Numerical Models Are Forms of Being

Notes on Oreskes, Shrader-Frechette, and Belitz (1994) and Lukács

Mantle plume modeling, from: https://earthsciences.anu.edu.au/research/research-projects/pulsing-mantle-plumes-causes-and-geological-consequences

In the succession of the economic categories, as in any other historical, social science, it must not be forgotten that their subject—here, modern bourgeois society—is always what is given, in the head as well as in reality, and that these categories therefore express the forms of being, the characteristics of existence, and often only individual sides of this specific society, this subject, and that therefore this society by no means begins only at the point where one can speak of it as such; this holds for science as well.

-Marx, 1973 [1858], p. 106

Oreskes, Shrader-Frechette, and Belitz (1994) have provided a landmark critique of epistemology in earth science. At the center of the co-authors’ contention is the problem of the verification of numerical models against empirical observations, which, they argue, is impossible. Defined as the correlation of a given model with the “truth” of “real world” phenomena, the semblance of any “verification”, the authors claim, obscures an underlying category error which conflates two very different kinds of systems: closed systems, such as those of logic and mathematics, and open systems, such as that of the earth. (NB: We will have reason to refuse this dichotomy below.)

Unlike closed systems, which they take to be defined axiomatically, the input parameters of the ‘earth system’ are, first, never completely known and, second, always subject to “extenuating circumstances.” This distinction, in turn, alters the respective criteria for the verification of truth claims of these different types of models in a fundamentally irreconcilable way. To illustrate, the co-authors provide the following example:

I say, ‘If it rains tomorrow, I will stay home and revise this paper.’ The next day it rains, but you find that I am not home. Your verification has failed. You conclude that my original statement was false. But in fact, it was my intention to stay home and work on my paper. The formulation was a true statement of my intent. Later, you find that I left the house because my mother died, and you realize that my original formulation was not false, but incomplete. It did not allow for the possibility of extenuating circumstances. Your attempt at verification failed because the system was not closed. (Oreskes, Shrader-Frechette, and Belitz, 1994, p. 641)

The truth content of closed systems is, in other words, qualitatively distinct from the truth content of open ones, and different criteria follows from different content. Most importantly, the truth content of open systems can never be deduced from a priori justifications alone: it can only ever be inferred through observation, no matter how ‘objective’ (read: impartial) those conclusions may seem (ibid., p. 642). Further, because these parameters always remain inferential, closed models inferred from the observation of open systems can never be definitively proven to be unique in their correspondence with the latter. If, as indeed often happens in earth science, two models can both produce outputs consistent with the same observation, forging any criterion that might verify one against the other takes us beyond empirical nature and depends instead upon non-scientific assertions of “symmetry, simplicity, and elegance, or personal, political, or metaphysical preferences” (ibid., p. 642).

In all, then, unverifiable, nonunique closed models of open systems cannot make any permanent claim to the truth content of the latter. They are at best heuristic guides: “Legitimately, all we can talk about is the relative performance of a model with respect to observational data, other models of the same site, and our own expectations based on theoretical preconceptions and experience of modeling other sites” (ibid., pp. 643-644). Only provisionally consistent with the ‘real world’, then, the authors conclude that models are “most useful when they are used to challenge existing formulations, rather than to validate or verify them” (ibid., p. 644).

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The peculiarity of this argument rests in the fact that, while verification is thus deemed categorically impossible, the ontological status of models vis-a-vis facts remains obscure. In short: where do these ‘closed’ models come from, if not ‘open’ material existence? With this inquiry in mind, the paper can be seen as a rather mundane rehearsal of Kant’s critique of epistemology, this time among earth scientists. Indeed, when pressed to give further characterization to this distinction between models and facts, the former end up appearing timeless—explicitly, they say models do not exist, likening them to a “novel” which “may resonate with nature” but is “not a ‘real’ thing” (ibid., p. 644). Hence, models from this vantage point appear to be formal and idealist abstractions with a permanently underspecified relationship to the reality they are supposed to represent. While direct observations of reality can confirm them provisionally, the former can never “demonstrate the veracity of a model or hypothesis, they only support its probability” (ibid., p. 643).

But this epistemological critique cannot help but provide an impoverished explanation of the relationship between model and fact, and hence cognition and reality. The central issue is that the limitations imposed here—within which thought restricts its “models,” qua forms of cognition, from the possibility of verification against ‘true’ reality—already and inexplicably depend upon a veritable claim about the world: in this case, the transhistorical, objective reality of the earth as an open system (and, conversely, logic as a closed one). How can one suggest the inadequacy of numerical models without already presupposing a truth about the reality of earth systems against which this inadequacy measures itself? And, in turn, by what criteria is this inadequacy ‘modeled’, and hence known and verified? The authors have no answer to this question, for its absence is what silently conditions the saliency of the argument: it is the impossibility of the verifying “numerical models” which verifies, albeit only negatively, the openness of earth systems.

