There are no facts, only interpretations
F. Nietzsche, 1901
Everything should be made as simple as possible, but not simpler Albert Einstein
The research presented in this thesis is hardly finished. On the contrary, it is of a highly exploratory nature, and as such it can be extended in many many ways. The paddler in its present incarnation is still in the early stages of its development; it has a very long evolutionary road ahead. It seems likely that, just like the system being modelled, the paddler and its habitat can be evolved indefinitely.
Due to the exploratory character of the research, and due to its "open end", it is impossible to draw one or a few final conclusions capturing the whole essence of the work. One can, however, very well draw conclusions regarding the solution of various interesting subproblems of survival in a changing environment.
1.3.4 a Guidelines for the modeller Toutes les g´en´eralisations sont dangereuses. Mˆeme celle-ci
Alexandre Dumas, fils
It is possible to extract some useful conclusions from the present state of the research.
First there is what might be called the compensation principle. This principle holds that there is not one, nor a few, optimal combination(s) of characteristics (parameters), but rather a whole range. Within this range, ill effects of a change in one parameter can be compensated for by changing another parameter that affects the same properties. Over the whole range, adequate behaviour results.
This principle has been observed mainly in the parameters specifying the paddler’s geometrical properties: see chapter 2. One example is the relation between the inter-ocular and the inter-paddle distances. In an animal that uses inter-ocular eye-response differences to determine directions, a larger inter-ocular distance can result in a higher directional sensitivity. A smaller inter-paddle distance causes the paddler to be less capable to turn fast. These effects can cancel each other out.
A second example comes from a small excursion not described in the following text. The excursion involved a related paddler species, sporting two pairs of paddles, both pairs receiving the same swim commands. The paddles of a paddler are fully specified by two parameters: their position on the body, and the direction in which they point. In a two- paddle paddler, there is a rather large range of combinations of these parameters for which the paddler fourages optimally. In a four-paddle paddler one finds two separate, slightly smaller ranges of combinations of these parameters. These two ranges reflect the specialisation of either the front or the rear paddle pair to steering paddles, with the other pair taking care mainly of forward locomotion.
30 CHAPTER1. INTRODUCTION
Second there is the importance of embedding physically inspired dynamics in the model. Such more or less realistic dynamics can enrich the behaviour displayed by the model. They can also allow simple solutions to certain problems; solutions,smart mechanisms, that make clever use of the physical properties of the system.
An example of the latter reason is given in chapter 5. In this chapter a speed control system is described that is intended to match the paddler’s actual speed to its intended speed. Here the problem arises how to compare measured ego-speed with the intended ego- speed that corresponds to the current swim commands. Ego-speed is measured through the drag excerted on a hair receptor by the water flow around the paddler’s body. This drag is subject to the same equations governing the drag experienced by the whole paddler, and thus the paddler’s speed. In short: the paddler’s speed is proportional to the square root of the thrust it generates; the ego-speed measurement is proportional to the square of the speed. The speed control system therefore only needs to know or learn the speed measurement corresponding to a given set of swim commands. Assuming that the generated thrust is proportional to the swim command, it can then directly "compute" a corrective gain factor on the basis of measured and expected speed.
How physically inspired dynamics can enrich the behaviour of a model can be illustrated with the light-adapting machinery of the diurnal paddler’s retina. Part of this machinery is a differentiator; not the mathematical beast16
, but a "leaky differentiator": a high-pass filter. Such a filter can be constructed by subtracting from an input a time-averaged copy of the same input: the output of a leaky integrator or low-pass filter. If the high-pass filter is to output its signal as a spike frequency, the choice for two output channels — ON and OFF— is a logical one. These channels can then be assigned different weights in subsequent processing.
The leaky integrator incorporated in the high-pass filter introduces a subtle difference be- tween this leaky differentiator, and its pure, mathematical, counterpart. Due to the memory in the leaky integrator, changes in input are signalled for a much longer time: the response becomesphasic-tonic. In case of increase of input — e.g. after something appears in the field of view — this only means that the presence of some object is signalled a little longer. When something disappears (an input drop to zero), after-images occur, which can mislead the paddler into assuming prey where there is none.
Paddlers that use theOFFchannel in their light-adapting machinery show a phenomenon
also known to occur in Planaria (F. Verheijen, personal communication): edge following, in which a steep gradient of (background) illumination is traced. This behaviour can be explained by the equal importance of entering or leaving a light or dark zone. As a result the paddler will return to the lighted region that the last of its two eyes just left, just as it will turn back toward the dark zone when the last of its eyes has entered the lighted region. The result: a paddler wiggling along the border between light and dark.
This leads to the third observation, the importance of the use of non-idealised components. It will be clear that no biological system incorporates ideal components: neither neurones, nor in sensory systems, nor in motor systems. Yet these non-ideal components are combined in such smart ways that the integrated (sub)systems are remarkably sensitive and robust. Part of the fun of neuro-ethological modelling lies in trying to reproduce the ideal by using non-ideal components, just as in nature.
One need not always try, however, to go for an ideal (sub)system. This is illustrated by the paddler’s motion detection system discussed in chapter 6. The elementary motion detector
1.3. AN OVERVIEW OF THIS THESIS 31