Third Time’s a Charm

8 February 2014

Saturday


geological eras of life

The Three Eras of Life on Earth

The Earth, it would seem, has been regularly reduced to biological penury throughout its long history, which has been punctuated by mass extinctions that have very nearly reduced biodiversity to zero. It is possible that, in the earliest history of life on Earth, when our planet was regularly bombarded by objects from space, and exposed to especially harsh conditions, life may have emerged multiple times, only to be wiped out again in short order. There would have been plenty of time for this to occur during the 550 million years prior to the emergence of the earliest life known to be continuous with our own.

The repeated denudation of the planet by mass extinctions constituted a kind of ecological succession on a grand scale. Each time life had to recover anew, and, in recovering, the surviving species (the “weeds” that were the most robust and which went on to colonize the denuded landscape and seascape) underwent dramatic periods of adaptive radiation until, in the global climax ecosystems prior to a mass extinction event, almost every niche for life has been filled — possibly several times over, leading to contested niches where multiple species compete for the same limited resources.

The history of life is such a reliable indicator of geological time that there is an entire discipline — biostratigraphy — given over to the dating of rocks by the fossils they contain. Once life becomes sufficiently complex to leave a record of itself in the rocks of our planet, the development of life is a sure guide to the age of the rocks that contain traces of this past life. Contemporary scientific geology largely got its start through biostratigraphy in the work of William Smith (called “strata Smith” by his contemporaries), whom I have previously mentioned in The Transplanetary Perspective.

Three of the major divisions of geological time are named for the eras of life that they comprise: Paleozoic (old life), Mesozoic (middle life), and Cenozoic (common, or recent, life). These divisions of geological time give a “big picture” view of the history of life on Earth. The mass extinction events at the end of the Permian and at the K-T boundary were so catastrophic that the Earth in the case of the end Permian extinction came perilously close to being sterilized, and while the K-T event (now known as the Cretaceous–Paleogene or K–Pg extinction event) was not as disastrous, it ended the dominion of the dinosaurs over most ecological niches and thereby gave mammals the opportunity to experience an explosive adaptive radiation.

cosmos 06

Million Year Old Civilizations

We know that intelligent life on Earth arose in the late Cenozoic era, but how clement were these earlier eras of life on Earth to intelligent life? If intelligent life had arisen in the Paleozoic, founded a civilization, and survived to the present, that civilization would be in excess of 250 million years old. If, again, intelligent life had arisen in the Mesozoic, founded a civilization, and survived to the present, that civilization would be in excess of 65 million years old. However, both of these counterfactual civilizations that did not happen would have almost certainly have been destroyed by the catastrophic mass extinctions that separated these eras of terrestrial life (unless they had taken adequate measures to mitigate existential risk, which would seem to be a necessary condition for any truly long-lived civilization).

The idea of a civilization a million or more years old was a theme discussed by Carl Sagan on several occasions. Here is an explicit formulation of the million-year-old civilization theme from Chapter XII, “Encyclopedia Galacitca,” from Sagan’s book Cosmos:

“What does it mean for a civilization to be a million years old? We have had radio telescopes and spaceships for a few decades; our technical civilization is a few hundred years old, scientific ideas of a modern cast a few thousand, civilization in general a few tens of thousands of years; human beings evolved on this planet only a few million years ago. At anything like our present rate of technical progress, an advanced civilization millions of years old is as much beyond us as we are beyond a bush baby or a macaque. Would we even recognize its presence? Would a society a million years in advance of us be interested in colonization or interstellar spaceflight? People have a finite lifespan for a reason. Enormous progress in the biological and medical sciences might uncover that reason and lead to suitable remedies. Could it be that we are so interested in spaceflight because it is a way of perpetuating ourselves beyond our own lifetimes? Might a civilization composed of essentially immortal beings consider interstellar exploration fundamentally childish?”

Carl Sagan, Cosmos, Chapter XII, “Encyclopaedia Galactica”

Human civilization could be considered as being more than ten thousand years old if we date the advent of civilization to the Neolithic Agricultural Revolution. This is an atypical way to think about civilization, but I have seen it in a few sources (Jacob Bronowski, I think, takes this view, more or less), and it is how I myself think about civilization. A civilization ten thousand years old or more is nothing to dismiss; persisting for ten thousand years is a non-trivial accomplishment. Yet the history of terrestrial civilization may be compared to the history of terrestrial life: there is a long period that is nearly stagnant, with painfully slow innovations, and then an event occurs — the Cambrian explosion for life, the industrial revolution for civilization — and what it means to be “alive” or “civilized” is radically altered.

Dating to the Neolithic Agricultural revolution is consistent with my recent suggestion in From Biocentric Civilization to Post-biological Post-Civilization that civilization could be minimally defined as a coevolutionary cohort of species. However, our industrial-technological civilization is barely more than two hundred years old. To consider the geologically insignificant period of time of one hundred years is to contemplate a period of time half again as long as the entire history of industrial-technological civilization. The kind of technological gains that industrial-technological civilization could experience over a period of a hundred years can be quite remarkable, as our experience of the past hundred years suggests.

This year, 2014, we experience the one hundred year anniversary of global industrialized warfare. Not long after, we will experience the hundred year anniversaries of digital computers, jet propulsion, rocketry, and nuclear technology. Some of these technologies have improved by orders of magnitude. Some have improved very little. If the coming century brings commensurate technological innovations (not to mention innovations in science that would drive these technological innovations), even if not all these developments experience exponential development, and many languish in a state of stagnation, our world and our understanding of the world will nevertheless be repeatedly revolutionized.

Given what we know about the rapidity of technological change — bequeathed to our industrial-technological civilization as a consequence of the STEM cycle — we ought to conclude that we can know almost nothing about what a million year civilization would be like, except in so far as we might be able to imagine only the most stagnant aspects of such a civilization. It would be beyond our ability to understand advanced technologies ten thousand years hence, just as our ancestors, only beginning to lay the foundations of agrarian-ecclesiastical civilization ten thousand years ago, could have understood our advanced technologies today. Understanding across these orders of developmental magnitude lie beyond the human zone of proximal development.

Octopus evolution

Counterfactual Civilizations

I have written previously that there is an earliest bound in the history of our universe for life, for intelligent life, and for civilization. It would not be possible to produce an industrial-technological civilization as we know it (i.e., a peer civilization) without heavier metallic elements, so that the emergence of industrial-technological civilization must minimally wait for the formation of Population I stars and their planetary systems. That being said, many population I stars have been around for billions of years, and there have consequently been billions of years for industrial-technological civilizations to emerge and to attain great age.

