7 December 2016
The full awareness of our sun being a star, and the stars being suns in their own right, was a development nearly coextensive with the entire history of science, from its earliest stirrings in ancient Greece to its modern form at the present time. During the Enlightenment there was already a growing realization of this, as can be seen in a number of scientific works of the period, but scientific proof had to wait for a few generations more until new technologies made available by the industrial revolution produced scientific instruments equal to the task.
The scientific confirmation of this understanding of cosmology, which is, in a sense, the affirmation of Copernicanism (as distinct from heliocentrism) came with two scientific discoveries of the nineteenth century: the parallax of 61 Cygni, measured by Friedrich Wilhelm Bessel and published in 1838, which was the first accurate distance measured to a star other than the sun, and the spectroscopy work of several scientists — Fraunhofer, Bunsen, Kirchhoff, Huggins, and Secchi, inter alia (cf. Spectroscopy and the Birth of Astrophysics) — which demonstrated the precise chemical composition of the stars, and therefore showed them to be made of the same chemical elements found on Earth. The stars were no longer immeasurable or unknowable; they were now open to scientific study.
The Ptolemaic conception of the universe that preceded this Copernican conception painted a very different picture of the universe, and of the place of human beings within that universe. According to the Ptolemaic cosmology, the heavens were made of a different material than the Earth and its denizens (viz. quintessence — the fifth element, i.e., the element other than earth, air, fire, and water). Everything below the sphere of the moon — sublunary — was ephemeral and subject to decay. Everything beyond the sphere of the moon — superlunary — was imperishable and perfect. Astronomical bodies were perfectly spherical, and moved in perfectly circular lines (except for the epicycles). Comets were a problem (i.e., an anomaly), because their elliptical orbits ought to send them crashing through the perfect celestial spheres.
This Ptolemaic cosmology largely satisfied the scientific, philosophical, moral, and spiritual needs of western thought from classical antiquity to the end of the Middle Ages, and this satisfaction presumably follows from a deep consonance between this conception of the cosmos and a metaphysical vision of what the world ought to be. Ptolemaic cosmology is the intellectual fulfillment of a certain kind of heart’s desire. But this was not the only metaphysical vision of the world having its origins (or, at least, its initial expression) in classical antiquity. Another intellectual tradition that pointed in a different direction was mathematics.
Mathematics was the first science to attain anything like the rigor that we demand of science today. It remains an open question to this day — an open philosophical question — whether mathematics is a science, one of the sciences (a science among sciences), or whether it is something else entirely, which happens to be useful in the sciences, as, for example, the formal propaedeutic to the empirical sciences, in need of formal structure in order to organize their empirical content. The sciences, in fact, get their rigor from mathematics, so that if there were no mathematical rigor, there would be no possibility of scientific rigor.
Mathematics has been known since antiquity as the paradigm of exact thought, of precision, the model for all sciences to follow (remembering what science meant to the ancients, which is not what it means today: a demonstrative science based on first principles), and this precision has been seen as a function of its formalism, which is to say its definiteness, it boundedness, its participation in the peras. Despite this there was yet a recognition of the infinite (apeiron) in mathematics. I would go further, and assert that, while mathematics as a rigorous science has its origins in the peras, it has its telos in the apeiron. This is a dialectical development, as we will see below in Proclus.
Proclus expresses the negative character of the infinite in his commentary on Euclid’s Elements:
“…the infinite is altogether incomprehensible to knowledge; rather it takes it hypothetically and uses only the finite for demonstration; that is, it assumes the infinite not for the sake of the infinite, but for the sake the infinite.”
Proclus, A Commentary on the First Book of Euclid’s Elements, translated, with an introduction and notes, by Glenn R. Morrow, Princeton: Princeton University Press, 1992, Propositions: Part One, XII, p. 223. This whole section is relevant, but I have quoted only a brief portion.
