26 March 2017
Science is a way to better understand the world, but science itself is not always easy to understand, and we often find that, after clarifying some problem through science, we must then clarify the science so that the science makes sense to us. Some call this science communication; I call it the pursuit of intuitive tractability.
While it is not part of science proper to seek intuitively tractable formulations, it is part of human nature to seek intuitively tractable formulations, as we are more satisfied with science formulated in intuitively tractable forms than with science that is not intuitively tractable. For example, there is, as yet, no intuitively tractable formulation of quantum theory, and this may be why Einstein famously wrote in a letter to Max Born that, “Quantum Mechanics is very impressive. But an inner voice tells me that it is not yet the real thing.”
When the concept of zero was introduced into mathematics, it was thought to be an advanced and difficult idea, but we now teach a number system starting with zero to children in primary school. In a similar way, the Hindu-Arabic system of numbers has displaced almost every other system of numbers because it is what I would paradoxically call an intuitive formalism, i.e., it is a formalization of the number concept that is both adequate to mathematics and closely follows our intuitive conception of number. Mathematics is easier with Hindu-Arabic numerals than other numbering systems because this numbering system is intuitively tractable. There are other formalisms for number that are equally valid and equally correct, but not as intuitively tractable.
The pursuit of intuitive tractability has also been evident in geometry, and especially the axiomatic exposition of geometry that begins with postulates accepted ab initio as self-evident, and which has been the model of rigorous mathematics ever since Euclid. Euclid’s fifth postulate, the famous parallel postulate, is difficult to understand and was a theoretical problem for geometry until its independence was proved, but whether or not the fifth postulate was demonstrably independent of the other postulates, Euclid’s opaque exposition did not help. Here is Euclid’s parallel axiom from the Elements:
“If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.”
Almost two thousand years later, in 1846, John Playfair formulated what we now call “Playfair’s axiom,” which tells us everything that Euclid’s postulate sought to communicate, but in a far more intuitively tractable form: “In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.” Once this more intuitively tractable formulation of the parallel postulate was available, Euclid’s formulation was largely abandoned. There is, then, a process of cognitive selection, whereby the most intuitively tractable formulations are preserved and the less intuitively tractable formulations are abandoned.
Those concepts that are the most intuitively tractable are those concepts that are familiar to us all and which are seamlessly integrated into ordinary thought and language. I have called such concepts “folk concepts.” Folk concepts that have persisted from their origins in our earliest evolutionary psychology up into the present have been subjected to the cognitive equivalent of natural selection, so that we can reasonably speak of folk concepts as having been refined and elaborated by the experience of many generations.
In a series of posts — Folk Astrobiology, Folk Concepts of Scientific Civilization, and Folk Concepts and Scientific Progress — I have considered the nature of “folk” concepts as they have been frequently invoked, and it is natural to ask, in the light of such an inquiry, whether there is a “folk Weltanschauung” that is constituted by a cluster of folk concepts that naturally hang together, and which inform the pre-scientific (or non-scientific) way of thinking about the world.
Arguably, the idea of a folk Weltanschauung is already familiar by a number of different terms that philosophers have employed to identify the concept (or something like the concept) — naïve realism or common sense realism, for example. What Husserl called “natürliche Einstellung” and which Boyce Gibson translated as “natural standpoint” and Fred Kersten translated as “natural attitude” could be said to approximate a folk Weltanschauung. Here is how Husserl describes the natürliche Einstellung:
“I am conscious of a world endlessly spread out in space, endlessly becoming and having endlessly become in time. I am conscious of it: that signifies, above all, that intuitively I find it immediately, that I experience it. By my seeing, touching, hearing, and so forth, and in the different modes of sensuous perception, corporeal physical things with some spatial distribution or other are simply there for me, ‘on hand’ in the literal or the figurative sense, whether or not I am particularly heedful of them and busied with them in my considering, thinking, feeling, or willing.”
Edmund Husserl, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy: First Book: General Introduction to a Pure Phenomenology, translated by Fred Kersten, section 27
Husserl characterizes the natural attitude as a “thesis” — a thesis consisting of a series of posits of the unproblematic existence of ordinary objects — that can be suspended, set aside, as it were, by the phenomenological procedure of “bracketing.” These posits could be identified with folk concepts, making the thesis of the natural standpoint into a folk Weltanschauung, but I think this interpretation is a bit forced and not exactly what Husserl had in mind.