Are there other constraints upon the emergence of life, intelligence, and civilization that move the boundary for the earliest possible emergence of these phenomena nearer to the present? Is there any reason to suppose, from our knowledge of the natural history of Earth and the complexity of the human brain, that intelligent life and civilization could not have arisen in earlier eras of life — Paleozoic intelligent life or Mesozoic intelligent life, which would, in turn, according to Civilization-Intelligence Covariance, give rise to Paleozoic civilization or Mesozoic civilization? Or, if not here on Earth, why not some other planet orbiting a population I star where life begins 550 million years after the formation of the planet?

Octopi, cuttlefish, and other cephalopods with large brains and highly sophisticated nervous systems — it takes a lot of raw neural processing power to do what some cephalopods do with their skin color — would seem to be ideal candidates for early terrestrial intelligent life. Octopi date back to the Devonian Period, more than 360 million years ago, during the Paleolithic Era, so that ancestors of this life form survived both the End Permian extinction and the K-T extinction (cf. Fossil Octopuses). Why didn’t cephalopods establish a counterfactual civilization during the Permian? There was certainly time enough to do so before the End Permian extinction.

Is a backbone, or something that can serve a similar function like an exoskeleton, a necessary condition for intelligence to issue in the production of civilization? Multicellular life forms without a backbone, or confined to an aquatic environment, might well develop intelligence, but would have a difficult time building a technological civilization — difficult, but not impossible. This is a question I considered previously in The Place of Bilaterial Symmetry in the History of Life and Counterfactuals Implicit in Naturalism.

If we should find life in the oceans below the icy surface of Europa, or any of the other moons in our solar system internally heated by gravitational forces, it would consist of life forms peculiarly constrained by their environment, i.e., possibly more constrained than terrestrial conditions, and therefore more likely to favor extremophiles. Oceanic lifeforms beneath a crust of ice many kilometers thick would not only have the technological disadvantage faced by any intelligent aquatic species, but would face the additional disadvantage of being cut off from the stars. Unable to physically see their place in the universe, such lifeforms might have an even more difficult time that we had in coming to understand the world. The mythology of such a life form would have to be very different from the mythologies created by early human societies, in which the stars typically played a prominent role. Any civilization that might be conjoined with such a mythology might constitute an extremophile civilization.

vitruvian_man

Inside the Charmed Circle

Many of the questions that I have posed above are variations on ancient themes of anthropocentrism, and from within the charmed circle of anthropocentrism it is difficult for us to see outside that circle. Our minds are quite literally defined by that circle, being the product of human biology, and our imagination is largely circumscribed by the limitations of our minds. But our minds are also capable, with effort, of passing beyond the charmed circle of anthropocentrism, identifying anthropic bias as such and transcending it.

For us, the third time life got a chance on Earth was the charm. Paleozoic life came and (largely) went without producing intelligence or civilization, as did Mesozoic life. It was not until Cenozoic life that intelligence and civilization emerged. But was this the result of mere contingency, or a function of some operative constraint — possibly even a constraint no one has even noticed because of its pervasive presence — that prevented intelligence and civilization from arising in earlier geological eras?

While there might be reason to believe that other forms of life will have something like a DNA structure, or that something like the transition from prokaryotic cells to eukaryotic cells will have taken place, but there is no particular reason to believe that the large scale structure of life on other worlds would have the terrestrial tripartite structure, since this big picture view of life on Earth was a result of particular mass extinction events that seem too contingent to characterize any possible emergence of life. However, there is reason to believe that there will be some mass extinction events afflicting life on other worlds, and at least some of these mass extinction events will result from large scale cosmological events. If solar systems form elsewhere in a process like the formation of our solar system, life elsewhere would also be exposed to asteroid impacts, comets, solar flares, and the like. This is one of the lessons of astrobiology.

That there will be constraints and contingencies that bear upon life we can be certain; but we cannot (yet) know exactly what these constraints and contingencies will be. This is a non-constructive observation: invoking the existence of constraints and contingencies without saying what they will be. What would a constructive approach to life’s constraints and contingencies look like? Is it necessary to adopt a non-constructive perspective where our knowledge is so lacking? As knowledge of the conditions of astrobiology and astrocivilization grows, may we yet adopt a constructive conception of them?

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Wednesday


Kant and the moral law 3

Immanuel Kant, in an often-quoted passage, spoke of, “…the starry heavens above me and the moral law within me.” Kant might have with equal justification spoken of the formal law within and the starry heavens above. There is a sense in which the formal laws of thought are the moral laws of the mind — in logic, a good thought is a rigorous thought — so that given sufficient latitude of translation, we can interpret Kant in this way — except that we know (as Nietzsche put it) that Kant was a moral fanatic à la Rousseau.

However we choose to interpret Kant, I would like to quote more fully from the passage in the Critique of Practical Reason where Kant invokes the starry heavens above and the moral law within:

“Two things fill the mind with ever new and increasing admiration and awe, the oftener and the more steadily we reflect on them: the starry heavens above and the moral law within. I have not to search for them and conjecture them as though they were veiled in darkness or were in the transcendent region beyond my horizon; I see them before me and connect them directly with the consciousness of my existence. The former begins from the place I occupy in the external world of sense, and enlarges my connection therein to an unbounded extent with worlds upon worlds and systems of systems, and moreover into limitless times of their periodic motion, its beginning and continuance. The second begins from my invisible self, my personality, and exhibits me in a world which has true infinity, but which is traceable only by the understanding, and with which I discern that I am not in a merely contingent but in a universal and necessary connection, as I am also thereby with all those visible worlds. The former view of a countless multitude of worlds annihilates as it were my importance as an animal creature, which after it has been for a short time provided with vital power, one knows not how, must again give back the matter of which it was formed to the planet it inhabits (a mere speck in the universe). The second, on the contrary, infinitely elevates my worth as an intelligence by my personality, in which the moral law reveals to me a life independent of animality and even of the whole sensible world, at least so far as may be inferred from the destination assigned to my existence by this law, a destination not restricted to conditions and limits of this life, but reaching into the infinite.”

