I.
Introduction
In the
history of scientific discovery, there have been examples of certain persons or
facets of their work being considered ‘out of step’ with the dominant
scientific or philosophical trends of the time. As such, they risk falling down
a deep well in our cultural landscape, with their work’s efficacy lost to
subsequent generations. If their work has merit, it may be considered ahead of
its’ time by future generations. The timing of a given theory or great idea is
largely determined by cultural and cognitive biases that favor the dominant
paradigm [1]. In other cases, ideas at the paradigmatic vanguard end up
resurrected in a more pragmatic way. The acceptance of such ideas occurs either
gradually or in one fell swoop at a later point in time. Let us keep
this in mind as we discuss Ronald C. Conant and W. Ross Ashby’s seminal work
“Every Good Regulator Theorem” [2] (EGRT):
“[The EGRT is]….a theorem is presented which shows, under
very broad conditions, that any regulator that is maximally both successful and
simple must be isomorphic with the system being regulated…….Making a model is
thus necessary.” [2]
The EGRT characterizes regulation with respect to cybernated
control systems. In the case of Ashby and Conant [3], the
EGRT developed within the context of several intersecting traditional fields.
These include algorithmics, information theory, systems theory, and behavioral
science. In such a context, models are exceedingly important. Given the
reliance of the EGRT concept on inference and propositional thinking, there is
an essential reliance on models. In fact, the EGRT exists at
such a high level of abstraction that even with a high degree of specification
may not be directly applicable in the real world [4]. However, there are
certain advantages of cybernetic modeling that make their cross-contextual
application useful.
Ashby's graphical formulation of the EGRT Theorem with original notation. COURTESY: [2].
II.
Background
Let us return to the notion of modeling as phenomenology.
Systems engage in modeling not simply to purposely regulate their environments,
but rather to reactively respond to input stimuli in a way that maintains
higher-level states [5]. This ability to model becomes part of their structure
at the most basic of levels, though it would be fair to say most modeling (in
the way we will use the word) is the result of cognitive processes. The constructivist might argue that such metacognitive dynamics [6] would influence one’s
proposed scientific model. Like Shakespeare’s Hamlet, however, the question of
whether or not to model (or be) is one of survival, whether that survival be
genetic or memetic. Rather than reviewing the proof step-by-step,
let’s discuss its potential significance in a variety of use-cases. In the
process, we will be transcending the traditional boundaries of autonomic,
‘choice’, or even cognitive.
Simply
put, the Every Good Regulator Theorem says that regulators operate on approximations (e.g. models) of the thing they are regulating. This
requires a mapping of the natural world to the model. While
one might consider the activities of encoding and translation to be inherently
cognitive, genomic systems also perform biological control functions in the
absence of cognition [7, 8]. In the biological control example, what matters is
not intent, but accuracy. Rather than an actively goal-oriented criterion, what we observe here is passively goal-oriented system output.
Accuracy of the approximated model influences the quality of regulation. Thus,
there need not be agency on the part of any single system component. Indeed, to
survive as a unit in an interrelated system, a regulating machine must
construct an interactive model that includes inputs, outputs, and feedback.
Let us consider a couple cases of regulatory dynamics, which
may be valuable in understanding the importance of this theorem. We can then
move on to what could this mean for both further theoretical development and
practical application. A good place to begin in cognitive science is game
theory [9]. One of the most simple, effective, and most explanatory strategies
in the Prisoners’ Dilemma game is the tit-for-tat strategy [10]. In this
2-player, 2x2 game, the tit-for-tat strategy is simple: ‘Do unto others as they
have done unto you’ after an initial good faith move of cooperation. The strategy
is simply to copy your opponent's behavior. If the opposing
agent cooperates, so does the tit-for-tat strategizing agent; if they defect,
the tit-for-tat strategist follows suit. The intended outcome of the strategy
is to move the exchange towards an equilibrium (though this is not the only
possible outcome, nor is the strategy perfect).
