A friend who had recently read some of my blog posts (eg, Consciousness as Computation, Social Systems are Computations that Minimize Uncertainty) just loaned me a copy of Angels Fear: Towards an Epistemology of the Sacred, by Gregory and Mary Catherine Bateson (the authors acknowledge the hubris of the title / topic in the book).
Angels Fear.
Written by a father & daughter, both of whom were anthropologists, the book touches on a wide variety of domains — anthropology, philosophy, engineering, cybernetics, information theory, computation, systems thinking, biology, mythology, religion — exactly my kind of book. Gregory Bateson spent a bunch of time as a resident at Esalen, and the first 30 pages or so of the book are new-age-y enough that you might be tempted to put it down pretty quickly, but the majority of the book is quite worthwhile if you’re interested in any of these sundry topics (and especially if you’re interested in the intersection of these / cross disciplinary thinking).
Angels Fear immediately called to mind two other books for me. There’s quite a bit of consideration about the limits of knowledge and problems of recursiveness that recall Douglas Hofstadter’s Gödel, Escher, Bach, and there is a bunch of systems thinking (eg, a consideration of how a resident uses a thermostat to govern temperature of a home) that recalls Donella Meadows’ Thinking in Systems. So if you enjoyed either of these, you may like _Angels Fear*.
Some of my favorite passages…
An example of a message that changes context of interaction, making a question impossible to answer:
The question “Do you love me?” doesn’t work, does it, any more than Joe Adam’s instructing you to record spontaneity or photographing prayer or prescribing sea snakes or even getting the violin one note at a time? They all masquerade as reporting, but they change the context of the interaction.
On free will and repressed knowledge:
FATHER: Look. The doctrine of “free will” is to action as the notion of “direct vision” is to perception — but “direct vision” makes perception into a passive business. “Free will” makes action more active.
In other words, we subtract or repress our awareness that perception is active and repress our awareness that action is passive — ? This is to be conscious?
And:
DAUGHTER: Daddy, you once said that you would derive consciousness from your analysis of the similarity between learning and evolution. Maybe that would help me see the relationship between the epistemological material and the cybernetic diagrams on the one hand, and the anecdotes and myths and questions of how we act in the world on the other.
FATHER: “How we act in the world.” Hmm. Well, I remain skeptical about both knowledge and action for very similar reasons. There is a double set of illusions — mirror images perhaps.
It is clear — as you know — that we do not see external objects and persons: “we” “see” images of those (therefore hypothetical) external entities. It is we who make the images. It is less clear — but must also be true — that we similarly do not have direct knowledge of our own actions.
We know (in part) what we intended.
We perceive (in part) what we are doing — we hear images of the sound of our own voices; we see or feel images of the motions of our limbs. We know not how we move our arms and legs.
In principle, our output is as indirectly known to us as our input. Ha!
Un-peeling the onion of logical types in biology:
But, then again, there is the question of whether the genotype conceivably provides an ability to learn to change the ability to tan. This would seem exceedingly unlikely, but the question must be asked when we are dealing with a creature subject to learning, to environmental impact. Insofar as the creature is subject to such an impact, it is always made so by the characteristics of its genotypic determination.
In the end, if we want to ask about tanning, or about any other phenomenon of environmental change or learning, the question we have to ask is the logical type of the specification provided by the genotype. Does it define skin color? Does it define the ability to change skin color? Does it define the ability to change the ability to change skin color? And so on. For every descriptive proposition which we may utter about a phenotype, there is a background of explanation which, at successive logical type levels, will always peel off into the genotype. The particular environment, of course, is still always relevant for explanation.
The point of world models:
That, of course, is exactly what a model is for — you see certain formal possibilities and look back to see whether they in fact illuminate something that occurs in the world.
Bateson’s rationale for thinking “in terms of a machine” exactly mirrors my own interest in the intersection of computationalism with the humanities and concepts like art and dignity:
FATHER: …. maybe anything that is therapeutic is also addictive.
DAUGHTER: You … I wish you wouldn’t keep letting the ideas spread out. I wish we could get to a concept of addiction that would explain the damage that gets done, the way people get hurt.