Immanuel Kant, Critique of Practical Reason, 1788, translated by Thomas Kingsmill Abbott, Part 2, Conclusion

This passage is striking for many reasons, not least among them them degree to which Kant has assimilated the Copernican revolution, acknowledging Earth as a mere speck in the universe. Also particularly interesting is Kant’s implicit appeal to objectivity and realism, notwithstanding the fact that Kant himself established the tradition of transcendental idealism. Kant in this passage invokes the starry heavens above and the moral law within because they are independent of the individual …

Moreover, Kant identifies both the starry heavens above and the moral law within not only as objective and independent realities, but also as infinitistic. Just as Kant the idealist looks to the stars and the moral law in a realistic spirit, so Kant the proto-constructivist invokes the “…unbounded extent with worlds upon worlds” of the starry heavens and the moral law as, “…reaching into the infinite.” I have earlier and elsewhere observed how Kant’s proto-constructivism nevertheless involves spectacularly non-constructive arguments. In the passage quoted above both Kant’s proto-constructivism and his non-constructive moments are retained in lines such as, “exhibits me in a world which has true infinity,” which by invoking exhibition in intuition toes the constructivist line, while invoking true infinity allows a legitimate role for the non-constructive.

When it comes to constructivism, we can see that Kant is conflicted. He’s not the only one. One might call Aristotle the first constructivist (or, at least, the first proto-constructivist) as the originator of the idea of the potential infinite, and here (i.e., in the context of the above discussion of Kant’s use of the infinite) Aristotelian permissive finitism is particularly relevant. (Aristotle would likely not have had much sympathy for intuitionistic constructivism, which its rejection of tertium non datur.)

The Greek intellectual attitude to the infinite was complex and conflicted. I have written about this previously in Reason in Moderation and Salto Mortale. The Greek quest for harmony, order, and proportion rejected the infinite as something that transgresses the boundaries of good taste and propriety (dismissing the infinite as apeiron, in contradistinction to peras). Nevertheless, Greek philosophers routinely argued from the infinity and eternity of the world.

Here is a famous passage from Democritus, who was perhaps best known among the Greek philosophers in arguing for the infinity of the world, making the doctrine a virtual tenet among ancient atomists:

“Worlds are unlimited and of different sizes. In some worlds there is no Sun and Moon, in others, they are larger than in our world, and in others more numerous. … Intervals between worlds are unequal. In some parts there are more worlds, in others fewer; some are increasing, some at their height, some decreasing; in some parts they are arising, in others failing… There are some worlds devoid of living creatures or plants or any moisture.”

Democritus, Fragments

…and Epicurus on the same theme of the infinity of the world…

“…there is an infinite number of worlds, some like this world, others unlike it. For the atoms being infinite in number, as has just been proved, are borne ever further in their course. For the atoms out of which a world might arise, or by which a world might be formed, have not all been expended on one world or a finite number of worlds, whether like or unlike this one. Hence there will be nothing to hinder an infinity of worlds.”

Epicurus, Letter to Herodotus

There were also poetic invocations of the idea of the infinity of the world, which demonstrates the extent to which the idea had penetrated popular consciousness in classical antiquity:

“When Alexander heard from Anaxarchus of the infinite number of worlds, he wept, and when his friends asked him what was the matter, he replied, ‘Is it not a matter for tears that, when the number of worlds is infinite, I have not conquered one?'”

Plutarch, PLUTARCH’S MORALS, ETHICAL ESSAYS TRANSLATED WITH NOTES AND INDEX BY ARTHUR RICHARD SHILLETO, M.A., Sometime Scholar of Trinity College, Cambridge, Translator of Pausanias, LONDON: GEORGE BELL AND SONS, 1898, “On Contentedness of Mind,” section IV

Like poetry, history had particular prestige in the ancient world, and here the theme of the infinity of the world also occurs:

“…Constantius, elated by this extravagant passion for flattery, and confidently believing that from now on he would be free from every mortal ill, swerved swiftly aside from just conduct so immoderately that sometimes in dictation he signed himself ‘My Eternity,’ and in writing with his own hand called himself lord of the whole world — an expression which, if used by others, ought to have been received with just indignation by one who, as he often asserted, laboured with extreme care to model his life and character in rivalry with those of the constitutional emperors. For even if he ruled the infinity of worlds postulated by Democritus, of which Alexander the Great dreamed under the stimulus of Anaxarchus, yet from reading or hearsay he should have considered that (as the astronomers unanimously teach) the circuit of whole earth, which to us seems endless, compared with the greatness of the universe has the likeness of a mere tiny point.

Ammianus Marcellinus, Roman Antiquities, Book XV, section 1

Like the quote from Kant quoted above, this passage is remarkable for its Copernican outlook, which shows that the ancients were not only capable of thinking in infinitistic terms, but also in more-or-less Copernican terms.

Lucretius was a follower of Epicurus, and gave one of the more detailed arguments for the infinity of the world to be found in ancient philosophy:

It matters nothing where thou post thyself,
In whatsoever regions of the same;
Even any place a man has set him down
Still leaves about him the unbounded all
Outward in all directions; or, supposing
moment the all of space finite to be,
If some one farthest traveller runs forth
Unto the extreme coasts and throws ahead
A flying spear, is’t then thy wish to think
It goes, hurled off amain, to where ’twas sent
And shoots afar, or that some object there
Can thwart and stop it? For the one or other
Thou must admit; and take. Either of which
Shuts off escape for thee, and does compel
That thou concede the all spreads everywhere,
Owning no confines. Since whether there be
Aught that may block and check it so it comes
Not where ’twas sent, nor lodges in its goal,
Or whether borne along, in either view
‘Thas started not from any end. And so
I’ll follow on, and whereso’er thou set
The extreme coasts, I’ll query, “what becomes
Thereafter of thy spear?” ‘Twill come to pass
That nowhere can a world’s-end be, and that
The chance for further flight prolongs forever
The flight itself. Besides, were all the space
Of the totality and sum shut in
With fixed coasts, and bounded everywhere,
Then would the abundance of world’s matter flow
Together by solid weight from everywhere
Still downward to the bottom of the world,
Nor aught could happen under cope of sky,
Nor could there be a sky at all or sun-
Indeed, where matter all one heap would lie,
By having settled during infinite time.

Lucretius, De rerum natura

The above argument is one that is still likely to be heard today, in various forms. If you go to the edge of the universe and throw a spear, either it is stopped by the boundary of the universe, or it continues on, and, as Lucretius says, For the one or other, Thou must admit. If the spear is stopped, what stopped it? And if it continues on, into what does it continue?

The contemporary relativistic cosmology has a novel answer to this ancient idea: the universe is finite and unbounded, so that space is wrapped back around on itself. What this means for the spear-thrower at the edge of the universe is that if he throws the spear with enough force, it may travel around the cosmos and return to pierce him in the back. There is nothing to stop the spear, because the universe is unbounded, but since the universe is also finite the spear will eventually cross its own path if it continues to travel. I do not myself think that the universe is finite and unbounded in precisely the way the many modern cosmologists argue, but I am not going to go into this interesting problem at the present time.