Of specific interest here is that the mechanics of the
strategy requires a model to be held in memory by the agent employing tit-for
tat (a 1-bit cooperate/defect model), regardless of the strategy employed by
the other agent (whether that be a more sophisticated maximizing strategy, or
random selections). While an economist might view this as free-riding behavior
by one of the two agents, the selection of tit-for-tat by both players can
produce a cooperative equilibrium, such as in the evolution of reciprocal
altruism in biological systems. The EGRT suggests that the greater the
memory for an agent, and the longer it has the opportunity to observe and
integrate the moves of its opponent, the greater its’ potential for effective
regulation.
Over time, this can lead to greater accuracy for the agent’s
cognitive model and a more stable equilibrium game outcome. Further, this
equilibrium state can be long-lasting, given extended memory capacity for more
detailed models, and may evolve towards ‘a conspiracy of doves’, within a game
of homo lupus homini. An
agent with a greater memory capacity can also employ more elaborate (or deeper)
strategies over time. This development of deeper strategies may also feedback
into modifying its model of the external world [11]. Overall, the capability to
regulate behavior of other players depends on the inferential and predictive
capacities of each player’s model: in a highly complex competitive game
environment, a good regulator has a superior model, or it will find itself
regulated by a competing agent in the game, especially as the behaviors get
more complex.
“The theorem has the interesting corollary that the living
brain, so far as it is to be successful and efficient as a regulator for
survival, must proceed, in learning, by the formation of a model (or models) of
its environment.” [2]
An example of a basic 2x2 payoff matrix characterizing the Prisoner's Dilemma.
COURTESY: "
Extortion in Prisoner's Dilemma", Blank on the Map blog, September 19 (2012).
III. Further
Considerations
Let us now consider a more complicated scenario where we
might be able to uncover the universal components of the EGRT phenomenology.
The context will be two people on a blind date (this can actually be a
complicated scenario). If one has been in one of these (terrifying) contexts,
then one can already see where we are going. The cognitive agents are
continually competing to increase the efficacy of their models of the other
agent, while also attempting to constrain the modeling of the other agent towards
a compact image they prefer. Although rarely implemented successfully, winning
strategies include accurately modeling the other actor and influencing the
state of their mental model. This can include both elaborate, multi-step
strategies, and simpler strategies, the complexity of which is does not
indicate their effectiveness. If the goal is a continuation of relations, the
acquisition and intentional obfuscation of information occurs at appropriate
times and in appropriate ways. Furthermore, this information has contextual
value. As in most scenarios involving imperfect or asymmetrical information
[12], your model must be superior to become the leader of the interaction [13],
and thus control of regulation.
Does regulation even require what we would call cognition?
This of course depends on our definition of cognition and regulation. However,
let us consider that a bacterium does not have a “cognitive” or mental model of
its environment, yet appears to have little trouble getting around and controlling
some aspects of its landscape. The similarities between chemotactic sensation
and mental models built upon multisensory stimuli serve as evidence for the
universal character of the EGRT. In fact, Heylighen [14] has proposed
that cybernetic regulation is a highly-generalized form of cognition. Yet do
thermostats or other mechanical systems possess anything approaching what we
consider cognition? While none of these has the cognitive capacity of a brain,
they do have information processing capabilities from their physical or
electronic structure, memory states, and crude models of how things ‘should’
be, towards which they regulate conditions. Non-cognitive systems possessing
these characteristics are obviously still capable of rudimentary communication,
control, decision making, and regulation, at least abstractly. We should also
expect some degree of continuity that crosses the boundary of the cognitive and
non-cognitive, since cognitive systems evolved from less intentional ones with
more rudimentary forms of behavioral control.
“...success in regulation implies that a sufficiently
similar model must have been built, whether it was done explicitly, or simply
developed as the regulator was improved.” [2]
IV.
Conclusion
Earlier, we had touched upon the history of scientific
discovery, and contextual model building. A scientific theory is simply a
model, and its value lies in its efficacy and repeatability (thus its’
trustworthiness and ability to aid in regulation). Theoretical models have
tended, historically, to shift from informal, conceptual models towards formal
mathematical ones (consider Comte’s Philosophy of Science). As a given model
acquires more data, and as those data create ever-more accurate model revisions
with higher fidelity. The overall capacity to aid regulation increases via
feedback. Thus, the model’s value to humans increases. However, as noted by the
example of ahead of their time thinking, scientific thought does not exist in a
vacuum, and the landscape conditions need to be aligned so that the model can
prove fruitful. Consider how we are witnessing an explosion in robust formal
mathematical and/or computer models either aiding or besting human cognitive
efforts [15, 16]. Informational revisions of the model often occur faster than
the landscape conditions change, so adaptive cross-contextual models may prove
more successful in dynamic situations, such as ones which are developed by
human thought and human cultural systems.
