AGI as shibboleth, symbols [reacting to Jack Clark]

Jack Clark has a LONG tweet stream on AI policy. Though I don’t agree with every tweet – would anyone? – it’s worth at least a quick look. I want to comment on two of the tweets.

AGI as shibboleth, and beyond

Discussions about AGI tend to be pointless as no one has a precise definition of AGI, and most people have radically different definitions. In many ways, AGI feels more like a shibboleth used to understand if someone is in- or out-group wrt some issues.

— Jack Clark (@jackclarkSF) August 6, 2022

Has AGI ever been anything other than a shibboleth? I believe the term was coined in the 1990s because some researchers felt that AI had become stale and focused on specialized domains, so-called “narrow” AI. The phrase “artificial general intelligence” (AGI) was as a banner under which to revive the founding goal of AI, to construct the artificial equivalent of human intelligence.

What researchers actually construct are mechanisms. But no one knows how to specify a mechanism or set of mechanisms for AGI. Oh, sure, there’s the Universal Turing machine which can, in point of abstract theory, compute any computable function. It may be a mechanism, but the idea so abstract that it provides little to no guidance in the construction of computer systems.

AGI, like AI before it, is an abstract goal, a beacon, without a procedure that will lead to it. No matter how vigorously you chase over the surface of the earth for the North Star, you’re never going to get there. And so AGI simply functions as a shibboleth. If you want into the club, you have to pledge allegiance to AGI.

But you don’t need to pledge allegiance in order to construct interesting and even useful systems. So why invent this unreachable goal? Is it just to define a club?

Meanwhile I’ve written a paper in which I define the idea of an artificial mind. I begin by defining mind:

A MIND is a relational network of logic gates over the attractor landscape of a partitioned neural network. A partitioned network is one loosely divided into regions where the interaction within a region is (much) stronger than the interactions between regions. Each of these regions will have many basins of attraction. The relational network specifies relations between basins in different regions.

Note that the definition takes the form of specifying a mechanism involving logic gates and a neural network. Given that:

A NATURAL MIND is one where the substrate is the nervous system of a living animal.

And:

An ARTIFICIAL MIND is one where the substrate is inanimate matter engineered by humans to be a mind.

There are other definitions as well as some caveats and qualifications.

However, those definitions come after 50 pages of text and diagrams in which I lay out the mechanisms that support those definitions. The paper is primarily about the human brain, but one can imagine constructing artificial devices that meet those specifications. Now, whether those specifications are the right specifications, that’s open for discussion. However that discussion turns out, it is a discussion about mechanisms, not myths and magic.

The paper:

Relational Nets Over Attractors, A Primer: Part 1, Design for a Mind, Version 2, Working Paper, July 13, 2022, pp. 76, https://www.academia.edu/81911617/Relational_Nets_Over_Attractors_A_Primer_Part_1_Design_for_a_Mind

Ah, symbols

Here’s a twofer:

Richard Sutton's The Bitter Lesson is one of the best articulations of why huge chunks of research are destined to be irrelevant as a consequence of scale. This makes people super mad, but also seems like a real phenomenon.

— Jack Clark (@jackclarkSF) August 6, 2022

It's the first tweet that interests me, but let’s look Richard Sutton’s bitter lesson. Here’s his opening paragraph:

The biggest lesson that can be read from 70 years of AI research is that general methods that leverage computation are ultimately the most effective, and by a large margin. The ultimate reason for this is Moore's law, or rather its generalization of continued exponentially falling cost per unit of computation. Most AI research has been conducted as if the computation available to the agent were constant (in which case leveraging human knowledge would be one of the only ways to improve performance) but, over a slightly longer time than a typical research project, massively more computation inevitably becomes available. Seeking an improvement that makes a difference in the shorter term, researchers seek to leverage their human knowledge of the domain, but the only thing that matters in the long run is the leveraging of computation. These two need not run counter to each other, but in practice they tend to. Time spent on one is time not spent on the other. There are psychological commitments to investment in one approach or the other. And the human-knowledge approach tends to complicate methods in ways that make them less suited to taking advantage of general methods leveraging computation. There were many examples of AI researchers' belated learning of this bitter lesson, and it is instructive to review some of the most prominent.

Sutton then goes on to list domains where there has proven so: chess, Go, speech recognition, and computer vision. He then draws some conclusions, which I want to bracket.

Note, however, that Sutton talks of researchers seeking “to leverage their human knowledge of the domain.” Is that what’s going on symbolic AI? Perhaps in expert systems, which may have been the most pervasive practical result of GOFAI. But I don’t think that’s an accurate general characterization. That’s not what was going on in computational linguistics, for example, or in much of the work on knowledge representation. That research was based on the belief that much of human knowledge is inherently symbolic in character and therefore that we must create models that capture that symbolic character.

Why did those models collapse? I think there are several factors involved:

1. Combinatorial explosion: Symbolic systems tend to generate large numbers of alternative with little or no way of choosing among them.

2. Hand coding: Symbolic systems have to be painstakingly hand-coded, which takes time.

3. Too many models, difficult to choose among them: This exacerbates the hand-coding problem.

4. Common sense has proven elusive: But then it has proven elusive for deep learning as well.

Perhaps the first problem can be solved through more computing power, though exponential search can easily outstrip the addition of CPU cycles and memory. The third problem is one for science, and is, I believe, entangled with the fourth one. The second problem is inconvenient, but, alas, if hand-coding is necessary, then it’s necessary. But perhaps if we’re clever....

On the fourth one, here’s what I said in my GPT-3 paper:

A lot of common-sense reasoning takes place “close” to the physical world. I have come to believe, but will not here argue, that much of our basic (‘common sense’) knowledge of the physical world is grounded in analogue and quasi-analogue representations. This gives us the power to generate language about such matters on the fly. Old school symbolic machines did not have this capacity nor do current statistical models, such as GPT-3.

Thus the problem is not specific to symbolic systems. It is quite general. It’s not at all clear that we can deal with this problem without having robots out and about in the world. I note that the working paper I mentioned in the previous section, Relational Nets Over Attractors, is about constructing symbolic structures over quasi-analog representations, which, following the terminology of Saty Chary, I characterize as structured physical systems.

Let’s return to Sutton’s paper. Here’s his final paragraph:

The second general point to be learned from the bitter lesson is that the actual contents of minds are tremendously, irredeemably complex; we should stop trying to find simple ways to think about the contents of minds, such as simple ways to think about space, objects, multiple agents, or symmetries. All these are part of the arbitrary, intrinsically-complex, outside world. They are not what should be built in, as their complexity is endless; instead we should build in only the meta-methods that can find and capture this arbitrary complexity. Essential to these methods is that they can find good approximations, but the search for them should be by our methods, not by us. We want AI agents that can discover like we can, not which contain what we have discovered. Building in our discoveries only makes it harder to see how the discovering process can be done.

I’m hesitant to think of symbol systems as being “simple ways to think about the contents of minds.” That strikes me as rhetorical overkill. But Sutton is right about “the arbitrary, intrinsically-complex, outside world.” He says that “we should build in only the meta-methods that can find and capture this arbitrary complexity.” Well, sure, why not?

But are we doing that now? That’s not at all obvious to me. it seems likely to me that the DL community is hoping that they’ve discovered the metamethods, or will do so in the near future, and so we don’t have to think about what’s going on inside either human minds or the machines we’re building. Well, if human minds use symbols, and it seems all but self-evident that we do – if language isn’t a symbol system, what is? – then the current repertoire of DL methods is not up to the task.

What meta-methods are needed to detect patterns of symbolic meaning and construct those quasi-analog representations?

My GPT-3 paper:

GPT-3: Waterloo or Rubicon? Here be Dragons, Version 4.1, Working Paper, May 7, 2022, 38 pp., https://www.academia.edu/43787279/GPT_3_Waterloo_or_Rubicon_Here_be_Dragons_Version_4_1

Why Are Symbols So Useful to Us? [Relational Nets]

I’ve been participating in the discussion of Yann LeCun’s recent position paper, A Path Towards Autonomous Machine Intelligence. My first comment was a long one, Why are symbols important? Because they index cognitive space.

