Lucretius once wondered in “On the Nature of Things “ why organisms seem1 to have goals, autonomy and agency, asserted by him as free will, if
[…] all movement is interconnected, the new arising from the old in a determinate order, if the atoms never swerve so as to originate some new movement that will snap the bonds of fate […]
Afterall, is there a difference between the complexity seen in organisms and in other dynamical systems which aren’t organisms, and if there is what type of difference is it? A quantitative gradient-like one (even admitting critical transitions), or a categorical one altogether? The former was taken by John von Neumann [7], and Robert Rosen argues in [2] in a more historical account, and in [3, 4] with more depth, for the latter2. And can one account for the complexity shown by organisms purely by physical law?
Schrödinger’s “What is Life?” [8] can arguably be read in two ways: either as re-affirmation of the undeniable success of molecular biology and adjacent fields over the past and present centuries, or as an indication that something still lies underneath unresolved3. That something has multiple ways to be stated, but could be put as: “How does a molecule become a message?” [9] (as per Pattee). This is the typical genotype-phenotype problem. Although the biggest problem is precisely understanding how systems which seem to have their symbolic (rate-independent) and physical (rate-dependent) domains completely coupled, stated as semiotic closure [10], have emerged (Deacon is an example which tries to give an account for this with his autogen [17, 18], which I try to describe here very briefly) and developed into present form. But such problem, which is commonly known as the symbol grounding problem [9] (and regarding the same problem in artificial systems [16]), should be taken seriously. As von Neumann noted [11], for a system to have open-ended evolvability, the constraints associated to the description of the system need to be detached from rate-dependent dynamics. Such (symbolic) constraints can’t be pre-stated by physical law (often called non-holonomic or non-integrable constraints), eventhough their material vehicles follow such laws. When we refer to material vehicles we are referring to the part of an object which is associated to rate-dependent dynamics. Every single structure or process, of course has some of its degrees of freedom associated to both. However, those that are usually associated to the description of such a system which displays self-repairing, self-replicating and self-maintaining properties, tend to be largely immutable to rate-dependent dynamics [12].
Pattee puts it as [12]:
We easily agree with Einstein that a Beethoven symphony cannot be appreciated as only “a graph of air pressures”, although in principle it has such a physical description. In the same way we understand Bohr that, “You don’t explain a tea party by quantum mechanics.” On the other hand, it is not so easy to understand why you cannot adequately explain genetics with biochemistry or enzyme catalysis with quantum mechanics. Because we believe no events at tea parties, in genes, or in enzymes violate any physical laws we might assume that their descriptions differ only in their degrees of complexity. What biosemiotics illustrates is that symbolic controls are categorically different from laws and that they are irreducible to physical laws even though their material vehicles obey the laws and have a correct physical description.
One is then presumably evading such symbol grounding problem when studying these “biological” processes as if they can be completely tracked through physical law. I say “biological”, because one might aswell be studying such processes outside of the correspondent organism. The causal structure of (and between) such processes is not being taken into account, and this is arguably the most important part. It’s the part which will inform us about that which can’t be tracked by physical law. Such (rate-independent) constraints show a logic, through which any of such constraints only makes sense within such system (organism). This is due to the impredicative organization organisms show [13, 15]4. It is inherently self-referential. Consider Kant [14], which was perhaps one of the first to capture this:
An organized being is then not a mere machine, for that has merely a motive power; but it possesses in itself formative power, and such a one, moreover, as it communicates to the materials, which do not possess it (it organizes them). Thus it requires no other purposive principle for its maintenance than the one which it itself produces. In such a product of nature, every part is thought as if it exists only by means of all the others, and so exists for the sake of the others and the whole, i.e., as an instrument (organ). And this reciprocal causation of the parts in the whole distinguishes a machine from an organized being. In the former, the parts only act on one another in turn (so that one part is the instrument of the motion of the other); but in the latter, the parts are reciprocally cause and effect of their form.
But of course, non-holonomic constraints and methods to deal with these are nothing new. Hertz was presumably one of the first to deal with such concerns [19], Eden [20] being another example, and overall extending to the school of analytical mechanics. However, should then we model a cell, or a minimal system which starts to show some of the interesting properties we associate with organisms, as a maximally (or optimally) constrained (non-holonomically) system [21]? Perhaps the better question is: should we model such systems as ones that are at least optimally constrained? This is, arguably, what control theory, cybernetics, and even some offshoots of these ideas into molecular biology, systems biology and adjacent fields, were (and are)5. And certainly these approaches can’t be denied their success. But that prior “at least” is doing some heavy work there. Although not being the intention of these approaches, they are evading the matter-symbol problem [22]. They are not giving a window into the primeval epistemic cut [23], of how the complementarity between physical and symbolic domains emerged - “How does a molecule become a message?” [9] - which is characteristic of systems we typically call organisms.
Von Neumann’s self-reproducing automaton led to a logical paradox when Rosen analysed it with a set-theoretic formalism [24], of the type - no function can belong to its own domain or range6 - as stated earlier by Wittgenstein [25]. Some attempts have been made at resolving such paradox, namely Guttman [26], and Löfgren [27] through the “objectification” of the corresponding impredicativities. However, in [29], there’s some light put on this paradox by reframing von Neumann’s self-replicating automaton with the use of a richer account of causation. That is, by using the four Aristotelian causes. Particularly, it’s realized by Hofmeyer that such paradox doesn’t hold, as efficient and formal causes don’t appear on the same level. The latter is usually associated with non-holonomic constraints and the former with rate-dependent dynamics (or controls of such). Very briefly, the Aristotelian causes are described as:
Material cause - What’s something made out of?
Efficient cause - What makes (produces) something?
Formal cause - What makes (what is it to be) something?
Final cause - What is the function of this something?
Accordingly, Hofmeyer understands that efficient causes (with respect to von Neumann’s universal constructor) always need to be “informed” or constrained by formal cause. If we take the example of Deacon’s autogen, already taking into account offloading of constraints of the system dynamics onto energy degenerate structures (here a nucleotide polymer), then the catalysts are the efficient cause, the substrate the material one, and the corresponding sequence which constrains such dynamics, is the formal cause. The final cause would presumably be associated to the teleological cause of self-manufacture of the system.
But what needs to be understood is that these symbolic constraints aren’t pre-stateable by physical law, much like the (non-holonomic) ones approached in the school of analytical mechanics. However, in organisms, there’s a self-referential logic to the generation of such constraints, by virtue of the self-manufacturing process of the system.
Where is then the new physics that Schrödinger and other contemporaries of his were looking for?
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[3] - Rosen, R. (1991). Life itself: a comprehensive inquiry into the nature, origin, and fabrication of life. Columbia University Press.
[4] - Rosen, R. (2000). Essays on life itself. Columbia University Press.
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