FATHER: Yes, well, that’s why we need to think in terms of a machine. So we can talk about the formal questions without moralizing or sentimentalizing. In any case, the shift of attention from individual to interactive process moves us away from questions of value. Instead of good or bad we can think in terms of “reversible” or “irreversible,” “self-limiting” or “self-maximizing.” We need to think in terms of two parts of a system, with some kind of interface between them.
On laws of perception:
Let me now indicate another necessity — namely, that where discontinuity is lacking or is blurred by statistical response of smaller units (e.g. populations of neurons), regularities like those described by the Weber-Fechner laws shall operate. If there be cybernetic systems on other planets so complex that we might be willing to call them organisms, then, surely, those systems must be characterized by a Weber-Fechner relationship whenever the relation across an interface is continuously variable on both sides.
What is asserted by the Weber-Fechner laws can be said in two ways:
Wherever a sense organ is used to compare two values of the same perceivable quantity (weight, brightness, etc.), there will be a threshold of perceivable difference below which the sense organ cannot discriminate between the quantities. This threshold of difference will be a ration, and this ratio will be constant over a wide range of values. For example, if the experimental subject can just discriminate between the perceived weight of thirty grams and the perceived weight of forty grams, then he will also just discriminate between three pounds and four pounds.
This is another way of saying that there will be a relation between input and sensation such that the quantity or intensity of sensation will vary as the logarithm of the intensity of the input. This relation seems to characterize the interfaces between environment and nerve wherever the interface is mediated by a sense organ. It is especially precise in the case of the retina, as shown long ago by Selig Hecht.
Interestingly, the same relation that characterizes afferent, or incoming, impulses was encountered by Norbert Wiener at the interface between efferent nerve and muscle.24 The isometric tension of the muscle is proportional to the logarithm of the frequency of neural impulses I the nerve serving that muscle.
So far as I know, there is no quantitative knowledge yet available of the relation between the response of an individual cell and the intensity of hormonal or other chemical messages impacting upon it. We do not know whether hormonal communication is Weber-Fechnerian.
As to the necessity of this Weber-Fechner relation in biological communication, the following consideration can be urged:
All digital information Is concerned with difference. In map-territory relations (of whatever kind, in the widest sense) that which gets from the territory to the map is always and necessarily news of difference. If the territory is homogeneous, there is no mark upon the map. A succinct definition of information is ä difference which makes a difference at a distance.
The concept of difference enters twice into understanding the process of perception: first, there must be a difference latent or implicit in the territory, and secondly, that difference must be converted into an event within the perceiving system — i.e. the difference must overcome a threshold, must be different from a threshold value.
The sense organs are like the lining of the stomach in functioning as filters to protect the organism from the violence or toxicity of the environment. They must both admit the ―news and keep out the excessive impact. This Is done by varying the response of the organ according to the intensity of the input. The logarithmic scale achieves precisely this: that the effect of inputs shall not increase according to their magnitude, but only according to the logarithm of their magnitude. The difference in effect between one hundred and one thousand units of input shall only equal the difference in effect one and ten units.
The information the organism requires (which will confer survival value) matches the logarithmic scale. The organism benefits by very great sensibility to very small impacts and does not need such precision in evaluating the gross. The hear a mouse in the grass or a dog bark a mile away — and still not be deafened by one‘s own voice shouting — that is the problem.
It seems that in all perception (not only in the biological) and in all measurement, there is something like a Weber-Fechner regularity. Even in man-made mechanical devices, the arithmetic sensitivity of the device falls of with the magnitude of the variable to be measured. A laboratory balance is only accurate in measuring comparatively small quantities, and error is usually computed as a percentage, i.e. as a ratio. (Interestingly, the Encyclopaedia Britannica carries a skewed curve of the variable product of two hundred repetitions of a chemical process25. Here the skewing is probably a result of the Weber-Fechner law operating in the measurement of the various ingredients. Human eyes (and possibly some balances) are affected equally by equal ratios. They are therefore more sensitive to difference on the subtractive side of any norm, and less sensitive to difference on the additive side)
It seems that the interface between nerve and environment is characterized by a deep difference in kind, i.e. in logical typing, between what is on one side of the interface and what is on the other. What is quantitative on the input side becomes qualitative and discontinuous on the perception side. Neurons obey an ̳all-or-nothing rule, and, to make them report continuous variation in a quantity, it is necessary to employ a statistical device — either the statistics of a population of neurons or the frequency of response of the single neuron.
