Cybernetics • Regulation In Biological Systems • Discussion 1

Re: Ontolog ForumJAPDM

JA:
We continue in pursuit of a system-theoretic answer to the question:  What are formalisms and all their embodiments in brains and computers good for?
PDM:
Could you also provide a brief answer to the question, through your analysis of the text you reference — we all suffer from attention deficit and may forget what you were trying to say at the beginning.

I know what you mean.  Brevity is the soul of wit, but the brief lives of mortal attention spans struggle to embody half of it.  I personally have trouble remembering what I was thinking a few days ago unless I wrote it down somewhere I can easily find again.

My question about the good of embodied formalisms was intended to call attention to a natural connection between Pragmatic Truth and Cybernetic Purpose.  Pragmatic ways of thinking about the role of representations in relating interpreters to objective realities naturally harmonize with systems thinking about the role of information in achieving the objectives of agents.  In either mode of thinking we tend to become quickly dissatisfied with disembodied abstractions, detached from dynamic context and meaningful purpose.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Cybernetics • Regulation In Biological Systems • Selection 5

Regulation In Biological Systems

Survival

Ashby Cybernetics Figure 10.5.2

10/5.[concl.]   To make the assumptions clear, here are some simple cases, as illustration.  (Inanimate regulatory systems are given first for simplicity.)

(1) The thermostatically-controlled water-bath.  E is its temperature, and what is desired (\eta) is the temperature range between, say 36° and 37°C.  D is the set of all the disturbances that may drive the temperature outside that range — addition of cold water, cold draughts blowing, immersion of cold objects, etc.  F is the whole regulatory machinery.  F, by its action, tends to lessen the effect of D on E.

(2) The automatic pilot.  E is a vector with three components — yaw, pitch, and roll — and \eta is the set of positions in which these three are all within certain limits.  D is the set of disturbances that may affect these variables, such as gusts of wind, movements of the passengers in the plane, and irregularities in the thrusts of the engines.  F is the whole machinery — pilot, ailerons, rudder, etc. — whose action determines how D shall affect E.

(3) The bicycle rider.  E is chiefly his angle with the vertical.  \eta is the set of small permissible deviations.  D is the set of those disturbances that threaten to make the deviation become large.  F is the whole machinery — mechanical, anatomical, neuronic — that determines what the effect of D is on E.

Many other examples will occur later.  Meanwhile we can summarise by saying that natural selection favours those gene-patterns that get, in whatever way, a regulator F between the disturbances D and the essential variables E.  Other things being equal, the better F is as a regulator, the larger the organism’s chance of survival.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Cybernetics • Regulation In Biological Systems • Selection 4

Regulation In Biological Systems

Survival

10/5.[cont.]   Now regard the system as one of parts in communication.  In the previous section the diagram of immediate effects (of cat and mouse) was (or could be regarded as)

Ashby Cybernetics Figure 10.5.1

We are now considering the case in which the diagram is

Ashby Cybernetics Figure 10.5.2

in which E is the set of essential variables, D is the source of disturbance and dangers (such as C) from the rest of the world, and F is the interpolated part (shell, brain, etc.) formed by the gene-pattern for the protection of E.  (F may also include such parts of the environment as may similarly be used for E\text{'s} protection — burrow for rabbit, shell for hermit-crab, pike for pike-man, and sword (as defence) for swordsman.)

For convenience in reference throughout Part III, let the states of the essential variables E be divided into a set \eta — those that correspond to “organism living” or “good” — and \text{not-}\eta — those that correspond to “organism not living” or “bad”.  (Often the classification cannot be as simple as this, but no difficulty will occur in principle;  nothing to be said excludes the possibility of a finer classification.)

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Cybernetics • Regulation In Biological Systems • Selection 3

Regulation In Biological Systems

Survival

10/5.   What is it survives, over the ages?  Not the individual organism, but certain peculiarly well compounded gene-patterns, particularly those that lead to the production of an individual that carries the gene-pattern well protected within itself, and that, within the span of one generation, can look after itself.

What this means is that those gene-patterns are specially likely to survive (and therefore to exist today) that cause to grow, between themselves and the dangerous world, some more or less elaborate mechanism for defence.  So the genes in Testudo cause the growth of a shell;  and the genes in Homo cause the growth of a brain.  (The genes that did not cause such growths have long since been eliminated.)

