we have recourse to principles that generalize the limited evidence to which we are privileged. The cosmological principle legitimizes our extrapolation from limited evidence to the universe entire. The principle of mediocrity legitimizes our extrapolation from a possibly exceptional moment to a range of ordinary cases and the most likely course of events. Conservation principles assure us that we can generalize from our limited experience of matter and energy to the behavior of the universe entire.

A recognition of the snapshot effect has long been with us, though called by other names. It has been a truism of philosophy, equally acknowledged by diverse (if not antagonistic) schools of thought, that our experiences constitute only a small slice of the actuality of the world. To cite two examples from the twentieth century, here, to start, is Bertrand Russell:

“…let us concentrate attention on the table. To the eye it is oblong, brown and shiny, to the touch it is smooth and cool and hard; when I tap it, it gives out a wooden sound. Any one else who sees and feels and hears the table will agree with this description, so that it might seem as if no difficulty would arise; but as soon as we try to be more precise our troubles begin. Although I believe that the table is ‘really’ of the same colour all over, the parts that reflect the light look much brighter than the other parts, and some parts look white because of reflected light. I know that, if I move, the parts that reflect the light will be different, so that the apparent distribution of colours on the table will change. It follows that if several people are looking at the table at the same moment, no two of them will see exactly the same distribution of colours, because no two can see it from exactly the same point of view, and any change in the point of view makes some change in the way the light is reflected.”

Bertrand Russell, The Problems of Philosophy, Chap. I, “Appearance and Reality”

Russell represents the tradition that would become Anglo-American analytical philosophy, temperamentally and usually also theoretically disjoint from European continental philosophy, which might well be represented by Jean-Paul Sartre. Nevertheless, Sartre opens his enormous treatise Being and Nothingness with a passage that closely echoes that of Russell quoted above:

“…an object posits the series of its appearances as infinite. Thus the appearance, which is finite, indicates itself in its finitude, but at the same time in order to be grasped as an appearance-of-that-which-appears, it requires that it be surpassed toward infinity. This new opposition, the ‘finite and the infinite,’ or better, ‘the infinite in the finite,’ replaces the dualism of being and appearance. What appears in fact is only an aspect of the object, and the object is altogether in that aspect and altogether outside of it.”

Jean-Paul Sartre, Being and Nothingness, translated by Hazel Barnes, Introduction: The Pursuit of Being, “I. The Phenomenon,” p. xlvii

Both Russell and Sartre in the passages quoted above are wrestling with the ancient western metaphysical question of appearance and reality. Both recognize a multiplicity of appearances and a presumptive unity of the objects of which the appearances are a manifestation. Seen in this light, the snapshot effect is a recognition that we see only an appearance and not the reality, and this reflection in turn embeds this simple observation in a metaphysical context that has been with us since the Greeks created western philosophy.

The snapshot effect means that our experiences are appearances, but our appreciation of appearances has grown since the time of Parmenides and Plato, and we see Russell and Sartre alike struggling to make out exactly why we should attach an ontological import to appearances — snapshots, as it were — when we know that they do no exhaust reality, and sometimes they betray reality.

The ontology of time and of history ought to concern us as much as the ontology of objects implicitly schematized by Russell and Sartre. A snapshot of time is an appearance of time, and as an appearance it does not exhaust the reality of time. Nevertheless, we struggle to do justice to this appearance — just as we struggle to do justice to our intuitions, for, indeed, a snapshot of time is an instance of sensible intuition — because the moment abstracted from time is still an authentic manifestation of time.

The “snapshot effect,” then, will be the term I will use to refer to the fact that human perceptions are a mere snapshot, perhaps representative or perhaps not, but perceptions which we tend to treat as normative, though we rarely take the trouble even to attempt to understand the extent to which our snapshot views of the world are, in fact, normative. There is, then, not only a metaphysical aspect to the snapshot effect, but also an axiological aspect to the snapshot effect, as our valuations are likely to be tied to, if not derived from, a snapshot in this sense.

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Grand Strategy Annex

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The Science and Technology of Civilization

In several contexts I have observed that there is no science of civilization, i.e., that there is no science that takes civilization as its unique object of inquiry. I wrote a short paper, Manifesto for the Scientific Study of Civilization, in which I outlined how I would begin to address this deficit in our knowledge. (And I’ve written several blog posts on the same, such as The Study of Civilization as Rigorous Science, Addendum on the Study of Civilization as Rigorous Science, and The Study of Civilization as Formal Science and as Adventure Science, inter alia.) Suppose we were to undertake a science of civilization (whether by my plan or some other plan) and thus began to assemble reliable scientific knowledge of civilization. Would we be content only to understand civilization, or would we want to employ our scientific knowledge in order to effect changes in the same way that scientific knowledge of other aspects of human life have facilitated more effective action?

Can we distinguish between a science of civilization and technologies of civilization? What is the difference between a science and a technology? One of the ways to distinguish science from technology is that science seeks knowledge, understanding, and explanation as ends in themselves, while technology employs scientific knowledge, understanding and explanation in order to attain some end or aim. Roughly, science has no purpose beyond itself, while technology is conceived specifically for some purpose. Thus if we wish to use scientific knowledge of civilization not only to understand what civilization is, but also to shape, direct, and develop civilization in particular ways, we would then need to go beyond formulating a science of civilization and to also construct technologies of civilization.

This distinction, while helpful, implies that technologies follow from science as applications of that science. This implication is misleading because technologies can appear in isolation from any science (other than the most rudimentary forms of knowledge). Epistemically, science precedes technology, but in terms of historical order, technology long preceded science. Our ancestors were already shaping stone tools millions of years ago, and by the time civilization emerged in human history and the first glimmerings of science can be discerned, technology was already well advanced. However, the greatest disruption in the history of civilization (to date) has been the industrial revolution, and the industrial revolution marks the point at human history in which the historical order of technology followed by science was reversed by the systematic application of science to industry, and since that time the most powerful technologies have been derived from following the epistemic order of starting with science and only then, after attaining scientific knowledge, applying this scientific knowledge to the building of technology.

Social Engineering for Preferred Outcomes

If we were to formulate a science of civilization today, it would be a science formulated in this post-industrialization historical context, and we would expect that we could converge on a body of knowledge about civilization that could then be applied reflexively to civilization as technologies in order to achieve whatever results are desired (within the scope of what is possible; assuming that there are intrinsic modal limits to civilization). At the same time, thinking of civilization in this way, and looking back over the historical record, we can easily see that there have been many technologies of civilization (i.e., technologies of civilization preceding a science of civilization) in use from the beginnings of large-scale social organization. (In an earlier post I called these social technologies, among which we can count civilization itself.)

Almost all civilizations have intervened in social outcomes in a heavy-handed way through social engineering. The inquisition, for example, was a form of social engineering intended to limit, to contain, to punish, and to expunge religious non-conformity. While this is perhaps an extreme example of social engineering through religious institutions, since most central projects of civilizations have been religious in character, most of human history has been marked by the use of religious institutions to shape and direct social life. Or, to take an example less likely to be controversial (religious examples are controversial both because those who continue to identify with Axial Age religious faiths would see this discussion as an affront to their beliefs, and also because religiously-based social engineering could be taken to be a soft target), law can be understood as a technology of civilization. From the earliest attempts at the regulation of social life, as, for example, with the code of Hammurabi, to the present day, systems of law have been central to shaping large-scale social organization.

