Unsolved Problems in Cybernetics, and Subjects for Exploration

Cylindrance

• Find sets of relations with corresponding sets of operators such that cylindrance is not increased.
• The relation between cylindrance and homomorphisms: what happens to cylindrance when a relation is "simplified"?
• Develop a theory of high-order interactions, whether in sets, communications, analyses of variance, differential calculus, etc.
• Relate the cylindrance of the environment to that of the brain that adapts to it.

Epistemology

• Can an additive measure be defined for the "complexity" of a machine, by starting with the axiom that two identical and unconnected machines should have a measure just twice that of the one?
• The Diagnosis and Homing problems (A. Gill) when the system studying them is itself a finite state machine.
• Develop a rigorous theory of how to "simplify" a system or machine, and apply it to the machine whose variables are continuous.
• Why, when there are such a vast number of possible binary relations, do we pick on a special few for consideration — equivalence, order, identity, single-valued, etc. —? These evidently have some special property: what is it?
• May the "meaning" of a message properly be identified with what the recipient does about it?

The Subjective

• What special relations does a system have to itself?
• What facts are relevant to the question whether a machine can feel pain?
• What facts are relevant to the question whether the Roman Empire was self-conscious?

Topology

• Construct a topology of machines in which "A is near B" corresponds to "machine A is 'like' machine B". Develop a suitable metric.
• How many topologies, defined by their open sets, are possible on a finite number of points? What is its order of magnitude as n → ∞?
• What relations hold between the local rules that determine connexion in a random net and the consequent large-scale patterns of connexion?

Finite State Machines

• The theory of complex equilibria and steady states, and their internal structures.
• Extend the theory (of the finite state machine) to the statistical case, over a population of machines.
• Are there properties peculiar to the Markovian machine (with input), or is it just a determinate system blurred?

The Polystable System

• Its properties, when isolated, as seen in various ways.
• Its responses, when disturbed by an input, as seen in various ways.
• The distribution of activity over a network of parts that show much clamping.
• The effects on a system of some variables being able to admit noise into the system.
• The properties of systems that store each memory at the site of its action.

The Random Net

• The relation between the specification of the parts and (after the parts have been joined) the shapes of the resulting confluents.
• Is there a relation between the distribution of loops formed by the connexions and the distribution of cycles it shows in its behavior?
• What are the conditions for the occurrence, in a random net, of cycles whose length is a large prime number?
• What invariants are there over such nets as Walker's? — like energy and angular momentum over Newtonian systems.
• Translate the properties of the wholly discrete random net to the case in which both variables and times are continuous.
• What are the differences between the two types:
• • (a) when the net's k internal connexions are unchanging in position?
  • (b) when there are k connexions at every moment, but their distribution changes with time?
• Extend the theory of why random nets tend to show habituation.
• Extend the theory of why random nets tend to change towards internal disconnexion.
• Are there critical degrees of connectedness between which it shows a behavioral analog of the "liquid" state?
• Will a random net show the sudden change associated with Reynold's [sic] number?
• Explain the "mesa" phenomenon of Minsky and Selfridge. (Proc. 4-th London Symp. on Information Theory; ed. Cherry, C. Academic Press, N.Y., 1961.)

Information Theory

• The non-ergodic and non-stationary cases.
• Characterise the error-controlled feedback regulator by the quantities of information flowing internally.
• Apply Shannon's tenth theorem (law of requisite transmission) to game theory.

Probability

• What is the probability that a linear system will be stable?
• (of 1) — To what order of magnitude does the probability tend as n tends to infinity?
• Extend Rubin & Sitgreaves' results to special cases with more constraints.

Physics

• Is it true that a steady thruput of energy tends to change a heterogeneous system toward such forms as maximally delay the escape of energy?
• Do the laws of physics force the systems governed by them to be of low cylindrance"? [sic]
• Make clear the relation between "order" as seen by the physicist and "order" as seen by the biologist.

Neuro-topology

• How can the topology of ordinary space (a three-dimensional Euclidean continuum) be represented on a network of neurons connected partly at random?

Physiology

• Does the brain have generators of "random" values, to get originality when making trials?
• What methods does the brain use, in serial adaptation, to ensure that later adaptations do not over-write, and spoil, earlier adaptations?
• Does pain, and the restlessness provoked by it, correspond to activity in second-order feedback (ultrastability)?
• What is the dynamic cnsequence [sic] of the layering so commonly seen in neural (especially sensory) tissue?

Psychology

• Can regression to simpler or earlier behavior be shown as a general property of dynamic systems?
• How fast does adaptation occur when it is composed of many small adaptations occurring simultaneously? Extend Lerner's result (velocity reduced to 1/√n) from the linear and additive to the discrete and arbitrary. (Lerner, I.M., Population Genetics and Animal Improvement. Cambridge Univ. Press, 1950.)
• Follows up various lines in:
• • (a) Recent Progress in Pscyhiatry [sic]; ed. Fleming, G.W.T.H., Churchill, London vol. 2, pp. 94-110, 1950.
  • (b) Ibid., vol. 3, pp. 94-117, 1958.
  • (c) Journal of Mental Science, 100, 114-124, 1954. — by W.R. Ashby.

Sociology

• Apply uncertainty analysis to find conditional transmissions in social activities.
• Can such "cerebral" activities as habituation, anticipation, conditioning, be demonstrated in contemporary social systems? — not as a personal but as a social or system event.
• (as 2) — in history?

Constructions

• Build a machine or organization that will beat the world Champion at chess.
• Build a model that will adequately represent Freud's theory of the neuroses.

Source

W. Ross Ashby, “Unsolved Problems in Cybernetics, and Subjects for Exploration”, unpublished classroom handout, reprinted in Roger Conant (ed.), Mechanisms of Intelligence: Ross Ashby’s Writings on Cybernetics (Seaside, CA: Intersystems Publications, 1981), pp. 429–432. Transcribed from the reprint; the typescript’s spelling and punctuation are preserved, with [sic] where it departs from the standard form.