Humberto Maturana, Francisca Varella and Heinz Von Foerster are all dead now. And I really thought their whimsical inquiry around human cognition may have died with them. And then I read this paper

It starts by saying ’Cognitive science is itself a cognitive activity. Yet, computational cognitive science tools are seldom used to study (limits of) cognitive scientists’ thinking.” ……I stopped reading here to check the authors and publication date, but it is recent and it wasn’t Heinz!!!! Feeling a little excited I read on….. ” Here, we do so using computational-level modeling and complexity analysis. We present an idealized formal model of a core inference problem faced by cognitive scientists: Given observations of a system’s behaviors, infer cognitive processes that could plausibly produce the behavior. We consider variants of this problem at different levels of explanation and prove that at each level, the inference problem is intractable, or even uncomputable. We discuss the implications for cognitive science.”

I haven’t read anything so wonderful since Heinz died in 2002. Granted I may have been looking in the wrong places and I thank the pandemic for revealing the nonsense in those places.

One of the really helpful things that Heinz spoke about was the difference between a trivial and a non trivial machine. “The trivial machine is all the rage among the followers of the notion of causality” he said in his conversations with Bernhard Poerksen.

The precondition for speaking about a cause and effect relationship, is that the rule of transformation is known. You have to know what makes the cause become the effect. In a simple machine there is an unconditional and unchangeable relationship between the input and output.

In medicine we have tried to turn snippets of the vast complexity of the non-trivial machine that is the human body into trivial sub unit machines. We have diagnoses that can be thought of as trivial machines and they are actually handled by doctors as if they are trivial machines. For example, diabetes can be diagnosed by a fasting blood glucose level. Above a certain reading it is diagnosed definitively, below a certain reading it can be excluded definitively and in between there’s another whole new world to turn glucose intolerance and insulin resistance into a trivial machine. The more unchangeable we make the relationship between treatment and effect the better the medicine.

It is such a satisfying field to work in if you like certainty and tidiness.

And so boring if you like uncertainty and messiness.

The medicalisation of human suffering has tried to follow the same path and as Heinz might say, it really is a horror show.

This lovely paper unpacks the horror and fictionally removes it and then, just as Heinz was prone to do, although possibly borrowed from Gregory Bateson’s metalogues, the authors use a fictional dialogue to explain what they mean. I’ll paste the metalogue herefor those who want the short version of the good bits of this lovely paper…….

“Unpacking the full implications of our results for cognitive science research practice is not easy, and we imagine that those reading this may have all kinds of questions, objections, or counter-intuitions. Given space limitations, we cannot possibly address them all. Instead, we unpack the implications of the results using a fictive dialogue, addressing the most likely concerns along the way. In the dialogue, Dr. Conjectura (denoted by C) plays the role of the skeptic who does not see the relevance of the results for their own practices. R relays our responses.
C: I appreciate you trying to help me achieve my research goals, but I can’t see how you are doing so. How are the theorems relevant to me? I am never in that ideal situation.
R: What ideal situation?
C: You formalized my inferential problems by assuming I have perfect, errorless observations. But my data are always incomplete and noisy.
R: The theorems show that in the ideal situation finding explanations consistent with the facts is not tractable. How can more uncertainty about the relevant facts make this problem easier? It seems it can only make it harder.
C: Fair. But you set an unrealistic standard for explanation. No explanation is perfect, but at best an approximation.
R: What do you mean exactly by ‘approximation’?
C: Well, for instance, explanations do not always need to be
consistent with all the data.
R: We need not assume such a high standard. Even if an explanation needs to be consistent with, say, half of the data,5 generating such ‘half-consistent’ explanations remains intractable.
C: Oh. That’s counter-intuitive.
R: I hope this takes away your worries about the idealizations we introduced? In general, many problems that are intractable to solve exactly are also hard to solve approximately, for various meanings of ‘approximation.’6
C: But I still do not understand. If you would just give me perfect, error-free observations, shouldn’t it be easy for me to infer the mechanism producing that data?
R: Explanation does not come for free. The number of possible mechanisms you could describe with language and mathematics is astronomical. Finding a description that pinpoints a mechanism consistent with the data is like finding a needle in a haystack: there exists no general efficient procedure for searching the space.
C: But I’ve already narrowed down the options. I’m looking only for explanations of a particular cognitive architecture type: [insert your favorite framework, e.g., ACT-R, Adaptive Toolbox, PDP, Subsumption-Architecture, etc.].
R: Our analyses encompass this view, as one option, by constraining the space of possible functions (the set F ) and algorithms (A), according to your architectural commit- ments. Even with such general a priori commitments, the space remains astronomically large for architectures with non-trivial computing power.
C: What do you mean by non-trivial?

R: Well, even if a system has few possible internal states and its behavior is fully governed by simple rules, generating explanations of its behaviors remains intractable.7 you think that human cognition is simpler than this?

C: No, likely more complex.
R: Then our intractability results apply to your work.
C: Are you saying my work is hopeless? I cannot hope to ever generate a satisfactory explanation for cognition?
R: I wouldn’t say hopeless. If you were to hit upon a satisfactory explanation through sheer luck, then you could recognize this.8
C: Sigh. That’s not much of a plan …
R: I don’t think you need to be any more discouraged by intractability than by the inherent uncertainty in your data, generalizations, and theory that you were already dealing with. But it does mean that your inferential work cannot be proceduralized in any efficient way. So best not try to make an algorithm, or an otherwise too-strict set of rules, to replace your scientific thinking.
C: Why not? What could go wrong?
R: You may fool yourself into thinking you are searching the whole space, while you are actually stuck in a small corner of an astronomical space outside your considera- tion. It may also cause you to assume that the system you are studying is simpler than you really believe, because otherwise your procedures would not converge efficiently.
C: Well if any procedure I might use will hold me back, what can I do?
R: I would endorse a meta-approach of not proceduraliz- ing. This is especially important now, as we increasingly focus on a too narrow set of methodological approaches in cognitive science.9 The best advice I can give pertains to the community: our only hope of understanding the mind is if the community allows for pluralism10 in approaches and an unbounded number of procedures different researchers may adopt.
C: Why unbounded?
R: Because it is known that intractable problems cannot
be solved by a fixed number of parallel procedures.11
C: But if we impose no limit on the number of approaches,
wouldn’t there be many bad ones?

R: Recognizing the need for and legitimacy of alternative approaches is a prerequisite to productive critique.12 So you can critique approaches on substantive grounds, but I must dissuade you from viewing any fixed (set of) proce- dure(s) as the right one and trying to convince others that they should adopt it too. I’ve noticed you grumbling about the too-subjective methods13 some of your colleagues are using, and I must encourage you to live and let live.14

……..And so, I humbly strive to live and let live……..