The Structure of Civilization through the Lens of Social Technologies

Elsewhere I have suggested that civilization can be understood as an institution of institutions. This is a very low resolution conception, but it has its uses. In the same spirit we can say that civilization is a social technology of social technologies, and this, too, is a very low resolution concept. I have also proposed that a civilization can be defined as an economic infrastructure linked to an intellectual superstructure by a central project (for example in my 2017 Icarus Interstellar Starship Congress presentation, The Role of Lunar Civilization in Interstellar Buildout). This conception of civilization is a bit more articulated, as it gives specific classes of social institutions that jointly constitute the social institution of civilization, and how these classes of institutions are related to each other.

In revisiting the question of civilization from the perspective of a science of civilization that might make technologies of civilization available, I have come to realize that the definition one gives of the structure of civilization will reflect (in part) the concepts employed in the analysis of civilization. What I have previously identified as the economic infrastructure and intellectual superstructure of civilization could mostly be classed under the concept of technologies of civilization, and this can be employed to present a structural model of civilization slightly different from that I have previous presented.

As noted above, technologies are purposive, and in order to organize purposive activity it is necessary to define or otherwise specify these purposes. This is the function of the central project of a civilization. From this perspective, the structure of civilization is a central project that delineates purposes and all the other institutions of civilization are social technologies that implement the purposes of the central project. This account of the structure of civilization does not contradict my definition of civilization in terms of superstructure and infrastructure joined by a central project, but it does give a distinctly different emphasis.

Partial and Complete Definitions of Civilization

There are many definitions of civilization that have been proposed. Civilization is a multivariant phenomenon (it is characterized by many different properties) and so each time we look at civilization a bit differently, we tend to see something a bit different. I have been thinking about civilization for many years, writing up my ideas in fragmentary form on this blog, and continually re-visiting these ideas and testing them for adequacy in the light of later formulations. In the above I have tried to show how different definitions of civilization (especially definitions of varying degrees of resolution) can be compatible and do not necessarily point to contradiction. However, this is does not entail that all definitions of civilization are compatible.

Formally, we will want to know which definitions of civilization are different ways of looking at the same thing, and thus ultimately compatible if we can fit them together properly within an overarching framework, and which definitions are not singling out the same thing, either because they fail to single out anything, or they fail to single out civilization specifically. Someone may set out to define civilization, and they end up defining culture or society instead (and perhaps conflating culture, society, and civilization). Some others may set out to define civilization and end up producing an incoherent definition that doesn’t allow us to converge upon civilizations in any reliable theoretical way. More often, attempts at defining civilization end up defining some part or aspect or property of civilization, but fail to illuminate civilization on the whole.

Partial definitions of civilization mean that the definition does not yet capture the big picture of civilization, but partial definitions can still be very helpful. As we have seen above, the institutions that jointly shape civil society can be distinguished between a class of institutions of the economic infrastructure (the ways and means of civilization) and a class of institutions of the intellectual superstructure (exposition of the ends and aims of civilization), but that all of these institutions can also be seen as falling within the same class of social technologies employed to implement the central project of a civilization.

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Grand Strategy Annex

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A Prehistory of the Overview Effect

Among many other contributions, E. O. Wilson is known for the Savannah Hypothesis, according to which human beings are especially suited, both biologically and cognitively, to life on the African savannah, which constituted the environment of evolutionary adaptedness (EEA) for our species. E. O. Wilson discusses this in the chapter “The Right Place” in his book Biophilia, in which he characterized this landscape as, “…the ideal toward which human beings unconsciously strive…” (pp. 108-109). Wilson developed this idea over much of this chapter, writing:

“…it seems that whenever people are given a free choice, they move to open tree-studded land on prominences overlooking water. This worldwide tendency is no longer dictated by the hard necessities of hunter-gatherer life. It has become largely aesthetic, a spur to art and landscaping. Those who exercise the greatest degree of free choice, the rich and powerful, congregate on high land above lakes and rivers and along ocean bluffs. On such sites they build palaces, villas, temples, and corporate retreats. Psychologists have noticed that people entering unfamiliar places tend to move toward towers and other large objects breaking the skyline.”

E. O. Wilson, Biophilia, Harvard University Press, 1984, p. 110 (I encourage reading the entire chapter, all of which is relevant to this discussion.)

In this context, the Savannah Hypothesis places human beings in a position to have an overview of the biome that constituted their EEA, that is to say, an overview of their relevant environment, the environment in which their differential survival and reproduction would mean either the continuation or the extinction of the species. As we know, human ancestors survived in such an environment for millions of years, and anatomically modern human beings passed through a bottleneck in such a landscape.

The African savannah was the landscape that played the most recent, and perhaps the most strongly selective role in the human mind and body, and there would be a high survival value attached to having an overview of this landscape. If we seek out prominences from which to take in a sweeping view, we do so for good reason.

Esther Quaedackers’ conception of little big histories.

Little Big Histories and Little Overviews

We can think of this biome overview as a “little overview,” which term I introduce in analogy to Esther Quadecker’s use of “little big histories,” that is to say, big histories that trace the development of some small topic (smaller than the whole of the universe) over cosmological time, from the big bang to the present day, and possibility also extending into the indefinite future. In the unfolding of our “little overviews” over time we have a prehistory of the overview effect as it is fully revealed when we see our homeworld from space.

Little overviews have played an important role in human history. The need for security and surveillance has resulted in the need for watchtowers and for the “crow’s nest” on a ship. Many of the most famous castles are built on high escarpments in order to command the view of the region, which, before telecommunications, was the only way in which to have a comprehensive survey. These precariously perched castles are thrilling to the romantic imagination, but they originally had a strategic purpose of giving an overview of a geographical region that was tactically significant in an age of fighting prior to modern technology. Anything that could happen on a battlefield could be taken in at a single glance.

Everyone will recall that the Persian king Xerxes had a throne erected from which we could watch the Battle of Salamis unfold as it happened. Byron immortalized the image in his Don Juan:

A king sate on the rocky brow
Which looks o’er sea-born Salamis;
And ships, by thousands, lay below,
And men in nations;—all were his!
He counted them at break of day —
And when the sun set where were they?

A culturally significant little overview is described in Petrarch’s account in a letter to his father of climbing Mount Ventoux, which is one of the most famous accounts of mountain climbing in western literature:

“…owing to the unaccustomed quality of the air and the effect of the great sweep of view spread out before me, I stood like one dazed. I beheld the clouds under our feet, and what I had read of Athos and Olympus seemed less incredible as I myself witnessed the same things from a mountain of less fame. I turned my eyes toward Italy, whither my heart most inclined. The Alps, rugged and snow-capped, seemed to rise close by, although they were really at a great distance…”

Francesco Petrarch, The Ascent of Mount Ventoux

It is something of a sport among historians to debate whether Petrarch was essentially medieval or already a modern mind in medieval times. Certainly there are intimations of modernity in Petrarch. The fact that Petrarch made his ascent of Mount Ventoux, that is to say, the spirit in which he made the ascent, was modern, though his response to the experience was not modern, but medieval. While on top Mount Ventoux Petrarch pulled out a copy of St. Augustine’s Confessions (a symbol both of antiquity and of Christendom) and opens to a passage that reads, “And men go about to wonder at the heights of the mountains, and the mighty waves of the sea, and the wide sweep of rivers, and the circuit of the ocean, and the revolution of the stars, but themselves they consider not.” Petrarch takes this as a rebuke to the worldliness implicit in his ambition to ascend the mountain, and he concluded his letter on the experience with this thought: “How earnestly should we strive, not to stand on mountain-tops, but to trample beneath us those appetites which spring from earthly impulses.”

