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

Gary Marcus and Our Innate Linguistic Capacity [Relational Net Primer]

During the period that I had been writing my primer on relational networks and attractor landscapes, Gary Marcus had taken to Twitter to challenge the deep learning community on the need for symbolic processing. I agree that symbolic processing is necessary for any device that is going to approximate or match the human capacity for abstract thought. However, as I’ve made clear in the primer, I don’t think that symbolic processing is primitive. Neural nets are primitive and symbolic processinig is implimented in them.

Marcus on Innateness

It is not clear to me just what Marcus thinks about this. At the beginning of chapter 6 of The Algebraic Mind[1], which is, I believe, his major theoretical statement, Marcus says (p. 143): “The suggestion that I consider in this chapter is that the machinery of symbol-manipulation is included in the set of things that are initially available to the child, prior to experience with the external world.” Later on he will reject the “idea that the DNA could specify a point-by-point wiring diagram for the human brain” (p. 156). After weaving his way through a mind-boggling network of evidence about development, Marcus offers (p. 165):

Genetically driven mechanisms (such as the cascades described above) could, in tandem with activity-dependence, lead to the construction of the machinery of symbol-manipulation—without in any way depending on learning, allowing a reconciliation of nativism with developmental flexibility.

At this point I’m afraid I’m driven to echo the great Roberto Duran and to say “no más”. It makes my head hurt.

Let me skip ahead to his final chapter, where he says (p. 172):

As I suggested in chapter 6, differences between the cognition of humans and other primates may lie not so much in the basic-level components but in how those components are interconnected. To understand human cognition, we need to understand how basic computational components are integrated into more complex devices—such as parsers, language acquisition devices, modules for recognizing objects, and so forth—and we need to understand how our knowledge is structured, what sorts of basic conceptual distinctions we represent, and so forth.

I agree with Marcus on that first sentence. I’m not so sure about some of the rest, though I do believe that last remark, after “so forth.” That structure what most of the primer is about.

Now, the word “modules” is most important in an intellectual tradition of which I’m skeptical. If by parser Marcus means the sorts of things that are the staple of classical computational linguistics, then I doubt that human brains have such things. That’s not an argument, and this isn’t the place to make one, but I will point out that, from its origins in the problem of machine translation in the 1950s until well into the 1970s, computational linguistics had little to no semantics to speak of – nor, for that matter, has it ever developed more than a smattering of semantics. Without semantics, syntax is what is left. If syntax is what you have, then you need a sophisticated and elaborate parser. I believe that human language is grounded in semantics, which is in turn grounded in perception and action, and that syntax supports semantics. Relatively little parsing, as such, is required.

As for the language acquisition device, we have already seen that Marcus believes symbol manipulation is available to children “prior to experience with the external world.” I certainly do not believe that the mind is a proverbial blank state. Infants do come into the world with some fairly specific perceptual and behavioral equipment. But whether or not that includes a language acquisition device, well, let me evade the issue by spining a tale.

Teaching Chimpanzees Language

This is a tale, not a true one, but a thought experiment. I invented it while thinking about the origins of language. I came up with this tale while thinking about various early attempts that had been made to teach chimpanzees language. All of them ended in failure [2]. In the most intense of these efforts, Keith and Cathy Hayes raised a baby chimp in their household from 1947 to 1954. But that close and sustained interaction with Vicki, the young chimp in question, was not sufficient.

Then in the late 1960s Allen and Beatrice Gardner began training a chimp, Washoe, in Ameslan, a sign language used among the deaf. This effort was far more successful. Within three years Washoe had a vocabulary of Ameslan 85 signs and she sometimes created signs of her own.

The results startled the scientific community and precipitated both more research along similar lines — as well as work where chimps communicated by pressing iconically identified buttons on a computerized panel — and considerable controversy over whether or not ape language was REAL language. That controversy is of little direct interest to me, though I certainly favor the view that this interesting behavior is not really language. What is interesting is the fact that these various chimps managed even the modest language that they did.