Other than the response to Lucretius in terms of relativistic cosmology, with its curved spacetime — a material response to the Lucretian argument for the infinity of the world — there is another response, that of intuitionistic constructivism, which denies the law of the excluded middle (tertium non datur) — i.e, a formal response to Lucretius. Lucretius asserted that, For the one or other, Thou must admit, and this is exactly what the intuitionist does not admit. As with the relativistic response to Lucretius, I do not myself agree with the intuitionist response to Lucretius. Consequently, I believe that Lucretius argument is still valid in spirit, though it must be reformulated in order to be applicable to the world as revealed to us by contemporary science. Consequently, I take it as demonstrable that the universe is infinite, taking the view of ancient natural philosophers.

Within the overall context of Greek thought, within its contending finitist and infinitistic strains, Greek cosmology was non-constructive, and the Greeks asserted (and argued for) the infinity of the world on the basis of non-constructive argument. Perhaps it would even be fair to say that the Greeks assumed the universe to be infinite in extent, and they at times sought to justify this assumption by philosophical argument, while at other times they confined themselves to the sphere of the peras.

Much of contemporary science is constructivist in spirit, though this constructivism is rarely made explicit, except among logicians and mathematicians. By this I mean that the general drift of science ever since the scientific revolution has been toward bottom-up constructions on the basis of quantifiable evidence and away from top-down argument. I made this point previously in Advanced Thinking and A Non-Constructive World, as well as other posts, though I haven’t yet given a detailed formulation of this idea. Yet the emergence of a “quantum logic” in quantum theory that does away with the principle of the excluded middle is a clear expression of the increasing constructivism of science.

In A Non-Constructive World I also made the point that the world appears to have both constructive and non-constructive features. In several posts about constructivism (e.g., P or not-P) I have argued that constructivism and non-constructivism are complementary perspectives on formal thought, and that each needs the other for an adequate account of the world.

In so far as contemporary science is essentially constructive, it lacks a non-constructive perspective on the phenomena it investigates. This is, I believe, intrinsic to science, and to the kind of civilization that emerges from the application of science to the economy (viz. industrial-technological civilization). By the constructive methods of science we can attain ever larger and ever more comprehensive conceptions of the universe — such as I described in my previous post, The Size of the World — but these constructive methods will never reach the infinite universe contemplated by the ancient Greeks.

How could the logical framework employed by a scientist have any effect over what they see in the heavens? Well, constructive science is logically incapable of formulating the idea of an infinite universe in any sense other than an Aristotelian potential infinite. No one can observe the infinite (in the philosophy of mathematics we say that the infinite is “unsurveyable”). And if you cannot produce observational evidence of the infinite, then you cannot formulate a falsifiable theory of an infinite universe. Thus the infinity of the world is, in effect, ruled out by our methods.

No one should be surprised at the direct impact the ethos of formal thought has a upon the natural sciences; one of the fundamental trends of the scientific revolution has been the mathematization of natural science, and one of the fundamental trends of mathematical rigor since the late nineteenth century has been the arithmetization of analysis, which has been taken as far as the logicization of mathematics. Logic and mathematics have been “finitized” and these finite formal methods have been employed in the rational reconstruction of the sciences.

I look forward to the day when the precision and rigor of formal methods employed in the natural sciences again includes infinitistic methods, and it once again becomes possible to formulate the thesis of the infinity of the world in science — and possible once again to see the world as infinite.

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The Epistemic Overview Effect

14 September 2013

Saturday


earth-from-space-1

OVERVIEW from Planetary Collective on Vimeo.

The Overview Effect

The “overview effect” is so named for the view of the earth entire — an “overview” of the earth — enjoyed by astronauts and cosmonauts, as well as the change in perspective that a few of these privileged observers have had as a result of seeing the earth whole with their own eyes.

One of these astronauts, Edgar Mitchell, who was on the 1971 Apollo mission and was the sixth human being to walk on the moon, has been instrumental to bringing attention to the overview effect, and has written a book about his experiences as an astronaut and how it affected his perception and perspective, The Way of the Explorer: An Apollo Astronaut’s Journey Through the Material and Mystical Worlds. A short film has been made about the overview effect, and an institution has been established to study and to promote the overview effect, The Overview Institute.

Here is an extract from the declaration of The Overview Institute:

For more than four decades, astronauts from many cultures and backgrounds have been telling us that, from the perspective of Earth orbit and the Moon, they have gained such a vision. There is even a common term for this experience: “The Overview Effect”, a phrase coined in the book of the same name by space philosopher and writer Frank White. It refers to the experience of seeing firsthand the reality of the Earth in space, which is immediately understood to be a tiny, fragile ball of life, hanging in the void, shielded and nourished by a paper-thin atmosphere. From space, the astronauts tell us, national boundaries vanish, the conflicts that divide us become less important and the need to create a planetary society with the united will to protect this “pale blue dot” becomes both obvious and imperative. Even more so, many of them tell us that from the Overview perspective, all of this seems imminently achievable, if only more people could have the experience!

We have a hint of the overview effect when we see pictures of the Earth as a “blue marble” and as a “pale blue dot”; those who have had the opportunity to see the Earth as a blue marble with their own eyes have been affected by this vision to a greater extent than we can presumably understand from seeing the photographs. Here is another description of the overview effect:

When people leave the surface of the Earth and travel into Low Earth Orbit, to a space station, or the moon, they see the planet differently. My colleague at the Overview Institute, David Beaver, likes to emphasize that they not only see the Earth from space but also in space. He has also been a strong proponent that we describe what then happens as a change in world view.

Deep Space: The Philosophy of the Overview Effect, Frank White

In the same essay White then quotes himself from his book, The Overview Effect: Space Exploration and Human Evolution, on the same theme:

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

Frank White has sought to give a systematic exposition of the overview effect in his book, The Overview Effect: Space Exploration and Human Evolution, which seeks to develop a philosophy of space travel derived from the personal experience of space by space travelers.

sunset

The Spatial Overview

There is no question in my mind that sometimes you have to see things for yourself. I have invoked this argument numerous times in writing about travel — no amount of eloquent description or stunning photographs can substitute for the experience of seeing a place for yourself with your own eyes. This is largely a matter of context: being in a place, experiencing a place as a presence, requires one’s own presence, and one’s own presence can be realized only as the result of a journey. A journey contextualizes an experience within the experiences required the reach the object of the journey. The very fact that one must travel in order to each a destination alters the experience of the destination itself.