With this medieval Christian response to a little overview there is much in common with the Stoic “view from above” thought experiment that I previously discussed in Stoicism, Sensibility, and the Overview Effect — the pettiness and smallness of the ordinary world of affairs, the need to transcend this smallness, the potential nobility of the human spirit in contrast to its actual corruption — though the specifically Christian elements are distinctive to Petrarch and place him a distance away from Marcus Aurelius’ disdain for the filth of the terrestrial life. Augustinian theology had declared the world good because God made it, so that the world could no longer be grandly dismissed as with the Stoics. It is the sinful human soul, and not the world, that is to be rebuked and chastised. This is the spirit that Petrarch brought to his experience of a little overview.

The Modern Overview Effect

We begin to encounter a more fully modern appreciation of little overviews in the earliest accounts of balloon aviation, where we find the distinctive relation between the attainment of a physical overview and a change in cognitive perspective, i.e., the idea that the two are tightly coupled. An early balloon flight pioneer, Fulgence Marion (a pen name used by Camille Flammarion), presents this relation plainly and simply: “We gave ourselves up to the contemplation of the views which the immense stretch of country beneath us presented.” Here the object of contemplate is the overview itself, which Marion describes in rapturous prose:

“The broad plains appeared before our view in all their magnificence. No snow, no clouds were now to be seen, except around the horizon, where a few clouds seemed to rest on the earth. We passed in a minute from winter to spring. We saw the immeasurable earth covered with towns and villages, which at that distance appeared only so many isolated mansions surrounded with gardens. The rivers which wound about in all directions seemed no more than rills for the adornment of these mansions; the largest forests looked mere clumps or groves, and the meadows and broad fields seemed no more than garden plots. These marvellous tableaux, which no painter could render, reminded us of the fairy metamorphoses; only with this difference, that we were beholding upon a mighty scale what imagination could only picture in little. It is in such a situation that the soul rises to the loftiest height, that the thoughts are exalted and succeed each other with the greatest rapidity.”

Fulgence Marion, Wonderful Balloon Ascents, or, the Conquest of the Skies, Chapter III

Petrarch was on the verge of just such an appreciation of the view from Mount Ventoux, one might even say that he felt this appreciation, but then turned from it in order to use the experience as a pretext to return to the Augustinian “inner man.”

Alexander von Humboldt, one of the great synthesizers of scientific knowledge of the 19th century, attempted to provide an explanation of the connection between overviews and cognitive changes. Criticizing Burke’s view that the feeling of the sublime arises from a lack of knowledge, Humboldt argues that past ignorance was responsible for the cosmological errors of antiquity, while our exultation at glimpsing an overview arises from our ability to connect ideas previously separate, so that the cognitive shift in the overview effect is due not to lack of knowledge, but to the expansion and integration of knowledge:

“The illusion of the senses… would have nailed the stars to the crystalline dome of the sky; but astronomy has assigned to space an indefinite extent; and if she has set limits to the great nebula to which our solar system belongs, it has been to shew us further and further beyond its bounds, (as our optic powers are increased,) island after island of scattered nebulae. The feeling of the sublime, so far as it arises from the contemplation of physical extent, reflects itself in the feeling of the infinite which belongs to another sphere of ideas. That which it offers of solemn and imposing it owes to the connexion just indicated; and hence the analogy of the emotions and of the pleasure excited in us in the midst of the wide sea; or on some lonely mountain summit, surrounded by semi-transparent vaporous clouds; or, when placed before one of those powerful telescopes which resolve the remoter nebulae into stars, the imagination soars into the boundless regions of universal space.”

Alexander von Humboldt, Cosmos: Sketch of a Physical Description of the Universe, London: Longman, Brown, Green, and Longmans, 1846, pp. 20-21

After Petrarch, the world was changed by the three revolutions — scientific, political, and industrial — and this changed context made possible the little overviews of Fulgence Marion and Alexander von Humboldt, who did not feel the need, as did Petrarch, to turn away to focus on the human soul and its cultivation of piety and salvation. Science changed the way that human beings understood the world, and their place in the world, so that subsequent mountain climbers saw the view of the world from the top of a mountain against a different conceptual background. Here is Julius Evola’s evocation of his contemplation of a little overview:

“…after the action, contemplation ensues. It is time to enjoy the peaks and heights from our vantage point: where the view becomes circular and celestial, where petty concerns of ordinary people, of the meaningless struggles of the life of the plains, disappear, where nothing else exists but the sky and the free and powerful forces that reflect the titanic choir of the peaks.”

Julius Evola, Meditations on the Peaks, “The Northern Wall of Eastern Lyskamm”

Evola’s attitude here more closely resembles that of the Stoic “view from above” thought experiment than Petrarch’s response to climbing Mount Ventoux, though Evola may have been consciously evoking the Stoic attitude, and was probably also influenced by Nietzsche, who spent much of his adult life in Switzerland and often rhapsodized on the views from mountain peaks.

It was a little overview that led to the explicit formulation of the overview effect, as Frank White described in the first chapter of the book in which he named and explicitly formulated the overview effect:

“My own effort to confirm the reality of the Overview Effect had its origins in a cross-country flight in the late 1970s. As the plane flew north of Washington, D.C., I found myself looking down at the Capitol and Washington Monument. From 30,000 feet, they looked like little toys sparkling in the sunshine. From that altitude, all of Washington looked small and insignificant. However, I knew that people down there were making life-or-death decisions on my behalf and taking themselves very seriously as they did so… When the plane landed, everyone on it would act just like the people over whom we flew. This line of thought led to a simple but important realization: mental processes and views of life cannot be separated from physical location.”

Frank White, The Overview Effect: Space Exploration and the Future of Humanity, third edition, American Institute of Aeronautics and Astronautics, Inc., 2014, p. 1

Here the modern overview conception is fully stated for the first time in terms amenable to scientific investigation. There is much that is continuous with the ancient and medieval responses to little overviews, and it may be taken as the telos upon which earlier modern accounts like those of Marion, von Humboldt, and Evola converge.

In the ancient, medieval, and modern responses to the overview effect there is both a common element as well as distinctive elements that derive from each period. In common is the sense of elevation above the merely mundane and of converging upon a “big picture” of the relationship between humanity and its homeworld; the distinctive elements arise from the valuation of our homeworld, of humanity, and the conception of the proper relationship between the two. The ancient response draws heavily upon Platonism, seeing the sublunary world as intrinsically less valuable than the superlunary world of the heavens, and humanity is understood to be the better as it tends toward the latter, and the worse as it tends to the former. The medieval response is to reflect on the meanness of human nature in contradistinction to the grandeur of God’s creation. The modern response, while retaining elements of earlier little overviews, begins to pare away the evaluative aspects to converge upon a theoretical expression of the core of the overview experience.

The Future of Little Overviews

Now that humanity is in possession of the overview effect in its most explicit and complete form, as some human beings have seen our homeworld entire with their own eyes, it might be thought that little overviews belong to the past. This would be misleading. The photographs that have brought the overview effect to millions if not billions of persons have been themselves little overviews — an overview that can be held in one’s hand, and which gives us a sense of the actual experience of the overview effect, without actually experiencing the full overview effect for ourselves (like a picture taken from the summit of a mountain by those who did not make the climb themselves). For the time being, the overview effect for most of us will be this little overview, and it remains to some future iteration of our technology to make this view universally available to those who desire it.

Other little overviews also continue to change our perspective on our world and our relation to the universe. The Hubble telescope deep field images — the Hubble Deep Field (HDF), Ultra Deep Field (HUDF), and eXtreme Deep Field (XDF) — are little overviews of the cosmos entire; little because they are a very small sample of the sky, but an overview more comprehensive than any previous human perspective on the universe. In one glance we can take in thousands of galaxies, many of them, like the Milky Way, with hundreds of billions stars each.