The string of earlier failures had led to a cessation of attempts. It seemed impossible to teach language to apes. It would seem that they just didn’t have the capacity. Upon reflection, however, the research community came to suspect that the problem might have more to do with vocal control than with central cognitive capacity. And so the Gardners acted on that supposition and succeeded where others had failed. It turns out that whatever chimpanzee cognitive capacity was, it was capable of orchestrating surprising behavior.

Note that nothing had changed about the chimpanzees. Those that learned some Ameslan signs, and those that learned to press buttons on a panel, were of the same species as those that had earlier failed to learn to speak. What had changed was the environment. The (researchers in the) environment no longer asked for vocalizations. The environment asked for gestures, or button presses. These the chimps could provide, thereby allowing them to communicate with the (researchers in the) environment in a new way.

It seemed to me that this provided a way to attack the problem of language origins from a slightly different angle.

How Aliens From Outer Space Brought Us Language

I imagined that a long time ago groups of very clever apes – more so than any extant species – were living on the African savannas. One day some flying saucers appeared in the sky and landed. The extra-terrestrials who emerged were extraordinarily adept at interacting with those apes and were entirely benevolent in their actions. These space aliens taught the apes how to sing and dance and talk and tell stories, and so forth. Then, after thirty years or so, the ETs left without a trace. The apes had absorbed the extra-terrestrials’ lessons so well that they were able to pass them on to their progeny generation after generation. Thus human culture and history were born.

Now, unless you actually believe in UFOs, and in the benevolence of their crews, this little fantasy does not seem very promising, for it is a fantasy about things that certainly never happened. But if it had happened, it does seem to remove the mystery from language’s origins. Instead of something from nothing we have language handed to us on a platter. We learned it from some other folks, perhaps they were short little fellows with green skin, or perhaps they were the more modern style of aliens with pale complexions, catlike pupils in almond eyes and elongated heads. This story hasn’t taught as anything new about just how language works, but one source of mystery has disappeared.

But, and here is where we get to the heart of the matter, what would have to have been true in order for this to have worked? Just as the chimps before Ameslan were genetically the same as those after, so the clever apes before alien-instruction were the same as the proto-humans after. The species has not changed, the genome is the same – at least for the initial generation. The capacity for language would have to have been inherent in the brains of those clever apes. All the aliens did was activate that capacity. Once that happened the newly emergent proto-humans were able to sustain and further develop language on their own. Thus the critical event is something that precipitates a reconfiguration of existing capabilities, a Gestalt switch. The rabbit has become a duck, or vice versa, the crone a young lady, or vice versa.

Where’s the Language Acquisition Device?

However, we’re not interested in the phylogenetic origins of language, we’re interested in how children acquire it. Whatever their genetic endowment, they live in a world surrounded by language speakers, and some of them are closely attuned to the infant’s needs, desires, and evoling capacities. It’s not clear to me just what specialized language acquisition device the infant needs.

The problem I have in thinking about this is very much like the problem I have identifying the acceleration subsystem in an automobile. I know that the engine has more effect on acceleration than the backseat upholstery, and the tires are more important than the cup-holders, but anything with mass affects the acceleration. Is there anything in the engine that is there specifically to enhance acceleration and nothing else, or is it a matter of proportion, strength, and adjustment of the components necessary to the engine?

That’s my problem with the idea of a language acquisition device. Given that infants are born with various perceptual capabilites (which Marcus recounts) it is not obvious whether or not we need anything more specific to language than, for example, the ability to track adult speech patterns that Condon and Sander reported in 1974 [3]. I think it’s a bit much to call that a language acquisition device. If you must have one, why not say that the human brain as a whole is, among many other things, a language acquisition device?

References

[1] Marcus, Gary F (2001). The Algebraic Mind (Learning, Development, and Conceptual Change). MIT Press. Kindle Edition.

[2] Linden, Eugene. (1974). Apes, Men, and Language. New York: Saturday Review Press, E. P. Dutton.