My opening paragraph:

I want to address the issue that your raise at the very end of your paper: Do We Need Symbols for Reasoning? I think we do. Why? 1) Symbols form an index over cognitive space that, 2) facilitates flexible (aka ‘random’) access to that space during complex reasoning.

My final paragraph is addressed to that second issue:

I really should say something about how symbols facilitate flexible access to cognition, but well, that’s tricky. Let me offer up a fake example that points in the direction I’m thinking. Imagine that you’ve arrived at a local maximum in your progression toward some goal but you’ve not yet reached the goal. How do you get unstuck? The problem is, of course, well known and extensively studied. Imagine that your local maximum has a name1, and that name1 is close to name2 of some other location in the space you are searching. That other location may or may not get you closer to the goal; you won’t know until you try. But it is easy to get to name2 and then see where that puts you in the search space. If you’re not better off, well, go back to name1 and try name3. And so forth. Symbol space indexes cognitive space and provides you with an ordering over cognitive space that is different from and somewhat independent of the gradients within cognitive space. It’s another way to move around. More than that, however, it provides you with ways of constructing abstract concepts, and that’s a vast, but poorly studied subject [1].

I really need to elaborate on that. Two discussions are needed: 1) one elaborates on the hill-climbing problem I mention, and 2) the other talks about syntax.

On the first, in an unindexed neural net all inference must proceed locally. In a space with billions and billions of dimensions, locality is obviously a very tricky matter. A local move on one dimension can easily put you in touch with locations on other dimensions which had been quite distant from your starting point. Still, an index constructed within the space gives you a set of vantage points which are outside the gradient structure of the network.

Syntax is one mechanism you have for moving around in index space. That’s what the syntax discussion needs to be about, how syntactic motion in index space can make it easier to move outside the local gradients in semantic space. But not here and now.

Nor is syntax the only mechanism available to you. You could move through a simple alphabetized list of word forms. Such a path would be arbitrary with respect to the gradients in semantic space, which is to say, such a path takes you outside semantic space.

What other mechanisms are there? How does rhyme in poetry figure into this?

More later.

[1] For some thoughts on various mechanisms for constructing abstract concepts, see William Benzon and David Hays, The Evolution of Cognition, Journal of Social and Biological Structures. 13(4): 297-320, 1990, https://www.academia.edu/243486/The_Evolution_of_Cognition

More Post-Publication Thoughts on the RNA Primer

This is a follow-up to a previous post: Some Post-Publication Thoughts on the RNA Primer [Design for a Mind]. Expect more follow-up posts. 

I’m talking about:

Relational Nets Over Attractors, A Primer: Part 1, Design for a Mind, https://www.academia.edu/81911617/Relational_Nets_Over_Attractors_A_Primer_Part_1_Design_for_a_Mind

I offer two sets thoughts, calibration, and paths ahead.

Calibration

By calibration I mean assessing, as well as I can, the signficance of the primer’s arguments and speculations in the current intellectual environment.

Gärdenfors’ levels of computation: In his 2000 book, Conceptual Spaces, Gärdenfors asserted that we need different kinds of computational processes for different different aspects of neural process:

On the symbolic level, searching, matching, of symbol strings, and rule following are central. On the subconceptual level, pattern recognition, pattern transformation, and dynamic adaptation of values are some examples of typical computational processes. And on the intermediate conceptual level, vector calculations, coordinate transformations, as well as other geometrical operations are in focus. Of course, one type of calculation can be simulated by one of the others (for example, by symbolic methods on a Turing machine). A point that is often forgotten, however, is that the simulations will, in general be computational more complex than the process that is simulated.

The primer outlines a scheme that involves all three levels, dynamical systems at the subconceptual level, Gärdenfors’ conceptual spaces at the conceptual level, and a relational network (over attractors) at the symbolic level. As far as I know, this is the only more or less comprehensive scheme that achieves that, though I have no reason to believe that others haven’t offered such proposals.

I note as well, that the arguments in the primer are quite different from those that Grace Lindsay considers in the final chapter of Models of the Mind, where she reviews three proposals for “grand unified theories” of the brain: Friston’s free energy principle, Hawkins, Thousand Brains Theory, and Tononi’s integrated information approach to consciousness. For what it’s worth I make no proposal about consciousness at all, though I do have thoughts about it, which are derived by a book published in 1973, Behavior: The Control of Perception by William Powers. Friston offers no specific proposals about how symbolic computation is implemented in the brain, nor, as far as I know, does Hawkins – I should note that I will be looking into his ideas about grid cells in the future.

Lindsay notes (pp. 360-361):

GUTs can be a slippery thing. To be grand and unifying, they must make simple claims about an incredibly complex object. Almost any statement about ‘the brain’ is guaranteed to have exceptions lurking somewhere. Therefore, making a GUT too grand means it won’t actually be able to explain much specific data. But, tie it too much to specific data and it’s no longer grand. Whether untestable, untested, or tested and failed, GUTs of the brain, in trying to explain too much, risk explaining nothing at all.

While this presents an uphill battle for GUT-seeking neuroscientists, it’s less of a challenge in physics. The reason for this difference may be simple: evolution. Nervous systems evolved over eons to suit the needs of a series of specific animals in specific locations facing specific challenges. When studying such a product of natural selection, scientists aren’t entitled to simplicity. Biology took whatever route it needed to create functioning organisms, without regard to how understandable any part of them would be. It should be no surprise, then, to find that the brain is a mere hodgepodge of different components and mechanisms. That’s all it needs to be to function. In total, there is no guarantee – and maybe not even any compelling reasons to expect – that the brain can be described by simple laws.

I agree. Whatever I’m proposing, it is not a simple law. Tt presupposes all the messiness of a brain that is “a mere hodgepodge of different components and mechanisms.” It is a technique for constructing another mechanism.

Christmas Tree Lights Analogy: Here I want to emphasize how very difficult understanding the brain has proven to be. It will remain so for the forseeable future. I’m calling on a post I did in 2017, A Useful Metaphor: 1000 lights on a string, and a handful are busted.

In line with that post, imagine that the problem of fully understanding the brain, whatever that means takes the form of a string of serial-wired Christmas Tree lights, 10,000 of them. To consider the problem solved all the lights have to be good and the string lit. Let us say that in 1900 the string is dark. Since then, say, 3472 bad bulbs have been replaced with good ones. Since we don’t know how many bad lights were in the string in 1900 we don’t know how many lights have yet to be replaced.

Let us say that, in the course of writing that primer, I’ve replaced 10 bad bulbs with 10 good ones. If 6518 had been good in 1900, then we’d have had 9990 good bulbs before I wrote the primer. With the primer the last 10 bad bulbs would have been replaced and SHAZAM! we now understand the brain.

That obviously didn’t happen. I take it as obvious that some of the bad bulbs had been replaced by 1900 since the study of the brain goes back farther than that. If there had been, say, 1519 good bulbs in 1900, then there would have been 4991 good bulbs before my paper (1519 in 1900 + 3472 since then). My 10 puts us past 5000 to 5001. We’re now more than halfway to understanding the brain. 

Play around with the numbers as you will, my point is that we have a lot more to do to understand the “hodgepodge of different components and mechanisms” that is the brain.

Will we be all the way in another century? Who knows. 

For extra credit: What if the number of bulbs in the string isn’t 10,000, but 100,000? All analogies have their limitations. In what way is this one limited by the need to posit a specific number of light bulbs in the string?

“Kubla Khan”: This is tricky and, come to think of it, deserves a post of its own. But, yes, I do think that work on the primer advanced my thinking about “Kubla Khan” by putting Gärdenfors’ idea of conceptual spaces in the forefront of my mind, which hadn’t been the case before in thinking about the poem. I’m now in a position to think about the poem as a structure of temporary conceptual spaces, in Gärdenfors’ sense, where the various sections of the poem are characterized by various dimensions. [As an exercise, you might want to plug this into my most recent paper on “Kubla Khan,” Symbols and Nets: Calculating Meaning in "Kubla Khan.")