Now, this criticism need not lead us to any relapse into the vulgar scientism which Oreskes, Shrader-Frechette, and Belitz sufficiently critique. But it does reveal the inadequacy of their (non-)explanation of the ontological status of numerical models. In other words, it reveals how the co-authors cannot grasp how categories of thought are not simply “fictions” but “forms of being, the characteristics of existence” (Marx, 1973 [1858], p. 106). It is trivially true that models can only ever approximate empirical observations (insofar as the former is always an abstract expression of the latter), hence that they do not maintain any permanent, fixed identity with them. And, no doubt, there is great confusion on this point in the history of earth science. Indeed, the earliest exploration geophysicists often treated geophysical maps as if they offered definitive, ‘exact’ accounts of the subsurface. This “unfortunate attitude,” as Wyckoff had lamented, led to the condemnation of entire prospecting regions should they not readily reveal the signatures of oil-bearing structures which prospectors were prepared to recognize (1944, p. 296).¹ But, to stress, this “unfortunate attitude” does not simply denote that conflating model with fact is a routine, mundane affair within the practice of earth science. It also evinces how all earth models are historically specific forms of consciousness.

As Lukács stresses in The Ontology of Social Being, critical recognition of the lack of any necessary correspondence between models and facts can easily fall back into neo-Kantianism, a la Oreskes, Shrader-Frechette, and Belitz (1994). But this is precisely why the Hungarian Marxist finds Hegel’s logic superior, by contrast, because it is “not a formal logic, but rather an inseparable intellectual union of logic and ontology” (1978, p. 20). Logic, in other words, is not a ‘closed system’ radically separated from the ‘open system’ of the earth. For Hegel, logical categories are “dynamic components of reality, as stages or steps along the road towards the self-attainment of Mind […] the movement in thought, in notion, judgment and syllogism is only the mental side of the intensive infinity of any object, relation or process” (ibid. pp. 21-22).² In contrast, Oreskes, Shrader-Frechette, and Belitz neglect any discussion of the history of the relationship between models and reality, in turn falling back into a methodological dualism.³ Indeed, history does not come up once in their article. Their critique of verificationism for open systems is presented merely as a proof of the logical fallacy of “affirming the consequent.”

However, Lukács also writes that Hegel falters insofar as he can be said to ignore the contradictory reality of social being (whether this is a fair criticism I will leave to the side). In turn, for the late Lukács (as well as Marx), while, on the one hand, Hegel’s “intellectual union” of logic and ontology progresses beyond Kant’s transcendental deduction, it also serves to mask the “genuine ontology” of social being Hegel had simultaneously proposed, one which does “not just grasp reality as dialectical but is itself dialectical in its structure and development” (Browne, 1990, p. 196). It is instead Marx who recognizes this “genuine ontology” from its necessary standpoint of labor, for it is only from this perspective (according to Lukács) that the recognition of the real dialectical structure of social being is possible, and wherein the apparent “hiatus between form and matter which bedevilled Kantianism” is both affirmed and negated (ibid., pp. 207-208). On the one hand, as Marx had insisted, labor “confronts nature as one of her own forces,” hence labor, as ‘form-giving fire,’ emerges from the matter to which it gives form (1977 [1857], p. 173). On the other hand, the “teleological positing” of labor, i.e. its self-conscious capacity to take up its own means and transform them into new ends, “determines a portion of existing reality as matter within the medium of a new labor process, thus creating a discontinuity implying a rupture or heterogeneity between form and matter” (Browne, 1990, p. 208). At once, then, labor exists in unity with nature while also being a particular differentiation of nature. There can in turn never be an ultimate coincidence between form and matter, and hence no pure identity between logic and ontology, but rather, these terms cohere only within a dialectical unity. What unfolds at the base of the metabolism of society and nature, in other words, is the continuous and contradictory process of labor objectifying itself, contradictorily, in things and thoughts.

To develop the stunted argument of Oreskes, Shrader-Frechette, and Belitz: from the vantage point of the dialectic of history, the logic of ‘closed systems’, even of universal mathematics, is thus objective and real only insofar as its becoming remains essential to its being.⁴ If and when this recognition fails, mathematics loses its correspondence to reality ‘as such’ (here, confirming Oreskes, Shrader-Frechette, and Belitz) and, instead, turns to represent a ‘closed system’, a “reality cocooned” by a universalizing, rational system of thought (Lukács, 1971 [1923], p. 129)—one quite different, we should add, from the “rich totality of many determinations and relations” which comprises the dialectical reproduction of the concrete in thought (Marx, 1973 [1858], p. 100). In either case, what is important to stress is that this cocooned reality is neither natural (in the sense of immediate) nor merely fictitious; it is a historical product. Indeed, the capacity of mathematized science to grasp so much of ‘objective reality’ represents a remarkable achievement in the concrete objectification of modern rationalism.