We can know of relationships, but we cannot know about the things related:
But, in fact, the problem of the eternal and the self-evident has not been entirely avoided by the mathematician‘s disclaimer in regard to axioms and definitions. I grant that the axioms and definitions are man-made and refer to nothing in particular in the material world. Indeed, I would insist that we do not know enough about the corporeal things of the world to guess even that the axioms might contain truths about things. But, after all, this book is not much concerned with truths about things — only with truths about truths, which the natural history of descriptive propositions, information, injunctions, abstract premises and the aggregate networks of such ideas. Above all, I am trying to build a natural history of the relations between ideas. It is irrelevant when mathematicians assert that their tautologies assert no truths about things, but explosively relevant when they assert that the steps and even the sequences of steps from the axioms to the detailed propositions are self-evident and, perhaps, eternal and true.
As to the referents of all this ratiocination and argument — the ―things— while I can know nothing about any individual thing by itself, I can know something about relations between things. As an observer, I am in a position resembling that of the mathematician. I, too, can say nothing about a single ting — I cannot even assert from experience that such exists. I can know only something about relations between things. If I say the table is ―hard, I am going beyond what my experience would testify. What I know is that the interaction or relationship between the table and some sense organ or instrument has a special character of differential hardness for which I have no ordinary vocabulary, alas, but which I distort by referring the special character of the relationship entirely to one of the components in it. In so doing, I distort what I could know about the relationship into a statement about a thing which I cannot know. It is always relationship between things that is the referent of all valid propositions. It is a man-made notion the ―hardness is immanent in one end of a binary relationship.
It is suggestive that the mathematicians are content to accept the idea that relationships between propositions can be self-evident, while they are unwilling to grant this status to the propositions themselves. And that position is precisely parallel to my own. I have great difficulty in discussing the vast mental organization of the world and great difficulty in discussing the parts of it, but it seems to me that we can, with care, talk about how that vast organization thinks. We can explore the kind of links it uses between its propositions, while we can never know whit it thinks about.
These links an patterns of relationship which I want to discuss are necessarily regular and form a part of the Eternal Verities, including the rules for joining together items of discourse, together with the natural history of what happens when items are joined together in inappropriate ways. I include in my field of investigation what the DNA says to the growing embryo and to the physiological body. I include what the structure of the brain says to the processes of thought. I include all discourse, which bonds together the phenomena of any ecosystem.
All communication implicitly builds upon assumed shared knowledge:
This preinstructed state of the recipient of every message is a necessary condition for communication. This book can tell you nothing unless you know nine-tenths of it already.
On freedom vs responsibility:
As you move from a narrower to a slightly wider determinism, you remain within the seemingly determined universe, but you can now stand off from the context in which you live and see that context. At this point you have to choose between better and worse. Not everything is so narrowly fixed for you. You become more like a bus that a tram. But you still have the illusion that if only you could reach the next order of freedom, if only you could stand off in another dimension, you would corner or over the next crest of the landscape. Freedom is always imagined to be round the next corner or over the next crest of the mental landscape. We go on doing research and thinking about all sorts of problems, as if we could one day reach the thought that would set us free.
The point of the limericks is not in either but in their juxtaposition. The naïveté of the tram, who thinks he would be free but for those constraining grooves, is demonstrated by the disillusion of the bus, who discovers the constraints and responsibilities of the next order of control. “Freedom” and “responsibility” are a complementary pair, such that an increase in the former will always bring with it an increase in the latter.
The superficial contrast between bus and tram is the fundamental determinism that both must face combine to provide a parable of the relation between youth and age and an instance of a very widespread and basic characteristic of many interfaces between mental systems.
If you find these bits interesting, you will probably enjoy the full book (it’s a fast read): Angels Fear: Towards an Epistemology of the Sacred. You may also enjoy these blog posts: Consciousness as Computation Social Systems are Computations that Minimize Uncertainty