Coming to an understanding of the big picture is likely to involve an ongoing dialectic by which we pass from experiences that present us with a more comprehensive perspective, and which serve as imaginative points of departure to contemplation of the cosmos entire, to little overviews that provide counterpoint to our personal experiences and which fill out the expansion of our imagination with greater detail and greater breadth and diversity than the personal experiences of any one individual. Those who can most seamlessly integrate and understand these sources of overviews as a whole, will come to the most comprehensive perspective that can be reconciled with the details and reality of ordinary experience.

Kurt Gödel 1906-1978

An Overview-Seeking Animal

We have all heard that man is a political animal, or a social animal, or a tool-making animal, and so on. We can add to this litany of distinctive human imperatives that man is an overview-seeking animal. The overviews we have attained, perhaps spurred onward by the evolutionary psychology that E. O. Wilson identified as the Savannah hypothesis, have allowed us to repeatedly transcend our previous perspectives, and with this transcendence of physical perspectives has followed a transcendence of cognitive perspectives, i.e., worldviews or conceptual frameworks. Recently in Einstein on Geometrical Intuition I quoted a passage from Gödel (one of my favorite passages, quoted many times) that is relevant to the transcendence of cognitive perspectives:

“Turing… gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive. What Turing disregards completely is the fact that mind, in its use, is not static, but is constantly developing, i.e., that we understand abstract terms more and more precisely as we go on using them, and that more and more abstract terms enter the sphere of our understanding. There may exist systematic methods of actualizing this development, which could form part of the procedure. Therefore, although at each stage the number and precision of the abstract terms at our disposal may be finite, both (and, therefore, also Turing’s number of distinguishable states of mind) may converge toward infinity in the course of the application of the procedure.”

“Some remarks on the undecidability results” (Italics in original) in Gödel, Kurt, Collected Works, Volume II, Publications 1938-1974, New York and Oxford: Oxford University Press, 1990, p. 306.

The seeking out of overviews, whether little overviews or grand overviews revealing our homeworld entire, is part of the method of actualizing our cognitive development by adding more terms to the sphere of our understanding. What Gödel approached from an abstract point of view the overview effect gives us from a concrete point of view.

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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

A Natural History of Overview Effects

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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The Franchise Problem

13 December 2017


‘Chairing the Member’ from William Hogarth’s series ‘Humours of an Election.’

Is an inclusive franchise a bug or a feature of democracy?

One of the unquestioned political values (if not ideals) of our time is not only that of liberal democracy, but, even more-so, liberal democracy with the broadest possible franchise. Many today regard the expansion of the franchise as one of the most important accomplishments of contemporary civil society and civil rights. Indeed, the limited franchise of democracies prior to the twentieth century expansion of the voting franchise is today regarded as a terrible moral stain on earlier societies. But what if a limited franchise were not a bug but rather a feature of early democracies? Can democracy even function with a universal franchise? We don’t know. Political societies in their contemporary form of a nearly universal franchise are historically very young, and we cannot yet say whether or not these political experiments will be successful.

Even to suggest a restriction on the franchise after a century of expansion is political heresy in the western world, but we may be forced into accepting some limitation on voting rights in order to salvage our societies, which seem bent on self-destruction. It is likely that the most we can do at this point in the history of western civilization is to salvage what can be salvaged from the Enlightenment project; more radically, western civilization may need to sever its relationship to the Enlightenment project and adopt some other ideological formation as its central project, and this would likely be a process as fraught as the Thirty Years’ War, which was one of the causes of the formation of the Enlightenment project. I think it would be preferable to experiment with different implementations of the Enlightenment project though different franchise regimes, when seen in comparison to the chaos that would ensue from entirely dispensing with the Enlightenment project. Thus, I am well aware that the present discussion lies outside the configuration of the Overton window as it functions in contemporary western societies, but I think that this discussion can be conducted in a rational way, and that it may suggest political experiments that have never yet been tried in the history of humanity.

Even before the age of the nearly universal franchise, democracy was believed to be unworkable. Plato and Aristotle had nothing good to say about democracy — after all, it had been democratic Athens that had condemned Socrates to death. In modern times there is a well-known quote from Alexander Fraser Tytler, often mis-attributed to Alexis de Tocqueville, suggesting that democracy is fatally flawed:

“A Democracy cannot exist as a permanent form of government. It can only exist until the voters discover they can vote themselves largess out of the public treasury. From that moment on the majority always votes for the candidate promising the most benefits from the public treasury with the results that Democracy always collapses over a loose fiscal policy, always to be followed by a dictatorship.”

While this was written before the nearly universal franchise of contemporary democracies, it points to a structural problem in democracies that is only made worse by the expanding scope of the franchise. The practical consequence of a nearly universal franchise is that voting rights have been given to an even greater number individuals who are not stakeholders in society except in so far as their “stake” in society is the value that they extract from the others in that society that produce value. Very few individuals are productive members of society — most consume more than they contribute to the common weal. It sounds cruel to say it, but this is a case in which we must eventually be cruel to be kind. The dependent members of a society will suffer more in the long run from the collapse of that society than they would suffer from being excluded from the franchise.

A democracy with a limited franchise has as its goal a franchise that is restricted to productive stakeholders in society. Limiting the vote to property owners was one way to accomplish this, and moreover this retained a connection to the feudal past, in which the lords of feudal estates were a law unto themselves in the decentralized power structure of feudalism. Nevertheless, democracy has deep roots in western society, and many of these feudal societies had democratic aspects that we fail to recognize as democratic today because of the severely restricted franchise. For example, when the aldermen of a town gathered to make a decision, this was an essentially democratic institution. Many such institutions existed on a local level, and they reached up all the way to the election of the Holy Roman Emperor, where the franchise was limited to prince-electors of the Holy Roman Empire electoral college. The Vatican retains a system like this to the present day, in which the College of Cardinals elects the Pope, not a mass ballot among Roman Catholics.

In past democratic societies, voting rights were restricted across categories of age, sex, and race, and these are precisely the categories that became the focus of identity politics in our own time. Since these past categories of franchise limitation have proved to be so divisive, the obvious political experiment is to attempt franchise limitations based on other categories (though it is easy to predict that any condition placed on voting would rapidly become stigmatized as a method employed by the powerful to shut out powerless sectors of society from ever gaining political power). Above the idea of limiting the franchise to property owners has been noted. Another idea that regularly recurs, and which is found in Heinlein’s Starship Troopers, is the limitation of the franchise to veterans. It would also be possible to limit the franchise to net taxpayers (those who pay more taxes to the government than the value they derive in government services, though this calculation would of course be controversial).

A thought experiment that may help us to think our way through the franchise problem is to consider the remaining restrictions on the expansion of the franchise. Most nation-states that hold elections have a minimum age limit for voting, and most restrict voting rights to citizens. What would it be like to remove these remaining restrictions on voting rights? What would a truly universal franchise be like? Suppose anyone from anywhere in the world could come to your nation-state and vote in your election, and further suppose that children of any age could vote. This would obviously run into serious problems. A toddler could not meaningfully vote, but a toddler’s parents could take a toddler into a voting booth and record the child’s vote.

The problem of children voting points to two very interesting questions:

1) If beings who cannot meaningfully vote were included in a universal franchise, why should we limit the franchise to human beings? A dog may not be able to meaningfully vote in an election (or stand for office), but a dog’s owner could register a dog’s vote, just as a parent could register a child’s vote before that child became old enough to resist having their vote taken by their parent. If this is a problem, why exactly is it a problem? Presumably it is a problem because kennel owners would breed themselves into a position of power in society, and we think this is more likely than parents producing so many children as to capture the vote in an election. However, a very rich individual could adopt a large number of children and thereby control a disproportionate voting bloc. Is this a bad thing? If there were requirements to assure the well being of the children (as there are), this could be to the benefit of orphans. However, if children were relevant to voting, there would be far fewer orphans because children would be more politically valuable than they are today.