[3] Condon, W.S., & Sander, L.W. (1974). Neonate movement is synchronized with adult speech: Interactional participation and language acquisition. Science, 183, 99-101.

“Kubla-Khan” in Light of the Relational Nets Primer

This is another post in my series of post-Relational-Net-Primer reflections.

“Kubla Khan”, as I’ve explained many times, originally in this piece first published in 1975, is what sent me chasing after computational semantics, in graduate school in the mid-1970s, and connected with my ongoing interest in the brain in a long article I published in 2003, “Kubla Khan” and the Embodied Mind. The nature of my interest is easily stated: Why does that poem have the structure that it does? I could launch out into a digression into just what kind of question that is – in what way does it differ from a similar question about sonnets? – but I won’t.

The Structure of “Kubla Khan”

Instead, I’ll present you with the structure (I list the whole poem in an appendix):

That diagram doesn’t present the rhyme scheme, which is also part of the puzzle, but you will find a discussion of that in the “Embodied Mind” paper. I inserted the long arrow to remind us that we read poems from beginning to end. We don’t have the overview perspective afforded by that diagram.

The diagram is simple enough. It is what linguists call a constituent structure tree, and it is over whole poem, which is 54 lines long. (Such trees are generally used in the analysis of sentence structure, not the structure of whole texts.) The first part, numeral 1 in the diagram, is 36 lines long, from line 1 to line 36. The second part, numeral 2 in the diagram, is 18 lines long, from line 37 to line 54. That divides the whole string into two parts. Each of those strings is in turn divided into substrings, as indicated by the tree. If you want to know how I arrived at the divisions, consult the “Embodied Mind” paper. But I will note that in many cases I did it by treating punctuation marks like brackets and braces in a mathematical expression. That is, my decision procedure was mindlessly mechanical.

Let’s take a simple arithmetic expression: 3 + 5 * 9. What’s the value of that expression? Unless you adopt a convention about the order in which you apply opperators, the expression is ambiguous and so could evaluate to either 56 or 48. We can eliminate the ambiguity by adding parenthese, giving us ‘(3 + 5) * 9’ or ‘3 + (5 * 9)’.

In looking at the poem, then, I assumed that the underlying process which determines the meaning of the string is segmented according to the boundaries between substrings. That’s not an odd assumption to make, but, given that we don’t understand that process, it must be considered an assumption. 

Note: I regard that tree structure as an analytic device, but not as something that is explicit in the underlying neural mechanisms. Just what those mechanisms are is not, of course, known. This should not be taken to mean that I do not think “Kubla Khan” is divided into substrings in the way indicated by that tree. It is, but that tree does not need to be a component of the mechanism that understands or that wrote the poem. For a discussion of this point see the discussion of description vs. catalysis in the opening of Sydney Lamb’s paper, Linguistic structure: A plausible theory, and Lamb’s discussion of descriptive vs. cognitive linguistics in Pathways of the Brain (1999).

What’s Remarkable About That Structure?

Notice that I’ve presented part of the tree in red. Looking at the red edges we see that the first part of the poem (ll. 1-36) is divided into three parts, the middle of those is, in turn, divided into three parts, and the middle of those, in turn, is divided into three. All other divisions are binary. The same thing is true of the second section (ll. 37-54).

If such structures were common we could say, “Oh, it’s just another one of those.” But, alas...we don’t know whether or not such structures are common, because literary critics don’t analyze poems like that. Still, as far as we know, such structures are not common. It certainly surprised me when I first discovered it.

So, that’s one thing, the fact that each part of them poem has a nested structure, like matryoshka dolls. By the time I’d discovered that structure, however, I’d taken an introductory course in computer programming, and so I thought I might be looking at the trace of some kind of nested loop structure. That is to say, I took it to be some kind of computational structure. I still do, though I no longer think it’s nested loops.

