Handling Critical Impasses in Interdisciplinary Work: a Case Study in Artificial Life

As work at the intersections of traditionally relatively insular fields develops with an ever quickening pace, the space for scientific perspectives to run askew gains many new degrees of freedom. One major site of interpretation conflict over the last couple of decades has been the intersection between systems biology and theory of computation; in particular, the research community studying artificial life has struggled to accept a common metalanguage within which theorists can ground their hopes and expectations for the results of their work. The 2006-2007 dispute between A. H. Louie, the student of pioneering mathematical biologist Robert Rosen, and Rosen’s critics Dominique Chu and Weng Kin Ho over the implications of his work for the future of synthetic life science serves as an instructive moment in the recent history of interdisciplinary consensus-building. In this paper I will focus on Louie’s initial rebuttal of Chu and Ho’s review of Rosen’s “central proof” and explore the response it evoked to evaluate its utility in the discursive defense of his school.[2]

First, a brief background is in order to frame the importance of this particular dispute. Robert Rosen was a biophysicist who studied under Nicolas Rashevsky at the University of Chicago in the late 1950s. In turn, Rosen passed down the principles of the school of relational biology he formulated together with Rashevsky to his own student, Aloisius Louie. With its foundations in the rather arcane new realm of category theory, the Rosen-Rashevsky school’s major contributions have gone untaught in most university biology and biochemistry curricula. But as Louie has spent much of his career illustrating, they carry profound implications for such questions as “What is life?” and “Is artificial life possible?”, the very questions “that drive the philosophical quest of artificial life” according to Chu and Ho.[3] However, as stated by Louie:

“The ‘central proof’ refers to the main conclusion of Robert Rosen’s book Life Itself, that a living system is not a mechanism and consequently must have noncomputable models.”[1]

Translated from the metalanguage of category theory into practical speech, the requirement of noncomputable models by living systems means that life cannot be authentically replicated by exclusively computational means. To many a hopeful computer scientist chasing cinematic fantasies of AI progeny, this result was unacceptable. So, naturally, mimicking the motivations of its institution, the MIT Press journal Artificial Life continued publishing articles which wildly contradicted Rosen’s conclusion decades later.

But it took until one such article had attacked Rosen’s theory head-on for Louie to step in and correct what he saw as unbridled confusion among the audience and authors of Artificial Life. This article, written in 2006 by Chu and Ho, was brazenly titled “A Category Theoretical Argument against the Possibility of Artificial Life: Robert Rosen’s Central Proof Revisited”. Louie would have none of it. His response in the following volume of the journal a year later took on a simpler title, “A Living System Must Have Noncomputable Models”, but gave no quarter in its dissection of the critics’ logic.

“Chu and Ho’s recent article in Artificial Life is riddled with errors. In particular, they use a wrong definition of Robert Rosen’s mechanism. This renders their ‘‘critical assessment’’ of Rosen’s central proof null and void.”[1]

Though curt, Louie does go on to present his arguments very neatly, exactingly demonstrating the sequence of redefined and misunderstood theorems that lead Chu and Ho to their “irrelevant” argument that Rosen’s work failed to discount the possibility “that organisms might be machines”.[1][2]

Louie begins with their problematic use of fundamental definitions: “To foreshadow what is to come, let me first point out that the category-theoretic definitions of product and coproduct are wrong (and cannot be explained away as simple misprints)” (second paragraph in Section 1 of [1]). His choice to place this before the “numerous other errors” he intends to unpack in his article reveals that he sees it as a key structural weak point in Chu and Ho’s analysis; one that entails a good portion of the logic of the others. And to emphasize its cruciality, he adds: “The proper definitions may be found in any introductory textbook in category theory.”

Then, Louie walks us through Rosen’s eight theorems regarding the relationships between the simulability of natural systems and their entailment patterns as such before pinpointing what he calls “the fatal error in the [sic] Chu and Ho’s article”, their unviable replacement of Rosen’s definition of the term “mechanism” and decision to use their own “wrong definition” instead (third and fourth paragraphs in Section 3 of [1]). A concept he belabors on his way to this judgment is that “Life is not definable by an algorithm” (fifth paragraph in Section 2 of [1]).

