The Physical Basis and Origin of Hierarchical Control

tags

Hierarchy

Notes

a physicist interested in the origin of life.

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If asked what the fundamental reason is for hierarchical organization, I suspect most people would simply say, "How else would you do it?"

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First there is the apparent paradox that hierarchical controls both limit freedom and give more freedom at the same time.

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legal constraints are necessary to establish a free society,

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constraints of spelling and syntax are prerequisites for free expression of thought.

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second problem about hierarchical constraints is that they always appear arbitrary to a large extent.

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hierarchical constraints or rules are embodied in structures that are to some extent "frozen accidents."

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Stravinsky writes in Poetics of Music, "The more constraints one im- poses, the more one frees one's self of the chains that shackle the spirit . . . " and he goes on, ". . . the arbitrariness of the constraint serves only to obtain precision of execution."

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any theory of hierarchical origins must ex- plain the origin of the type of constraints that are both arbi- trary and effective in the sense of giving freedom to the collection.

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hierarchical organization is foreign to most physics, but common to all the biological sciences. On the other hand, if we want to understand origins we must begin at a simple enough level so that hierarchical controls are not already inherent

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Structural versus Control Constraints

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the origin of those control constraints that free living matter to evolve along innumerable pathways that non-living mat- ter, following the same detailed laws of motion, cannot fol- low.

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it is the control hierarchy that is the distinguishing characteristic of life.

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authority relation of the upper level over the elements of the lower levels. It is this original functional meaning I want to preserve, but without the original Divine implica- tions.

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description of the physical basis of structural hierarchies as well as a theory of their origin. His theory depends on the relative assembly times for elements with certain probabili- ties of association and dissociation. This time is drastically shortened if there exist stable substructures.

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approxi- mate treatment of the dynamics of many hierarchical struc- tures which Simon calls "near-decomposability." The simplicity and solvability of most physical equations depend on making these approximations.

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The collection of subunits that forms the upper level in a structural hierarchy now also acts as a constraint on the motions of selected individual subunits. This amounts to a feedback path between levels.

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cells do not simply aggregate to form the individual, as atoms aggregate to form crystals. There are chemical messages from the collections of cells that constrain the detailed genetic expression of individual cells that make up the collection. Although each cell began as an autono- mous, "typical" unit with its own rules of replication and growth, in the collection each cell finds additional selective rules imposed on it by the collection, which causes its differ- entiation.

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the authority relation of the hierarchy is often popularly expressed by referring to DNA as the "master molecule" of life, but here again we must emphasize that there is no intrinsic chemical property of DNA that allows it to hold this office. It is the integrated collection of "ordinary" molecules we call the cell that endows DNA with this authority.

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shifts the emphasis from one level or another to the hierarchical interface between levels.

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most biologists today hold strongly to the strategy of looking at the molecular structures for the answers to the question of "how it works." Nevertheless, it is surprising and discouraging to find so many biologists who, finding this strategy productive, mistake it for a theory of life.

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quite seriously, "If we can find all the facts, why do we need a theory?"

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the structure-function problem is still very much with us in biology, in spite of our new knowledge of molecular details.

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function or control can only arise through some selective loss of detail.

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In the collection where it exerts some control it is not just a physical structure—it func- tions as a message, and therefore the significance of this message does not derive from its detailed structure but from the set of hierarchical constraints

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What is a Control Device?

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the concept of control involves a more active dynamical role than simply limiting the available space in which matter can move.

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clearer description of the degree of constraint that gives rise to a control hierarchy.

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an effective control event cannot be simply a passive, spatial constraint, but must actively change the rate of one particu- lar event, reaction, or trajectory

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the operation of the con- straint must be repeatable without leading to the freezing up of the system.

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we must be very careful not to evade the problem by formalizing it.

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even though we have another word to describe control, we have no idea of how control con- straints actually originate. What we need to do is look more closely at the physical basis

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What Is a Constraint?

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there is the force of gravity and electric fields that enter into the equations of motion and determine how the system will move in the course of time. These fundamental forces do indeed "limit the freedom" of the particles, but the fact is that they leave the particles no freedom at all.

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The forces of constraint to a physicist are unavoidably associated with a new hierarchical level of description.

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forces of constraint are not the detailed forces of individual particles, but forces from collections of particles or in some cases from single units averaged over time. In any case, some form of statistical averaging process has replaced the microscopic details. In physics, then, in order to describe a constraint, one must relinquish dynamical description of detail. A constraint requires an alternative description.

