ABSTRACT
This chapter and the next two address the view that the methodologies of physics can be cast into a very general form that is applicable to all systems. As noted, this is not a reductionistic view that seeks to express all phenomena in terms of a standard set of elementary physical laws and boundary conditions. Rather it is the belief that the methodological strategies of the physical sciences can be extended to encompass the events connected with complex (biological) systems as well as simple (physical) systems. As will become apparent, the decisive idea is that of "flow." The path taken here from a simple system to a complex system begins with an understanding of mass-dependent causes of flow, passes through an appreciation of the stable geometric properties to which flows give rise, and ends with the observation that mass-independent characterizations of flow function as the informational basis for animal activity. The path is cluttered, however, with issues of measurement and modeling. Some of these issues are the concern of the present, prefatory chapter.
Any biological system succumbs to analysis at a number of scales, where the scale of any given analysis refers to its ordinal position in an extensive dimension of magnitude. The most commonly cited scales of analyses are the macroscopic and microscopic, but more specific distinctions in scale can be drawn. For 15example, with regard to a locomoting animal it is commonplace to note a scale at which the body segments, their associated torques, and their motions are the variables to be measured, and an immediately lower scale at which the muscles, their oxygen perfusion, and their tensile states are the objects of analysis. Scales of analyses contrast in terms of the number and type of components to which they refer; muscles outnumber body segments, for example, and the lower scale's states of perfusion are not duplicated at the upper scale. This contrast can invite a number of others, most notably contrasts in metrics (roughly, real valued "distance functions"), unit quantities (those adopted as standards of measurement), and levels of abstraction (degree of specificity or generality in the measurement of a scale's properties).
All natural systems conform to this image of a progression of scales of analyses. Further, and relatedly, any natural system, whether it is the system of interest in full or in part, can be regarded alternatively as an individual system (e.g., an atomism) or as a set of systems (e.g., a continuum), as Chapter 3 underscores. Whatever the regard, issues will arise concerning the selection of metrics, units, and level of abstraction.
Another class of problems that arises for a multiple-scale analysis of a system, assuming that the division into scales is principled, is that of how to construct models that relate different scales of analysis. With respect to biological systems, there is no single agreed-upon answer, although it is popular to construct models that use computational/representational linkages: The state of affairs at one scale of analysis is the basis for computing the state of affairs at the next scale of analysis (which is usually an ordinally lower scale when the system produces output and an ordinally higher scale when the system receives input). This approach to modeling is continuous with arithmetic formalisms. It favors a symbolic interpretation of a scale of analysis and of the relation among scales, and it begs many questions. Is there a more principled basis for interpreting and relating scales? The strategy pursued in physical science is to link scales of analyses through the symmetries associated with conservations. These symmetries do not change with changes in a system's description that are incurred by analyses at multiple scales. The model for biomechanical organization to be pursued here rests on a methodological commitment to symmetries and conservations as the common thread linking scales of organization in complex (biological) systems.
