26

3

Regulation and Control

can also be quantified, provided that function and structure are quantifiable. The

dependency of whole-system function on the components of an arbitrarily chosen

piece of the system can then be measured. The less that dependency itself depends on

components outside the chosen piece, the more the function of that piece is localized

(i.e., the more modular it is). If the dependencies are represented as second derivatives

of function with respect to pairs of parameters (the Hessian matrix of fitness), modules

can be identified as those collections of parameters that are concentrated around the

diagonal of the matrix.

Problem. Quantify the regularity, modularity, and hierarchicality for a variety of

artificial and natural systems.

3.8

Autonomy and Heterarchical Architecture

Autonomy or “autonomous unity” has been seen as the essential, characteristic fea-

ture of life (Varela et al. 1974). These authors introduced the idea of the autopoietic

organization, in which a “network of interactions of components” (which, in a single

cell, could be its biochemical reactions) participates recursively in the same network

that produced them. This idea of recursiveness, or self-referentiality, is a fairly obvi-

ous feature of the working of the human brain. After McCulloch and Pitts published

their famous study of the hierarchical logic of information processing (McCulloch

and Pitts 1943), ² later they came to realize that an adequate description of neural

activities requires a heterarchical structure (McCulloch 1945). Self-reference only

derives from heterarchically structured systems (Kaehr and von Goldammer 1988).

As Fig. 14.1 shows, the relationship between genes and proteins is also self-

referential, the genes being inert and functionless without the proteins that they

encode working to express the genes.

3.9

Biological Information Processing

The living information processor par excellence is of course the brain, but informa-

tion processing by individual cells such as an amoeba has recently been scrutinized

and computational methods extracted from its behaviour. ³ Conversely, biophysico-

chemical information processing means constructing information processors using

biological components such as lipid bilayer membranes and enzymes. ⁴ Working

integrated information processing systems are typically based on a planar membrane

of thicknessupper LL in which an enzyme is homogeneously immobilized. Their operation

2 Cf. the von Neumann computer model.

3 Nakagaki et al. (2009); see also Umedachi et al. (2010).

4 Valleton (1990).