2 the evolution in the brain
2.6 The evolution of signal patterns in the brain
In the brain the evolution of DNA-messages is replaced by an evolution of signal patterns and the phenotypic landscape is replaced by a mental landscape, the complexity of which will hardly be second to the former. The metaphor with the mental landscape is based on the assumption that certain signal patterns give rise to a better well-being or performance. For instance, the control of a group of muscles leads to a better pronunciation of a word or performance of a piece of music.
2.7 Neural networks
Artificial neural networks are attempts to model the central nervous system, in which the nerve cells send showers of pulses to each other. Such a network may consist of interconnected components that are able to add or multiply signal values, and may therefore be simulated on computers. The reason is that nerve cells may add signals in the sense that they send a pulse after having received a certain number of pulses from other nerve cells. A kind of multiplication may take place in the synapses, where the contact area to the next cell may increase or decrease so that signals may, in principle, be amplified or attenuated (see Levine, references).
Different networks may be controlled by different algorithms and it has also been shown that such networks are able to learn certain things. Our choice of algorithm is in accordance with the brain model of Matti Bergström and MacLean, where the brain - during the course of evolution – has been divided into three main parts: (1) The brain stem, (2) the cortex, and between those (3) the limbic system.
2.8 Signal patterns
As in the case in telecommunication, signal patterns in the brain may be modeled as a pile of parameter values in series or parallel. For example, a pattern of 28 parameter values in a sequence (as in figure 2.2 below) may be seen as a point in a 28-dimensional space. For the sake of simplicity it will here be assumed that different signal values are sent in parallel. We restrict ourselves to a graphic demonstration of the process in two dimensions. Thus, an individual signal pattern determined by two parameters (for example those framed in figure 2.2) may in a picture be represented by a point, where the first parameter is the shortest distance from the point to the left edge of the picture, while the second parameter is the distance from the point to the bottom edge of the picture.
Figure 2.2.
Figure 2.3 shows a small limbic system with two models of visible nerve cells having two synapses each (the triangular w-boxes) and a circular nucleus with a + sign. The purpose here is to show that already this very simple circuit is capable of solving relatively difficult two-dimensional problems efficiently. But of course, the real brain is tremendously more complex than that.
In the w-boxes the signals may be attenuated or amplified, i. e. multiplied by the w-coefficient. It may be that more natural cells are needed to carry out the operations of the model cells, because they also include addition and multiplication of negative numbers.
The brain stem is here supposed to deliver normally distributed independent random numbers g1 and g2. After having passed the limbic system the resulting signal pattern consisting of x1 and x2 enters the cortex for evaluation. If the pattern is not acceptable, the process continues with a new random pattern. On the other hand, if the pattern is for some reason acceptable, then the entities in the box at the bottom of the figure will be updated according to the equations. But the brain will hardly carry out any such calculations; they may rather be a result of physical and chemical reactions. A general derivation of these equations is given in section 7, simulation of normal adaptation.
m1 = 0.9 m1 + 0.1 x1; m2 = 0.9 m2 + 0.1 x2;
w11 = 0.9 w11 + 0.1 y1g1; w12 = 0.9 w12 + 0.1 y1g2;
w21 = 0.9 w21 + 0.1 y2g1; w22 = 0.9 w22 + 0.1 y2g2;
Figure 2.3.
The reasons for this choice are that (1) it is equivalent to our model of phenotypic evolution, (2) it obeys the Hebbian rule of associative learning and (3) it may fulfill the conditions of optimality according to the theorems of efficiency and adaptation, i. e. it carries out a simultaneous maximization of mean fitness and mean information of signal patterns. The Hebbian rule states that the synaptic transmission between neurons is strengthened if the neurons are simultaneously active while the system is in a state of well-being, otherwise the transmission may be weakened.