But let’s save that for another post. For this I just note that, as I have explained in various places (e.g. Into Lévi-Strauss and Out Through “Kubla Khan”), my interest in “Kubla Khan” that has been a major component of my interest in the computational view of mind and its realization in the brain. “Kubla Khan” is the touchstone by which I judge all else...sorta’. We’re making progress.

Paths Ahead

How do I understand some of the implications of the primer? Here’s some quick and dirty notes.

Understanding the brain: Here the issue is: How do we go from my speculative account to empirical evidence? One route, but certainly not the only one, is to start looking at recent evidence for the semantic specialization of the neocortex. I cited some of this work in the primer, but did not attempt to relate it to the relational network notation in a detailed way. That must be done, but I’m not the one to do it. Or, rather, I cannot do it alone. For one thing, my knowledge of neocortical anatomy isn’t up to the job. While that can be remedied, that’s not enough. The task needs the participation of bench scientists, investigators who’ve done the kind of work that I’ve cited, as they’re the ones with a sensitive understanding of the empirical results.

Long-Term “pure” AI: The primer says clearly that symbolic computation is central to human cognition. But it also says that it is derived from, implemented in, neural nets. That is the position the Lecun argued in his recent paper with Jacob Browning, What AI Can Tell Us About Intelligence. What does that imply about future research?

I think it means new architectures, new architectures for learning and for inference. What those might be....

Near and Mid-term applied AI: I think that’s as it has always been: If you have to solve a problem, now, use the best tool you can find. AI systems built on the kind of model suggested by the primer are not currently available, to my knowledge. If you need symbolic computation as well as a neural network, pick the best hybrid architecture you can find.

Some Post-Publication Thoughts on the RNA Primer [Design for a Mind]

I’m talking about:

Relational Nets Over Attractors, A Primer: Part 1, Design for a Mind, https://www.academia.edu/81911617/Relational_Nets_Over_Attractors_A_Primer_Part_1_Design_for_a_Mind

While I’ve got some ideas about what might go into Part 2, some of which I’ve mentioned in a Coda to Part 1, I have no definite plans to go to work on it.

What I’ve been thinking about is the scope of the piece. It’s not the first time I’ve written seriously about the brain. I’ve got a good bit of material in my book on music, Beethoven’s Anvil, and in several articles. The most important of those, by far, is the one David Hays and I published in 1988, Principles and Development of Natural Intelligence. That article is about the whole brain, developing five principles and relating them to: behavior, computational principle, neuroanatomy, phylogeny, and ontogeny.

I bring that up three times in the primer. The first time is in the introduction, where I introduce Mirian Yevick’s work, which is the basis of our fourth principle (figural). Then I mention it in discussing language, the fifth principle (indexing). Finally I introduce the modal principle (first) while discussing types of minds in order to make that point that, while the primer is about the cortex, it does not assume that the cortex is somehow isolated or autonomous. On the contrary, activity in the cortex is affected by the whole brain, with the modal principle being the deepest example. For it is implemented in the reticular formation, which is the phylogenetically oldest part of the brain. And yet it affects, in a broad way, what areas of the cortex are active during any given stretch of time.

So, the paper implies the action of the whole brain, not just the cortex. What does the primer add to what Hays and I did in Principles? It provides a way of thinking about how the cortex implements highly differentiated cognitive processes and, in particular, natural language semantics. And natural language semantics is the lever through which the mind develops abstract concepts and elaborates on them over the long-haul of cultural evolution. That’s what’s new in the primer.

And that, it seems to me, “closes the space” on how the mind works, at least informally. The burden of working out how abstract concepts are developed will not, of course, fall directly on neural analysis. We’ll need other mechanisms for that. That’s why I introduced the relational network notation. That’s how we’re going to have to understand the mind’s construction of concepts. There is the logic inherent in the notation itself, and there are the implications of that logic for neurodynamics.

On the one hand we have global neurodynamics, something Freeman talked about. But then we have the local neurodynamics of the cortical neurofunctional areas (NFAs). I am assuming that the the dynamics of each NFA have a measure of autonomy from both global dynamics and from adjacent NFAs. Otherwise it makes no sense to select them as units for analysis. Sure, each cortical NFA receives inputs from other cortical NFAs and sends outputs to them (to and from subcortical NFAs as well). But the activity with an NFA is dominated by signals passed between neurons within it.

And then we have grand mal epileptic seizures, which often start locally in one hemisphere, but then engulf the entire brain. Local autonomy is lost. But then so is consciousness.

More later.

Relational Nets Over Attractors, A Primer: Part 1, Design for a Mind

New working paper. Title above, links, abstract, table of contents, preface, and appendix below.

Academia.edu: https://www.academia.edu/81911617/Relational_Nets_Over_Attractors_A_Primer_Part_1_Design_for_a_Mind
SSRN: https://ssrn.com/abstract=4141479
ResearchGate: https://www.researchgate.net/publication/361421487_Relational_Nets_Over_Attractors_A_Primer_Part_1_Design_for_a_Mind

Abstract: Miriam Yevick’s 1975 holographic logic suggests we need both symbols and networks to model the mind. I explore that premise by adapting Sydney Lamb’s relational network notation to represent a logical structure over basins of attraction in a collection of attractor landscapes, each belonging to a different neurofunctional area (NFA) of the cortex. Peter Gärdenfors provides the idea of a conceptual space, a low dimensional projection of the high-dimensional phase space of a NFA. Vygotsky’s account of language acquisition and internalization is used to show how the mind is indexed. We then define a MIND as a relational network of logic gates over the attractor landscape of a neural network loosely partitioned into many NFAs. An INDEXED MIND consists of a GENERAL network and an INDEXING network adjacent to and recursively linked to it. A NATURAL MIND is one where the substrate is the nervous system of a living animal. An ARTIFICIAL MIND is one where the substrate is inanimate matter engineered by humans to be a mind; it becomes AUTONOMOUS when it is able to purchase its compute with services rendered.

Preface: Notation as Speculative Engineering 2
1. How it Began: Symbols, Holograms, and Diagrams 3
2. A Semantic Net vs. A Relational Network over Attractors 12
3. Simple Animals, Attractor Landscapes, and Lamb’s Notation 18
4. Some Basic Constructions 27
5. Language, Inner Speech, and Thought 38
6. Kinds of Minds 49
Coda: Topics for Further Exploration 62
Appendix: The Idea in 14 Statements 67
References 69

Preface: Notation as Speculative Engineering

I write this paper as a kind of philosopher, a speculative engineer. I am an engineer because I am curious about how to design and build things. I speculate because that is the only way to enact what I attempt in this paper. W. Ross Ashby wrote Design for a Brain. I write in that spirit, but my topic is a bit different: design for a mind.

I propose a diagrammatic notation convention as a crucial design tool. It is a convention that relates patches of cortical tissue with a classical model derived from mid-century computational lingistics. My aim is to provide a way of thinking about how a meshwork of neurons can give rise to symbolic thought. Think of the notation as a collection of Lego pieces for a mind.

There’s the bricks and mortar, and there’s the whole building. You can’t create a building simply by piling up bricks and morter. You have to design it first. That’s what this is paper about, the tools you need to design the building.

As such it is a simplification, an idealization. I have had to leave much out of account. Setting aside the things I do not know, and the things I’d don’t know that I do not know, incorporating all that I do know – not to mention things I but know about, more or less, would have made it impossible for me to do much of anything at all. Organization is the problem, gathering these many and various things, these ideas, facts, models, observations, what have you, gathering them together and laying them out in a coherent order, that is the problem.

It is my belief that by pushing through, if not to completion, at least to some kind of closure is the best way bring order to this material. Get it one place where we can see and examine it. Then and only then does it make sense to ferret out the many things I have missed or gotten wrong. In this case, closure means an explicit definition of what a mind is. That in turn leads to definitions of artificial and natural minds, and autonomous artificial minds.

Are those definitions correct? They may be useful without being correct. They are best thought of as being provisional, a means to deeper conceputalization and more refined definitions. The only way to measure their limitations is to try them out and see what becomes visible.

Appendix: The Idea in 14 Statements

1. I assume that the cortex is organized into NeuroFunctional Areas (NFAs), each of which has its own characteristic pattern of inputs and outputs. It does not appear that NFAs are sharply distinct from one another. Their boundaries can be revised – think of cerebral plasticity.

