Information, Entropy, and Nervous System

INFORMATION, ENTROPY, AND NERVOUS SYSTEM FERNANDO RAMON FERRANDO* Inthis paper certainwell known features ofthe nervous activity are discussed in an attempt to approach them from the point ofview ofthermodynamics and theory of information. The meaning of certain concepts such as Prigogine's or Boltzmann's formulae in relation to the nervous function has been particularly emphasized. Since these concepts may not be familiar to all readers, a brief introduction to them will precede the exposition ofthe theories here supported. 1. Introduction: Fundamental Concepts in Theory of Information and Thermodynamics a. signals and messages Any information process that takes place in our mind is based upon two signals, two informative elements: yes and no. This seems to have a parallel in the all-or-nothing responses that one finds throughout the nervous system . For example, in the retina the photosensitive cells either receive or do not receive photons; the depolarization in one point ofa nervous conducting membrane is either transmitted to other regions or not transmitted. The existence of membranes where conduction is décrémentai, as in the case ofdendrites, does not invalidate this statement. In any case, the sum of impulses reaching the nerve cell is either followed by firing ofits axon or is not. The nerve cell either sends an impulse to other regions ofthe nervous system or fails to do so. Even in the more complex case ofgroups ofinteracting neurons, the final result is either a definite type ofresponse, a complex movement, for example, or any other type ofresponse which is not that reflex movement. Firing and non-firing nervous elements may appear in a variety ofcombinations . From the standpoint ofthe mathematical theory ofinformation, * Facultad de Ciencias, Universidad de Salamanca, Spain. 296 Fernando Ramon Ferrando · Information, Entropy, and Nervous System Perspectives in Biology and Medicine · Spring 1962 each of these combinations can be considered as a message. There are a number ofpossible messages which depend on the number ofnervous elements involved. The calculation ofthis number is easy in this particular case because we are dealing with a binary system where only two elementary types ofresponse exist: firing and non-firing. Let us represent yes and no by + and — . A definite message—for instance , "yes, no, no, yes, no"—would appear as H-----------1----- . Each ofthese positive or negative symbols is defined as a signal, and the number ofsignals as the length ofthe message. In this way, the length of the message above written is five. It is evident that the number ofpossible messages (P) with two types of signals and length five is 2 X 2 X 2 X 2 X 2 = 25. In general, we have P = 2N where Pis the number ofpossible messages in a binary system ofa given length N. B.information When a definite message is recorded, its information is measured in bits, the latter being related to the number ofsignals used and to the length Nof the message. Intheparticularcaseofa binary system, where onlytwo kinds of signals are used, the information measured in bits coincides with the length N ofthe message. This is not the case in other information systems where more than two types ofsignals exist. C.ORGANIZATION AND ENTROPY The concept ofinformation is mathematically equivalent to the concept of organization. An example could be a collection of nails which, for the sake ofsimplicity, will be considered here as parallel to one another. This collection will form an organization where the position ofthe points and heads can be considered as a message. But, on the other hand, this organization or information can be destroyed. The nails can be thrown so that, when collected again, the original organization is lost. It is important to underline that before throwing the nails we do not know in which way they will end. One crystal ofsodium chloride has its atoms arranged in an orderly way. This organization measured in bits can be calculated if, among other data, the number of molecules ofthe crystal is known. When this one is dissolved or melted, its organization is lost. We do not know any longer the orientation ofthe N dissolved molecules or, more precisely, ofthe N pairs of ions originated. We do not know what the message they represent...