THE PHYSICAL BASIS AND ORIGIN OF HIERARCHICAL CONTROL

If it were only as simple as that. The analytic approach to understanding simplicity, Pattee said, turns out to be very complex. "We really do not mean just 'simplicity'," as he stated it, "...The simplification that results from the hierarchical constraints of an organization must be balanced by how well it functions." In the analytical approach Pattee notes two basic problems that must be overcome.

What are the central prúoblems about hierarchical systems? First there is the apparent paradox that hierarchical controls both limit and give more freedom at the same time. The constrúaints of the genetic code on ordinary chemistry make possible the diversity of living forms. At the next level, the additional constraints of genetic repressors make possible the integrated development of functional organs and multicellular individuals, At the highest levels of control we know that legal constraints are necessary to establish a free society, and constraints of spelling and syntax are prerequisites for free expression of thought.
A second problem about constraint is that they always appear arúbitrary to a large extent. as far as we can see, the same type of life could exist wúith a number of different genetic codes--that is, with different assignments of nucleic acid codons to amino acids, molecules that perform the function of messengers, such as hormones or activator molecules, appear to have only arbitrary relation to what they control. Other hierarchical rules are more obviously conventions. We know we can drive oneither the left or right side of the road as long as there is collective agreement, just as we know we can give the same instructions in many different languages using different alphabets. In other words, hierarchical constr:aints or rules are embodied in str:uctures that are to some extent "frozen accidents"

Searching for a physical basis for the origin of hierarchical control programs is essentially a search for the origin of life. In Pattee's words, "...The origin of those control constraints that free living matter to evolve along innumerable pathways that non-living matter, following the same detailed laws of motion cannot follow, in other words, although wúe recognize structural hierarchies in both living and non-living matter, it is the control hierarchy that is the distinguishing characteristic of life:"

The origin and development of' structural hierarchies has been dealt with by the authors we have discussed up to this point, We have number hierarúchies, that is crystals made up of stable atoms, organisms made up of cells with high autonomous stability. We have hierarchies of dynamic time scales, short time associated with small structures and strong forúces, and long times associated with large structures and weak forces. We can often write dynamical equations for any single level by approximating that one particle is typical of the collection, that fast motion on lower levels are averaged out and that slow motions on higher levels are constant.

This is what Simon called near-decomposability. However well this might operate in analyzing structural hierarchies, Pattee tells us that hierarchical control systems are not that simple:

In a control hierarchy the upper level exerts a specific, dynamic constraint on the details of the motion at lower level, so that the fast dynamics of the lower level cannot simply be averaged out. The collection of subunits that forms the upper level in a structural hierarchy now also acts as a constraint on the motion of selected individual subunits. This amounts to a feedback path between levels. Therefore the physical behavior of a control hierarchy must take into account at least two levels at a time, and wúhat is worse, the one particle approximation fails because the constrained subunits are atypical.

As described by Bonner, cells do not simply aggregate as molecules do to form crystals. Chemical messages from the collection of cells constrain the action of the cell according to the genetic control program. In the same way, while we live according to certain patterns determined by our personal life-style, society constrains us to live according to some authority, however we define that authority. Another important point is that there is nothing special about the molecules, or for that matter, the men, that provide that constraint.

The interesting problem of the origin of hierarchical control is to explain how such ordinary molecules and men can evolve such extraordinary authority as members of a collection. Or to put the problem in other words, how do structures that have only common physical properties achieve special functions in a collection? This statement of the problem shifts the emphasis from one level or another to the hierarchical interface between levels.

Pattee saw that the problem of understanding hierarchical control arises to a great extent from our classical acceptance of the relationship between structure and function. In his words, "Therefore most biologists today hold strongly to the strategy: of looking at the molecular structure for the answers to the question of 'How it wúorks'." This, he said, is analogous to a mathemetician trying to deduce the nature of computation from the ways computer hardware is wired together. "The problem," as he put it, "is precisely at the interface level between the detail of the structure and the abstraction of the function." It is at this point that he explained that function or control can only arise through "selective loss of detail."