Perhaps closer to what I am getting at than the Husserlian natural attitude is what Wilfrid Sellars has called the manifest image of man-in-the-world, or simply the manifest image. Sellars’ thought is no easier to get a handle on than Husserl’s thought, so that one never quite knows if one has gotten it right, and one can easily imagine being lectured by a specialist in the inadequacies of one’s interpretation. Nevertheless, I think that Sellers’ manifest image is closer to what I am trying to get at than Husserl’s natürliche Einstellung. Closer, but still not the same.
Sellars develops the idea of the manifest image in contrast to the scientific image, and this distinction is especially given exposition in his essay Philosophy and the Scientific Image of Man. After initially characterizing the philosophical quest such that, “[i]t is… the ‘eye on the whole’ which distinguishes the philosophical enterprise,” and distinguishing several different senses in which philosophy could be said to be a synoptic effort at understanding the world as a whole, Sellars introduces terms for contrasting two distinct ways of seeing the world whole:
“…the philosopher is confronted not by one complex many dimensional picture, the unity of which, such as it is, he must come to appreciate; but by two pictures of essentially the same order of complexity, each of which purports to be a complete picture of man-in-the-world, and which, after separate scrutiny, he must fuse into one vision. Let me refer to these two perspectives, respectively, as the manifest and the scientific images of man-in-the-world.”
Wilfrid Sellars, Philosophy and the Scientific Image of Man, section 1
Sellars’ distinction between the manifest image and the scientific image has been quite influential. A special issue of the journal Humana Mente, Between Two Images: The Manifest and Scientific Conceptions of the Human Being, 50 Years On, focused on the two images. Bas C. van Fraassen in particular has written a lot about Sellars, devoting an entire book to one of the two images, The Scientific Image, and has also written several relevant papers, such as “On the Radical Incompleteness of the Manifest Image” (Proceedings of the Biennial Meeting of the Philosophy of Science Association,Vol. 1976, Volume Two: Symposia and Invited Papers 1976, pp. 335-343). All of this material is well worth reading.
Sellars is at pains to point out that his distinction between manifest image and scientific image is not intended to be a distinction between pre-scientific and scientific worldviews (“…what I mean by the manifest image is a refinement or sophistication of what might be called the ‘original’ image…”), though it is clear from this exposition that the manifest image, however refined and up-to-date, has its origins in a pre-scientific conception of the world. (“It is, first, the framework in terms of which man came to be aware of himself as man-in-the-world.”) The essence of this distinction between the manifest image and the scientific image is that the manifest image is correlational while the scientific image is postulational. What this means is that the manifest image “explains” the world (in so far as it could be said to explain the world at all) by correlations among observables, while the scientific image explains the world by positing unobservables that connect observables “under the surface” of things, as it were (involving, “…the postulation of imperceptible entities”). Sellars also maintains that the manifest image cannot postulate in this way, and therefore cannot be improved or refined by science, although it can improve on itself by its own correlational methods.
I do not yet understand Sellars well enough to say why he insists that the manifest image cannot incorporate insights from the scientific image, and this is a key point of divergence between Sellars’ manifest image and what I above called a folk Weltanschauung. If a folk Weltanschauung consists of a cluster of tightly-coupled folk concepts (and perhaps a wide penumbra of associated but loosely-coupled folk concepts), then the generation of refined scientific concepts can slowly, one-by-one, replace folk concepts, so that the folk Weltanschauung gradually evolves into a more scientific Weltanschauung, even if it is not entirely transformed under the influence of scientific concepts. Science, too, consists of a cluster of tightly-coupled concepts, and these two distinct clusters of concepts — the folk and the scientific — might well resist mixing for a time, but the human mind cannot keep such matters rigorously separate, and it is inevitable that each will bleed over into the other. Sometimes this “bleeding over” is intentional, as when science reaches for metaphors or non-scientific language as a way to make its findings understood to a wider audience. This is part of the pursuit of intuitively tractable formulations, but it can also go very wrong, as when scientists adopt theological language in an attempt at a popular exposition that will not be rejected out-of-hand by the Great Unwashed.