To be sure, this situation does not prevent the scientist from recognizing “objectively and correctly an objective partial cohesion in reality,” but the point is that this is not the same as “being in a position to say anything true and dialectical about the reality of that ‘world of appearance’ whose parts [the scientist] researches correctly” (Lukács, 2002, p. 125). The mathematized science scrutinized by Oreskes, Shrader-Frechette, and Belitz, in other words, can certainly arrive at correct, dependable claims about reality without for this reason being able to offer any justification of the grounds on which it is able to do so. This is because, while it perceives the immediate appearance of isolated ‘facts’ reduced to their “purely quantitative essence, to their expression in numbers and numerical relations,” it never turns to regard these facts from the standpoint of the “concrete unity of the whole” (Lukács, 1971 [1919], p. 6). For as long as “we are not in a position to demonstrate concretely the historical genesis of the emergence of our perceptions out of their material basis, i.e. not only that they are, but what they are, and how, etc.,” as Lukács writes, “our mode of looking is lacking an important objective moment of the dialectic: history” (1971 [1923], p. 117).

It is indeed precisely the tendency toward formalism within modern science (up to and including its critique, as is well articulated by Oreskes, Shrader-Frechette, and Belitz above) which ought to signal to us the obfuscation of the “historical genesis” of modern science. Through the reification of bourgeois consciousness, history comes to appear accidental to science rather than an “essential, objective moment of the dialectic.” Against this elision of history, we ought to follow Lukács in insisting that scientific advancement is reflective of and historically mediated by the ontology of social being.

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With all this in mind, it seems to me we can say something much more interesting about the relationship between the proliferation of ‘closed’ numerical models in earth science and the notion of ‘open’ natural systems than what is argued by Oreskes, Shrader-Frechette, and Belitz. Rather than treating the two as external to and independent of one another, I want to leave here with the suggestion that they intimately imply one another and, further, that the existing form of their dialectical relationship is grounded in technological transformations which took place over the course of the 20^th-century. Put bluntly, the open-system/closed-model dialectic is essential to the midcentury emergence of systems theory and describes how problems of statistical analysis have been framed ever since.

One too brief example: in the second part of his two-volume autobiography, I Am a Mathematician (1956), Norbert Wiener describes this predicament with great clairvoyance as he recounts his enjoyment gazing upon the Charles River while strolling along its banks at MIT. While the “moods” of the waters were “always delightful to watch,” he writes, they had “another meaning” to the mathematician and physicist (ibid., p. 33). This is because any adequate mathematical description of the motion of the surface of the Charles, with its waves ranging wildly and continuously across spectra of frequency, strength, and length, appeared to be so brilliantly irreducible to any closed algebraic function. In response, Wiener asks:

How could one bring to a mathematical regularity the study of the mass of ever shifting ripples and waves, for was not the highest density of mathematics the discovery of order among disorder? […] What descriptive language could I use that would portray these clearly visible facts without involving me in the inextricable complexity of a complete description of the water surface? This problem of the waves was clearly one for averaging and statistics […] (ibid., p. 33)

Citing our “limited measuring instruments,” the determinism which characterizes the “great physical tradition of Newton” is therefore ruled by Wiener to be an inadmissible starting point in describing something as complex and chaotic as the surface of the Charles (ibid., p. 34). Perfect knowledge of its motion being unattainable, the “working physicist” has no choice but to assume a “physics of probability” which keeps open “many different universes simultaneously,” in turn attempting to describe the movement of the water’s turbulence as a statistical formalization of fundamentally stochastic and interminably complex processes. Of course, the statistical mechanics Wiener is drawing on here precedes modern computing by a century, and very complex earth models had in turn been theoretically devised for some time. Their application was stunted, however, because, as Enders Robinson had once put it bluntly, “the solutions were impossible” (qtd. in Goldstein, 2021). An “open-system” mathematics was too complex for manual computational processes.

Yet, again during middle decades of the 20^th-century, “more realistically complex, even chaotic, views” of the deep structure of the Earth emerged (Brown, 2013, p. 253). Early oil prospectors had an outspoken influence on this epistemological transformation (Anduaga, 2016)—as did changes to the technological mediation of the subsurface. Indeed, the very recognition of complexity was not independent of but conditioned by the advancement of techniques for statistical modeling which informed the design of modern computers for oil exploration. Formalization of geostatistics, however, was not feasible until there was, first, technical means of producing, processing, and interpreting sufficient amounts of observational data and, second, the economic imperative to do so. Modern computing gave rise to precisely this possibility, not, pace Wiener, by mirroring some complexity ‘found in nature’ but by giving a concrete, objective form to the idealist notion of mathematical complexity—which, in turn, allowed for the translation of classical problems of integral calculus into discrete problems of time series analysis and, moreover, digital computer programming.