Now, look at the diagram. The last line of the first par, line 36, is “A sunny pleasure-dome with caves of ice!” Now look at the second part, the middle of the middle or the middle, that is to say, the structural center. That’s line 47: “That sunny dome! Those caves of ice!” It’s almost an exact repedition of line 36. What’s that line doing in that place?

Now, these questions would have one valence if, upon consulting Coleridge’s notebooks, we found notes where he laid this scheme out and gave his reasons for so doing. But no such notes exist and, as you may know, Coleridge himself disavowed the poem, saying it came to him in an opium dream. He just channeled the vision but played no active role in writing it.

You can believe what you will about that, the point is that we have no evidence that this structure reflects conscious planning on Coleridge’s part. It’s sources are unconscious. That’s what I’m trying to figure out.

Now, at this point you might wonder what’s happening in the structural center of the first part (1.222). A mighty fountain is breaking ground, spewing rocks into the air, and giving rise to the sacred river, Alph. And that leads to the question: What’s that fountain have in common with that line that both of them occupy the structural center of their respective parts of the poem? That’s a very good question, but I’m going to leave it alone. If you’re curious, consult “Embodied Mind.” I want to stick with that one repeated line.

Semantic Dimensions in “Kubla Khan”

Let’s return to the first part of the poem. The first of its three parts (1.1) is characterized by an emphasis on spatial orintation and location and the visual mode. The second part (1.2) is characterized by an emphasis on sound and on time. The third part (1.3) encompasses both sight and sound, time and space. That is, it weaves the two worlds of 1.1 and 1.2 together. There is, of course, more going on. Part 1.1 has Kubla Khan as the major agentive force while 1.2 has that fountain. Neither Kubla nor the fountain are present in 1.3, but their creations, the dome and the river, both are.

Let us think of each section of the poem as being organized along the kinds of dimensions that Peter Gärdenfors uses in his account of semantics (Conceptual Spaces, 2001; The Geometry of Meaning, 2014). The various words in the poem each is located in some conceptual space characterized by certain dimensions. The thing to do, then, would be to examine the dimensions evoked by each part of the poem. While I have done quite a detailed analysis of the poem (again, see “Embodied Mind”), I have yet to undertake that.

But I do want to look at the last two line of the first part from that point of view. We have:

It was a miracle of rare device,
A sunny pleasure-dome with caves of ice!

I suggest that “miracle” marks one end of a dimension while “rare device” marks the other end. Similarly, “sunny pleasure-dome” marks one end of a dimension while “caves of ice” marks the other end of that dimension. Think of these as derived or virtual dimensions; they aren’t basic to the semantic system, but arise in the context of this poem.

While I didn’t conduct my analysis in terms of dimensions, the terms I did use make it plausible to think of those two last lines as encapsulating or being emblematic of the entire semantic space evoked in the previous lines. I now suggest that those two line are a two-dimensional projection of the semantic space evoked in the first part of “Kubla Khan.”

Now we are in a position to think about what’s going on in line 47, which repeats 36. First, remember that we are dealing with the human brain not a digital computer. “Kubla Khan” can be read aloud in two to two-and-a-half minutes (I’ve timed myself). While individual neurons fire quickly and so are either on or off in a time measured in milliseconds, millions and millions of neurons would be involved in reading a poem. Thus as one reads through the poem activation is going to spread through 100s of millions of neurons, generating increased activity throughout that population. So that last line, the one that’s repeated in the second part of the poem, it is going to ‘resonate’ with the entire first part of the poem – something I suggested in Symbols and Nets: Calculating Meaning in “Kubla Khan”. So, when that line is repeated in the second part, it brings that resonance with it, almost as though the ‘meaning’ of the first part is ‘injected’ into the second part in line 47, something I describe in “Embodied Mind”.

Neural Evidence, Please

That seems plausible enough, but could we get actual evidence of such a thing operating in the brain? I strongly suspect that one day we will. Here’s a brief email exchange I had with the late Walter J. Freeman early in this century:

Walter,

I've had another crazy idea. I've been thinking about Haken's remark that the trick to dealing with dynamical systems is to find phenomena of low dimensionality in them. What I think is that that is what poetic form does for language. The meaning of any reasonable hunk of language is a trajectory in a space of very high dimensionality. Poetic form “carves out” a few dimensions of that space and makes them “sharable” so that “I” and “Thou” can meet in aesthetic contemplation.