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these two alternative languages, dynamics and statistics, have never been combined in an elegant way,

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the problem has proven exceedingly obscure at the most fundamental level— namely, the interface between quantum dynamics and mea- surement statistics.

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measurement requires an alternative descrip- tion,

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the structure is really a solution of the equations of motion, and the fact that the energy and time are not simultaneously measurable is not the result of collective forces or an averaging process, but an essential condition of the fundamental dynamical language of quantum mechanics.

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So the question arises: How many chemical bonds do we need before we can speak of a constraint? Of course there is no exact number, such as 10 or 10,000.1 believe there is only a very pragmatic answer that one can give: I would say that a dynamical collection is described as a constraint when there exist equations or rules in a simpler form that direct or control the motions of selected particles. Of course the dynamical equations must still tell us in principle how the whole system will evolve in time, without involving the concept of constraint.

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an equation of con- straint in physics in an alternative description of the micro- scopically complex and deterministic motions that gains in simplicity or utility by selectively ignoring certain dynamical details.

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This kind of classification or selective neglect of detail still requires an intelligent physicist with a problem to solve.

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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.

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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.

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The Principle of Classification of Details

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The Principle of Optimum Loss of Detail

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This type of rate control is accom- plished by flexible (non-holonomic) constraints that can be neither too tight nor too loose. If they are too tight, we see more or less rigid bodies with no "function," whereas if they are too loose we see only "boundary conditions" that have no definite, repeatable effect on the elements of the collection.

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hierarchical control appears in collec- tions of elements within which there is some optimum loss of the effects of detail.

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hierarchical controls arise from a degree of internal constraint that forces the elements into a collective, simplified behavior that is independent of selected details of the dynamical behav- ior of its elements. It is the combination of the independence of the constraints on the microscopic dynamics along with the simplification of the collective dynamics which creates what we recognize as integrated behavior or function.

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The Principle of Statistical Closure

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In dynamical systems, any error in initial conditions eventually leads to chaos, while in statistical systems only chaos in initial condi- tions leads to simple behavior. What we need for hierarchical control is something in between these extremes, or more precisely, a combination of both.

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emphasize what I interpret as the most fundamental aspect of hierarchical control. It is in the nature of a "juxtaposition of disparate categories,"

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a collection of element types that may combine or interact with each other individually in many ways, but that nevertheless persist as the same collection when looked at in detail over a long period of time.

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What I mean by statistical closure, on the other hand, is a collection of elements that is established and that persists largely because of the rates of their combination. This in turn implies a population dynamics for the elements and therefore a real-time dependence.

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Examples of Statistical Closure

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it may be possible to imagine a strictly discrete, deterministic automaton model of biological development,

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But apparently nature does not do it that way. The indi- vidual cell switches off or on or regulates much of its growth according to concentrations or gradients of concentrations of "message molecules," and this is fundamentally a statistical process.

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the statistical nature of the remarkable molecular devices that make this "scheme" work —the enzymes.

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The enzymes control the rate of selected reactions, and rate control is not a dynamical, but a statistical concept.

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We said this behavior in a hierarchical constraint re- sults in the control of the detailed motions of selected degrees of freedom. This is precisely the nature of enzymes. At the functional level, we speak of the enzyme "recognizing" its substrate, which means that its many collisions with other molecules have no regular effect, and even many degrees of freedom of the substrate are ignored in the binding and catalytic steps. However, at the functional level the operation of the enzyme is specific and repeatable—the same enzyme molecule producing the same catalytic reaction over and over.

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the cell is too complex to have come into existence spontaneously. The general hierarchical origin problem is to find the simplest or most probable natural collection of elements which exhibits statistical closure.

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The Origin Problem

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it is difficult to find examples of incipient hierarchical control or observe the spontaneous growth of hierarchical control.

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critics who do not find the theory of natural selection a satisfying or sufficient explanation for the major evolutionary innovations that have occurred, in particular the origin of new hierarchical control levels.

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It is easy to say that a code will be "frozen" when any change is lethal, but the problem arises in the preliminary stages before the coding constraints appear frozen.

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A physical theory of the origin of hierarchical control levels would be a derivation of these principles from a combi- nation of the existing fundamental laws, both dynamical and statistical. It would explain how complex collections of in- teracting 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 the genotypes (descriptions) and phenotypes (functions) are generated by the constraints of a genetic code. As yet such a physical theory does not exist.

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