To be present in a landscape means that all of one’s senses are engaged: one not only sees, but one sees with the whole of one’s peripheral vision, and when one turns one’s body in order to take in more of the landscape, one not only sees more of the landscape, but one feels one’s body turn; one smells the air; one hears the distinctive reverberations of the most casual sounds — all of the things that remind us that this is not an illusion but possesses all the chance qualities that mark a real, concrete experience.

I have remarked in other posts that one of the distinctive trends in contemporary philosophy of mind is that of emphasizing the embodiedness of the mind, and in this context the embodied mind is a mind that is inseparable from its sensory apparatus and its sensory apparatus is inseparable from the world with which it is engaged. When our eyes hurt as we look at the sun we are reminded by this visceral experience of sight — one might say overwhelming sight — that we experience the world in virtue of a sensory apparatus that is made of essentially the same materials as the world — that there is an ontological reciprocity of eye that sees and sun that shines, and it is only because the two share the same world and are made of the same materials that they stand in a relation of cause and effect to each other. We are part of the world, of the world, and in the world.

Presumably, then, to the present in space and feel oneself kineasthetically in space — most obviously, the feeling of a micro-gravity environment once off the surface of the earth — is part of the experience of the overview effect, as is the dramatic journey into orbit, which must remind the viewer of the difficulty of attaining the perspective of seeing the world whole. This is the overview effect in space.

temporal overview

The Temporal Overview

There is also the possibility of an overview effect in time. For the same reason that we might insist that some experiences must be had for oneself, and that one must be present spatially in a spatial landscape in order to appreciate that landscape for what it is, we might also insist that a person who has lived a long life and who has experienced many things has a certain kind of understanding of the temporal landscape of life, and it is only through a conscious knowledge of the experience of time and history that we can attain an overview of time.

The movement in contemporary historiography called Big History (which I have written about several times, e.g., in The Science of Time and Addendum on Big History as the Science of Time) is an attempt to achieve an overview experience of time and history.

I have observed elsewhere that we find ourselves swimming in the ocean of history, but this very immersion in history often prevents us from seeing history whole — which is an interesting contrast to the spatial overview experience, which which contextualization in a particular space is necessary to its appreciation and understanding. But contextualization in a particular time — which we would otherwise call parochialism — tends to limit our historical perspective, and we must actively make an effort to free ourselves from our temporal and historical contextualization in order to see time and history whole.

It is the effort to free ourselves from temporal parochialism, and the particularities and peculiarities of our own time, that give as a perspective on history that is not tied to any one history but embraces the whole of time as the context of many different histories. This is the overview effect in time.

Knowledge Tree

The Epistemic Overview

I would like to suggest that there is also an epistemic overview effect. It is not enough to be told about knowledge in the way that newspaper and magazine articles might tell a popular audience about a new scientific discovery, or in the way that textbooks tell students about the wider world. While in some cases this may be sufficient, and we must rely upon the reports of others because we cannot construct the whole of knowledge on our own, in many cases knowledge must be gained firsthand in order for its proper significance to be appreciated.

Elsewhere (in P or not-P) I have illustrated the distinction between a constructive and a non-constructive point of view being something like the difference between climbing up a mountain, clambering over every rock until one achieves the summit (constructive) versus taking a helicopter and being set down on the summit from above (non-constructive). (I have taken this example over from French mathematician Alain Connes.) With this image in mind, being blasted off into space and seeing the mountain from orbit is a paradigmatically non-constructive experience, and it is difficult to imagine how it could be made a constructive experience.

Well, there are ways. Once space technology becomes widely distributed and accessible, if a person were to build their own SSTO from off-the-shelf parts and then pilot themselves into orbit, that would be something like a constructive experience of the overview effect. And if we go on to create a vibrant and vigorous spacefaring civilization, making it into orbit will only be the first of many steps, so that a constructive experience of space travel will be to “climb” one’s way from the surface of the earth through the solar system and beyond, touching every transitional point in between. It has been said that the journey of the thousand miles begins with a single step — this is very much a constructivist perspective. And it holds true that a journey of a million miles or a billion miles begins with a single step, and that first step of a cosmic voyage is the step that takes us beyond the surface of the earth.

Despite the importance and value of the constructivist perspective, it has its limitations, just as the oft-derided non-constructive point of view has its particular virtues and its significance. Non-constructive methods can reveal to us knowledge that is disruptive because it is forced upon us suddenly, in one fell swoop. Such an experience is memorable; it leaves an impression, and quite possibly it leaves much more of an impression that a painstakingly gradual revelation of exactly the same perspective.

This is the antithesis of the often-cited example of a frog placed in a pot of water and which doesn’t jump out as the water is slowly brought to a boil. The frog in this scenario is a victim of constructivist gradualism; if the frog had had a non-constructive perspective on the hot water in which he was being boiled to death, he might have jumped out and saved himself. And perhaps this is exactly what we need as human beings: a non-constructive (and therefore disruptive) perspective on a the familiar life that has crept over us day-by-day, step-by-step, and bit-by-bit.

An epistemic overview of knowledge can give us a disruptive conception of the totality of knowledge that is not unlike the disruptive experience of the overview effect in space, which allows us to see the earth whole, and the disruptive experience of time that allows us to see history whole. Moreover, I would argue that the epistemic overview is the ultimate category — the summum genus — that must contextualize the overview effect in space and in time. However, it is important to point out that the immediate visceral experience of the overview effect may be the trigger that is required for an individual to begin to seek the epistemic overview that will give meaning to his experiences.

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Sunday


A couple of days ago in describing my pilgrimage to Kinn I suggested that the phenomenon of pilgrimage is a Wittgensteinian “form of life,” and as a form of life we may understand it better if we confine ourselves to the material infrastructure while setting aside the formal superstructure that surrounds the form of life we call pilgrimage. But in a fine-grained account of pilgrimage we must distinguish between those forms of pilgrimage that, when taking the long view of the big picture, become conflated.

As I attempted to show, in different ways, in Epistemic Orders of Magnitude and P or not-P, both la longue durée and the fine-grained view have their place in our epistemic development — respectively, and roughly, they represent the non-constructive and the constructive perspectives on experience — and we ought to be equally diligent in exploring the consequences of each perspective, since we have something important to learn from each.