2) If the votes of very young children would necessarily be mediated by their parents, the child’s vote could simply be legally conferred upon the parent or guardian until that child reaches a certain age. This points to possible alternatives to contemporary franchise conventions: an individual (or a couple) could have as many votes as they have dependent children, for example. This could be administered in many different ways. Each adult might have a vote, and then one parent (or both) might have an additional number of votes corresponding to their number of dependent children. In a more radically natalist regime, the only votes could be the votes that parents exercise on behalf of their dependent children, and no adult automatically has a vote simply in virtue of being an adult. Individuals would have an opportunity to vote only when they could prove themselves to be a parent presently caring for a dependent child, which would achieve the end of having the only voters being those who are stakeholders in the future of the society in question. Additionally, this would incentivize child-rearing at a time of declining fertility rates. (Full disclosure: I have no children, so I would not be eligible to vote under such a franchise regime.)

I do not think it is likely that any contemporary political regime would adopt any of the franchise experiments suggested above in regard to parents exercising a vote on behalf on their children, but it is an interesting idea, and it points to other political experiments that could be made.

A political entity might actively manage the scope of its franchise throughout its history, changing voter qualifications as conditions change, and circumstances appear to warrant a different composition of the electorate. For example, if the age distribution of a society becomes too weighted toward the elderly, as is projected to occur in most if not all industrialized nation-states in the near future, a nation-state may choose to implement not only a lower age limit to voting, but also an upper age limit for voting. An active management of the franchise might be continual changes in both lower and upper age limits to voting eligibility.

Given the generous supply of political data, it would not be difficult for data scientists to comb through well-documented elections and to determine, ex post facto, what the result of a given election would have been if the franchise regime had been altered. If general rules could be derived from this kind of research, an analysis of the contemporary political landscape would determine the ideal composition of the electorate required to obtain a certain result. However, this meta-electoral process would itself be undemocratic. Some managerial body (or some individual) would have to determine the desired result and, on the basis of the desired result, then stipulate the constitution of the electorate, and it is difficult to imagine how such a regime could come about under contemporary social conditions.

The important exception to the above observation on the difficulty of managing an electorate under contemporary conditions is the European Union, which has de facto pursued a course like this. The political elites have made a determination of the desired end, and votes are held until the desired result is achieved. While it could be argued that this procedure has produced an unprecedented unification of Europe, it has also produced a backlash, most obviously manifested by the Brexit vote for Britain to leave the EU. The political class of Britain is staunchly opposed to this, and seem to be going about Brexit negotiations in a disingenuous fashion, while the “Remainers” continue to agitate for another vote, on the hope that this will reverse the first vote, and then we would have a return to EU business as usual, when votes are simply held until the desired result is obtained. This system does not involve tailoring the electorate in order to achieve the desired result; instead, the wording of the measures to be decided (clear or confusing as necessitated by circumstance), the date selected for the vote (convenient or inconvenient), the campaign for the vote, and threats of disaster should the vote not go according to plan, have been the methods employed to shape a putatively democratic society along non-democratic lines.

The reader may interpret the above remarks as hostile to the European Union, but while I find aspects of the European Union to be problematic, I admire the Europeans for having undertaken their grand political experiment in the constitution of a European superstate at a time when few nation-states are willing to experiment politically. The Europeans are using the tools they have at their disposal in order to attempt a reform of liberal democracy. Though this experiment is imperfect, as are all political experiments, there is much that we can learn from it. It is this spirit of political experimentation that he needed to order to test alternative voting franchise regimes such as those suggested above, and to prevent a society from becoming so politically stagnant that change becomes inconceivable.

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Grand Strategy Annex

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Digging Up the Anthropocene

29 November 2017


Photograph by Ben Roberts.

A recent paper, The Working Group on the Anthropocene: Summary of evidence and interim recommendations, by Jan Zalasiewicz and twenty-four additional authors, considers the case for the formalization of the Anthropocene as a chronostratigraphic/geochronologic unit, i.e., a periodization of geological time. Since “Anthropocene” was proposed by Paul Crutzen in 2000 as a geological period marked by the impact of human beings upon the Earth, geologists have been attempting to determine if the geological record will someday bear the distinctive traces of human activity and whether (and this an interesting future contingent) geologists might someday be able to reliably locate and identify the Anthropocene boundary in the geological record. The emerging consensus is that there is, “…a clear synchronous signal of the transformative influence of humans on key physical, chemical, and biological processes at the planetary scale.” These synchronous signals are described as follows:

“A range of potential proxy signals emerged as potentially important during the analysis, for instance the spherical carbonaceous particles of fly ash (Rose, 2015; Swindles et al., 2015), plastics (Zalasiewicz et al., 2016), other ‘technofossils’ (Zalasiewicz et al., 2014a, 2016) and artificial radionuclides (Waters et al., 2015), changes to carbon and nitrogen isotope patterns (Waters et al., 2016) and a variety of fossilizable biological remains (Barnosky, 2014; Wilkinson et al., 2014). Many of these signals will leave a permanent record in the Earth’s strata.”

The Working Group on the Anthropocene: Summary of evidence and interim recommendations, by Jan Zalasiewicz, et al., Anthropocene, Volume 19, September 2017, Pages 55-60.

Will paleontologists of the future someday dig up technofossils, and from these technofossils attempt to reconstruct an entire technological infrastructure, much as we today reconstruct an extinct species from a single preserved vertebra or rib, and around the resulting organism we seek to reconstruct the entire vanished ecosystem in which that extinct species made its home?

Recently I was prompted to think about the Anthropocene from a paleontological perspective by a Twitter post by Ben Roberts, which included images of automobiles being degraded by weathering (these photographs are included in this post). In response to these images I wrote that I would like to see what the fossils of these automobiles would look like in ten million years. This caused me to think about the possibility of the artifacts of human civilization that might be preserved over geological scales of time. The signals mentioned above in the paper quoted all constitute microfossils that would begin to appear in the geological record for the first time with the advent of the Anthropocene, but I also wonder if larger artifacts might be preserved in the geological record.

Photograph by Ben Roberts.

The tissues of organisms — sometimes even soft tissues — are preserved in the geological record through several different processes. While it is unlikely that human artifacts would be fossilized by replacement and recrystallization or by adpression, it seems possible that technological fossils could be formed through permineralization or through casts and molds. It is easy to imagine that the hulk of an automobile, a train, or even an entire industrial facility might fill with sediment, and though the steel would rust away, that rust would be preserved in situ more or less in its finished form by the sediment hardening into sedimentary rock around it. A careful paleontologist thus might be able to excavate an entire locomotive by means of rust encased in sedimentary rocks.

Of course, fossils are rare, and most artifacts will be eroded away rather than fossilized. Moreover, technofossils are likely to be even more rare than natural fossils. Given our interest in our own past, and our technological abilities to recover artifacts, human beings will continually recover our own remains from the historical period. The fossil record that remains to be discovered will depend upon whether civilization is merely transient or whether it will prove to be enduring. In the case of civilization being a transient historical phenomenon (note that civilization could endure for another 10, 20, or 30 thousand years or more and still be “transient” from the perspective of paleontology), the process of recovering artifacts that would otherwise be fossilized will come to be end. There likely will be a few cases at least of human artifacts in sedimentary basins that eventually are preserved by some process or another. Human artifacts will ultimately be preserved in ice, in snow, in a glaciers, covered in sand on beaches and deserts, covered by landslides on land, as well as being preserved in the oceans, in deep, cold anoxic waters, as well as underwater covered in mud. There is a good chance that many ancient ships lost at sea have been entirely covered over by sand, mud, and silt, and are not likely to be located within our own historical period, thereby saved for far future paleontologists specializing in the excavation of technofossils.