There is no question that the apeiron appeared on the inferior side of the Pythagorean table of opposites, but it is also interesting to note what Proclus says earlier on:
“The objects of Nous, by virtue of their inherent simplicity, are the first partakers of the Limit (περας) and the Unlimited (ἄπειρον). Their unity, their identity, and their stable and abiding existence they derive from the Limit; but for their variety, their generative fertility, and their divine otherness and progression they draw upon the Unlimited. Mathematicals are the offspring of the Limit and the Unlimited…”
Proclus, Commentary on the First Book of Euclid, Prologue: Part One, Chap. II
Here the apeiron appears on an equal footing with the peras, both being necessary to mathematical being. “Mathematicals” are born of the dialectic of the finite and the infinite. Both of these elements are also found (hundreds of years earlier) in the foundations of geometry. As the philosophers produced proofs that there could be no infinite number or infinite space, Euclid spoke of lines and planes extended “indefinitely” (as “apeiron” is usually translated in Euclid). Even later when the Stoics held that the material world was surrounded by an infinite void, this void had special properties which distinguished it from the material world, and indeed which kept the material world from having any relation with the void. The use of infinities in geometry, however, even though in an abstract context, force one to maintain that space locally, directly before one, is essentially of the same kind as space anywhere else along the infinite extent of a line, and indeed the same as space infinitely distant. All spaces are of the same kind, and all are related to each other. This constitutes a purely formal conception of the uniformity and continuity of nature. One might interpret the subsequent history of science as redeeming, through empirical evidence, this formal insight.
The infinite is the “internal horizon” (to use a Husserlian phrase) and the telos of mathematical objects. Given this conception of mathematics, the question that I find myself asking is this: what was the mathematical horizon of the Greeks? Did the idea of a line or a plane immediately suggest to them an infinite extension, and did the idea of number immediately suggest the infinite progression of the series, or were the Greeks able to contain these conceptions within the peras, using them not unlike we use them, but allowing them to remain limited? Did ancient mathematical imagination encompass the infinite, or must such a conception of mathematical objects (as embedded in the infinite) wait for the infinite to be disassociated from the apeiron?
The wait was not long. While the explicit formulation of the mathematical infinite had to wait until Cantor in the nineteenth century, Greek thought was dialectical, so regardless of the nature of mathematical concepts as initially conceived, these concepts inevitably passed into their opposite numbers and grew in depth and comprehensiveness as a result of the development of this dialectic. Greek thought may have begun with an intellectual commitment to the peras, and a desire to contain mathematics within the peras, consequently an almost ideological effort to avoid the mathematical infinite, but a commitment to dialectic confounds the demand for limitation. It is, then, this dialectical character of Greek thought that gives us the transition from purely local concepts to a formal concept of the uniformity of nature, and then the transition from a formal conception of uniformity to an empirical conception of uniformity, and this latter is the cosmological principle that is central to contemporary cosmology.
The cosmological principle brings us back to where we started: To say that the sun is a star, and every star a sun, is to say that the sun is a star among stars. Earth is a planet among planets. The Milky Way is a galaxy among galaxies. This is not only a Copernican idea, it is also a formal idea, like the formal conception of the uniformity of nature. (In A Being Among Beings I made a similar about biological beings.) To be one among others of the same kind is to be a member of a class, and to be a member of a class is to be the value of a variable. Quine, we recall, said that to be is to be the value of a variable. This is a highly abstract and formal conception of ontology, and that is precisely the importance of the formulation. This is the point beyond which we can begin to reason rigorously about our place in the universe.
We require a class of instances before we can draw inductive inferences, generalize from all members of this class, or formalize the concept represented by any individual member of that class. This is one of the formal presuppositions of scientific thought never made explicit in the methodology of science. We could not formulate the cosmological principle if we did not have a concept of “essentially the same,” because the “same” view that we see looking in any direction in the universe is not identically the same, but rather essentially the same. Of any two views of the universe, every detail is different, but the overview is the same. The cosmological principle is not a generalization, not an inductive inference from empirical evidence; it is a formal idea, a regulative idea that makes a certain kind of cosmological thought possible.
