Remarks on Chu-Ho 2006/2007

The recent paper by Chu and Ho prompt me to remark on both of their papers. I find numerous errors which void their argument and I discuss additional points.

The original central complaint in Chu-Ho 2006, section 5 [1]:

The problem of this becomes clear when one attempts to recover information about the mapping implemented by the component [tex]small{f_{i_0}}[/tex] if this component is described in terms of the [tex]small{x_{f_{i_0}}}[/tex]. By the same token, given a set of states, how can one decide whether or not they actually do implement a mapping or not? Our conclusion is that one cannot. To see this, consider an implementation of the system in Figure 6. Specifically, assume an implementation of this system in an N-dimensional cellular automaton (CA). By the assumption of mechanism, such a CA is guaranteed to exist.

This premise in itself is faulty. The definition of a Rosennean mechanism is plainly stated by Rosen as follows[2]:

We shall say that a natural system N is a mechanism if all of its models are simulable.

A CA is not a natural system. It is a formal system. Certainly, we can agree that a CA can be implemented in some kind of natural system. But this is irrelevant. A mechanism is a natural system, it is not whatever formal system might possibly be implemented in that natural system. Therefore, their central complaint fails out of the gate.

They then go on to present the scenario:

     Let us now assume a slightly different scenario. Specifically, assume that the system in Figure 6 is implemented in the part of G that corresponds to the summand K’, while we assume now that all the cells of K are kept in a quiescent state. Now, the state variable [tex]small{k_l}[/tex] still describes some state of K, but it does not describe a mapping any more; this is so because we assumed that K is an empty system (all cells in the quiescent state). On the other hand, we would now have to assume that the corresponding state [tex]small{k_l}[/tex]’ of the subsystem K’ does implement a mapping. 
     This example thus seems to indicate that whether or not a state implements a function does depend on the context of the system as a whole. This however is in clear contradiction to the requirement that the state description be a complete description.

The postulated senario is already built upon an incorrect understanding of mechanism, so it is already invalid. But it is also worth pointing out that this scenario relies upon the use of CA states, where such “states” can be “quiescent”, such that the system is “empty”. The state-based descriptions to which Rosen refers, however, are those described at length in an entire chapter (“The Concept of State”) devoted to the topic[2]. These are the Newtonian-type state-based descriptions, which are based upon the Newtonian paradigm. More importantly, the entailments of the particles are encoded in such a state-based descriptions using the inherent recursion of the formalism as well as in the form of impressed forces. In the CA scenario, the entailments which drive the CA are not in the CA “state” descriptions, but instead reside hidden among the states of the software which underlies and drives the CA. Thus, there is additional misunderstanding of “state-based description”.

From this incorrect argument, they conclude:

Altogether, it seems that Rosen’s proof does not hold and we are still entitled to conclude that organisms might be machines.

As I have shown, no such conclusion can be drawn from their argument since it rests on an erroneous understanding of mechanism and additionally, an erroneous understanding of state-based description

There is an additional conceptual point worth bringing up. Relational descriptions of Rosennean machines can be thought of as abbreviations for the entailments among the state descriptions which underlie them. As is illustrated repeatedly in chapter 9 (“Relational Theory of Machines”) of [2], the relational encodings are a shorthand description of the state descriptions of the underlying particles and the entailment relations between them. Rosen says at the beginning of chapter 9:

Our first result will be to show explicitly that machines in general admit relational descriptions. We will in fact see in detail how the relational descriptions arise from, and are related to, their underlying “physics” as we have developed it in the preceding chapter.

That machines admit relational descriptions simply means that there exists a way to partition and label the existing state description. Such partitioning and labeling does not inform us of any dynamics that are not already in the state description, nor does it constitute a separate model which cannot be refined to the state description. Importantly, there is no more entailment in the relational description of a machine than is present in the underlying state description. It is instead simply an abstracted view of the entailment relations between sets of  states in the machine. Obviously, if the state description were to lack entailment relations, then so too will there be no entailments in the abstracted view, and so the relational description will be empty. Thus, even if their argument were not already entirely invalid, their conclusion based upon an inability to deduce a relational description from a “quiescent” system fails since it presents a vacuous challenge.


Moving forward to the 2007 Chu-Ho paper[3], the authors state:

To the contrary, our claim in [1] has never been to provide a definite argument about Rosen’s work, but rather to attempt to present it free from jargon, increase its accessibility, and provide a critical assessment of the central theorem.

However, in the abstract of [1], they flatly state: “The conclusion of this article is that Rosen’s central proof is wrong.” This is quite a contrast from the assertion here that they never claimed to provide a definite argument about Rosen’s work. Also, the notion that they have somehow increased the accessibility of Rosen’s arguments or made them jargon-free fails given their erroneous understandings of Rosen as I have shown above, and as Louie has further described[4].

They continue:

     We still believe that Rosen’s work is of high potential significance  for our understanding of of life and specifically the relation between life and algorithmic systems. Yet, in order to have any real impact on the way we think about life, Rosen’s arguments need to be reevaluated and most of all restated in a language that avoids confusing and unjustified misnomers (such as metabolism and repair for what are really just arrows.)

What is most bizarre here is the claim that “metabolism and repair” are just “confusing and unjustified misnomers”. The entire basis for the development of the (M,R)-system models is motivated by idea the that they are models of organisms, and thus the models are built based upon actual organismic functions, i.e., metabolism and repair. These models did not arise out of thin air — they are not just abstract arrow diagrams to which labels were attached post hoc. Their assertion would be like saying that the chemical symbols on a Krebs cycle model are just confusing misnomers – after all, its really just arrows.

Finally, both papers are interested in Rosen’s work for only one reason, and that is because Rosen’s work  asserts the logical impossibility of creating computational (i.e., Turing machine based) artificial life. This runs contrary to various efforts in the artificial life community to do just that: create computationally-based artificial life. The authors ask the following questions:

Hence there are two big questions that drive the philosophical quest of artificial life:

  • What is life?

  • Is artificial life (in the sense of a computational system being alive) possible?

I assert that these are far from just being philosophical questions. Without an operational definition of life, the question “when (i.e., on what grounds) will you know that you have succeeded in creating computationally-based artificial life?” cannot be answered. Moreover, the question “when (i.e., on what grounds) will you know that you have not succeeded in creating computationally-based artificial life?” cannot be answered. This makes such an enterprise one of folly. There must be an operational definition of life if the enterprise is to have any scientific meaning.

I further assert that if it is made a precondition that artificial life can be computationally based, then the operational definition of life employed must likewise be so constrained; otherwise, the criteria in such a definition could not be fulfilled by a computer program. That is, the definition must be able to be stated in the form of an algorithm and it must be shown that the algorithm halts. It would of course, also have to be shown that such a definition applies universally to all biological life forms. Ultimately, it is only upon determination of such an algorithmic definition of life that the enterprise of creating computationally-based artificial life will be scientifically meaningful.



[1] Chu, D. & Ho, W. 2006. A category theoretical argument against the possibility of artificial life. Artificial Life, 12(4):117-135.

[2] Rosen, R. 1991. Life Itself.  

[3] Chu, D. & Ho, W. 2007. The Localization Hypothesis and Machines. Artificial Life, 13(3):229-302.

[4] Louie, A. 2007. A Living System Must Have Noncomputable Models. Artificial Life, 13(3):293-297.

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