ABSTRACT
This chapter is concerned with four models of pattern perception: (a) the Dodwell Model, (b) the System-Theoretical Approach, (c) the Reenpaii Model, and (d) the Hoffman Model (LTG/NP—the Lie transformation group approach to neurophysiology).
Three points are stressed in regard to the mathematical descriptions of these models:
Progress within the fields of biological research has been extraordinarily rapid, creating a considerable lag in incoiporating new achievements. Therefore, parallel biotheoretical models are likely to prevail.
There has been much confusion in discussing theoretical models because the levels of description (e.g., metric level, statistical level) have not been kept sufficiently apart. We shall probably never arrive at theories which are truly universal, because of the different explanatory tasks of the models concerned.
A false enthusiasm for “universal models” is also rooted in the popularity of reductionism. Hoffman's model, if mathematically valid, has an explanatory value quite independent of whether or not the “geometric orbits or trajectories” can be neurophysiologically interpreted.