I tried to suggest a similarly comprehensive synthesis yesterday in A Meditation upon the Petroglyphs of Ausevik, when remarking that an extrapolation of a personal philosophy of history, when drawn out to a sufficient extent coincides with the history of the world entire. In other words, non-constructivism represents the furthest reach of constructivist thought, which immediately suggests the contrary perspective, i.e., that constructivism represents the furthest reach of non-constructive thought. Constructivism is non-constructivism in extremis; non-construtivism is constructivism in extremis. To translate this once again into historico-personal terms, the history of the world entire coincides with an intimately personal philosophy of history when the former is extrapolated to the greatest extent of its possible scope.

In a fine-grained account of pilgrimage (in contradistinction to pilgrimage understood in outline, in the context of la longue durée), at the level of personal experience that is constructive because every detail is of necessity immediately exhibited in intuition and nothing whatsoever is demonstrated, we can distinguish many forms of pilgrimage. There are religious pilgrimages, such as the Sunnivaleia, there are personal pilgrimages, such as my pilgrimage to Kinn, there are aesthetic pilgrimages, such as when the custom dictated the young gentlemen of good families and fortune would take the “Grand Tour” of Europe, there are political pilgrimages, as when a candidate for office visits a politically significant place — and there are even philosophical pilgrimages. I have previously made some minor philosophical pilgrimages, as when I sought out Kierkegaard’s grave in Copenhagen and similarly visited Schopenhauer’s grave in Frankfurt. Today I made another philosophical pilgrimage, by visiting the small town of Skjolden, where Wittgenstein spent time working on the ideas that would later becomes the Tractatus Logico-Philosophicus.

In the letters that Wittgenstein subsequently exchanged with his acquaintances in Skjolden (which have, of course, been published along with the rest of his correspondence), the people of Skjolden almost always close their letters by observing that Skjolden is as it always was and ever will be, essentially unchanged in the passage of time. I wrote about this previously in The Charms of Small Town Norway. It seems to be true that life changes very slowly, almost imperceptibly, in the fjord country of Norway, as life always changes slowly in isolated, mountainous regions the world over. The peoples who retreat from the onrushing advance of civilization to the margins of the world where they will not be bothered, are not the kind of peoples who wish to indulge in change for the sake of change. It is this latter attitude that typifies industrial-technological civilization, which is still largely confined to the regions of the world fully given over to agricultural civilization. The margins of the world before industrialization largely coincide with the margins of the world after industrialization.

Wittgenstein, I think, left little impact upon Skjolden. He didn’t make waves, as it were, and didn’t want to make waves. Life in Skjolden is probably little changed in essentials from when Wittgenstein isolated himself in a small, bare hut at the end of a fjord in order to think and write about logic. I think that Wittgenstein would have liked this — or, at least, that he would have preferred this near absence of influence. The fjords are unchanged since Wittgenstein lived here, even if life has been modernized, and they still provide a refuge for those who would seek a world largely untouched by what Wittgenstein in his later years would call, “the main current of European and American civilization,” from which he felt profoundly alienated.

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Nazca to Ica

23 January 2012

Monday


A short distance north of Nazca, along the Panamericana, and situated between the designs of the “hands” (“manos“) and the “tree” (“arbol“), there is a tower (the “Torre Mirador”) that can be climbed, probably about 40 or 50 feet in height, in order to view some part of the lines of Nazca without flying over them. This close-up view of the lines clearly reveals the construction methods that I quoted yesterday (in Lines in the Desert) from Mason’s The Ancient Civilizations of Peru — stones have been removed from within geometrically defined areas and the removed stones have been piled at the edges of the designs. The piled stones not only represent the space cleared, but the piles themselves serve to make the demarcation between cleared and non-cleared areas all the more obvious, making the distinction more visually striking.

This construction technique was also used at nearby Palpa, and continues to be effective in the present day, as driving along the Panamericana (once outside the archaeologically preserved area) one sees a variety of messages spelled out in the desert, from the initials and names of individuals to fairly elaborate advertisements for small roadside stores.

In my naïveté I though that any intrepid visitor of sufficient curiosity might walk out into the desert and and look at the construction of the lines for themselves, but the desert has been fenced off along the Panamericana to prevent further damage to the lines, and once made aware of the threat it becomes immediately obvious how damaged many of the lines and figures are, which accounts for some of the difficulty in seeing some of the patterns from the air. Some — but not all.

Much is revealed by a close inspection (as one can gain from the tower along the Panamericana) that is lost in a distant view from the air, just as much is revealed in a distant inspection from the air that is close in the close-up view from near the ground. This is a perfect concrete illustration of what I was recently writing about in relation to the distinction between constructive and non-constructive thought (in P or not-P). In this post (on my other blog) I employed an image taken from Alain Connes to illustrate the constructive/non-constructive distinction such that the constructive perspective is like that of a mountain climber while the non-constructive perspective is like that of a visitor who flies over the summit of a mountain laboriously climbed by the other.

Any thorough investigation will want to make use of both perspectives in order to obtain the most comprehensive perspective possible — even though each perspective has its blind spots and its shadows that compromise our perspective on the whole. Indeed, it is precisely because each perspective incorporates deficits specific to the perspective that one will want to supplement any one perspective without another perspective with a different set of specific deficits. Between two or more fundamentally different perspectives on any one state-of-affairs there is the possibility of constructing the comprehensive conception that is excluded by any one perspective in isolation.

The two perspectives offered on the Nazca lines by the tower and an airplane flyover also reminded me of a point that I imperfectly attempted to make in my post on Epistemic Orders of Magnitude, in which I employed aerial photographs of cities in order to demonstrate the similar structures of cities transformed in the imagine of industrial-technological civilization. This similarity in structure may be masked by one’s experience of an urban area from the perspective of passing through the built environment on a human scale — i.e., simply walking through a city, which is how most people experience an urban area.

Now, in light of what I have subsequently written about constructivism, I might say that our experience of a built environment is intrinsically constructive, except for that of the urban planner or urban designer, who must see (or attempt to see) things whole. However, the urban planner must also inform his or her work with the street-level “constructive” perspective or the planning made exclusively from a top-down perspective is likely to be a failure. Almost all of the most spectacular failures in urban design have come about from an attempt to impose, from the top down, a certain vision and a certain order which may be at odds with the organically emergent order that rises from the bottom up.

This reflection gives us yet another perspective on utopianism, which I have many times tried to characterize in my attempts to show the near (not absolute) historical inevitability of utopian schemes transforming themselves upon their attempted implementation into dystopian nightmares — the utopian planner attempts to design from a purely non-constructive perspective without the benefit of a constructive perspective. This dooms the utopian plans to inevitable blindspots, shadows, and deficits. The oversights of a single perspective then, in the fullness of time, create the conditions for cascading catastrophic failure.