Photograph by Ben Roberts.

Human beings have been building structures and leaving artifacts for thousands of years, of course — sufficient time for many of these structures to be abandoned, covered over, forgotten, and subsequently revealed once again to the light of day by archaeology. The extensive remains of the Indus Valley civilization were forgotten in this way, only to be rediscovered in the twentieth century, and the knowledge of the Minoan civilization had been reduced to mere legend when its palaces were eventually excavated. These remains have been subject to weathering and degradation, but some are in a remarkable state of preservation, though they have not been buried for millions of years, or subjected to the temperatures and pressures that result from being contained in geological strata. An insufficient time has passed for there to be a fossil record of human civilization, even though there is an archaeological record of human civilization.

Up until the industrial revolution, human industry was mostly carried out on a modest scale and resulted in little impact on the environment. Most materials employed were biodegradable and have disappeared over scales of historical time. I have previously observed that traces of Roman lead production have been preserved in the ice of Antarctica, and I would not be surprised to learn that silver processing at Potosí in the early modern period also left detectable traces. One might understand these examples as very early anticipations of later industrial processes carried out on a far larger scale. With the advent of technologies made possible by the systematic application of science to industry, new and unprecedented materials were invented and employed in industrial-scale applications. Some of these are the materials cited in the paper quoted above as the distinctive signals of the Anthropocene. While the recent paper cited above singled out a spike of artificial radionuclides, an earlier paper specifically mentioned plastics:

“Plastics are already present in sufficient numbers to be considered as one of the most important types of ‘technofossil’ that will form a permanent record of human presence on Earth.”

“The geological cycle of plastics and their use as a stratigraphic indicator of the Anthropocene,” by Jan Zalasiewicz, et al.

Contemporary industrial processes are sufficiently sophisticated to produce distinctively new technogenic materials (like Chernobylite) and on a scale to distribute the products of industry globally, and so to leave a planetary trace of human activity. It remains only for time, heat, and pressure to transform these distinctive traces into technofossils.

Photograph by Ben Roberts.

That the global deposition of a distinctive Anthropocene layer begins in earnest in the twentieth century (and specifically in the mid-twentieth century) is significant. The authors of the paper write:

“This mid-20th century level seems to serve best the prime requirement for a chronostratigraphic base of high-precision global synchroneity… Human activities only came to have an effect that was both large and synchronous, and thus leave a clear (chrono-) stratigraphic signal, in the mid-20th century. A wide range of evidence from this time indicates the rapid increase in scale and extent of global human impact on the planetary environment, also clearly recognizable from a wide range of synchronous stratigraphic indicators.”

The Working Group on the Anthropocene: Summary of evidence and interim recommendations, by Jan Zalasiewicz, et al.

It is interesting to note how this mid-20th century boundary (as geologists would call it; I might call it a “threshold”) corresponds to other boundaries (or thresholds) in human development. For example, in the Before Present (BP) time scale frequently employed in the sciences, the “present” for purposes of radiometric dating has been set as 01 January 1950, as radiometric dating became practical at about this time. A neat mid-century point of reference fit well with the actual date of the availability of the technologies of radiometric dating.

Recently in Radio Technology and Existential Risk I discussed what we may call “Sagan’s Thesis,” viz. that nuclear and radio technology are tightly-coupled, so that the invention of radio technology means both that the inventors of the technology can see and be seen in the cosmos, and that the inventors soon will be able to build nuclear weapons and so be enabled to destroy themselves. Radio, then, is both an existential risk and an existential opportunity, thus marking a threshold of technological maturity in the history of an intelligent species:

“Radio astronomy on Earth is a by-product of the Second World War, when there were strong military pressures for the development of radar. Serious radio astronomy emerged only in the 1950s, major radio telescopes only in the 1960s. If we define an advanced civilization as one able to engage in long-distance radio communication using large radio telescopes, there has been an advanced civilization on our planet for only about ten years. Therefore, any civilization ten years less advanced than we cannot talk to us at all.”

Carl Sagan, The Cosmic Connection: An Extraterrestrial Perspective, Chap. 31

While radio astronomy sensu stricto is not likely to leave any trace in the fossil record (though the wreckage of radio telescopes might be found), it will leave a lasting mark on civilization, and may (under some circumstances) transform a civilization. A changed civilization that endures for geological scales of time will leave a transformed trace of itself in the geological record. And for humanity, this change began near the mid-20th century boundary — about the same time as we began to use nuclear weapons, which is consistent both with Sagan’s Thesis and with a mid-20th century boundary for the Anthropocene.

The consilience of these several factors — planetary-scale anthropogenic impacts, radio technology, and nuclear technology (which includes both nuclear weapons and radiometric dating) — distinctively manifesting themselves on a global scale in the middle of the twentieth century, constitute “synchronous signals” not only for stratigraphy, but also for civilization on historical scales of time. In other words, the Anthropocene marks not only a geological periodization, but also a new stage in the development of civilization.

Train cemetery, Uyuni, Bolivia

In his original 1964 paper that introduced the idea of “types” of civilization, “Transmission of Information by Extraterrestrial Civilizations,” Kardashev defined a Type I civilization as a civilization at, “a technological level close to the level presently attained on the earth.” (Here I ask the reader to set aside imaginative characterizations of Type I civilizations that have been elaborated by individuals who have never bothered to read Kardashev’s paper.) As this paper was written in 1964, a mid-20th century boundary for the Anthropocene corresponds nicely with the level of technological development close to that attained by civilization at this time. We could, then, identify a Type I civilization with a civilization that produces an Anthropocene-like boundary on its homeworld (i.e., the equivalent of the Anthropocene for some other intelligent species but defined in an non-anthropocentric way).

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Grand Strategy Annex

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Thursday — Thanksgiving Day

Studies in Formal Thought:

Albert Einstein (14 March 1879 – 18 April 1955)

Albert Einstein (14 March 1879 – 18 April 1955)

Einstein’s Philosophy of Mathematics

For some time I have had it on my mind to return to a post I wrote about a line from Einstein’s writing, Unpacking an Einstein Aphorism. The “aphorism” in question is this sentence:

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

…which, in the original German, was…

“Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nict sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit.”

Although this sentence has been widely quoted out of context until it has achieved the de facto status of an aphorism, I was wrong to call it an aphorism. This sentence, and the idea it expresses, is entirely integral with the essay in which it appears, and should not be treated in isolation from that context. I can offer in mitigation that a full philosophical commentary on Einstein’s essay would run to the length of a volume, or several volumes, but this post will be something of a mea culpa and an effort toward mitigation of the incorrect impression I previously gave that Einstein formulated this idea as an aphorism.

The first few paragraphs of Einstein’s lecture, which includes the passage quoted above, constitute a preamble on the philosophy of mathematics. Einstein wrote this sententious survey of his philosophy of mathematics in order to give the listener (or reader) enough of a methodological background that they would be able to follow Einstein’s reasoning as he approaches the central idea he wanted to get across: Einstein’s lecture was an exercise in the cultivation of geometrical intuition. Unless one has some familiarity with formal thought — usually mathematics or logic — one is not likely to have an appreciation of the tension between intuition and formalization in formal thought, nor of how mathematicians use the term “intuition.” In ordinary language, “intuition” usually means arriving at a conclusion on some matter too subtle to be made fully explicit. For mathematicians, in contrast, intuition is a faculty of the mind that is analogous to perception. Indeed, Kant made this distinction, implying its underlying parallelism, by using the terms “sensible intuition” and “intellectual intuition” (which can also be called “outer” and “inner” intuition).