So, what does this mean? One standard analytic technique is to discover binary oppositions in the text and see how they are treated. In KK [“Kubla Khan”] Coleridge has a pile of them, human vs. natural, male vs. female, auditory vs. visual, expressive vs. volitional, etc. So, I'm thinking of making a table with one column for each line of the poem and then other columns for each of these “induced” dimensions. I then score the content of each line on each dimension, say +, - and 0. That set of scores, taken in order from first to last line, is the poem’s trajectory through a low dimensional projection or compression of the brain's state space.

The trick, of course, is to pull those dimensions out of the EEG data. Having a sound recording of the reading might be useful. What happens if you use the amplitude envelope of the sound recording to “filter” the EEG data?

Later,

Bill B

Not crazy, Bill, but technologically challenging! Will keep on file and get back to you.

Walter

I can live with technologically challenging. Instrumental technique has advanced since we had that exchange. Is it yet up to the job? I don’t know. But surely one day it will be.

More later.

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.

Welcome to the Fourth Arena @3QD

That’s my latest article at 3 Quarks Daily:

Welcome to the Fourth Arena – The World is Gifted, https://3quarksdaily.com/3quarksdaily/2022/06/welcome-to-the-fourth-arena-the-world-is-gifted.html

I suggest that we may be moving into a new Cosmic Arena, from inanimate Matter (1), to Life (2), to Culture (3), to . . . just what? Let’s simply call it the Fourth Arena while we’re figuring it out.

A Complex Universe

I begin by arguing that the universe is basically complex. Here’s a recent tweet that makes the point:

Good reminder (by Gabor Vattay): pic.twitter.com/M88IBFGN0r

— Luiz Pessoa (@PessoaBrain) June 20, 2022

Beyond that, read the article.

We need to rethink how we live

But I will leave you with the question that Michael Liss posed to me, and my answer to him. The question:

Bill, how does society adapt to the potential that so many who worked in jobs that required human interaction/conversation find their careers made obsolete? We've had waves of displacement in the past, but mostly at the "mechanical" level--artisans who were pushed out because of industrialization, farm work replaced by machinery, even secretaries replaced by word-processors and spell checks. This has pushed some people to reach higher, but a lot of the rest accept jobs in low-wage industries, and find their status and family's potential for advancement diminished. Businesses, driven by profit motive, will adapt or close, but government can't do that. When a large section of the population in both traditionally blue and white collar jobs realize that their government either has no answers, or is beholden to a few, what next for civil society?

My reply:

That’s a complicated question, Michael, and I might have to write a book, albeit a compact one, in order to come up with an answer. I can’t answer it now. But I can say a few things that I’d have to take into consideration.

I’d start out with a famous remark Keynes made in a 1930 essay, “Economic Possibilities for our Grandchildren,” in which he argued that a 15-hour workweek should suffice for all our economic needs.

Yet there is no country and no people, I think, who can look forward to the age of leisure and of abundance without a dread. For we have been trained too long to strive and not to enjoy. It is a fearful problem for the ordinary person, with no special talents, to occupy himself, especially if he no longer has roots in the soil or in custom or in the beloved conventions of a traditional society. To judge from the behaviour and the achievements of the wealthy classes today in any quarter of the world, the outlook is very depressing! For these are, so to speak, our advance guard-those who are spying out the promised land for the rest of us and pitching their camp there. For they have most of them failed disastrously, so it seems to me—those who have an independent income but no associations or duties or ties—to solve the problem which has been set them.

I feel sure that with a little more experience we shall use the new-found bounty of nature quite differently from the way in which the rich use it today, and will map out for ourselves a plan of life quite otherwise than theirs.