Historically speaking, it is not difficult to see how this comes about. After the astonishing planned cities of early antiquity, many from prehistoric societies that have left us little record except for their admirably regular and disciplined town plans, Europeans turned to a piecemeal, organic approach to urbanism. Once this approach was rapidly outgrown when cities began their burgeoning growth with the advent of the Industrial Revolution, it was a natural response on the part of Haussman-esque planners to view organic urbanism as a “failure” that necessitated replacement by another model that envisioned the already-built environment as a tabula rasa to be re-built according to rational standards. Cities henceforth were to be wholly planned to address to inadequacies of the medieval pattern of non-planning, which could not cope with cities with populations that now numbered in the millions.

I have observed elsewhere (in my Political Economy of Globalization) that many ancient prehistoric societies were essentially utopian constructions over which a god-king presided as a living god, present in the flesh among his people, and indeed some of the most striking examples of ancient town planning date from societies that exhibited (or seem to have exhibited) this now-vanished form of order. For only where a god-king is openly acknowledged as such can a social order based upon living and present divinity within the said social order be possible.

Nazca, however, does not seem to have been based on this social plan of a divinely-sanctioned social order which can bring utopian (and therefore likely non-constructive, top-down) planning into actual practice because of the physical presence of the god in the midst of his people. The book that I cited yesterday, The Ancient Civilizations of Peru by J. Alden Mason, has this to say of Nazca society:

“…the general picture seems to be one of a sedentary democratic people without marked class distinctions or authoritarianism, possibly without an established religion. There is less difference in the ‘richness’ or poverty of the graves, and women seem to be on an equality with men in this respect. The apparent absence of great public works, of extensive engineering features, and of temple pyramids implies a lack of authoritarian leadership. Instead, the leisure time of the people seems to have been spent in individual production, especially in the making of quantities of perfect, exquisite textiles and pottery vessels. This seems to indicate a strong cult of ancestor-worship. Cloths on which an incredible amount of labor was spent were made especially for funerary offerings and interred with the dead. The orientation seems to have been towards individualized religion rather than towards community participation, dictation, coercion, and aggression.”

J. Alden Mason, The Ancient Civilizations of Peru, Penguin Books, 1968, p. 85

Such egalitarian societies focused on the satisfaction of consumer demands were rare in the ancient world, but we should not be surprised that it was an egalitarian society, organized constructively from the bottom up, that produced the astonishing lines in the desert of the Nazca. Without an aerial perspective, the making of these lines was a thoroughly constructivistic undertaking, not even counter-balanced by a non-constructive perspective, which has only been obtained long after the Nazca civilization has disappeared, leaving only traces of itself in the dessicated sands of the desert.

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While I am posting this a couple of days after the fact, this entire account was written in longhand on the day here described.

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Tuesday


Kardashev Scale

The Kardashev scale is a method of measuring an advanced civilization's level of technological advancement... first proposed in 1964 by the Soviet Russian astronomer Nikolai Kardashev... a Type I civilization has achieved mastery of the resources of its home planet, Type II of its solar system, and Type III of its galaxy. (from Wikipedia)

I have mentioned the Kardashev scale for ranking the technological achievements of civilization based on their ability to utilize energy resources in several posts: A Quick Note on Heideggerian Cosmological Eschatology, Two Conceptions of Civilization, Humanity’s Responsibility for Itself, and Intimations of Mature Civilization. Kardashev was thinking big when he formulated this civilizational metric, and that gives his idea a visionary dimension.

In A Half Century of Human Spaceflight I mentioned Kardashev again, and then went on to suggest my own technological measure of civilization based upon space travel metrics. There I formulated the following:

A Stage 0 spacefaring civilization is a non-spacefaring civilization in which life is largely dictated by regional geography.
A Stage 1 spacefaring civilization has the kind of minimal capacity that we now possess to loft satellites and human beings into orbit, and even to visit nearby heavenly bodies such as the moon.
A Stage 2 spacefaring civilization might be defined as one that had established a permanent, self-sustaining presence off the surface of the world of its biological origin.
A Stage 3 spacefaring civilization would have achieved practical and durable interstellar travel.
A Stage 4 spacefaring civilizations would be defined in terms of practical and durable inter-galactic travel.
A Stage 5 spacefaring civilizations would be defined in terms of practical and durable travel within the multiverse (i.e., among discrete universes).

I have gone into much greater detail on these stages of spacefaring civilization in The Moral Imperative of Human Spaceflight.

Not surprisingly, I prefer my own measure to that of Kardashev’s for several reasons. One of the reasons that I didn’t mention in the post in which I developed this idea is the ambiguity of the Kardashev metric in terms of actual vs. comparable energy usage. A carefully constructivist account of Kardashev would insist that a Type II civilization is “a civilization that is able to harness all of the power available from a single star” (from Wikipedia) and that all of this energy must in fact come from that star. In other words, given a strict conception of a Type II civilization, a civilization utilizing energy quantitatively equivalent to but not identical to the actual energy produced by a single star would not constitute a Type II civilization. I have read some accounts that confuse tapping the power of a star with harnessing the energy equivalent to a star. These are very different measures, but apparently these kind of conceptual slips routinely go unnoticed.

My formulation avoids this ambiguity that follows from a failure to distinguish between constructive and non-constructive conceptions. However, what these two measures of civilization — Kardashev’s and mine — have in common is that they are technological measures, and that they are readily quantifiable.

The obvious alternative to a quantitative measure would be a qualitative measure, though how any metric could be fixed on a qualitative measure is difficult to say. Many people have pointed out that the greatest poets aren’t always the greatest builders, with the implied contrary that the monuments we see now of past civilizations that were great builders represent building only, and that there may have been civilizations of great poetic monuments who left no similarly impressive remains. (A technological metric for measuring civilization is implicitly a principle of technological selection, i.e., a kind of observation selection effect.) We certainly couldn’t measure the achievement of a poetic civilization in terms of the quantity of poetry produced, since production may be in inverse proportion to quality.

Perhaps even more elusive would be a measure of civilization on moral metrics. This is not only elusive, but, like any qualitative measure, would be highly controversial. I have discussed this in posts such as The Very Idea of Higher Civilization. It is considered impolite and impolitic to measure and compare the moral or aesthetic worth of distinct civilizations, mostly because representatives of Western civilization did this so loudly and abrasively up until the nineteenth century.

