In a recent article in 'Artificial Life', Chu and Ho suggested that Rosen's central result about the simulability of living systems might be flawed. This argument was later declared ''null and void'' by Louie. In this article the validity of Louie's objections are examined

Chu, Dominique

Ho, W.

English

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UnThe Localization Hypothesisand Machinescorrec authofn 2007 Massachusetts Institute of Technology* Corresponding author.Dominique Chu*Computing LaboratoryUniversity of KentCanterbury CT2 7NFUnited KingdomD.F.Chu@kent.ac.ukWeng Kin HoSchool of Computer ScienceUniversity of BirminghamBirmingham B15 2TTUnited KingdomW.K.Ho@cs.bham.ac.ukKeywords(M,R) systems, Robert Rosen, simulability,analytic models, synthetic modelsAbstract In a recent article in Artificial Life, Chu and Ho suggestedthat Rosen’s central result about the simulability of living systemsmight be flawed. This argument was later declared ‘‘null and void’’ byLouie. In this article the validity of Louie’s objections are examined.tedr proo1 Introduction!---not final versionThe field of artificial life is very diverse, with contributions ranging from systems biology to theo-retical research into the origin of life to robotics. Yet although artificial life research predominantlyuses methodologies from computer science and mathematics, there is also a strong philosophicalcomponent in the artificial life research agenda.This philosophical aspect of the field has been very much connected to the attempt to createliving systems in silico. Such an attempt leads to a fundamental question: Given a specific com-putational system, how do we decide whether or not it is alive? Or alternatively, how do we dis-tinguish between systems that behave like living systems (‘‘lifelike systems’’) and systems that aretruly alive?As it turned out, this question is not an easy one to answer. Despite many attempts, nobodyhas yet been able to identify a single set of criteria to demarcate living systems from nonlivingsystems.The attempt to create life in silico has so far not been a great success. No examples of com-putational systems that would, at least at an intuitive level, satisfy even a significant minority ofresearchers as an example of life have been found. This might be taken as an indication that there issomething about life that cannot be captured in computational models. Hence there are two bigquestions that drive the philosophical quest of artificial life. What is life? Is artificial life (in the sense of a computational system being alive) possible?Artificial Life 13: 1–4 (2007)UnQ1The Localization Hypothesis and MachinesD. Chu and W. K. Ho2 If Living Systems Must Have Uncomputable Models, Then Artificial Lifeis ImpossibleThe work of one scientist claims to give definite answers to both of those questions. In his book LifeItself [3] Robert Rosen gives a ‘‘comprehensive inquiry into the nature, origin and fabrication of life.’’The central results of this book are (i) a demarcation criterion for living systems and (ii) a proof thatwhatever qualifies as a living system must have models that are not ‘‘simulable.’’ (Note that‘‘simulable’’ sensu Rosen might not directly map to everybody’s intuitive understanding of the word,yet it is certainly true that according to Rosen, all computer programs are simulable and havesimulable models.) Therefore a central result of Rosen’s work is that artificial life, in the above sense,is impossible.Louie [2] criticized a similar statement we made in [1]:cFigu2Let me reiterate the fact that Rosen did not say that artificial life is impossible, only that lifeis noncomputable. [2, Section 5]!orrected author proof---not final versionWhethe or not Louie is correct depends on what one thinks encompasses artificial life. Rosen’sresults are relevant for computational artificial life, but probably not for wet artificial life. Given that thefield of artificial life is predominantly (if not exclusively) concerned with computational artificial lifeand given the context of our statement in [1], we wrongly assumed that it was clear that we onlyreferred to computational artificial life.We would now like to respond to Louie’s more substantial objections against the core contributionsof [1], namely our argument that Rosen’s central results might in fact not be relevant at all.3 Is Rosen Correct?In order to arrive at his central result, Rosen constructed a minimal relational model of a cell; thismodel is usually referred to as the (M,R) system (for metabolism-repair system). ‘‘Relational’’ essentiallymeans that the model consists of blocks and arrows connecting the blocks. The justification forassuming that the model is indeed a model of a cell is that it has a certain closure property (‘‘closedwith respect to efficient causation’’). Rosen’s central argument consists then in showing that systemsthat have this closure property cannot be fully captured by computational models.The task we undertook in [1] was both to clarify Rosen’s central proof and to evaluate its validity;more specifically, we indicated in what sense analytic and synthetic models form categories, andsecondly we reconstructed and assessed Rosen’s proof while avoiding jargon. This critical assessmentuncovered a potential flaw of Rosen’s argument but was later declared ‘‘null and void’’ by Louie [2].We will not repeat the details of our argument from [1] here, but only summarize its overallstructure; for details the reader is referred to [1, Section 5].1. Assumption: Figure 1 (which is the same as Figure 6 in [1] and Figure 9D.1 in [3]) is a machine.re 1. A relational model of a machine. See also Figure 6 in [1].Artificial Life Volume 13, Number 3UnThe Localization Hypothesis2. Assumption: In machines a function (which would correspond to the dotted arrow in Figure 1)is located in an identifiable part of the machine (the localization hypothesis; see [3, Section 8G]).3. All machines are mechanisms, and for all mechanisms it is the case that all models are simulable.4. All models simulable implies analytic models = synthetic