It's quite clear that we have utterly failed on that last count. Those of us with jobs devote more time than ever to them. The convenience of email has made us available to our employers 24/7 365. And while the necessity of working from home during the pandemic has led many to question the wisdom of going into the office 5 days a week for 8 to 10 hours a day plus commute time, I’m not at all sure how that’s going to work out. I should think the boss class will do its best to see that distant-work tech means that work haunts you wherever you are, 24/7 365.

And people will put up with it? Why? Because they don’t, in the end, know how to use their leisure. I’m sure Netflix and the rest will do their best to keep us supplied with binge-worthy video. But, come on? Is that life?

I got a shock when my father took early retirement at 62; he was in perhaps the earliest cohort who had that option. He spent his career as an engineer with Bethlehem Mines. He was very good, and certainly loved (aspects of) his job. And still he retired as soon as he could.

How did he spend his time? He spent an enormous amount of time playing solitaire. Every day, several hours a day. This was an intelligent man, with many interests, golf, stamp collecting, wood-working, and he read a lot. And, yet, when he had the time to devote to them, he spent it playing solitaire. Yes, he did play golf, more often, he found some guys to play bridge with, he ramped up his stamp collecting, but never did anything with his wood-working. So he spent less and less time at solitaire, but it never tapered off to zero.

And he’s not alone. I’ve read articles about retirement coaches, people who work with retired executives and such to help them figure out how to spend their time when they’re retired. I’m pretty sure these coaches to not work for minimum wage. I suspect they’re more likely to charge lawyers’ rates, though probably not at the top of the range. The only people who can afford those rates would be highly skilled people working relatively high on the totem pole. Why for god’s sake do those people need help unwinding? Why don’t they just buy some Hawaiian shirts and join the Jimmy Buffett parrot-head crowd – which, by the way, some of them are doing. As you may know, Buffett has become rich from various businesses, the most recent of which is retirement communities for people who want to sit around with friends sipping margaritas and eating cheese burgers in paradise.

More Keynes:

When the accumulation of wealth is no longer of high social importance, there will be great changes in the code of morals. We shall be able to rid ourselves of many of the pseudo-moral principles which have hag-ridden us for two hundred years, by which we have exalted some of the most distasteful of human qualities into the position of the highest virtues. We shall be able to afford to dare to assess the money-motive at its true value. The love of money as a possession—as distinguished from the love of money as a means to the enjoyments and realities of life—will be recognised for what it is, a somewhat disgusting morbidity, one of those semicriminal, semipathological propensities which one hands over with a shudder to the specialists in mental disease. All kinds of social customs and economic practices, affecting the distribution of wealth and of economic rewards and penalties, which we now maintain at all costs, however distasteful and unjust they may be in themselves, because they are tremendously useful in promoting the accumulation of capital, we shall then be free, at last, to discard.

THAT’s what we’ve got to think about.

Now, yes, we’ve got global warming to deal with. We aren’t going to be able to do that by simply munching on paradise cheese burgers. That’s going to take a lot of work, though of what kind and by whom and where, that’s somewhat up in the air. And we’ve got to do better on pandemic preparedness, which is a matter of both political will and bureaucratic will (the CDC and FDA failed us miserably). And then there’s the specter of war. Somehow in the middle of all that we need to rethink who and what we are.

And then there’s these new machines. What do they mean for the law, your profession? What aspects of the law require a high-level of face-to-face interaction? There’s acquiring clients and maintaining the relationship. There’s the actual back-and-forth of negotiation. And there’s litigation, which may require theatrical skills as well. But there’s an awful lot of routine paperwork of varying skill level. You’ve got to review warehouses full of documents and produce boilerplate prose. I’m guessing that lot of that is done by paralegals and junior associates, many of whom are bored witless. That can all be replaced, is being replaced, but computer systems. I know that document discovery has gone way beyond keyword search (I’ve got a cousin in the legal AI business). I’d think that the latest AI chatbots can be trained up to draft boilerplate and I assume people are working on it now, though I have no idea whether or not any of it is being deployed.