Intuition as employed in this formal sense has been, through most of the history of formal thought, understood sub specie aeternitatis, i.e., possessing many of the properties once reserved for divinity: eternity, immutability, impassibility, and so on. In the twentieth century this began to change, and the formal conception of intuition came to be more understood in naturalistic terms as a faculty of the human mind, and, as such, subject to change. Here is a passage from Gödel that I have quoted many times (e.g., in Transcendental Humors), in which Gödel delineates a dynamic and changing conception of intuition:

“Turing… gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive. What Turing disregards completely is the fact that mind, in its use, is not static, but is constantly developing, i.e., that we understand abstract terms more and more precisely as we go on using them, and that more and more abstract terms enter the sphere of our understanding. There may exist systematic methods of actualizing this development, which could form part of the procedure. Therefore, although at each stage the number and precision of the abstract terms at our disposal may be finite, both (and, therefore, also Turing’s number of distinguishable states of mind) may converge toward infinity in the course of the application of the procedure.”

“Some remarks on the undecidability results” (Italics in original) in Gödel, Kurt, Collected Works, Volume II, Publications 1938-1974, New York and Oxford: Oxford University Press, 1990, p. 306.

If geometrical intuition (or mathematical intuition more generally) is subject to change, it is also subject to improvement (or degradation). A logician like Gödel, acutely aware of the cognitive mechanisms by which he has come to grasp logic and mathematics, might devote himself to consciously developing intuitions, always refining and improving his conceptual framework, and straining toward developing new intuitions that would allow for the extension of mathematical rigor to regions of knowledge previously given over to Chaos and Old Night. Einstein did not make this as explicit as did Gödel, but he clearly had the same idea, and Einstein’s lecture was an attempt to demonstrate to his audience the cultivation of geometrical intuitions consistent with the cosmology of general relativity.

Einstein’s revolutionary work in physics represented at the time a new level of sophistication of the mathematical representation of physical phenomena. Mathematicized physics began with Galileo, and might be said to coincide with the advent of the scientific revolution, and the mathematization of physics reached a level of mature sophistication with Newton, who invented the calculus in order to be able to express his thought in mathematical form. The Newtonian paradigm in physics was elaborated as the “classical physics” of which Einstein and Infeld, like mathematical parallels of Edward Gibbon, recorded the decline and fall.

Between Einstein and Newton a philosophical revolution in mathematics occurred. The philosophy of mathematics formulated by Kant is taken by many philosophers to express the conception of mathematics to be found in Newton; I do not agree with this judgment, as much for historiographical reasons as for philosophical reasons. But perhaps if we scrape away the Kantian idealism and subjectivism there might well be a core of Newtonian philosophy of mathematics in Kant, or, if you prefer, a core of Kantian philosophy of mathematics intimated in Newton. For present purposes, this is neither here nor there.

The revolution that occurred between Newton and Einstein was the change to hypothetico-deductivism from that which preceded it. So what was it that preceded the hypothetico-deductive conception of formal systems in mathematics? I call this earlier form of mathematics, i.e., I call pre-hypothetico-deductive mathematics, categorico-deductive mathematics, because the principles or axioms now asserted hypothetically were once asserted categorically, in the belief that the truths of formal thought, i.e., of logic and mathematics, were eternal, immutable, unchanging truths, recognized by the mind’s eye as incontrovertible, indubitable, necessary truths as soon as they were glimpsed. It was often said (and is sometimes still today said), that to understand an axiom is ipso facto to see that it must be true; this is the categorico-deductive perspective.

In mathematics as it is pursued today, as an exercise in hypothetico-deductive reasoning, axioms are posited not because they are held to be necessarily true, or self-evidently true, or undeniably true; axioms need not be true at all. Axioms are posited because they are an economical point of origin for the fruitful derivation of consequences. This revolution in mathematical rigor transformed the landscape of mathematical thought so completely that Bertrand Russell, writing in the early twentieth century could write, “…mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” Here formal, logical truth is entirely insulated from empirical, intuitive truth. It is at least arguable that the new formalisms made possible by the hypothetico-deductive method are at least partially responsible for Einstein’s innovations in physics. (I have earlier touched on Einstein’s conception of formalism in A Century of General Relativity and Constructive Moments within Non-Constructive Thought.)

If you are familiar with Einstein’s lecture, and especially with the opening summary of Einstein’s philosophy of mathematics, you will immediately recognize that Einstein formulates his position around the distinction between the categorico-deductive (which Einstein calls the “older interpretation” of axiomatics) and the hypothetico-deductive (which Einstein calls the “modern interpretation” of axiomatics). Drawing upon this distinction, Einstein gives us a somewhat subtler and more flexible formulation of the fundamental disconnect between the formal and the material than that which Russell paradoxically thrusts in our face. By formulating his distinction in terms of “as far as,” Einstein implies that there is a continuum of the dissociation between what Einstein called the “logical-formal” and “objective or intuitive content.”

Einstein then goes on to assert that a purely logical-formal account of mathematics joined together with the totality of physical laws allows us to say something, “about the behavior of real things.” The logical-formal alone can can say nothing about the real world; in its isolated formal purity it is perfectly rigorous and certain, but also impotent. This marvelous structure must be supplemented with empirical laws of nature, empirically discovered, empirically defined, empirically applied, and empirically tested, in order to further our knowledge of the world. Here we see Einstein making use of the hypothetico-deductive method, and supplementing it with contemporary physical theory; significantly, in order to establish a relationship between the formalisms of general relativity and the actual world he didn’t try to turn back the clock by returning to categorico-deductivism, but took up hypothetic-deductivism and ran with it.

But all of this is mere prologue. The question that Einstein wants to discuss in his lecture is the spatial extension of the universe, which Einstein distills to two alternatives:

1. The universe is spatially infinite. This is possible only if in the universe the average spatial density of matter, concentrated in the stars, vanishes, i.e., if the ratio of the total mass of the stars to the volume of the space through which they are scattered indefinitely approaches zero as greater and greater volumes are considered.

2. The universe is spatially finite. This must be so, if there exists an average density of the ponderable matter in the universe that is different from zero. The smaller that average density, the greater is the volume of the universe.

Albert Einstein, Geometry and Experience, Lecture before the Prussian Academy of Sciences, January 27, 1921. The last part appeared first in a reprint by Springer, Berlin, 1921

It is interesting to note, especially in light of the Kantian distinction noted above between sensible and intellectual intuition, that one of Kant’s four antinomies of pure reason was whether or not the universe was finite or infinite in extent. Einstein has taken this Kantian antimony of pure reason and has cast it in a light in which it is no longer exclusively the province of pure reason, and so may be answered by the methods of science. To this end, Einstein presents the distinction between a finite universe and an infinite universe in the context of the density of matter — “the ratio of the total mass of the stars to the volume of the space through which they are scattered” — which is a question that may be determined by science, whereas the purely abstract terms of the Kantian antimony allowed for no scientific contribution to the solution of the question. For Kant, pure reason could gain no traction on this paralogism of pure reason; Einstein gains traction by making the question less pure, and moves toward more engagement with reality and therefore less certainty.