Despite my differences with Sellars, I am going to here adopt his terminology of the manifest image and the scientific image, and I will hope that I don’t make too much of a mess of it. I will have more to say on this use of Sellars’ concepts below (especially in relation to the postulational character of the scientific image). In the meantime, I want to use Sellars’ concepts in a exposition of intuitive tractability. Sellars’ uses the metaphor of “stereoscopic vision” as the proper way to understand how we must bring together the manifest image and the scientific image as a single way of understanding the world (“…the most appropriate analogy is stereoscopic vision, where two differing perspectives on a landscape are fused into one coherent experience”). I think, on the contrary, that intuitively tractable formulations of scientific concepts can make the manifest image and the scientific image coincide, so that they are one and the same, and not two distinct images fused together. A slightly weaker formulation of this is to assert that intuitively tractable formulations allow us to integrate the manifest image and the scientific image.
Now I want to illustrate this by reference to the overview effect, that is to say, the cognitive effect of seeing our planet whole — preferably from orbit, but, if not from orbit, in photographs and film that make the point as unmistakably as though one were there, in orbit, seeing it with one’s own eyes.
Before the overview effect, we saw our planet with the same eyes, but even after it is proved to us that the planet is (roughly) a sphere, hanging suspended in space, it is difficult to believe this. All manner of scientific proofs of the world as a spherical planet can be adduced, but the science lacks intuitive tractability and we have a difficult time bringing together our scientific concepts and our folk concepts of the world — or, if you will, we have difficulty reconciling the manifest image and the scientific image. The two are distinct. Until we achieve the overview effect, there is an apparent contradiction between what we experience of the world and our scientific knowledge of the world. Our senses tell us that the world is flat and solid and unmoving; scientific knowledge tells us that the world is round and moving and hanging in space.
Once we attain the overview effect, this changes, and the apparent contradiction is revealed as apparent. The overview effect shows how the manifest image and the scientific image coincide. The things we know about ordinary objects, which shapes the manifest image, now applies to Earth, which is seen as an object rather than as surrounding us as an environment with an horizon that we can never reach, and which therefore feels endless to us. Seen from orbit, this explains itself intuitively, and an explicit explanation now appears superfluous (as is ideally the case with an axiom — it is seen to be true as soon as it is understood). The overview effect makes the scientific knowledge of our planet as a planet intuitively tractable, transforming scientific truths into visceral truths. One might say that the overview effect is the lived experience of the scientific truth of our homeworld. In this particular case, we have replaced a folk concept with a scientific concept, and the scientific concept is correct even as intuition is satisfied.
The use of the overview effect to illustrate the manifest and scientific images, and their possible coincidence in a single experience, is especially interesting in light of Sellars’ insistence that the scientific image is distinctive because it is postulational, and more particularly that it postulates unobservables as a way to explain observables. When, in a scientific context, someone speaks of unobservables or “imperceptible entities” the assumption is that we are talking about entities that are too small to see with the naked eye. The germ theory of disease and the atomic theory of matter both exemplify this idea of unobservables being observable because they are smaller than the resolution of unaided human vision. We can only observe these unobservables with instruments, and then this experience is mediated by complex instruments and an even more complex conceptual framework so that no one ever speaks of the “lived experience” of particle physics or microbiology.
In contrast to this, the Earth is unobservable to the human eye not because it is too small, but because it is too large. When shown scientific demonstrations that the world is round, we must posit an unobservable planet, and then identify this unobservable entity with the actual ground under our feet. This is difficult to do, intuitively speaking. We see the world at all times, but we do not see it as a planet. We do not see enough of the world at any one moment to see it as a planet. Enter the overview effect. Seeing the Earth whole from space reveals the entity that is planet Earth, and if one has the good fortune to lift off from Earth and experience the process of departing from its surface to then see the same from space, this makes a previously unobservable postulate into a concretely experienced entity.
We are in the same position now vis-à-vis our place within the Milky Way galaxy, and our place within the larger universe, as we were once in relation to the spherical Earth. Our accumulated scientific knowledge tells us where we are at in the universe, and where we are at in the Milky Way. We can even see a portion of the Milky Way when we look up into the night sky, but we cannot stand back and see the whole from a distance, taking in the Milky Way and pointing of the position of our solar system within one of the spiral arms of our galaxy. We know it, but we haven’t yet experienced it viscerally. We have to posit the Milky Way galaxy as a whole, the Virgo supercluster, and the filaments of galaxies that stretch through the cosmos, because they are too large for us to observe at present. They are partially observed, in the way we might say that an atom is partially observed when we look at a piece of ordinary material composed of atoms.
