On the Appearance of Design

Participating in a messy discussion at scienceforums.net as Hrvoje1, I couldn't help the feeling that the legitimate question of mathematical description of design still eludes scientific community, as well as that of mathematical description of life. Regardless of the question if these two are connected, I have searched a bit for the information on who tackled it so far, and of course found tons of material, some is seminal such as Schrödinger's What is Life?, in a sense that he was among the first physicists to deal with it in a longer essay, and Constructor Theory of Life by Marletto, in a sense that she and Deutsch went further than anyone else in their investigation, that I already knew, however there is also Chris Adami, Fritjof Capra, ... and many others. There is also Elsberry and Shallit versus Dembski discussion/critique Information Theory, Evolutionary Computation, and Dembski's Complex Specified Information, that I didn't study very carefully, but still careful enough to spot that they claim the following:
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 he never gives a positive account of design; we do not learn from reading his works what Dembski thinks design is. In 'The Design Inference' he simply defines design as the complement of regularity and chance, and the possibility that this complement is in fact empty is not seriously addressed. In 'No Free Lunch', he gives a process-oriented account of design:
(1) A designer conceives a purpose.
(2) To accomplish that purpose, the designer forms a plan.
(3) To execute the plan, the designer specifies building materials and assembly instructions.
(4) Finally, the designer or some surrogate applies the assembly instructions to the building materials.
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Now, although that account of design maybe didn't impress Elsberry and Shallit, or Deutsch and Marletto, who although address the same question of design as Dembski, never mention him at all, answering that way basically non existing challenge (to their Neo-Darwinian views), that Elsberry and Shallit's comment made me think of the quality of my account of design, given in that scienceforums.net discussion. Which is distilled from Deutsch and Marletto's theory, as they do not give a positive account of design either, but they do give a positive account of a system that appears to be designed:
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Consider a recipe R for a possible task T. A sub-recipe R0 for the task T0 is fine-tuned to perform T if almost any slight change in T0 would cause T to be performed to a much lower accuracy. (For instance, changing the mechanism of insulin production in the pancreas even slightly, would impair the overall task the organism performs.) A programmable constructor V whose repertoire includes T has the appearance of design if it can execute a recipe for T with a hierarchical structure including several, different subrecipes, fine-tuned to perform T. Each fine-tuned sub-recipe is performed by a sub-constructor contained in V : the number of fine-tuned sub-recipes performable by V is a measure of V's appearance of design. This constructor-theoretic definition is non-multiplicative, as desired.
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So, the appearance of design of a programmable constructor V is a measure of its complexity, related with a number of sub-constructors it can be hierarchically decomposed to, each of which has to perform accurately in order for V to perform accurately. In my opinion that definition deals more with a robustness of V, as there is nothing said about the possibility of maintenance, ie how V recovers from the situation when T0 is not accurately performed, by itself, or if external maintenance is required. It is also about its stability, as a slight change in sub-constructor accuracy of performing its task T0, leads to significant degradation of accuracy of V's performance of T. It certainly does not explain the difference between designed programmable constructor and the one that just appears to be designed.
 That leads to a slightly bizarre situation that a world renowned physicist dedicates a whole paper to investigation of a notion that she never defines directly, although she tries to define precisely what constitutes the appearance of that notion. To be fair, that paper is not exactly about design, it is about life, and its precise mathematical description, while for the "real" design, it somehow looks as if the author thinks it does not need to be addressed (or that it does not exist) at all. If we suppose that is because she thinks explanation is embarrassingly simple, namely, real design is essentially same as the appearance of design, apart from the fact that it is produced by human, then it is not clear who should be more embarrassed, the one who asks for such simple explanations, or the one who comes up with such definitions. Besides that, that does not correspond exactly to the usual notion of designed thing, which is something envisaged and built purposefully to fit accurately certain goal, regardless of its programmability or automatic behavior. Like a glass of water, that is notably different from any naturally occuring receptacles, although it does not conform to a supposed Marletto’s definition of a designed object. And of course, life then cannot be designed because people could not have been present at the moment of earliest stage of its evolution, as they are result of the same process at later stage, and there is nothing else by definition in the universe that could have designed it.
In that discussion on scienceforums.net, I started from the point of view that automata theory is a theory of designed systems, that are built upon physical laws that act as a basis for their functioning, but their behavior is furthermore determined by the idea of designers about the purpose of automata which is built into them, in terms of constructor theory, these ideas are recipes for the tasks these automatic constructors and their sub-constructors are supposed to perform. Well, not just into that software part of constructors, these ideas are also built into their hardware. And one cannot fully describe and understand functioning of, let's say an electro mechanical automatic device, just by understanding laws of mechanics and laws of electromagnetism, because that component of understanding is only necessary, but not sufficient. Because, automata contain the element of design, that is not contained in physical laws, which is a key to their understanding. According to that view, phenomena that can be explained solely and entirely in terms of physical laws, such as clouds, or rain, or rivers within their natural streambed, are not designed. That looked kind of obvious to everyone, nobody actually objected to that claim. However, I started to question it myself, and took as the example Cellular Automata (CA) theory, which is a source of inspiration for many people for different reasons. And not only inspiration, but also the framework applied in concrete examples:
Packard Snowflakes on the von Neumann Neighborhood by Brummitt,Delventhal and Retzlaff
The Cellular Automaton Interpretation of Quantum Mechanics by Gerard 't Hooft
I was interested only in the question if CA models designed systems in contrast to the models that describe physical systems (such as theory of gravity), since these two (snowflakes and QM) seemed to me as counterexamples. For the appearance of design within CA, there must be a freedom of choice of production rules for the next generation of cells, while for the appearance of a physical law, there must be no such liberty of choosing the rules that guide a physical system from the current state to the next one, they should be preset, or predefined for the whole universe. However, if we constrain a little bit the computation rules for CA, such as for example if we focus only on linear CA, then on the one that allows only two possible cell states, and let's say that they depend in the next generation solely on the current state of the cell itself and of its two nearest neighbours, that is two adjacent cells, then we get only 256 possible computation rules for such a system. And if we finally narrow down our interest further to only one, let's say Rule 110, due to its interesting behavior on the boundary between stability and chaos, we can analyze its evolution in the same way using our logical apparatus as we analyze motion of physical systems that obey physical laws. And if we give ourselves the freedom and imagine the existence of ultimate multiverse that contains every mathematically possible universe under different laws of physics, then we can conclude that nothing really distinguishes between designed systems and physical systems, they both just appear to be one way or the other. That really is a great conclusion, however, we don't have much proof of existence of any other universe but the one we exist in, and if we allow the possibility that we have a free will, then we are really able to "design a designed system", that doesn't just appear to be designed. Or, in Elsberry and Shallit's words, maybe there really exists in nature a third category, that is neither pure physical regularity nor chance?