2. I assume that the operations of each NFA are those of complex dynamics. I have been influenced by Walter Freeman (1999, 2000) in this.

3. A low dimensional projection of each the phase space for each NFA can be modeled by a conceptual space as outlined by Peter Gärdenfors.

4. Each NFA has its own attractor landscape. A primary NFA is one driven primarily by subcortical inputs. Then we have secondary and tertiary NFAs, which involve a mixture of cortical and subcortical inputs. (I am thinking of the standard notions of primary, secondary, and tertiary cortex.)

5. Interaction between NFAs can be approximated by a Relational Network over Attractors (RNA), which is a relational network defined over basins in multiple linked attractor landscapes.

6. The RNA network employs a notation developed by Sydney Lamb (1961) in which the nodes are logical operators, AND & OR, while ‘content’ of the network is carried on the arcs.

7. Each arc corresponds to a basin of attraction in some attractor landscape.

8. The output of a source NFA is ‘governed’ by an OR relationship (actually exclusive OR, XOR) over its basins. Only one basin can be active at a time. [Provision needs to be made for the situation in which no basin is entered.]

9. Inputs to a basin in a target NFA are regulated by an AND relationship over outputs from source NFAs.

10. Symbolic computation arises with the advent of language. It adds new primary attractor landscapes (for phonetics & phonology, and morphology) and extends the existing RNA. The overall RNA is roughly divided into a general network and a lingistic network.

11. Word forms (signifiers) exist as basins in the linguistic network. A word form whose meaning is given by physical phenomena are coupled with an attractor basin (signifier) in the general network. This linkage yields a symbol (or sign). Word forms are said to index the general RNA.

12. Not all word forms are directly defined in that way. Some are defined by cognitive metaphor (Lakoff and Johnson 1981). Others are defined by metalingual definition (David Hays 1972). I assume there are other forms of definition as well (see e.g. Benzon and Hays 1990). It is not clear to me how we are to handle these forms.

13. Words can be said to index the general RNA (Benzon & Hays 1988b).

14. The common-sense concept of thinking refers to the process by which one uses indices to move through the general RNA to 1) add new attractors to some landscape, and 2) construct new patterns over attractors, new one or existing ones.

Miriam Yevick on why both symbols and networks are necessary for artificial minds

Miriam Yevick was a mathematician who corresponded with physicist David Bohm in the 1950s and went on to publish a very interesting article on the formal structure of perception and cognition: Holographic or fourier logic [1]. The abstract:

A tentative model of a system whose objects are patterns on transparencies and whose primitive operations are those of holography is presented. A formalism is developed in which a variety of operations is expressed in terms of two primitives: recording the hologram and filtering. Some elements of a holographic algebra of sets are given. Some distinctive concepts of a holographic logic are examined, such as holographic identity, equality, contaminent and “association”. It is argued that a logic in which objects are defined by their “associations” is more akin to visual apprehension than description in terms of sequential strings of symbols.

In 1978 she commented on an article by John Haugeland, The nature and plausibility of Cognitivism, and spells out the implications of her idea for cognition ([2] p. 253):

The author here points out a distinction between two modes of understanding our environment: the first identifies objects by quasi-linguistic representations; the other apprehends objects by means of nonarticulate skills. This dichotomy; which is undoubtedly related to the complexity of the concrete objects to be recognized or manipulated, was projected as follows by von Neumann (1966, pp. 51-54): “certain objects are such that their description is more complex than the object itself.”

We can explicate this proposition on a theoretical level in the domain of optical patterns. (See Yevick, 1975op. cit.). Such patterns or objects are thin, white regions on a black background. These can be simple (regular), like the outlines of rectangles; or complex, like the outlines of Chinese characters or random-like motions. The following holds true: a complex object requires a long (sequential, quasi-linguistic) description but yields a sharp recognition (auto-correlation) spot under holographic filtering; hence it is identified most readily by holographic recognition, or holistically. A simple object requires a short (quasi-linguistic) description but yields a diffuse recognition spot; hence it is identified most readily by quasi-linguistic representation or description.

Description and holographic recognition thus appear as two (complementary) modes of identifying an object: the more complex the object, the longer its description and the sharper its auto-correlation spot, and vice versa. The more complex the physiognomy of a person, the more unique, and hence sharper, its identity and ease of recall; the more simple, the more common and hence “unidentifiable.” Perfect holographic recognition obtains for a totally “random object”, that is, one with an infinitely long description; for a perfectly sharp point the opposite is true.

Suppose that one is given a store of objects with which one is familiar, a holographic recognition device, and a quasi-linguistic mode of representation; one is then presented with an arbitrary object to be “identified.” An approximate match is obtained either by producing a description of acceptable length or by holographic recognition of a subset of similar (associated) objects from the store. The mode of identification that will be more appropriate then depends on the complexity of the unknown object. If it is simple, we "know" it by a short linguistic description; if it is complex, by the "associations” it evokes.

If we consider that both of these modes of identification enter into our mental processes, we might speculate that there is a constant movement (a shifting across boundaries) from one mode to the other: the compacting into one unit of the description of a scene, event, and so forth that has become familiar to us, and the analysis of such into its parts by description. Mastery, skill and holistic grasp of some aspect of the world are attained when this object becomes identifiable as one whole complex unit; new rational knowledge is derived when the arbitrary complex object apprehended is analytically described.

She goes on to point out that the same distinction holds in the domain of abstract objects (254):

A careful scrutiny of the various presentations leading to Godel’s result reveals that the “abstract objects” that are the entities under discussion in a formal system actually occur in two modes: as objects identified by bold- faced pictures or shapes or marks on paper, and as objects generated recur- sively from certain zero-entities, recognized in some way by their rank, that is, the first of a certain list (Quine, 1950); an expression of length one (Shoenfield, 1967); a sequence of one symbol (Godel, Pred. 15 in van Heijenoort, 1970; Mendelson, 1964); entities generated by a successor operation on a pair of arguments (Kleene, 1970, pp. 247, 251-252; Pred. Dn 1 should read: y≍0). We recognize abstract objects of the first kind byosten- sion (holistically); those of the second kind are recognized by sequential generation or description. But whereas in the case of concrete objects discussed above, it is possible to assert that these two modes of (approximate) identification refer to the same object, the abstract objects have no identity recognizable beyond their formal mode of representation or generation. Thus, going beyond Haugeland’s remark and using the word “mode” for his “dimension,” we note that the mixing of modes is already present in the argu- ment that yields Godel’s undecidability result: it rests essentially on the identification of abstract objects (“formal numerals”) recognized in two dis- connected modes. The well-known confusion between Mention and Use reappears here as a confusion between showing and telling or display and enumeration, that is, as a mixing of dimensions.

The following quotation from Freudenthal (1960), who attempted to construct a language, “Lincos,” aimed at cosmic communication, clearly projects the irreducible duality: “We have agreed to abstain as much as possible from showing (concrete things or images of concrete things) but we cannot entirely abstain from it. Our first message will show numerals as an in– troduction to mathematics. Such an ostensive numeral, meaning the natural number n, consists of n peeps with regular intervals; from the context the reader will conclude that it aims aishowing just the natural number n.”

For minds to communicate or to do formal mathematics, they must possess both a quasi-linguistic (sequential, rational) and a holistic (ostensive, associative) dimension.

This has an obvious bearing on the current controversy in artificial intelligence between partisans of a pure neural network approach and those who argue that symbols are necessary as well. Neural networks exemplify Holographic or fourier logic, literally so in the case of convolutional neural networks. But symbolic reasoning is necessary as well. They apply to different classes of objects.

David Hays and I gave Yevick’s work an important place in our papers on the natural intelligence [3] and metaphor [4].

