Page 411 - Deep Learning

394 Notes to Pages 6–10

sciences. Ormerod (1998) applies complex system concepts to social and eco-
nomic behavior. Bak (1996) has something to say about all these fields.
10. Weinberg (1977).
11. See Callander (1978) for a review of research on river meandering.
12. The contrast between reversible and irreversible processes is now seen by many
scientists as fundamental for understanding nature; see, e.g., Denbigh (1989)
for a review of different types of irreversible processes and Prigogine (1997) for
a strong statement of the role of irreversibility in the material world. The first
physical science in which lack of reversibility played a central role was thermo-
dynamics, although Uffink (2003) has questioned the oft-claimed link between
irreversibility (“time’s arrow”) and the Second Law of Thermodynamics (i.e., the
statement that entropy is always increasing). In biology, species have of course
been seen as historical entities ever since Darwin. See Gould (2002), Chapter 2,
for a reading of Darwin as the inventor of a historical methodology for biology.
13. Regarding the values of physical constants, astrophysicist Neil de Grasse Tyson
(2004) writes: “… in recent decades a lot of physicists have been looking for evi-
dence that constants don’t hold for all eternity. … there’s practically a cottage
industry of physicists desperately seeking fickle constants. Some are looking for a
change across time; others, for the effects of a change in location; still others are
exploring how the equations operate in previously untested domains” (p. 24). For
a cosmological theory based on the assumption that the universe, including the
basic physical constants, evolves, see, e.g., Smolin (1992).
14. Callander (1978): “Rivers carry the products of erosion as well as water, and in
meanders, some sediment is transported by scour and fill. Scour takes place on
the outer banks of the bends and deposition on the inner banks …” (p. 129).
15. “Self-organization is a process in which a pattern at the global level of a system
emerges solely from numerous interactions among the lower-level components of
the system … the pattern is an emergent property of the system, rather than a
property imposed on the system by an external ordering influence … emer-
gent properties are features of a system that arise unexpectedly from interac-
tions among the system’s components …” (Camazine et al., 2001, p. 8, italics in
original).
16. See Bonabeau et al. (1997). Ormerod (1998) compares anthills with human eco-
nomic and social behavior.
17. For example, a firm is a set of interacting employees and can hence be repre-
sented as a network with individuals as nodes and communication channels
(face-to-face contacts, e-mail, etc.) as links. But firms interact in the relevant
market, so a market (or at least some markets) can be represented as a network
with firms as nodes and interactions as links. In this case, an interaction might be
that a person leaves one firm and becomes an employee of another. The processes
of exchanging E-mails and of exchanging employees are very different in their
material details, but they both generate network structures. Particular network
phenomena such as the small-world effect (Watts, 1999) might appear at either
level, because they are independent of the material properties of the nodes and
links. This point was made by von Bertalanffy (1968/1973) in an earlier incarna-
tion of complex systems theory.