Incomplete Nature Part 20

CHAPTER 6: CONSTRAINT.

1. W. Ross Ashby (1962), p. 257.

2. A notion that can be compared with the indeterminacy of modern quantum physics.

3. C. S. Peirce, Collected Papers, Vols. 16 (193135), 1:16, 4:1.

4. More subtly, in chapter 11 when we return to consider the concept of work-i.e., that which is necessary to change things in non-spontaneous ways-we will discover that it takes constraint to produce work; and in chapters 12 and 13 we will discover that constraint is also the defining attribute of information.

5. A non-linear equation is one in which one or more variables in that equation take on the value of the result of performing the calculation that the equation specifies. Thus, given an initial value, the same calculation is repeatedly performed, with each successive calculation incorporating the resultant value of the previous calculation as the updated value of that variable. A cla.s.sic example is the calculation of compounded interest, in which the interest on a princ.i.p.al is added to the remaining princ.i.p.al to yield the new princ.i.p.al on which the next calculated interest value is based, and so forth.

6. Robert Laughlin would even extend this logic to make it a basic factor distinguis.h.i.+ng quantum from cla.s.sical dynamics (though I am not qualified to a.s.sess this claim). As has been understood for nearly a century, although quantum fluctuations are ubiquitous and inject irreducible indeterminateness into all quantum-level interactions, these noiselike effects typically wash out above the atomic scale to produce material interactions that are nearly indistingushable from those predicted by Newtonian dynamics.

CHAPTER 7: HOMEODYNAMICS.

1. Curiously, there were efforts to explain gravitation in efficient causal terms following Newton and before Einstein. One theory hypothesized that the gravitational "force" might occur due to a kind of s.h.i.+elding effect. Laplace imagined that there were vast numbers of particles careening around the universe, constantly b.u.mping into solid matter and moving it about, a bit like atoms in Brownian motion. An object isolated in s.p.a.ce would be evenly b.u.mped on all sides and would therefore remain at rest. Two objects brought into close proximity would, in contrast, partially s.h.i.+eld one another from collisions on the sides facing each other, and this would produce an asymmetrical force on each, propelling them together.

2. You might also say that gravitational-inertial ma.s.s is itself just a local warp in s.p.a.ce-time, though this is not the standard interpretation.

3. This partial isolation of properties and the possibility of linking previously isolated dimensions of change, like transforming heat into linear motion in a heat engine, will be explored in extensive detail in chapter 11, as it pertains to the concept of work.

4. The a.n.a.logy between Newtonian and thermodynamic interactions is actually closer than might first be apparent. Real billiard b.a.l.l.s also have microscopic atomic structure, and the transfer of momentum from one to the other is mediated by a transient distortion of the relations.h.i.+ps between atoms that is quickly propagated through each ball during the exchange of momentum. In this respect, this transient period of atomic-level deformation leading up to elastic rebound is a.n.a.logous to the period of heat transfer between contiguous media, and the resultant state of whole ball movement is a.n.a.logous to the new equilibria that the two media settle into. And although the heat (i.e., average molecular momentum) in each medium may be equivalent after interaction, if they are composed of different numbers of molecules, the total amount of molecular momentum in each will be appropriate to this difference.

5. The term phase s.p.a.ce initially referred to graphs that depict the way variables like temperature and pressure interact to determine the change in phase (e.g., from liquid to gas).

6. The metaphor of a warped phase s.p.a.ce is actually not the way attractors are usually graphed. More commonly, the s.p.a.ce is Euclidean and attractors show up as areas of more dense trajectories. Indeed, this a.n.a.logy is only heuristic because the dimensionality of a thermodynamic system of even modest size is high and thus quite beyond depiction. This way of thinking about the attractor bias in trajectory orientation is intended to highlight the geometric nature of the causality.

7. It can be objected that the so-called modern scientific paradigm being invoked here is actually a hundred-year-old pre-relativistic and pre-quantum understanding of causality. This is in fact the case. Does this mean that these concepts and this way of fractionating the notion of causality are irrelevant to modern physics, or that these distinctions are likely to be undermined by considering them in light of more contemporary physical theory? I don't think so. I suspect that pursuing a similar logic in an a.n.a.lysis of quantum-level and relativistic processes might indeed help explain some of the more paradoxical aspects of these processes. This is a matter that would at least require another book, and for the purpose of making sense of the teleological features of life and mind, I believe that these extremes of scale in s.p.a.ce, time, and energy are not relevant. We need go no further than cla.s.sical statistical mechanics to make sense of these phenomena.

8. C. S. Emmeche, S. Kppe, and F. Stjernfelt, Levels (2000), p. 31.

9. Whether we can identify homeodynamic processes at even deeper quantum levels is unclear to me, though I suspect that some variant of these reciprocal orthograde-contragrade dynamical relations.h.i.+ps will even apply in this strange domain as well.

CHAPTER 8: MORPHODYNAMICS.

1. Peirce's 1898 series of Harvard lectures to which he was invited by William James. Reprinted in Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898 (1992), Cambridge, MA: Harvard University Press, p. 258.

2. Paul Weiss (1967).

3. Literally, "in gla.s.s," meaning in a laboratory experiment performed within a dish, not within an organism.

4. Note that dependence on what occurred previously in the sequence also describes the additive logic of the Fibonacci series.