References

[1] Yevick, Miriam Lipschitz, Holographic or fourier logic, Pattern Recognition, Volume 7, Issue 4, December 1975, Pages 197-213, https://doi.org/10.1017/S0140525X00074458

[2] Yevick, Miriam L., The two modes of identifying objects: descriptive and holistic for concrete objects; recursive and ostensive for abstract objects. Brain and Behavioral Sciences, 1(2), 253-254. 1978, doi.org/10.1017/S0140525X00074148

[3] William Benzon and David Hays, Principles and Development of Natural Intelligence, Journal of Social and Biological Structures, Vol. 11, No. 8, July 1988, 293-322, https://doi.org/10.1016/0140-1750(88)90061-9

[4] William Benzon and David Hays, Metaphor, Recognition, and Neural Process, The American Journal of Semiotics, Vol. 5, No. 1 (1987), 59-80, https://www.academia.edu/238608/Metaphor_Recognition_and_Neural_Process.

Eureka! Have I Found It? How to Model the Mind, that Is. [Symbols and Nets]

Since roughly the last week in April, when I applied for an Emergent Ventures grant (which was quickly, but politely, turned down), I have been working hard on revising and updating work on a system of notation which I sketched out in 2003 and posted to the web in 2010, 2011. I am referring to what I then called called an Attractor Network, but now call a Relational Network over Attractors (RNA) because I found out that neuroscientists already talk about attractor networks, which are not the same as what I’ve got in mind. The neuroscientists are referring to a network of neurons whose dynamics tend toward an attractor. I am referring to a network that specifies relationships between a very large number of attractors (hence, it is constructed over them).

Anyhow, by the time Emergent Ventures had turned me down, I was committed to the project, which has gone well so far. I had no particular expectations, just a general direction. I’ve been looking, and I’ve found some interesting things, encouraging things. Or, if you will, I’ve been puttering around, assembling bits and pieces here and there, and an interesting structure has begun to emerge.

Lamb Notation

The idea has been to develop a new notation for representing semantic structures in network form. Actually, the notation is not new; it had already been developed by Sydney Lamb in the 1960s. He developed it to model the structures of a stratificational grammer. I’ve been adapting it to model semantics.

I am doing that by assuming that the cerebral cortex is loosely divided into functionally distinct regions which I call neurofunctional areas (NFAs). The activity of these NFAs is to be modeled by complex dynamics (Walter Freeman) and a low-dimensional projection of each NFA phase space can be modeled by a conceptual space (Peter Gärdenfors). Each NFA is thus characterized by an attractor landscape.

The RNA (relational net over attractors) is a network where the nodes are logical operators (AND, OR) and the edges are basins of attraction in the NFA attractor landscapes. This is not the place to explain what that actually means, but I can give you a taste by showing you three pictures.

This is a simple semantic structure expressed in a “classical” notation from the 1970s:

It depicts the fact that both beagles and collies are varieties (VAR) of dog. The light gray nodes at the bottom are perceptual schemas, while the dark gray nodes at the right are lexemes. The white nodes are cognitive.

Here’s a fragment of one of Lamb’s networks:

The triangular nodes are AND while the brackets (both pointing up and down) are OR. The content is carried on the edges.

This RNA network takes the information expressed in the semantic network and expresses it using AND and OR nodes.

I am not even going to attempt to explain just how that works. Suffice it to say that it seems a bit more visually complicated than the old notation and thus harder to read. It also expresses more informatation. Those AND and OR nodes specify processing while no processing is specified in the classical diagram.

I am finding it more demanding to work with. In part that is because I haven’t drawn nearly so many RNA diagrams, perhaps 100 or so as compared to 1000s. But also, in drawing RNAs I have to imagine these structures being somehow laid out on a sheet of cortex, which is tricky. It would be even trickier if I were working with data about the regional functional anatomy of the cortex at my elbow, trying to figure just where each NFA is on the cortical sheet. Eventually, that will have to be done, but right now I’m satisfied just to draw some diagrams.

Crazy and Not So Crazy

The fact that I intend these diagrams as a very abstract sketch of functional cortical anatomy means that they have fairly direct empirical implications that the old diagrams never had. Of course, we were always committed to the view that we were figuring out how the human mind worked and so  eventually someone would have to figure out where and how those structures were implemented in the brain. Well, now is eventually and these new diagrams are a tool for figuring out the where and how.

And that, I suppose, is a crazy assertion. Everyone who knows anything knows that the brain is fiercely complicated and we’re never going to figure it out in a million years but anyhow we have to a waste a billion euros building a damned brain model that tells us a bit more than diddly squat, but not a whole hell of a lot more. But then what I’m doing costs nothing more than my time. Excuse the rant.

As I said, it’s crazy of me to propose a way of thinking about how high-level cognitive processes are organized in the brain. But I’m only proposing, and I’m doing it by offering a conceptual tool, a notation, that helps us think about the problem in a new way. I don’t expect that the constructions I propose are correct. I ask only that they are coherent enough to lead us to better ones.

There’s one further thing and this is not so crazy: This notation, in conjunction with 1) my assertation that it is about complex cortical dynamics, and 2) and Lev Vygotsky’s account of language development, gives us a new way of thinking about a debate that is currently blazing away in a small region of the internet: How do we model the mind, neural vectors, symbols, or both? If both, how? I am opting for both and making a fairly specific proposal about how the human brain does it. The question then becomes: What will it take to craft an artificial device that does it? If my proposal ends up taking 14K or 15K words and maybe 30 diagrams, well it deals with a very a complicated problem.

Here is the draft introduction, Symbols, holograms, and diagrams, to the working paper. With that, I’ll leave you with a brief sketch of my proposal.

The Model in 14 Propositions

1. I assume that the cortex is organized into NeuroFunctional Areas (NFAs), each of which has its own characteristic pattern of inputs and outputs. As far as I can tell, these NFAs are not sharply distinct from one another. The boundaries can be revised – think of cerebral plasticity.

2. I assume that the operations of each NFA are those of complex dynamics. I have been influenced by Walter Freeman in this.)

3. A low dimensional projection of each NFA phase space can be modeled by a conceptual space as outlined by Peter Gärdenfors.

4. Each NFA has its own attractor landscape. A primary NFA is one driven primarily by subcortical inputs. Then we have secondary and tertiary NFAs, which involve a mixture of cortical and subcortical inputs. (I’m thinking of the standard notions of primary, secondary, and tertiary cortex.)

5. Interaction between NFAs is defined by a Relational Network over Attractors (RNA), which is a relational network defined over basins in multiple linked attractor landscapes.

6. The RNA network employs a notation developed by Sydney Lamb in which the nodes are logical operators, AND & OR, while ‘content’ of the network is carried on the arcs. [REF/LINK to his paper.]

7. Each arc corresponds to a basin of attraction in some attractor landscape.

8. The output of a source NFA is ‘governed’ by an OR relationship (actually exclusive OR, XOR) over its basins. Only one basin can be active at a time. [Provision needs to be made for the situation in which no basin is entered.]

9. Inputs to a basin in a target NFA are regulated by an AND relationship over outputs from source NFAs.

10. Symbolic computation arises with the advent of language. It adds new primary attractor landscapes (phonetics & phonology, morphology?) and extends the existing RNA. Thus overall RNA is roughly divided into a general network and a lingistic network.

11. Word forms (signifiers) exist as basins in the linguistic network. A word form whose meaning is given by physical phenomena are coupled with an attractor basin (signifier) in the general network. This linkage yields a symbol (or sign). Word forms are said to index the general RNA.

12. Not all word forms are defined in that way. Some are defined by cognitive metaphor (Lakoff and Johnson). Others are defined by metalingual definition (David Hays). I assume there are other forms of definition as well (see e.g. Benzon and Hays 1990). It is not clear to me how we are to handle these forms.

13. Words can be said to index the general RNA (Benzon & Hays 1988).

14. The common-sense concept of thinking refers to the process by which one uses indices to move through the general RNA to 1) add new attractors to some landscape, and 2) construct new patterns over attractors, new or existing.

Symbols, holograms, and diagrams

I am currently revising and updating some work I did over a decade ago. The new document is tentatively titled: Relational Nets Over Attractors, A Primer: Part 1, Basics. This a draft of the introduction.

Introduction: Symbols, holograms, and diagrams

As I have indicated in the Preface, this primer is about a notational convention. I adopted the convention to solve a problem. This introduction is about the problem I am trying to solve.