There is, however, a conceivable “moral” measure that is at least in part quantifiable and perhaps slightly less controversial than any measure of aesthetic excellence or virtue in conduct. What I have in mind is a measure of the extent to which we take responsibility for our own destiny, rather than simply riding the wave of history like a surfer on the crest of a wave he did not create and which he does not control.

Whether we call it the cunning of reason (as in Hegel) or the invisible hand (as in Adam Smith) or the unconscious (as in Freud), there has been a recognition among subtle thinkers that human beings are following promptings and drives and instincts, scarcely knowing what they are doing (this position is sometimes equated with soft determinism). If it happens on occasion to add up to civilization and to great works of art, we’re ahead of the game. If it also happens, on occasion, to issue in cataclysmic wars and ingeniously diabolical forms of suffering, then it becomes a little more difficult to glibly assert that we are ahead of the game.

In other words, human beings are mostly subject to events that befall us, and even when we carefully plan for the future, and take proactive steps to shape our lives and the destiny of the world, the unintended consequences of our actions often are more profound and far-reaching than the intended consequences that we planned to bring about.

It seems to me that a truly mature civilization could be measured by the extent to which both individuals and social groups take responsibility for their own destiny, and moreover pursue this proactive sense of responsibility to the extent that unintended consequences are understood to count against our efforts, and that the only honestly measurable “success” of a civilization are those intended consequences brought to fruition with a minimum of unintended consequences. Further, a mature civilization (or the measure of a mature civilization) might also involve steps taken in the amelioration of unintended consequences.

Even on the intuitive and practical level of ordinary life we are not ignorant of the possibility of this degree of self-responsibility. For example, among people who are serious about playing pool, and not just hitting balls into pockets, you must name your shot (“eight ball in the corner pocket”), and if some other ball goes into some other pocket as an unintended consequence of your shot, this is dismissed as “sloppy” and the ball is extracted from its pocket and put back on the table.

Are we prepared, as a civilization, or will we someday be prepared, to aspire to the ethos of the pool hustler?

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I have gone into Kardashev in much more detail in my Centauri Dreams post What Kardashev Really said.

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A Non-Constructive World

19 April 2009


An imaginary illustration of Protagoras teaching.

An imaginary illustration of Protagoras teaching.

Further Ontological Ruminations

In yesterday’s Ontological Ruminations: Six Protagorean Propositions on the Nature of Man and the World I laid down several ontological principles of a Quasi-Protagorean bent. Protagoras (ca. 490– 420 BC; Greek: Πρωταγόρας), you will recall, was one of the greatest of the Presocratics, and was famous for having said, “Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not.” This is one of those rare philosophical quotations that is sufficiently famous to have survived more than two thousand years and is recognized even by those with no interest in philosophy. So when I noted yesterday that the presence of man in the world as an agent constituting the world, it was, in essence, a Protagorean observation.

Beyond the immediate Protagorean interest, my six propositions of yesterday also suggested the non-constructive character of the world, but this requires explanation to make any sense whatsoever. When I speak of constructive and non-constructive in this forum, I mean the terms in their logical, and not their social, signification. What is the logical significance of constructive and non-constructive? That is difficult to easily sum up.

Constructivism in logic, mathematics, and formal thought generally is an embarras de richesse: there are a remarkable number of distinct formulations of constructivism as well as degrees of constructivism. I was just skimming several philosophical reference works for a simple and comprehensive definition of constructivity that would cover its various manifestations, and I couldn’t find anything satisfying.

There are logical approaches to constructivism, some of which involve logic without the Law of the Excluded Middle and others of which forbid the use of “existence” axioms that posit an entity without giving a method for constructing the entity, and there are finitist approaches to constructivism that deny or limit infinitistic propositions or methods, or which confine legitimate thought to finite assertions, and there are again predicative forms of constructivism that proscribe the use of impredicative definitions and methods.

Hopefully from the above (which is admittedly rather compressed and inexact) it should at least emerge that constructivists generally place limits on formal (or ontological) thought that would not otherwise be observed.

Constructive thought is pervasively influential today for a variety of reasons, ranging from essentially constructive nature of computer science, which makes itself felt in our lives in countless ways today because of the role of computers in our lives, to the increasingly constructivistic character of the sciences.

Physics has been turned into a constructivist undertaking without much notice of this profound change in perspective, yet it retains patently idealistic strains within the generally constructive drift—especially the presumption of the rationality of the world, i.e., its amenability to rational explanation, and mathematization of physics and its consequent idealizations and simplifications. Take, for example, the claim of the impossibility of travel at the velocity of light — if a philosopher deduced properties of the world from mathematical equations he would be a laughing stock, but physicists do so with impunity.

Physicists have taken the mantle of speculation from philosophers; science today is much more speculative than philosophy ever was, and the careful pedanticism of contemporary philosophers looks like a parody of scientific method intended to elicit laughter.

Moreover, the world itself seems constructive. Indeed, the constructivity of the world on a quantum scale is dramatically demonstrated by the failure of the law of the excluded middle and bivalence for quantum states: the logic of quantum theory is a logic without tertium non datur.

We see the extent to which the world is constructive when we contemplate the gradual, piecemeal way in which any actuality would need to approach any infinity. Just as we cannot reach aleph null by adding one repeatedly to any arbitrarily large number, so we cannot attain infinite mass by adding increments of mass to any arbitrarily large mass, nor can we shrink any arbitrarily small but finite quantity to nothing by gradually reducing it in size by a finite number of steps.

In mathematics, these limits have not the same function that they have in physics, because we can conduct thought experiments in which time and temporal processes have no place. But all that it subject to the laws of physics is also subject to the laws of time, and time will not allow us more than a constructive infinity of successively adding discrete quantities a finite number of times. This process can only yield an infinite result after the passage of an infinite quantity of time.

For all that, the world is still non-constructive, and even incorrigibly non-constructive.

The particular non-constructive aspect of the world that featured in yesterday’s exposition was the impredicativity of the world. An impredicative definition defines a given entity in terms of a whole of which it is a part. Impredicative reasoning makes use of impredicative definitions, and such are not terribly unusual. Any definition of an individual man that refers to all men is an impredicative definition, since the class of all men includes the individual so defined. And, more to the point in the present context, the world constructed by an agent who is part of that world is a non-constructive conception.

Not only is the world non-constructive and impredicative, but it is also indefinable in the traditional Aristotelian sense. In Aristotle, a term is defined by citing its genus and differentia. But the world has neither genus or differentia, and therefore cannot be defined. The world is a totality the eludes capture in formal thought. Or, as I put it in my Variations on the Theme of Life: “The world” is a metaphor for a concept that cannot be made literal.

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