5. For a recent demonstration of the spontaneous formation Fibonacci spirals in a non-organic material, see Li et al. (2005, 2007).

6. Ashby later cautioned against a too literal interpretation of self-organization for reasons a.n.a.logous to those discussed here.

7. Benard (1900).

8. For example, hexagonal close packing occurs spontaneously when same-size b.a.l.l.s are packed together tightly on a planar surface.

9. For the sake of narrative flow, after having painstakingly dissected Benard cell dynamics, I will simplify each of the following accounts, ignoring the many subtle differences that make their emergence slightly disa.n.a.logous to Benard cell emergence, and focusing mainly on the major features that exemplify their logic of constraint transfer and amplification.

CHAPTER 9: TELEODYNAMICS.

1. David Bohm, "Some Remarks on the Notion of Order" (1968), p. 34.

2. Ulanowicz (2009) argues that the dynamics of living systems contradict the fundamental axioms of Newtonian dynamics.

3. See Ilya Prigogine, Introduction to Thermodynamics of Irreversible Processes (1955).

4. Dewar in Whitfield (2005), p. 907.

5. Kleidon, in ibid.

6. Swenson (1989), p. 46.

7. E. D. Schneider and J. J. Kay (1997), p. 165.

8. See Stuart Kauffman (2000).

9. Maturana and Varela (1980).

10. Bickhard (2003).

11. See John von Neumann (1966), p. 67.

12. See E. V. Koonin (2000).

13. See R. Gil et al. (2004).

14. See recent reviews in Ra.s.smussen et al. (2004) and also Szathmary et al. (2005).

15. T. R. Cech (1986).

16. But see Frietas and Merkle (2004) for a review of the state of this research.

17. See, e.g., Anet (2004); Andras and Andras (2005); de Duve (1996); Kauffman (1995); and Morowitz (1992).

CHAPTER 10: AUTOGENESIS.

1. Immanuel Kant, The Critique of Judgment (1790), Sect. 65, p. 558.

2. Kauffman (2000).

3. Eigen and Schuster (1979).

4. Kant (1790), Sect. 65, p. 557.

5. See Deacon (2004, 2005, 2007).

6. Though neither are literally self-replication. Both require reciprocal relations.h.i.+ps between molecules; and even if RNA molecules are able to a.s.sume both template and catalytic functions, they can't do both at once, even in the simplest cases envisioned. See the more detailed critical discussion of this concept in chapter 14.

7. Von Uexkull (1957).

8. Francisco J. Varela (1992), p. 11.

CHAPTER 11: WORK.

1. From a textbook on thermodynamics: H. C. Van Ness, Understanding Thermodynamics (1969).

2. Gergory Bateson, Steps to an Ecology of Mind (1972), p. 453.

3. I.e., there is total energy symmetry across time in accordance with the first law of thermodynamics.

4. The curious fact that it takes work to change or produce constraints, and that constraints are required to do work, is discussed as an important clue to what Stuart Kauffman describes as the missing "theory of organization," in his book Investigations (2000).

CHAPTER 12: INFORMATION.

1. John Collier (2003), p. 102.

2. Franz Brentano (1874), Psychology from an Empirical Standpoint, pp. 8889.

3. Indeed, this is what makes self-organizing dynamics so intriguing and makes living dynamics often appear planned and executed by an external or invisible agency.

4. Shannon based his a.n.a.lysis on the model of a transmission channel such as a telephone line with a fixed limit to the variety and rate of signals that it could carry. This model system will be used throughout the discussion to be consistent with Shannon's terminology; but the a.n.a.lysis equally applies to anything able to convey information, from text on a page to physical traces used as clues in a criminal investigation.

5. Thus the probability of appearance of each character at each position is maximally uncorrelated with all others, as is the movement of each molecule in a gas at equilibrium. This justified calling both conditions maximum entropy.

6. See Warren Weaver and Claude Shannon (1949).

7. See Deacon (2007, 2008).

8. For example, negentropy plays a central role in Erwin Schrodinger's famous essay What Is Life?

CHAPTER 13: SIGNIFICANCE.

1. Personal communication from Stuart Kauffman. See also Kauffman et al. (2008).

2. This does not necessarily mean that there is a loss of functionality accompanying this reduction. In fact, in biology just the opposite is true. The functional features of protein molecules are mostly a function of their three-dimensional structure. This is a secondary consequence of the different properties of their const.i.tuent amino acids (coded in the DNA) and how these properties in this order interact with one another and with the surrounding chemical milieu. Because of this, a protein embodies a considerably higher potential Shannon entropy than does the DNA sequence that codes for it. This contributes to an enormous amplification of information from genome to cellular organization.

3. See, e.g., Karl Popper (2003) and Donald T. Campbell (1974).

4. E.g., Fred Dretske (1988) and Ruth Millikan (1984).

5. See, e.g., critiques by Mark H. Bickhard (1998, 2000, 2003, and 2005).

6. Although other organisms sharing the same ecosystem may comprise a significant source of relevant selection "pressures," they do not generally directly modify the information pa.s.sed from generation to generation, but simply impose complex changing boundary conditions on one another. Parasites, predators, and opposite-s.e.x conspecifics may however exert a more direct constraining influence.

7. See Charles Sanders Peirce (193135).