I could say that I’m trying to understand how the brain works. That is true, but it is too broad. It would be better to say that I am trying to understand how a mind is implemented in the brain. That word, “implemented,” is carefully chosen. Though the word is common enough, I take it from computing, where one talks of implementing a program in a particular high-level programming language. One may also talk of implementing a high-level language in the low-level language for a particular processor. Higher levels are implemented in lower levels.

While some would talk of the mind as emerging from the operations of the brain, I prefer to look at it from the other direction; the mind is implemented in the brain. Beyond that I think it is best to see how this problem developed in my early intellectual life.

I studied ‘classical’ symbolic semantics with the late David Hays in the Department of Linguistics at Bufflo back in the mid-1970s. One day we were discussing a diagram that looked something like Figure 1:

Figure 1: Birds have parts.

It is a simple diagram, asserting that the typical bird consists of various parts (CMP = component), in this case, head, body, left wing, right wing, and tail. If you wish, you can imagine other components as well, two legs, and maybe a neck, a beak, and so forth. We were discussing the problem presented by having to account for a bird’s feathers:

Figure 2: Feathers.

Figure 2 shows a number of feathers for the left wing. Surely the left wing has more than eight feathers, no? How many? What about the feathers for the right wing, for the body, the head, the tail, the legs? Moreover, feathers are not primitive parts; they have shafts to which barbs are attached. Do we have to represent all those as well?

Perhaps you are thinking, that can’t possibly be right. We don’t think about all those hundreds if not thousands of parts for each and every bird. No, we don’t. But the logic inherent in this kind of symbolic representation says that we have to get the parts list right.

I had an idea. And that time we have been studying a book by William Powers, Behavior: The Control of Perception. He argued that the mind/brain employed a fundamentally analog, rather than digital, representation of the world. I suggested something like this:

Figure 3: Bird in perception and cognition.

Figure 3 shows a cognitive system where the typical bird is represented by a node, just as in Figures 1 and 2. That node is linked to a perceptual system that is, following Powers, analog in nature. The system contains a sensorimotor schema that is analog in character. It is connected to the cognitive node with a representation (REP) arc.

If you wish, we can then add some further structure to the cognitive depiction along with some other adjustments, as we see in Figure 4:

Figure 4: Parts of a bird in cognition and perception.

In cognition we see the same structure we had in Figure 1. Each node in that structure is connected to the appropriate part of the sensorimotor schema by a representation arc. We can think of the cognitive structure as digital and symbolic in character where the perceptual scheme has a quasi-analog character, which we’ll get to shortly. The bird itself is in the external world.

What of all the feathers, and their parts? you ask. They’re in the perceptual representation, all you have to do is look closely.

Well, that’s not quite correct. All the parts are there in the physical bird, and we are free to examine it at whatever level of detail we choose. Hunters, taxidermists, butchers, naturalists, aritists and illustrators will choose a relatively high level of detai. The rest of us can be satisfied by a crude representation.

And thus we had proposed a solution to what would become known as the symbol grounding problem, though I do not believe the term was known to us at the time. The cognitive system is digital and symbolic in character and is linked to a perceptual system that is analog in character. Given that, the cognitive system need not be burdened with accounting for all the detail inherent in the world. The perceptual system can handle much of it. But it need not handle all of it, only enough to distinguish between one object and another. If we only need to tell the difference between birds and mammals, that’s not much detail at all. If we need to distinguish between one kind of bird and another, between robins and starlings, eagles and owls, and so forth, then more detail is required. Most of the differentiating detail will be in the respective sensorimotor schemas, only some of it need be represented in cognition. Unless, of course, you are one of those people with a particularly strong interest in birds. Then you will develop rich sensorimotor schemas and reconstruct them in cognition at a high level of detail. While you may well count every feather in a wing or a tail, you are unlikely to count every barb in every feather. But you will know they are there and have the capacity to count them if it becomes necessary.

Hays went on to develop a model of cognition – Cognitive Structures (1981) – built on basic on this basic idea: Cognition is grounded in an analog perceptual (and motor) system that is in direct contact with the world. And some years after that he and I became curious about the brain and wrote a paper outlining that curiosity, “Principles and Development of Natural Intelligence” (1988). We suggested five principles. We called the fourth one the figural principle introduced the work of the mathematician Miriam Yevick in the course explicating it (pp. XX-XX):

The figural principle concerns the relationship between Gestalt or analogue process in neural schemas and propositional or digital processes. In our view, both are necessary; the figural principle concerns the relationship between the two types of process. The best way to begin is to consider Miriam Yevick's work (1975, 1978) on the relationship between ‘descriptive and holistic’ (analogue) and ‘recursive and ostensive’ (digital) processes in representation.

The critical relationship is that between the complexity of the object and the complexity of the representation needed to ensure specific identification. If the object is simple, e.g. a square, a circle, a cross, a simple propositional schema will yield a sharp identification, while a relatively complex Gestalt schema will be required for an equivalently good identification (see Fig. 5). Conversely, if the object is complex, e.g. a Chinese ideogram, a face, a relatively simple Gestalt (Yevick used Fourier transforms) will yield a sharp identification, while an equivalently precise propositional schema will be more complex than the object it represents. Finally, we have

Figure 5: Yevick's law. The curves indicate the level of representational complexity required for a good identification.

those objects which fall in the middle region of Figure 5, objects that have no particularly simple description by either Gestalt or propositional methods and instead require an interweaving of both. That interweaving is the figural principle.

We then went on to explicate that figural principle in some detail.

But we need not enter into that here. I introduced it only as a way of introducing Yevick’s distinction between two types of identification, one ‘descriptive and holistic’ (analogue) and the other ‘recursive and ostensive’ (digital). Yevick wrote about visual identification. In the annoying, if not flat-out hubristic, way of theoreticians, Hays and I generalized her distinction to every modality. I will continue with that generalization in this paper, where I will refer to the one process as symbolic and the other in various says, but connectionist will do as perhaps the most general term.

And that brings me to a controversy currently afoot in the world of artificial intelligence. To be sure, that is not my primary concern, which is and remains the human mind and nervous system, but is very much on my mind. As Geoffrey Hinton, a pioneer in connectionist models, declared in a interview with Karen Hao, “I do believe deep learning is going to be able to do everything” (MIT Technology Review, 11.3.2020). And deep learning operates in the connectionist world of artificial neural networks.

It is my belief that the highest-level processes of human intelligence are best conceived in symbolic terms, but that the basic processes in the brain are not symbolic in character. They are based on the “big vectors of neural activity” that Hinton talks about. My objective in this paper is to present a way of thinking about how those neural vectors can serve as the basis of symbolic structures and processes. Turned in the other direction: How do we implement symbolic processes on a connectionist foundation?

That is my subject in this paper. Consider this tripartite distinction made by Peter Gärdenfors:

Symbolic models: Based on a given set of predicates with known denotation. Representations based on logical and syntactic operations. [...]
Conceptual spaces: Based on a set of quality dimensions. Representations based on topological and geometrical notions. […]
Connectionist models: Based on a (uninterpreted) inputs from receptors. Distributed representations by dynamic connection weights. [...]

Let us think of a connectionist model as mediating between perception an the external world (in Figure 4 above). It performs a process of data compression. But there is also a categorization aspect to that process. That is a function of conceptual spaces, which are central to Gärdenfors’ thinking. They mediate the relationship between perception and cognition.

I will have relatively little to say about connectionist models. I have been strongly influenced by the ideas about complex neurodynamics developed by the late Walter Freeman and I will assume his approach, or something similar, is reasonable. He investigated how medium-scale patches of tissue in the olfactory cortex reacted to odorants. Thus I assume that I am dealing with mesoscale patches of corticial tissue, which I will call neurofunctional areas (NFAs).

I will also assume that each NFA corresponds to one of Peter Gäedenfors’ conceptual spaces. If you will, the geometry of each conceptual space is a low dimensional projection of the high dimensional space of the connectionist dynamics. For the purposes of this paper I am willing to take Gärdenfors’ work on those spaces at face value.

Given those assumptions, I am proposing a notional convention that will allow us to see how symbolic computation can be implemented in cortical tissue. While I am proposing this convention, it is not a convention I have invented. Rather, I have adapted it from the work of Sydney Lamb, a linguistic of David Hays’s generation and who was a friend of his.

