Figure 5. Two time slices from the Bénard experiment. The first time slice (left) shows the homogeneous or disordered "Boltzmann regime" where entropy is produced by heat flow from the disordered collisions of the molecules (by conduction), and the second (right) shows entropy production in the ordered regime. Spontaneous order arises when the field potential is above a minimum critical threshold and stochastic microscopic fluctuations are amplified to macroscopic levels and hundreds of millions of molecules begin moving coherently together. Since the emergence of order is thus stochastically seeded at the microscopic level (a generic property of autocatakinetic systems meaning the starting point is never precisely the same twice) there is great variability during the early stages of the ordering process. As time goes on the system goes through a generic developmental process of selection which includes such dynamics as spontaneous fissioning of cells and competitive exclusion until the system reaches a final state of regularly arrayed hexagonal cells (not shown). From R. Swenson, 1989b, Systems Research 6, p. 192. Copyright 1989 by Pergamon Press. Reprinted by permission.
extraphysical "makers"). Figure 5 shows two time slices in the now well-known Bénard experiment which consists of a viscous liquid held in a circular dish between a uniform heat source below and the cooler temperature of the air above. The difference in temperatures constitutes a potential (or thermodynamic force F) the magnitude of which is determined by the extent of the difference. When F is below a critical threshold the system is in the disordered or linear "Boltzmann regime", and a flow of heat is produced from source to sink (entropy is produced) as a result of the disordered collisions of the molecules (conduction) and the macroscopic state appears smooth and homogeneous (left). As soon as F is increased beyond a critical threshold, however, the symmetry of the disordered regime is broken and order spontaneously emerges as hundreds of millions of molecules begin moving collectively together (right).
      According to Boltzmann's hypothesis of the second law such states are infinitely improbable, but here, on the contrary, order emerges with a probability of one, that is every time F is increased above the critical threshold. What is the critical threshold? It is simply the minimum value of F that will support the ordered state. Just as the empirical record suggests that life on Earth, the global ordering of the planet, occurred as soon as minimum magnitudes of critical thresholds were crossed (e.g., an Earth cool enough so its oceans would not evaporate in the origin of life, or the levels of order that

apparently arose as soon as minimal levels of atmospheric oxygen were reached), so too here spontaneous ordering occurs as soon as it gets the chance. But what is the physical basis for such opportunistic ordering?

Return to the Balance Equation of the Second Law

Returning to the balance equation of the second law provides the first clue. The intrinsic space-time dimensions for any system or process are defined by the persistence of its component relations. Since in the disordered regime there are no component relations persisting over greater distances or longer times than the distances and times between collisions (mean free path distances and relaxation times) it is easy to see that the production of order from disorder thus increases the space-time dimensions of a system. In the Bénard case, for example, the intrinsic space-time dimensions of the disordered regime are on the order of 10-8 centimeters and 10-15 seconds respectively. In stark contrast, the new space-time level defined by the coordinated motion of the components in the ordered regime is measured in whole centimeters and seconds, an increase of many orders of magnitude. Bertalanffy and Schröedinger emphasized that as long as an autocatakinetic system produces entropy fast enough to compensate for its development and maintenance away from equilibrium (its own internal entropy reduction) it is permitted to exist. With the understanding of the relation between intrinsic