The connection between “finite syntactic algorithms” (methods of navigating networks of causal entailment of systems in a finite number of steps) and Rosen’s synonymous concepts of “simulable” or “computable” is left implicit in Louie’s article because readers are assumed to understand that something can be computed or simulated only if there is some algorithm by which to perform its computation or simulation. The notion becomes less obvious with the introduction of the metalanguage of category theory, because numerous systems treated by it will contain many models—for example, an autonomous robot may contain a model for its environment, models for its various modes of motion, and a model for recognizing certain voice commands—in which case, according to the definition both Louie and Chu and Ho cite, all such models must be simulable for the whole system to be considered a mechanism.[1][2] In turn, as Louie emphasizes, knowing that a system is a mechanism does not distinguish whether or not it is living, but instead places it within the class of systems whose semantic functions (which in life might include metabolism, emotion, cognition, etc.) can be modeled “by computation alone”.[1] Louie then points out that neither Chu and Ho’s recapitulation of Rosen’s definition of a mechanism nor their use of it to discuss the possibility of artificial life constitute an appropriate interpretation of the work they intend to criticize. Hence Louie’s characterization of Chu and Ho’s article as being “riddled with errors” is evidently justified.[1]

But the tone of Louie’s conclusion toward the end of his article, albeit stern, shows that he is concerned with more than just correcting flawed reasoning; he wants the research community at large to open their eyes to a broader range of possibilities than can be achieved by pure computation. In his closing statements, he writes:

“Artificial life does not have to be limited to what a computing machine can do algorithmically. The first step is to admit that not everything is computable, that is, throw away the Cartesian and Newtonian machine metaphor. One must loosen the mechanist constraints and assert the existence of natural systems with nonsimulable models.”[1]

This remark is meant less to admonish the addressees of his paper than to critique the misguided old Cartesian and Newtownian schools of thought that still foster validation bias for mechanistic perspectives in the academic culture of life and cognitive science. In this way, it works to contextualize the harsh exactitude of the rest of his paper. Through my own limited correspondence with A. H. Louie and review of his writing, it is my opinion that his work overall aims to help liberate the philosophy of biology from the rampant reductionist thinking that accompanied the rapid ascent of the computational paradigm to supremacy in the epistemic landscape of post-industrial capitalism. On his own website, Louie summarizes his complaints about reductionism and “mechanistic dogma”:

“The failure of presumptuous reductionism is that of the inability of a small surrogate universe to exhaust the real one. Equivocations create artefacts. The limits of mechanistic dogma are very examples of the restrictiveness of self-imposed methodologies that fabricate non-existent artificial ‘limitations’ on science and knowledge.”[4]

Bearing in mind this tenet of his, it becomes apparent why Louie chose Chu and Ho’s alleged refutation as the site of an ideological battle, and why he pulled out all the stops in his use of the source text: more egregious than simply failing to understand Rosen’s conclusion, the critics were imposing a naive paradigmatic limitation on what impressionable readers might follow them in defining as “life”. This particular limitation is embodied in the quote Louie placed for emphasis at the end of his article, where Rosen had said of the von Neumannian mechanists’ tired notion of life: “The idea was that by serially endowing a machine with more and more of the simulacra of life, we would cross a threshold beyond which the machine would become an organism. The same reasoning is embodied in the artificial intelligence of today, and it is articulated in Turing’s Test. This activity is a sophisticated kind of curve-fitting, akin to the assertion that since a given curve can be approximated by a polynomial, it must be a polynomial.”[1]


  1. Louie, A. H. (2007). A living system must have noncomputable models. Artificial Life, 13(3), 294-297. 
  2. Chu, D., & Ho, W. K. (2006). A category theoretical argument against the possibility of artificial life: Robert Rosen’s central proof revisited. Artificial Life, 12(1), 117–134.
  3. Chu, D., & Ho, W. K. (2007). The localization hypothesis and machines. Artificial Life, 13(3), 1-4.
  4. Louie, A. H. Relational Biology, A. H. Louie: Mathematical Biologist. https://ahlouie.com/relational-biology/ [accessed 14 September, 2019]

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