Symbols and Nets: Debriefing

It’s been several days since I’d uploaded my most recent run on “Kubla Khan” to the web: Symbols and Nets: Calculating Meaning in “Kubla Khan.” It feels like I’m done tweaking it, so it’s time for a debriefing.

• First I ask: If I’d read this paper early in my career, what would I have made of it? (Cf. Borges on the curious case of Menard and the Quixote.)
• Then: Just what did I mean when I said (to myself): It’s all over but the details?
• Finally, some further thoughts on the methodological postscript.

Would BB69 or BB72 Have Understood It?

Once we get past the introduction, which is in straight prose, the dialog containes six diagrams, all of them transparently derived from diagrams in my 1972 MA thesis, “THE ARTICULATED VISION: Coleridge's ‘Kubla Khan’.” There is relatively little in there about the work that I’ve done since then. Perhaps the most important bit is a phrase from a recent interview with Geoffrey Hinton, “big vectors of neural activity.” And there’s some computer tech stuff about addresses that I may not have known then. So why did it take me 50 years to write that dialog?

Could I have written it 10 years ago? Back then there wouldn’t have been that Hinton interview I alude to, nor would I have done all the thinking I’ve done about machine learning and artificial neural nets. None of that is in there, but it is implicit in what I wrote and why I wrote it. The same goes for all the cognitive network stuff I did with Dave Hays in the mid-1970s. For me, in 2022, that dialog implies a lot that I’ve learned over the course of half a century (has it been that long, really?). None of that would have been available to BB69 (Bill Benzon in 1969), before I’d written my thesis, or to BB72, after I’d written it.

BB72 would recognized the diagrams as his work, and would have been angry if they weren’t attributed to him – but in this counter-factual he would have been given full credit for them. BB72 certainly saw those nested trees as possible evidence of nested loops in some kind of computation, so I don’t know how he would have taken the concluding dismissal of that possibility. I should also say that BB72 was still somewhat under the influence of Chomsky and attempted to account for those trees with two re-write rules, like this:

T --> B + T + B
B --> B + B

But he didn’t take much satisfaction from them. They seemed rather empty.

I’m not sure what he would made of that dismissal, not do I think it matters. But I do think he would have found the dialog interesting. The question is, would having read it changed his next steps? He’d still have been curious about it all and still would have set off to graduate school with the intention of figuring it out. Would that dialog have changed how he went about it?

That’s hard to say. But what would have been available to him back in the 1970s? He had to work through computational semantics to learn that that wouldn’t solve that problem, though it allowed him to publish a paper about a Shakespare sonnet (129). Would reading that dialog have saved him from doing that? I doubt it. Besides, doing that work proved interesting and useful, just not for THAT problem. And knowing it wouldn’t solve THAT problem is itself useful.

Let’s ask a different question. Let’s bring BB72 forward into the present and have him read that dialog. Now what would he do? The possibilities before him are quite different, though access to that Old School cognitive science would have been tricky. Would he have looked at it? Who knows?

What about BB69? Let’s make it the summer of 1969, after he’d written a senior-year term paper on “Kubla Khan” and had become committed to working out a structuralist account of the poem, but had not yet worked through it to discovering the structure in those diagrams. He would certainly have checked the diagrams for himself. Beyond that, his situation isn’t much different from that of BB72, except that he hadn’t worked over the poem, time and again, until he finally gave up on the binary-structuralist analytic approach and he got the idea to check line-end punctuation. That’s the idea that led to those diagrams. What did BB72 learn from that work that BB69 hadn’t? Does it matter?

I’m not sure it does. BB69 would have verified those diagrams. And he’d certainly have gone looking for similar structures in other poems by Coleridge and then later, poems by other poets. He would have set out to do the kind of work that’s necessary to discovering those diagrams. That’s the important point.

So why haven’t other literary critics independently figured out how to do what BB70 had done?

It’s All Done but the Details

What the hell does that mean? I DON’T think it means that we’re on the edge of figuring out “Kubla Khan,” and by implication, a whole lot more. I DO think it means that if and when I decided to take another detailed look at the poem, I’ll come up with something interesting. Just what, I don’t know.

In my working paper, Calculating meaning in “Kubla Khan” – a rough cut, I had a this chart:

What we’re looking at is a combination of compositional concatenation and convolutional gestalting – this is not the place to explain what those might mean. But I think I will be able to say something about that process that I couldn’t have when I wrote the paper in 2017. Just what...we’ll see when I do it. But see the next section...

Methodology: Cathedrals and Building Materials

The point I was making in the postscript on method (pp. 18 ff.) can be exemplified like this: You’re a linguistic. You know everything there is to know about sentence-level linguistics (assuming, for the sake of argument, the the idea of a sentence is self-evidently useful), from phonetics and phonology up through syntax. But that’s not going to tell you how a connected discourse is put together. You can analyze each sentence-level string in the discourse but, when you’ve done that for the whole discourse, you still don’t know how and why the discourse was put together. That involves consideration that are invisible at the sentence level.

Now, does it make sense to investigate discourse level structure when you don’t have well-settled means of describing and analyzing sentence-level strings? Yes, why not? You just have to be careful how you do it. You want to construct your discourse accounts in terms that are at least commensurate with one or some sentence-level accounts.

That’s what I’m up to with “Kubla Khan.” I know that ultimately we’re going to have to have recourse to neuroscience in order to figure out what’s going on. But the neuroscientists haven’t got a clue about what’s going on in phenomena like “Kubla Khan.” So working at the level of the poem in terms that are commensurate, ultimately, with neuroscience, that’s tricky. Speculative. But someone’s got to do it. And it’s not like we’ve got to go straight to neuroscience in one fell swoop. There’s other levels of description and analysis available.

So, I’m interested in understanding a cathedral. You guys understand stone blocks, morter, and so forth. I’ve just got to keep an eye on what you’re up to while I’m thinking about the overall design. And you might want to look up every now and then to see where it’s going.

A postscript on method [Symbols and Nets: Calculating Meaning in “Kubla Khan” ]

Yesterday I gave notice of my new working paper on "Kubla Khan." Today I'm posting the methodological post script.

* * * * *

I can hear the voices now:

Naa, naa, you’re crazy!
You can’t do science like this, too speculative.
Speculative? He’s out to lunch!
On the moon! – “To the moon, Alice, too the moon!”
That’s not how it’s done, son.

How’s WHAT done?

Psychology, neuroscience, linguistics, AI, figuring out the mechanisms of the mind. Those things are complicated. We have to take it a piece at a time, get the details right –

You don’t think I know that? I read the technical literature, been doing it for years, decades. And you know what?

What?
What?
What?

As interesting as a lot of your stuff is, you guys haven’t told me jack shit that’s really useful in figuring out what’s going on in “Kubla Khan.”

But that’s not what we’re trying to do?

Why not?

Because it’s too complicated. We’re not ready.

Well, when are you going to be ready?

I don’t know.
50, 87, 199 years, who knows?
These things take time.

Horse pucky! You know what I hear? I hear you saying, “We’re not worthy.” No, you’re not. Neither am I. No one’s worthy. It’s not about worthyness. It’s about work, and desire, and vision. It’s about risk and speculation. Do you think we can understand the mind?

No, it’s beyond us.

You, you get out! You’ve given up. Come back when you’re sober.

I’d like to think we can understand the mind. But it’s hard, really hard. We’ve chased a lot of rabbits down holes, spilt a lot of milk, got lost on a lot of garden paths, ‘lotta water under the freakin’ bridge –

Enough with the cliches! Let’s say I want to build a cathedral. So I hire the best stone masons, the best carpenters and plumbers, the best electricians, the best glazers, and so on. I gather them together on site and give them the best materials. “Now build me a cathedral,” I say, “Build me a cathedral.” What do you think’s going to happen?

Hmmmm... Not much.
Confusion.
Fighting maybe.

Why?

You need a plan. You can’t build a cathedral from the ground up with just materials and skills. You need to know how to put all those things together.