Our postulational scientific image of the universe in which we live is redeemed for intuition by experiences that put us in a position to view these entities with our own eyes, and so to see them in an intuitively tractable manner. Perhaps one of the reasons that quantum theory remains intuitively intractable is that the unobservables that it posits are so small that we have no hope of ever seeing them, even with an electron microscope.
Ultimately, intuitively tractable formulations of formerly difficult if not opaque scientific ideas is a function of the conceptual framework that we employ, and this is ultimately a philosophical concern. Sellars suggests that the manifest and scientific conceptual framework might be harmonized in stereoscopic vision, but he doesn’t hold out any hope that the manifest image can be integrated with the scientific image. I think that the example of the overview effect demonstrates that there are at least some cases when manifest image and scientific image can be shown to coincide, and therefore these two ways of grasping the world are not entirely alien from each other. Cosmology may be the point of contact at which the two images coincide and through which the two images can communicate.
The pursuit of intuitive tractability is, I submit, a central concern of scientific civilization. If there ever is to be a fully scientific civilization, in which scientific ways of knowing and scientific approaches to problems and their solutions are the pervasively held view, this scientific civilization will come about because we have been successful in our pursuit of intuitive tractability, and we are able to make advanced scientific concepts as familiar as the idea of zero is now familiar to us. Since the question of a conceptual framework in which rigorous science and intuitively tractable concepts can be brought together is not a scientific question, but a philosophical question, the contemporary contempt for philosophy in the special sciences is invidious to the effective pursuit of intuitive tractability. The fate of scientific civilization lies with philosophy.
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● The Overview Effect and Intuitive Tractability
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18 March 2017
Many years ago, reading a source I cannot now recall (and for which I searched unsuccessfully when I started writing this post), I came upon a passage that has stayed with me. The author was making the argument that no sciences were consistent except those that had been reduced to mere catalogs of facts, like geography and anatomy. I can’t recall the larger context in which this argument appeared, but the observation that sciences might only become fully consistent when they have matured to the point of being exhaustive but static and uninteresting catalogs of facts, implying that the field of research itself had been utterly exhausted, was something I remembered. This idea presents in miniature a developmental conception of the sciences, but I think that it is a developmental conception that is incomplete.
Thinking of this idea of an exhausted field of research, I am reminded of a discussion in Conversations on Mind, Matter, and Mathematics by Jean-Pierre Changeux and Alain Connes, in which mathematician Alain Connes distinguished between fully explored and as yet unexplored parts of mathematics:
“…the list of finite fields is relatively easy to grasp, and it’s a simple matter to prove that the list is complete. It is part of an almost completely explored mathematical reality, where few problems remain. Cultural and social circumstances clearly serve to indicate which directions need to be pursued on the fringe of current research — the conquest of the North Pole, to return again to my comparison, surely obeyed the same type of cultural and social motivations, at least for a certain time. But once exploration is finished, these cultural and social phenomena fade away, and all that’s left is a perfectly stable corpus, perfectly fitted to mathematical reality…”
Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics, Princeton: Princeton University Press, 1995, pp. 33-34
To illustrate a developmental conception of mathematics and the formal sciences would introduce additional complexities that follow from the not-yet-fully-understood relationship between the formal sciences and the empirical sciences, so I am going to focus on developmental conceptions of the empirical sciences, but I hope to return to the formal sciences in this connection.
The idea of the development of science as a two-stage process, with discovery followed by a consistent and exhaustive catalog, implies both that most sciences (and, if we decompose the individual special sciences into subdivisions, parts of most or all sciences) remain in the discovery phase, and that once the discovery phase has passed and we are in possession of an exhaustive and complete catalog of the facts discovered by a science, there is nothing more to be done in a given science. However, I can think of several historical examples in which a science seemed to be converging on a complete catalog, but this development was disrupted (one might say) by conceptual change within the field that forced the reorganization of the materials in a new way. My examples will not be perfect, and some additional scientific discovery always seems to have been involved, but I think that these examples will be at least suggestive.