This
ability to cross the boundary between cognitive and non-cognitive with models
may challenge either our informal, colloquial conception of cognition or the
universality criterion of the formal EGRT. As both features of cognition and
more universal mechanisms, information processing, memory, communication, and
selection can occur without any kind of cognitive superstructure. Perhaps the
context of what we call “cognition” is too limiting. What about human cognition
then is truly universal, and what is unique to a certain set mechanisms and
representational models? For example, are models of so-called cellular
decision-making [17] an unduly anthropomorphic representation of cellular
differentiation and metabolism, or is it drawing upon a common set of universal
properties that can only be abstracted from the system by an appropriate model?
Rather than trying to solve this philosophical puzzle now, let us take leave to consider that a deep truth like the one perhaps contained within the formalism of the EGRT should make us question scientific knowledge in a manner akin to reconsidering our firmly-held beliefs. It should make us reconsider how well we understand the relationship between nature and our own conceptual models. In that, it kindles the same spark from which all great scientific theories alight: It leads us to more questions, new ways of thinking about things, and guides us towards more accurate, repeatable, and otherwise ‘good’ models.
“Now that we know that any regulator (if it conforms to the qualifications given) must model what it regulates, we can proceed to measure how efficiently the brain carries out this process. There can no longer be question about whether the brain models its environment: it must.” [2]
References:
[1] Kuhn, T.
Structure of Scientific Revolutions. University of Chicago Press (1962).
[2] Conant, R.C. and Ashby, W.R. Every good regulator of a system must be a model of that system. International Journal of Systems Science, 1(2), 89–97 (1970).
[3] Ashby, W.R.
Introduction to Cybernetics.
Chapman and Hall (1962).
[4] Fishwick, P. The
Role of Process Abstraction in Simulation. IEEE Transactions on Systems, Man,
and Cybernetics, 18(1), 18-39 (1988).
[5] Brooks, R.
Intelligence Without Representation. Artificial Intelligence, 47,
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[6] Kornell, N. Metacognition in Humans and Animals. Current
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[7] Ertel, A. and Tozeren, A. Human and mouse switch-like genes share
common transcriptional regulatory mechanisms for bimodality. BMC Genomics,
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[8] Gormley, M. and Tozeren, A. Expression profiles of switch-like genes
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[9] Gintis, H. Game
Theory Evolving. Princeton University Press (2000).
[10]
Imhof, L.A., Fudenberg, D., and Nowak, M.A.
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[11] Liberatore, P. and Schaerf, M. Belief Revision and Update: Complexity of
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[12] Rasmussen, E.
Games and Information: an introduction to game theory. Blackwell
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[13] Simaan, M. and Cruz, J.B. On the Stackleberg Strategy in Nonzero-Sum
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[14] Heylighen, F.
Principles of Systems and Cybernetics: an evolutionary perspective. CiteSeerX, doi:10.1.1.32.7220 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.7220 (1992).
[15] LeCun, Y., Bengio, Y., and Hinton, G. Deep Learning.
Nature, 521, 436-444 (2015).
[16] Ferrucci, D., Brown, E., Chu-Carroll, J., Fan, J.,
Gondek, D., Kalyanpur, A.A., Lally, A., Murdock, J.W., Nyberg, E., Prager, J.,
Schlaefer, N., and Welty, C. Building
Watson: an overview of the DeepQA project. AI Magazine, Fall (2010).
[17] Kobayashi, T.J., Kamimura, A. Theoretical aspects of cellular
decision-making and information-processing. Advances in Experimental Medicine
and Biology, 736, 275-291 (2012).
UPDATE (9/30): During the editorial process, Rob and I had a discussion about using the word "alight" (in the final paragraph). I was not sure about the correct word usage, but Rob assured me that it was being used correctly in this context. But to back this up even further (and to gratuitously insert an informatics Easter Egg), here is the Google Ngram history of "alight" usage since 1800.
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