It was the shift from categorico-deductivism to hypothetico-deductivism, followed by Einstein’s “completion” of geometry by the superaddition of empirical laws, that allows Einstein to adopt a methodology that is both rigorous and scientifically fruitful. (“We will call this completed geometry ‘practical geometry,’ and shall distinguish it in what follows from ‘purely axiomatic geometry’.”) Where the simplicity of Euclidean geometry allows for the straight-forward application of empirical laws to “practically-rigid bodies” then the simplest solution of Euclidean geometry is preferred, but where this fails, other geometries may be employed to resolve the apparent contradiction between mathematics and empirical laws. Ultimately, the latter is found to be the case — “the laws of disposition of rigid bodies do not correspond to the rules of Euclidean geometry on account of the Lorentz contraction” — and so it is Riemannian geometry rather than Euclidean geometry that is the mathematical setting of general relativity.

Einstein’s use of Riemannian geometry is significant. The philosophical shift from categorico-deductivism to hypothetico-deductivism could be reasonably attributed to (or, at least, to follow from) the nineteenth century discovery of non-Euclidean geometries, and this discovery is an interesting and complex story in itself. Gauss (sometimes called the “Prince of Mathematicians”) discovered non-Euclidean geometry, but published none of it in his lifetime. It was independently discovered by the Hungarian János Bolyai (the son of a colleague of Gauss) and the Russian Nikolai Ivanovich Lobachevsky. Both Bolyai and Lobachevsky arrived at non-Euclidean geometry by adopting the axioms of Euclid but altering the axiom of parallels. The axioms of parallels had long been a sore spot in mathematics; generation after generation of mathematicians had sought to prove the axiom of parallels from the other axioms, to no avail. Bolyai and Lobachevsky found that they could replace the axiom of parallels with another axiom and derive perfectly consistent but strange and unfamiliar geometrical theorems. This was the beginning of the disconnect between the logical-formal and objective or intuitive content.

Riemann also independently arrived at non-Euclidean geometry, but by a different route than that taken by Bolyai and Lobachevsky. Whereas the latter employed the axiomatic method — hence its immediate relevance to the shift from the categorico-deductive to the hypothetico-deductive — Riemann employed a metrical method. That is to say, Riemann’s method involved measurements of line segments in space defined by the distance between two points. In Euclidean space, the distance between two points is given by a formula derived from the Pythagorean theorem — d = √(x2x1)2 + (y2y1)2 — so that in non-Euclidean space the distance between two points could be given by some different equation.

Whereas the approach of Bolyai and Lobachevsky could be characterized as variations on a theme of axiomatics, Riemann’s approach could be characterized as variations on a theme of analytical geometry. The applicability to general relativity becomes clear when we reflect how, already in antiquity, Eratosthenes was able to determine that the Earth is a sphere by taking measurements on the surface of the Earth. By the same token, although we are embedded in the spacetime continuum, if we take careful measurements we can determine the curvature of space, and perhaps also the overall geometry of the universe.

From a philosophical standpoint, it is interesting to ask if there is an essential relationship between the method of a non-Euclidean geometry and the geometrical intuitions engaged by these methods. Both Bolyai and Lobachevsky arrived at hyperbolic non-Euclidean geometry (an infinitude of parallel lines) whereas Riemann arrived at elliptic non-Euclidean geometry (no parallel lines). I will not attempt to analyze this question here, though I find it interesting and potentially relevant. The non-Euclidean structure of Einstein’s general relativity is more-or-less a three dimensional extrapolation of the elliptic two dimensional surface of a sphere. Our minds cannot conceive this (at least, my mind can’t conceive of it, but there may be mathematicians who, having spent their lives thinking in these terms, are able to visualize three dimensional spatial curvature), but we can formally work with the mathematics, and if the measurements we take of the universe match the mathematics of Riemannian elliptical space, then space is curved in a way such that most human beings cannot form any geometrical intuition of it.

Einstein’s lecture culminates in an attempt to gently herd his listeners toward achieving such an impossible geometrical intuition. After a short discussion of the apparent distribution of mass in the universe (in accord with Einstein’s formulation of the dichotomy between an infinite or a finite universe), Einstein suggests that these considerations point to a finite universe, and then explicitly asks in his lecture, “Can we visualize a three-dimensional universe which is finite, yet unbounded?” Einstein offers a visualization of this by showing how an infinite Euclidean plane can be mapped onto a finite surface of a sphere, and then suggesting an extrapolation from this mapping of an infinite two dimensional Euclidean space to a finite but unbounded two dimensional elliptic space as a mapping from an infinite three dimensional Euclidean space to a finite but unbounded three dimensional elliptic space. Einstein explicitly acknowledges that, “…this is the place where the reader’s imagination boggles.”

Given my own limitations when it comes to geometrical intuition, it is no surprise that I cannot achieve any facility in the use of Einstein’s intuitive method, though I have tried to perform it as a thought experiment many times. I have no doubt that Einstein was able to do this, and much more besides, and that it was, at least in part, his mastery of sophisticated forms of geometrical intuition that had much to do with his seminal discoveries in physics and cosmology. Einstein concluded his lecture by saying, “My only aim today has been to show that the human faculty of visualization is by no means bound to capitulate to non-Euclidean geometry.”

Above I said it would be an interesting question to pursue whether there is an essential relationship between formalisms and the intuitions engaged by them. This problem returns to us in a particularly compelling way when we think of Einstein’s effort in this lecture to guide his readers toward conceiving of the universe as finite and unbounded. When Einstein gave this lecture in 1922 he maintained a steady-state conception of the universe. About the same time the Russian mathematician Alexander Friedmann was formulating solutions to Einstein’s field equations that employed expanding and contracting universes, of which Einstein himself did not approve. It wasn’t until Einstein met with Georges Lemaître in 1927 that we know something about Einstein’s engagement with Lemaître’s cosmology, which would become the big bang hypothesis. (Cf. the interesting sketch of their relationship, Einstein and Lemaître: two friends, two cosmologies… by Dominique Lambert.)

Ten years after Einstein delivered his “Geometry and Experience” lecture he was hesitantly beginning to accept the expansion of the universe, though he still had reservations about the initial singularity in Lemaître’s cosmology. Nevertheless, Einstein’s long-standing defense of the counter-intuitive idea (which he attempted to make intuitively palatable) of a finite and unbounded universe would seem to have prepared his mind for Lemaître’s cosmology, as Einstein’s finite and unbounded universe is a natural fit with the big bang hypothesis: if the universe began from an initial singularity at a finite point of time in the past, then the universe derived from the initial singularity would still be finite any finite period of time after the initial singularity. Just as we find ourselves on the surface of the Earth (i.e., our planetary endemism), which is a finite and unbounded surface, so we seem to find ourselves within a finite and unbounded universe. Simply connected surfaces of these kinds possess a topological parsimony and hence would presumably be favored as an explanation for the structure of the world in which we find ourselves. Whether our formalisms (i.e., those formalisms accessible to the human mind, i.e., intuitively tractable formalisms) are conductive to this conception, however, is another question for another time.

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An illustration from Einstein’s lecture Geometry and Experience

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Studies in Formalism

1. The Ethos of Formal Thought

2. Epistemic Hubris

3. Parsimonious Formulations

4. Foucault’s Formalism

5. Cartesian Formalism

6. Doing Justice to Our Intuitions: A 10 Step Method

7. The Church-Turing Thesis and the Asymmetry of Intuition

8. Unpacking an Einstein Aphorism

9. The Overview Effect in Formal Thought

10. Einstein on Geometrical intuition

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Wittgenstein's Tractatus Logico-Philosophicus was part of the efflourescence of formal thinking focused on logic and mathematics.

Wittgenstein’s Tractatus Logico-Philosophicus was part of an early twentieth century efflorescence of formal thinking focused on logic and mathematics.

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Grand Strategy Annex

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