To understand this, Pattee said that we require a clear realization of what he means when he uses the term "hierarchical control". For example, given a solution of salt water, the sodium and chlorine atoms are free to move about in three dimensions, they have three translational degrees of freedom. Af'ter some time has passed some may have gathered to form a crystal. Those ions that nowú land on the surface of that crystal have fewer degrees of freedom. It forms a collective constraint on the individual ions. This does not mean it is a hierarchical control device because the constraint leads to a fixed crystalline structure.

In the case of screw-dislocation crystal growth, there are imperfections in the crystal grow'th, This constraint, while preserving its screw structure, speeds up the binding of ions by an enormous factor. Thus it provides a more active control process. Yet, eventually it still results in a fixed rigid structure. In order to arrive at a control system that approximates those found in living systems, we need a set of constraints that holds between certain degrees of freedom but does not result in rigid bodies, More than that, because a balloon constrains the gas inside it without freezing into a rigid body, it results in a boundary condition, not a hierarchical control.

What we need to find, then, is a clearerúdescription of the degree of constraint that gives rise to a control hierarchy, We can state two conditions that must be satisfied. First, an effective control event cannot be simply a passive spatial constraint, but must actively change the rate of one particular event, reaction, or trajectory relative to the unconstrained rates. This condition is fulfilled by most devices that we normally associate with existing control systems--for example, switches and catalysts. Second the operation of the constraint must be repeatable wúithout leading to the freezing up of the system, Another way to say this is that control constraints must limit the trajectories of the system in a rúegular way without a corresponding freezing out of its conf'igurational degrees of freedom.

The term "constraint" normally means a forcible limitation of: freedom. The force of gravity limits the freedom of a falling body but it leaves the body no freedom at all. We need a concept of constraint that acts to increase freedom. This is where the concept of a hierarchy plays a significant part. The law of motion relates the detailed trajectory or state of the system to dynamical time. In a hierarchical constraint, the language is about a situation in which the dynamic detail has been purposely ignored.

Let me say that a hierarchical constraint is established by a particular kind of new rule that represents not merely a structure but a classification of microscopic degrees of freedom of the lower level it controls. The classification may take many f'orms which an intelligent observer might define as averages of microscopic variables, or as selection of a fewúsensitive degrees of freedom, or as a redefinition of the system. But in some sense, the appearance of a natural constraint implies an internal classification process that is selected on the basis of simplicity, utility, or function of this alternative description.

One of the fundamentals of hierarchical control programs is selective neglect of certain details, In Bonner's description of neogenesis, he brought up the concept of the "development test," It is the purpose of these tests to turn on specific genes and ignore the rest. Here is the second point that Pattee makes. It is not just a selective loss of detail that gives rise to hierarchical control programs but the optimum loss of detail. This implies that if there is a point in the gradient of detail that wúill cause the system to operate more efficiently then normal evolutionary forúces will tend to move the system toward that point. Constraints that are too tight result in rigid bodies, constraints that are too loose result in boundary conditions that have no repeatable effect on the system.

Hierarchical controls arise from a degree of internal constraint that is independent of' selected details of' the dynamical behavior of its elements.

Hierarchical controls arise from a collection of elements but act on individuals of that collection. Pattee called this "statistical closure", or in his own words, "... a collection of elements that is established and that persists largely because of the rates of their combination," He also said that, "This in turn implies a population dynamics for the elements and therefore a real-time dependence. Furthermore, the rates of specific combinations of elements must be controlled by collections of the elements of the closed set."

An example of statistical closure would be, "It is a well-known principle of evolution that natural selection does not operate deterministically on individuals, but statistically on the breeding population. The effect of natural selection, however, must be recorded in the hereditary memory of the individual organismso Thereforúe, selection is a collective restraint that limits the detailed structure of the individual elements of the collection and establishes a statistically closed set, which wúe call the breeding population."

We cannot understand the nature of biological hierúarchies simply by a finer look at molecular structure, by the solution of detailed equations of motion, nor by the application of non-equilibrium statistical thermodynamics.

A physical theory of hierarchic control would be at the interface between levels.

It would explain how complex collections of interacting elements spontaneously separate out persistent and coherent descriptions and functions under the constraints that relate them. The origin of life is the lowest level of this process where genotypes (descriptions) and phenotypes (functions) are generated by the constraints of a genetic code. As yet such a physical theory does not exist.