Formal principles like this are present throughout the sciences, though not often recognized for what they are. Bessel’s observations of 61 Cygni not only required industrialized technology to produce the appropriate scientific instruments, these observations also presupposed the mathematics originating in classical antiquity, so that the nineteenth century scientific work that proved the stars to be like our sun (and vice versa) was predicated upon parallel formal conceptions of universality structured into mathematical thought since its inception as a theoretical discipline (in contradistinction to the practical use of mathematics as a tool of engineering). Formal Copernicanism preceded empirical Copernicanism. Without that formal component of scientific knowledge, that scientific knowledge would never have come into being.
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19 March 2012
This post has been superseded by Eo-, Eso-, Exo-, Astro-, which both corrects and extends what I wrote below.
The Philosophical Significance of Astrobiology as a
Cosmological Extrapolation of Terrestrial Biology
In yesterdays’ Commensurable Perspectives I finished with this observation:
Ecology is the master world-narrative that unifies the sub-narratives employed by individual species in virtue of their perceptual and cognitive architecture. Ultimately, astrobiology would constitute the universal narrative that would unify the ecological narratives of distinct worlds.
The naturalistic narrative has the power to unify even across species and across worlds. This power may not be particularly evident at present, but in the long term future of our species (if our species does in fact have a long term future) this power will prove to be crucial.
If indeed astrobiology is the universal narrative of life, that gives astrobiology a privileged position among the sciences. That is a tall order. But what is astrobiology? At one time I had heard both the terms “exobiology” and “astrobiology” and I was not quite clear about the exact difference between the two, or how each was defined. Thereby hangs a tale. The distinction between the two is in fact a very interesting story, and it is a story to which an entire book has been devoted, The Living Universe: NASA and the Development of Astrobiology, by Steven J. Dick and James E. Strick.
I urge the reader to get this book and peruse it for yourself for the detailed version of the emergence of astrobiology as a scientific discipline. I will give only the bare bones of that story here, which will be only enough to grasp the crucial concepts involved. And our interest is in the concepts, not the personalities.
Exobiology is the older term, introduced by Joshua Lederberg (first used in a public lecture in 1960), and contrasted by him to eobiology. Exobiology has some currency in the public mind, but I didn’t know about eobiology until I read about the history of the discipline. However, the contrast between the two terms is conceptually important. Exobiology is concerned with biology off the surface of the earth, while eobiology is biology on the surface of the earth. (cf. p. 29) In other words, all biological science prior to human spaceflight was eobiology, even if we didn’t know that it was eobiology. Another way to formulate this distinction is to say that eobiology is the biology of the terrestrial biosphere, while exobiology is the biology of everything else.
In the book The Living Universe: NASA and the Development of Astrobiology the authors give a lot of background on the internal politics and budgeting of NASA and how this affected the emergence of astrobiology. It is an interesting story, but I will not go into it here, as our interest at present is exclusively with the conceptual infrastructure of the discipline. Suffice it to say that in 1996 the first attempts were made to define astrobiology (cf. p. 202), and within a couple of years there was a virtual Astrobiology Institute.
“Astrobiology is the study of the origin, evolution, distribution, and future of life in the universe. This multidisciplinary field encompasses the search for habitable environments in our Solar System and habitable planets outside our Solar System, the search for evidence of prebiotic chemistry and life on Mars and other bodies in our Solar System, laboratory and field research into the origins and early evolution of life on Earth, and studies of the potential for life to adapt to challenges on Earth and in space.”
“The study of the living universe. This field provides a scientific foundation for a multidisciplinary study of (1) the origin and distribution of life in the universe, (2) an understanding of the role of gravity in living systems, and (3) the study of the Earth’s atmospheres and ecosystems.”
The important lesson to take away from this is that astrobiology is the more comprehensive concept, and that in fact we can consider astrobiology the union of eobiology and exobiology. This sounds simple enough (and it is), but it is important to understand the conceptual leap that has been taken here.