Prior to the great discoveries of cosmology in the early twentieth century, after which astronomy became indissolubly connected to astrophysics, astronomy seemed to be converging slowly upon an exhaustive catalog of all stars, with the limitation on the research being simply the resolving power of the telescopes employed to view the stars. One could imagine a counterfactual world in which technological innovations in instrumentation supplied nothing more than new telescopes able to resolve more stars, and that the task of astronomy was merely to supply an exhaustive catalog of stars, listing their position in the sky, intrinsic brightness, and a few other facts about the points of light in the sky. But the cataloging of stars itself contributed to the revolution that would follow, particularly when the period-luminosity relationship in Cepheid variable stars was discovered by Henrietta Swan Leavitt (discovered in 1908 and published in 1912). The period-luminosity relationship provided a “standard candle” for astronomy, and this standard candle began the process of constructing the cosmological distance ladder, which in turn made it possible to identify Cepheid variables in the Andromeda galaxy and thus to prove that the Andromeda galaxy was two million light years away and not contained within the Milky Way.
Once astronomy became scientifically coupled to astrophysics, and the resources of physics (both relativistic and quantum) could be brought to bear upon understanding stars, a whole new cosmos opened up. Stars, galaxies, and the universe entire were transformed from something static that might be exhaustively cataloged, to a dynamic and changing reality with a natural history as well as a future. Astronomy went from being something that we might call a Platonic science, or even a Linnaean science, to being an historical science, like geology (after Hutton and Lyell), biology (after Darwin and Wallace), and Paleontology. This coupling of the study of the stars with the study of the matter that makes up the stars has since moved in both directions, with physics driving cosmology and cosmology driving physics. One result of this interaction between astronomy and physics is the illustration above (by Jennifer Johnson) of the periodic table of elements, which prominently exhibits the origins of the elements in cosmological processes. The periodic table once seemed, like a catalog of stars, to be something static to be memorized, and divorced from natural history. This conceptualization of matter in terms of its origins puts the periodic table in a dramatically different light.
As the cosmos was once conceived in Platonic terms as fixed and eternal, to be delineated in a Linnaean science of taxonomical classification, so too the Earth was conceived in Platonic terms as fixed and eternal, to be similarly delineated in a Linnaean science of classification. The first major disruption of this conception came with geology since Hutton and Lyell, followed by plate tectonics and geomorphology in the twentieth century. Now this process has been pushed further by the idea of mineral evolution. I have been listening through for the second time to Robert Hazen’s lectures The Origin and Evolution of Earth: From the Big Bang to the Future of Human Existence, which exposition closely follow the content of his book, The Story of Earth: The First 4.5 Billion Years, from Stardust to Living Planet, in which Hazen wrote:
“The ancient discipline of mineralogy, though absolutely central to everything we know about Earth and its storied past, has been curiously static and detached from the conceptual vagaries of time. For more than two hundred years, measurements of chemical composition, density, hardness, optical properties, and crystal structure have been the meat and potatoes of the mineralogist’s livelihood. Visit any natural history museum, and you’ll see what I mean: gorgeous crustal specimens arrayed in case after glass-fronted case, with labels showing name, chemical formula, crystal system, and locality. These most treasured fragments of Earth are rich in historical context, but you will likely search in vain for any clue as to their birth ages or subsequent geological transformations. The old way all but divorces minerals from their compelling life stories.”
Robert M. Hazen, The Story of Earth: The First 4.5 Billion Years, from Stardust to Living Planet, Viking Penguin, 2012, Introduction
This illustrates, from the perspective of mineralogy, much of what I said above in relation to star charts and catalogs: mineralogy was once about cataloging minerals, and this may have been a finite undertaking once all minerals had been isolated, identified, and cataloged. Now, however, we can understand mineralogy in the context of cosmological history, and this is as revolutionary for our understanding of Earth as the periodic table understood in terms of cosmological history. It could be argued, in addition, that compiling the “particle zoo” of contemporary particle physics is also a task of cataloging the entities studied by physics, but the cataloging of particles has been attended throughout with a theory of how these particles are generated and how they fit into the larger cosmological story — what Aristotle would have called their coming to be and passing away.
