A schematic diagram ofbifurcation appears in Fig.34.1, reproduced from
Nicolis and Prigogine ( 1989 , p. 73). Highlighting their thesis of indeterminacy,
Nicolis and Prigogine make the following comment upon the model:
A ball moves in a valley, which at a particular pointkcbecomes branched and leads to
either of two valleys, branches b1 and b2 separated by a hill. Although it is too early for
apologies and extrapolations...it is thought provoking to imagine for a moment that instead
of the ball in Figure [1] we could have a dinosaur sitting there prior to the end of the
Mesozoic era, or a group of our ancestors about to settle on either the ideographic or the
symbolic mode of writing. (p. 73)Although, due to system perturbations andfluctuations, it is impossible to precisely
ascertain causes in advance, retrospectively, of course, wefind the‘cause’there in
the events that lead up to an event, in the sense that we look backwards and point to
plausible antecedent factors that contributed to its occurrence. While therefore not
undetermined by prior causes, the dislocation of linear deterministic trajectories and
Fig. 34.1 Mechanical
illustration of the
phenomenon of bifurcation
(from Nicolis and Prigogine
1989 , p. 73)
34 Complexity and Learning: Implications for Teacher Education 511