References

Anduaga, A., 2016. Geophysics, Realism, and Industry: How Commercial Interests Shaped Geophysical Conceptions, 1900-1960. Oxford University Press, Oxford. https://doi.org/10.1093/acprof:oso/9780198755159.001.0001

Brown, Larry D., 2013. “From layer cake to complexity: 50 years of geophysical investigations of the Earth.” Geological Society of America. Special paper 500: The Web of Geological Sciences: Advances, Impacts, and Interactions. Edited by Bickford, M.E., pp. 233-258. https://doi.org/10.1130/2013.2500(07)

Browne, Paul. 1990. “Lukács’ later ontology.” Science & Society 54 (2), pp. 193-218. https://www.jstor.org/stable/40403069

Goldstein, A., 2021. Enders Robinson: an interview conducted by Andrew Goldstein.” Interview #326 for the Center for the History of Electrical Engineering, The Institute of Electrical and Electronics Engineers, Inc. Available at https://ethw.org/Oral-History:Enders_Robinson

Lukács, Georg. 1971 (1923). History and Class Consciousness: Studies in Marxist Dialectics. Translated by Rodney Livingstone. Cambridge, MIT Press.

Lukács, Georg. 1978. The Ontology of Social Being: Hegel’s False and His Genuine Ontology. Translated by David Fernbach. London, Merlin Press.

Marx, Karl. 1973 (1857). Grundrisse. Translated by Martin Nicolaus. New York, Vintage Books.

Oreskes, Naomi, Shrader-Frechette, Kristin, Belitz, Kenneth. 1994. “Verification, validation, and confirmation of numerical models in the earth sciences.” Science 263(5147), pp. 641-646. https://doi.org/10.1126/science.263.5147.641

Wiener, Norbert. 1956. I Am a Mathematician: The Later Life of a Prodigy. Cambridge, MIT Press.

Wyckoff, R.D. 1944. “Geophysics looks forward.” Geophysics 9(3), pp. 287-298. https://doi.org/10.1190/1.1445080

1. As Wyckoff continues in the specific case of seismography: “the seismograph interpreter must piece together literally thousands of control points derived from elusive reflection events with possibilities of distortions and complex travel paths. And he is practically alone in his understanding of the problem. Under such conditions and in anticipation of the ever-present lash of criticism he is forced into a conservative attitude. And yet, the industry calls upon geophysics to find stratigraphic traps. The location of such traps by means of the seismograph is not an impossibility but it will be accomplished only by understanding and wholeheartedly accepting the risks that face the interpreter. When such an attitude is adopted, then and only then will an experienced interpreter dare present some of the obscure features he so frequently encounters in his data” (1944, p. 296).

2. It should be noted that the sense Lukács ascribes to ontology is distinct from that of its traditional sense, of the study of Being beyond appearance, contingency, and history. As Paul Browne notes, Lukács’ “ontology is concerned with the actually existing conditions of concrete reality, rather than the possibilities and principles of cognition of reality, and seeks to transcend this level of immediate concreteness by elucidating the various different forms of being which converge in it. Ontology implies a historical understanding of its object, a reconstruction of complexes in their real development, rather than some logical deduction of categories […] Lukács is thus far removed here from the metaphysics of the Subject, the Origins and the End which haunts the imaginations of post-structuralists” (1990, p. 196).

3. Hegel remarks: “If nature is only matter, and not subject and object, then no scientific construction of it is possible, for this requires that knower and known are one” (“Difference of Fichtean and Schellingian Systems”, p. 105). Lukács will take issue with this suggestion in The Ontology of Social Being, namely, in the identity of subject and object, which the Hungarian Marxist dismisses as a “philosophical myth” (1978, p. 29). It is important to note that this is a significant development away from his own endorsement of the proletariat as “subject-object” in History and Class Consciousness (see also Browne, 1990).

4. “Thus we perceive that there is something highly problematic in the fact that capitalist society is predisposed to harmonise with scientific method, to constitute indeed the social premises of exactness. If the internal structure of the ‘facts’ of their interconnections is essentially historical, if, that is to say, they are caught up in a process of continuous transformation, then we may indeed question when the greater scientific inaccuracy occurs. [Is it] when I conceive of the ‘facts’ as existing in a form and as subject to laws concerning which I have a methodological certainty (or at least probability) that they no longer apply to these facts? Or is it when I consciously take this situation into account, cast a critical eye at the ‘exactitude’ attainable by such a method and concentrate instead on those points where this historical aspect, this decisive fact of change really manifests itself?” (Lukács, 1971 [1919], p. 7).