From the perspective of astrobiology, earth sciences are only fragments of far larger and more comprehensive sciences. Just as all biology was once eobiology, the same observation can be made in regard to the other earth sciences, and the same tripartite conceptual distinction can be brought to the other earth sciences. We can formulate eogeology and exogeology unified in astrogeology; we can formulate eohydrology and exohydrology unified in astrohydrology; we can formulate eovulcanology and exovulcanology unified in astrovulcanology; we can formulate eoclimatology and exoclimatology unified in astroclimatology. All of these are cosmological extrapolations of earth sciences. One suspects that, in the future, the prefixes will be dropped and we will return to climatology simpliciter, e.g., but while the conceptual revolution is underway it is important to retain the prefixes as a reminder that science is no longer defined by the boundaries of the earth.
I assert that this is a conceptual leap of the first importance because what we have with astrobiology is the formulation of the first truly Copernican science; astrobiology includes eobiology but it is not exhausted by eobiology; it is supplemented by exobiology. The earth, for obvious reasons, remains important to us, but it no longer dictates the center of our science. All mature sciences will eventually need to take this Copernican turn and dethrone the earth from the center of its concern.
We can take a further step beyond this conceptual formulation of Copernican sciences by observing that traditional earth sciences began as local enterprises, and it has only been in recent decades that truly global sciences have emerged. These global sciences have culminated in objects of scientific study that take the world entire as their object. Thus biology has converged upon study of the biosphere; hydrology has converged on study of the hydrosphere; glaciology has culminated in the study of the cryosphere. Copernican sciences based on the model of astrobiology can go one better than this, transcending earth-defined “-spheres” in favor of more comprehensive concepts.
When I spoke last year on “The Moral Imperative of Human Spaceflight” at the NASA/DARPA 100 Year Starship Study symposium it was my intention to spend some time on the emergence of Copernican sciences, but I didn’t have enough time to elaborate. I cut most of that material out and still was rushed. The point that I wanted to make there was that the concepts of the biosphere, the lithosphere, the geosphere, hydrosphere, cryosphere, atmosphere, anthrosphere, sociosphere, noösphere, and technosphere are essentially Ptolemaic concepts. (If the proceedings of the symposium are published, and if my paper is included, this contains my first sketch of Copernican sciences as transcending these earth-defined “-spheres.”) The Copernican Revolution entails the formulation of Copernican concepts to supersede Ptolemaic concepts, and this work is as yet unfinished. In some spheres of human thought, it has scarcely begun.
One way to transcend our Ptolemaic concepts and to replace them with Copernican concepts, and thus to extend the ongoing shift to a truly Copernican perspective, is to substitute for the earth-defined “-spheres” a conception of the object of the sciences not dependent upon the earth, and this can be done by defining, respectfully, biospace (in place of the biosphere), lithospace, geospace, hydrospace, cryospace, atmospace, anthrospace, sociospace, noöspace, and technospace. In so far as we can facilitate the emergence of Copernican sciences, we can contribute to the ongoing Copernican Revolution, which will someday culminate in a Copernican civilization (if we do not first destroy ourselves).
We can pass beyond the earth sciences and the natural sciences and similarly extend our conceptions of a the social and political sciences. Although concepts from the social sciences are not usually expressed in geocentric terms — except for the above-mentioned anthrosphere, sociosphere, noösphere, and technosphere (which are not employed very often) — our social and political thought is usually even more tied to planetary prejudices than the concepts of the natural sciences. Thus we can extend our conception of politics by distinguishing between eopolitics and exopolitics, both of which are subsumed under astropolitics. Similarly, we can formulate eoeconomics and exoeconomics, subsumed by astroeconomics, eostrategy and exostrategy, subsumed by astrostrategy, and so forth.
As a final note, it is ironic that the breakthrough to a Copernican science should occur first with biology, because biology was among the latest of the sciences to actually attain a scientific status. Prior to Darwin, biological theories were essentially theological theories with but a few exceptions. Darwin put biology on a firm biological footing and created the discipline in its modern scientific form. Thus biology was among the last of the sciences to attain a modern scientific form, though it was the first to attain to a Copernican form.
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This post has been superseded by Eo-, Eso-, Exo-, Astro-.
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