The best contemporary example of a science still in its initial phases of discovery and cataloging is the relatively recent confirmation of exoplanets. On my Tumblr blog I recently posted On the Likely Existence of “Random” Planetary Systems, which tried to place our current Golden Age of Exoplanet Discovery in the context of a developing science. We find the planetary systems that we do in fact find partly as a consequence of observation selection effects, and it belongs to the later stages of the development of a science to attempt to correct for observation selection effects built into the original methods of discovery employed. The planetary science that is emerging from exoplanet discoveries, however, and like contemporary particle physics, is attended by theories of planet formation that take into account cosmological history. However, the discovery phase, in terms of exoplanets, is still underway and still very new, and we have a lot to learn. Moreover, once we learn more about the possibilities of planets in our universe, hopefully also we will learn about the varied possibilities of planetary biospheres, and given the continual interaction between biosphere, lithosphere, atmosphere, and hydrosphere, which is a central motif of Hazen’s mineral evolution, we will be able to place planets and their biospheres into a large cosmological context (perhaps even reconstructing biosphere evolution). But first we must discover them, and then we must catalog them.
These observations, I think, have consequences not only for our understanding of the universe in which we find ourselves, but also for our understanding of science. Perhaps, instead of a two-stage process of discovery and taxonomy, science involves a three-stage process of discovery, taxonomy, and natural history, in which latter the objects and facts cataloged by one of the special sciences (earlier in their development) can take their place within cosmological history. If this is the case, then big history is the master category not only of history, but also of science, as big history is the ultimate framework for all knowledge that bears the lowly stamp of its origins. This conception of the task of science, once beyond the initial stages of discovery and classification, to integrate that which was discovered and classified into the framework of big history, suggests a concrete method by which to “cash out” in a meaningful way Wilfrid Sellars’ contention that, “…the specialist must have a sense of how not only his subject matter, but also the methods and principles of his thinking about it, fit into the intellectual landscape.” (cf. Philosophy and the Scientific Image of Man) Big history is the intellectual landscape in which the sciences are located.
A developmental conception of science that recognized stages in the development of science beyond classification, taxonomy, and an exhaustive catalog (which is, in effect, the tombstone of what was a living and growing science), has consequences for the practice of science. Discovery may well be the paradigmatic form of scientific activity, but it is not the only form of scientific activity. The painstakingly detailed and disciplined work of cataloging stars or minerals is the kind of challenge that attracts a certain kind of mind with a particular interest, and the kind of individual who is attracted to this task of systematically cataloging entities and facts is distinct from the kind of individual who might be most attracted by scientific discovery, and also distinct from the kind of individual who might be attracted to fitting the discoveries of a special science into the overall story of the universe and its natural history. There may need to be a division of labor within the sciences, and this may entail an educational difference. Dividing sciences by discipline (and, now, by university departments), which involves inter-generational conflicts among sciences and the paradigm shifts that sometimes emerge as a result of these conflicts, may ultimately make less sense than dividing sciences according their stage of development. Perhaps universities, instead of having departments of chemistry, geology, and botany, should have departments of discovery, taxonomy, and epistemic integration.
Speaking from personal experience, I know that (long ago) when I was in school, I absolutely hated the cataloging approach to the sciences, and I was bored to tears by memorizing facts about minerals or stars. But the developmental science of evolution so intrigued me that I read extensively about evolution and anthropology outside and well beyond the school curriculum. If mineral evolution and the Earth sciences in their contemporary form had been known then, I might have had more of an interest in them.
What are the sciences developing into, or what are the sciences becoming? What is the end and aim of science? I previously touched on this question, a bit obliquely, in What is, or what ought to be, the relationship between science and society? though this line of inquiry is more like a thought experiment. It may be too early in the history of the sciences to say what they are becoming or what they will become. Perhaps an emergent complexity will arise out of knowledge itself, something that I first suggested in Scientific Historiography: Past, Present, and Future, in which I wrote in the final paragraph:
We cannot simply assume an unproblematic diachronic extrapolation of scientific knowledge — or, for that matter, historical knowledge — especially as big history places such great emphasis upon emergent complexity. The linear extrapolation of science eventually may trigger a qualitative change in knowledge. In other words, what will be the emergent form of scientific knowledge (the ninth threshold, perhaps?) and how will it shape our conception of scientific historiography as embodied in big history, not to mention the consequences for civilization itself? We may yet see a scientific historiography as different from big history as big history is different from Augustine’s City of God.
It is only a lack of imagination that would limit science to the three stages of development I have outlined above. There may be developments in science beyond those we can currently understand. Perhaps the qualitative emergent from the quantitative expansion of scientific knowledge will be a change in science itself — possibly a fourth stage in the development of science — that will open up to scientific knowledge aspects of experience and regions of nature currently inaccessible to science.
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