models:5. If analytic models = synthetic models, then the system is state-space based [1, Section2.4.1].6. If Figure 1 represents a state-space based system, then it is not compatible with the localizationhypothesis.7. Conclusion: Machines cannot both imply the localization hypothesis and be state-space based.The conclusion was later declared ‘‘null and void’’ by Louie [2] on the following grounds:!corrected author proof---not final version1. The argument in [1] constructs an example of a system that contradicts Rosen’s conclusion. YetRosen’s conclusion was mathematically proven; hence the whole argument is ‘‘null and void.’’2. The definition of mechanisms in [1] (mechanisms as the class of systems where analyticmodels = synthetic models) is wrong; hence any conclusions drawn from this definitionmust be ‘‘null and void.’’3. The discussion by Chu and Ho was based on an incorrect representation of closed systems (i.e.,Figure 7 in [1] is wrong).Let us start with the third point. First of all, even if Figure 7 in [1] were indeed incorrectlyreproduced, it would not make any difference t the discussion or conclusion in [1], because thespecifics of the figure are never used. Secondly, Louie’s criticism is in fact incorrect. The reader caneasily convince herself that Figure 7 in [1] is formally identical to Figure 9F.3 in [3].As to the first point raised by Louie: We think that it represents a misunderstanding of theargument. First of all, we disagree with the strong statement that there cannot be any counter-examples to mathematical proven facts. A counterexample to a mathematical theorem (if correct) isjust the same as a proof that the theorem is incorrect. Hence, if a theorem is believed to be proven,but a counterexample exists, then the proof must be wrong. Hence there is no reason to dismissconstructions out of hand on the ground that they contradict a known theorem.In any case, alleging the use of counterexamples to disprove Rosen’s central theorem amounts toa misunderstanding of our argument in [1]. Instead of constructing a counterexample to Rosen’scentral result, we used one of Rosen’s own examples of a machine (in fact, the simplest relationalmodel of a machine) and investigated its properties. Admittedly, our argument is not to beconsidered a formal mathematical proof, but it is certainly not affected by Louie’s first objection.As to the second objection: While Louie might be correct in pointing out that the definition ofa mechanisms in [1] was inaccurate, that inaccuracy would be inconsequential for the argumentwe made. Let us explain why: Louie complained that we defined a mechanism as equivalentto analytic models = synthetic models, while in fact only the implication mechanism Zanalytic models = synthetic models is true. Let us, for the sake of the argument, assume heis correct in this criticism. While pointing out the alleged inaccuracy, Louie also grants us the sameprivilege as Humpty Dumpty claims for himself, namely, that we can choose a word to meanwhatever we like, ‘‘neither more nor less.’’ We accept this privilege but, in order not to confuse thereader, we will distinguish between R mechanisms (mechanisms defined according to Rosen, i.e.,only the implication holds) and CH mechanisms (equivalence holds).In order to understand the difference between R mechanisms and CH mechanisms in relationto the argument in question in [1], it is useful to review once again the basic chain of implicationsArtificial Life Volume 13, Number 3 3UnThe Localization Hypothesis and MachinesD. Chu and W. K. Hocorrecton which our objection to Rosen relies. This chain is as follows: machine Z mechanism Zsynthetic = analytic Z state space based Z Ilocalization hypothesis. Another im-plication is used, namely: machine Z localization hypothesis.The reader will immediately see that at no point in the above chain does the implicationanalytic = synthetic Z mechanism appear. Hence if the above argument is correct for CHmechanisms, it is so for R mechanisms. Thus, by invoking the Humpty Dumpty privilege, weconclude that Louie’s objection is immaterial for our argument in [1].4 ConclusionWe do not believe that Louie’s objections per se force an alteration of our conclusions in [1]. This—of course—does not mean that [1] is beyond all doubt. To the contrary, our claim in [1] has neverbeen to provide a definite argument about Rosen’s work, but rather to attempt to present it free fromjargon, increase its accessibility, and provide a critical assessment of the central theorem.We still believe that Rosen’s work is of high potential significance for our understanding of lifeand specifically the relation between life and algorithmic systems. Yet, in order to have any realimpact on the way we think about life, Rosen’s arguments need to be reevaluated and most of allrestated in a language that avoids confusing and unjustified misnomers (such as metabolism andrepair for what really are just arrows). Our contribution in [1] was meant as a first step in thisdirection. Future work will need to address among other things the following questions:ed author pr Which biological systems are clear realizations of (M,R) systems in biology? Which aspects of those systems cannot be captured by computational simulation? What exactly leads to a failure of the localization hypothesis in organisms? How do familiar concepts, such as emergence, relate to Rosen’s observations?oof-References --not final v1. Chu, D., & Ho, W. (2006). A category theoretical argument against the possibility of artificial life.Artificial Life, 12(4), 117–135.2. Louie, A. (2006). A living system must have noncomputable models. Artificial Life, this issue.3. Rosen, R. (1991). Life itself. New York: Columbia University Press.ersion!Artificial Life Volume 13, Number 34Uncorrected author proof---not final version!AUTHOR QUERYAUTHOR PLEASE ANSWER QUERYDuring the preparation of your manuscript, the question listed below arose.Kindly supply the necessary information.1. Please check if the proposed running head is okay.END OF QUERY

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