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Cybernetics • Regulation In Biological Systems • Selection 2

Regulation In Biological Systems

Survival

10/4.   What has just been said is well enough known.  It enables us, however, to join these facts on to the ideas developed in this book and to show the connexion exactly.

For consider what is meant, in general, by “survival”.  Suppose a mouse is trying to escape from a cat, so that the survival of the mouse is in question.  As a dynamic system, the mouse can be in a variety of states;  thus it can be in various postures, its head can be turned this way or that, its temperature can have various values, it may have two ears or one.  These different states may occur during its attempt to escape and it may still be said to have survived.  On the other hand if the mouse changes to the state in which it is in four separated pieces, or has lost its head, or has become a solution of amino-acids circulating in the cat’s blood then we do not consider its arrival at one of these states as corresponding to “survival”.

The concept of “survival” can thus be translated into perfectly rigorous terms, similar to those used throughout the book.  The various states (M for Mouse) that the mouse may be in initially and that it may pass into after the affair with the cat is a set M_1, M_2, \ldots, M_k, \ldots, M_n.  We decide that, for various reasons of what is practical and convenient, we shall restrict the words “living mouse” to mean the mouse in one of the states in some subset of these possibilities, in M_1 to M_k say.  If now some operation C (for cat) acts on the mouse in state M_i, and C(M_i) gives, say, M_2, then we may say that M has “survived” the operation of C, for M_2 is in the set M_1, \ldots, M_k.

If now a particular mouse is very skilled and always survives the operation C, then all the states C(M_1), C(M_2), \ldots, C(M_k), are contained in the set M_1, \ldots, M_k.  We now see that this representation of survival is identical with that of the “stability” of a set (S.5/5).  Thus the concepts of “survival” and “stability” can be brought into an exact relationship;  and facts and theorems about either can be used with the other, provided the exactness is sustained.

The states M are often defined in terms of variables.  The states M_1, \ldots, M_k, that correspond to the living organism are then those states in which certain essential variables are kept within assigned (“physiological”) limits.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Cybernetics • Regulation In Biological Systems • Selection 1

Regulation In Biological Systems

10/3.   The foundation.   Let us start at the beginning.  The most basic facts in biology are that this earth is now two thousand million years old, and that the biologist studies mostly that which exists today.  From these two facts follow a well-known deduction, which I would like to restate in our terms.

We saw in S.4/23 that if a dynamic system is large and composed of parts with much repetition, and if it contains any property that is autocatalytic, i.e. whose occurrence at one point increases the probability that it will occur again at another point, then such a system is, so far as that property is concerned, essentially unstable in its absence.  This earth contained carbon and other necessary elements, and it is a fact that many combinations of carbon, nitrogen, and a few others are self-reproducing.  It follows that though the state of “being lifeless” is almost a state of equilibrium, yet this equilibrium is unstable (S.5/6), a single deviation from it being sufficient to start a trajectory that deviates more and more from the “lifeless” state.  What we see today in the biological world are these “autocatalytic” processes showing all the peculiarities that have been imposed on them by two thousand million years of elimination of those forms that cannot survive.

The organisms we see today are deeply marked by the selective action of two thousand million years’ attrition.  Any form in any way defective in its power of survival has been eliminated;  and today the features of almost every form bear the marks of being adapted to ensure survival rather than any other possible outcome.  Eyes, roots, cilia, shells and claws are so fashioned as to maximise the chance of survival.  And when we study the brain we are again studying a means to survival.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Pragmatic Theory Of Truth • 18

Re: Pragmatic Theory Of Truth • (14)(16) • (17)
Re: Peirce ListTom Gollier

We do not live in axiom systems.  We do not live encased in languages, formal or natural.  There is no reason to think we will ever have exact and exhaustive theories of what’s out there, and the truth, as we know, is “out there”.  Peirce understood there are more truths in mathematics than are dreamt of in logic and Gödel’s realism should have put the last nail in the coffin of logicism, but some ways of thinking just never get a clue.

That brings us to the question:

  • What are formalisms and all their embodiments in brains and computers good for?

For that I’ll turn to cybernetics …

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