Right. It’s the same with the mind. You guys have the skills and materials. And I’ve got, well I don’t have a plan, but I’ve got this poem, Coleridge’s “Kubla Khan.” And I know a lot about it, not just what I’ve put up there in that dialog, if you reach right out of this dialog, you’ll find some papers listed in Appendix 3. There’s a large literature on the poem. There’s stuff there too, though not much of it has been crafted with the cognitive and neurosciences in mind, much less deep learning and artificial intelligence. Work toward it.

Work toward it?

Yeah. Dream a little. If you wanted to get there – “Kubla Khan” – from wherever here is for you, what’s the first step you would take? And the next? What kind of cooperation are you going to need from others, from me?

But it’s just so hard. We’ve worked so long.

Is it all work? Haven’t there been some fun times, some excitement?

You’re right. Some of it has been fun.

So, keep on truckin’. We’ll get there.

In the distance –

Heigh-ho, heigh-ho, it’s off to work we go...
Ditty dump di dum, woopsie ding dong daddy,
Heigh-ho,
Heigh-ho,
Heigh-ho,
Heigh-ho!

Symbols and Nets: Calculating Meaning in “Kubla Khan”

A new working paper. Title above, abstract, table of contents, and introduction below. Download at: Academia.edu: https://www.academia.edu/78967114/Symbols_and_Nets_Calculating_Meaning_in_Kubla_Khan_
SSRN: http://ssrn.com/abstract=4106687
ResearchGate: https://www.researchgate.net/publication/360525548_Symbols_and_Nets_Calculating_Meaning_in_Kubla_Khan 

* * * * * 

Abstract: This is a dialog between a Naturalist Literary Critic and a Sympathetic Techno-Wizard about the interaction of symbols and neural nets in understanding “Kubla Khan,” which has an extraordinary structure. Each of two parts is like a matryoshka doll nested three deep, with the last line of the first part being repeated in the middle of the second. They start talking about traditional symbol processing, with addressable memory, and nested loops, and end up talking about a pair of interlinked neural nets where one (language forms) is used to index the other (meaning). 

In search of “Kubla Khan” 2
Fee fi fo fum, I smell computation 4
Calculating over symbols 8
Calculating over a neural net 10
Two linked networks in the mesh 14
Speculative Engineering: A postscript on method 17
Appendix 1: The text of “Kubla Khan” 18
Appendix 2: Rhyme and sense in the first part of “Kubla Khan” 20
Appendix 3: My Work on Coleridge 21 

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Symbols and Nets  

...At this moment he was unfortunately called out by a person on business from Porlock, and detained by him above an hour, and on his return to his room, found, to his no small surprise and mortification, that though he still retained some vague and dim recollection of the general purport of the vision, yet, with the exception of some eight or ten scattered lines and images, all the rest had passed away like the images on the surface of a stream into which a stone has been cast, but, alas! without the after restoration of the latter!
– Samuel Taylor Coleridge, Preface to “Kubla Khan” 

 In search of “Kubla Khan”

This dialog marks progress in my third attempt to comprehend the structure of Coleridge’s “Kubla Khan.” My 1972 Master’s Thesis marks my first attempt: “THE ARTICULATED VISION: Coleridge's ‘Kubla Khan’”. I read everything I could find about the poem in the Johns Hopkins library. Two essays held my attention. The one by Humphrey House, from his Clarke Lectures, pointed out that no one would ever have thought the poem incomplete without Coleridge’s preface. In the other one, “’Kubla Khan,’ Proto-Surrealist Poem,” Kenneth Burke argued that the poem so defied Coleridge's aesthetic theories that he did not know what to make of it, arguing that it was a ”poetized psychology.”

I updated my thesis work with a 1988 essay I published in Language and Style, “Articulate Vision: A Structuralist Reading of ‘Kubla Khan’.” I tossed out some of the philosophical language and updated it with some cognitive network diagrams, but it was fundamentally the same work. It was an analysis of the poem’s utterly remarkable structure, a structure which no one had seen despit all the attention that had been given to the poem.

Though I hadn’t realized it at the time, that thesis marked my break from what I now think of as standard literary criticism, which centers on interpreting a text’s meaning. I focused on the text’s form and used meaning as a way to examine form. Whereas the profession had moved beyond structuralism to various post-structuralisms, I had moved beyond it to the cognitive sciences. But I branded my essay “structuralist” both to signal its intellectual roots and as a touchstone literary critics could recognize.

Decades passed until, early in the new millenium, I took another pass at “Kubla Khan.” I published “’Kubla Khan’ and the Embodied Mind,” PsyArt: A Hyperlink Journal for the Psychological Study of the Arts (2003). This was considerably longer than my 1988 article, more prose and many more diagrams, and a section where I speculated on the neural underpinnings of the poem. But I remained focused on the structure I had identified in my 1972 thesis, and which my interlocutors examine in the first section of their dialogue below, “I smell computation.”

I paired that with a later essay, “Talking with Nature in ‘This Lime-Tree Bower My Prison,’” PsyArt, November (2004). That poem has a motif, gazing upon the sun, which is closely related to the “sunny dome” of “Kubla Khan” and a glimpse into a “still roaring dell” that resonates with the “deep romantic chasm” of “Kubla Khan.” A decade later I discussed these conjunctions in an unpublished working paper, “STC, Poetic Form, and a Glimpse of the Mind” (2013) – where “unpublished” means not published in the formal academic literature; but I posted it online, as I have this dialog.

At that time I thought perhaps I had gone as far as I could with Coleridge. There was certainly more to be done, but I couldn’t see how to do it. And the I began reading about machine learning and artificial neural nets, which set me to thinking. In December, 2017, I issued a working paper, “Calculating meaning in ‘Kubla Khan, – a rough cut,” Version 2. Here’s how I characterize calcuation (pp. 2-3):

Roughly speaking then, to calculate the meaning of a text is to construct a coherent pattern of signifieds as prompted by the that text. [...] I assume this process involves both composition and convolution. Composition is the primary process and for many texts it may be the only process. I sometimes think of composition as “the freight train” model of meaning, where meanings are discrete entities, each of which is packed into a freight car, and the cars assembled into a train. In fact, nothing in a relational network functions like this, but it will serve as a crude metaphor to underpin the following discussion.

Here is how I characterize convolution (p. 5):

Still, what do I mean by convolve? I’m going to tap-dance through this one. Some years ago David Hays and I published a paper on metaphor, “Metaphor, Recognition, and Neural Process” [7], in which we argued that ‘robust’ metaphor (as opposed to ‘dead’ metaphor) works by convolving the tenor and the vehicle. At the time we were influenced by Karl Pribram’s notion of neural holography, which we explain (somewhat) in the paper. Note that neural tissue is active tissue. Individual neurons are always active, but more so at some times than others. Convolution is thus a process involving the interaction of meshworks of neurons, perhaps arranged in a specific architecture.

Convolution is a very important operation in the world of artificial neural nets, used mostly for processing images. But then, “Kubla Khan” conjures up rich visual imagery.

Thus began my third attempt to understand the mechanisms behind “Kubla Khan.” This dialog continues that attempt. I have created two interlocutors, a Naturalist Literary Critic (NLC) and a Sympathetic Techno-Wizard (STW). I conceive of this Naturalist Literary Critic as one who examines literary works in the way that a naturalist examines life forms. I first explained my conception in a long post at The Valve in 2010, which is now defunct. It’s now on New Savanna, “’NATURALIST’ criticism, NOT ‘cognitive’ NOT ‘Darwinian’ – A Quasi-Manifesto”. Nor, I might add, is it formalist, Marxist, deconstructionist, feminist, or any other form of interpretive criticism. It is, if you will, post-interpretive.

As for the Sympathetic Techno-Wizard, they’re expert in various forms of natural language processing, machine learning, and artificial intelligence, which I am not, except for my early-career adventure into Old School computational semantics. Nonetheless, as I alone am writing this dialog, I have to play the role of STW, which implies that they say what I want/need them to say. One of my major intellectual goals is to take a topic that has resisted technical development and transmute it into a form where it is accessible to investigators who have technical skills that I lack. That has been one motive driving my work on “Kubla Khan” from the very beginning. I offer this dialog in the hope that some real techno-wizards will read it and take me up on it.