The periodic table, color-coded by the source of the element in the solar system. By Jennifer Johnson.

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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