Meanwhile Neal Stephenson has written a smashing book in The Diamond Age, in which a young girl is given an interactive book that helps her mature. And we’ve got bots cranking out some very interesting images. We’ve got lots to work with.

But we’ve got to revise our conception of what makes a good life. Let’s take Keynes seriously.

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.

Hyperviscosity and Bathtub Philosophy [complex neural dynamics, really]

This was originally published 11.30.12, but I'm bumping it to the top of the queue because I'm thinking about the general idea of the fluid mind. Here's a working paper, From Associative Nets to the Fluid Mind,

https://www.academia.edu/9508938/From_Associative_Nets_to_the_Fluid_Mind

A couple of mornings ago I had a good idea while lounging in the tub. A good idea, but not a great or surprising idea. Good’s enough.

As I explained a year or so ago, I do a lot of thinking while lounging in the tub in the morning—or, for that matter, at other times of the day, on occasion. So this was not at all unusual. Still, I thought I’d post a brief note to the blog, you know, just to note the cognitive utility of hanging out in the tub. ‘Cause tending to one’s mind is important, but a rather obscure and tricky business.

Alas, I forgot to do so. And I forget just now which good idea I had that day, though I have a sense that I did act on it. Anyhow, it happened again today. So I made a point of writing a note this time.

Today’s insight is simple, that I could, and perhaps even should and will, talk about manga and anime at the end of my next, and I hope penultimate post, on pluralism. Working title for the post: Facing up to Relativism: Pluralist Axiology.

A mouthful, that: “axiology.” It’s basically a cover term for ethics and aesthetics. What’s a pluralist got to say about the fact that different peoples have different Life Ways?

Negotiation, that’s what. Latour talks about it in “Exploring Common Worlds” in Politics of Nature. While I had no specific itinerary in mind when I set out on this venture into OOO-land, I certainly didn’t expect to find myself with an occasion to talk about cartoons. But now...

* * * * *

Enough. This is about the bathtub, not about a post I’m going to write sometime in the next several days (I hope).

 

What is it about bathtub lounging that’s so congenial to meandering thought, to reverie? And why’s such thought useful?

It’s certainly not about working out details, about dotting i’s and crossing t’s. That requires sustained attention. Bathtub thinking seems to allow things to float to the surface and there wander around and mingle together.

I like to think of the mind as fluid, and has having many different viscosities at once. Call it hyperviscosity. Some things move very slowly, like chilled molasses, only slower. Other things move rapidly, like gas in a flame. But, in the mind, these things are all going on at once and consciousness, well, it attends sometimes to the fast things, sometimes to the slow things, and sometimes to the glacial things.

It’s not just that, in the tub, you really don’t have anything else to do; it’s not just the open time. It’s also the warm water. That’s important. It doesn’t have any effect on the brain’s temperature, of course, as that’s regulated to be body temperature, but the relaxation does have an effect on the overall state of the mind.

Tub thinking seems to affect the dynamics of hyperviscosity. The different viscosities tend to segment into different layers. Tub thinking gets the layers to interact with one another.

I’m thinking that some very slow things move just a bit faster and creep up a layer or three. Some of the fastest things dissipate and get out of the way. Other slow down, even way down, and sing. Thus there’s a gentle turnover in the depths and surfaces of the mind.

Hyperviscosity, of course, is just a metaphor.

Just a metaphor.

Nothing to it.

The time-space extent of human experience in the cosmos

Can't stop thinking about this pic.

"Human experience of space and time in the physical world."

[Eureka! by RJ Blin-Stoyle, 1997] pic.twitter.com/GC3HwxKyoT

— Daniele Grattarola (@riceasphait) June 12, 2022

The Fourth Arena 2: New beings in time

Yesterday I suggested that we are at the edge of a new era in cosmic history, at least our local version of it, for we have little idea what’s been happening with life on other planets in other solar systems in other galaxies or even if such life exists or has existed. The arena of matter started 14 billion years ago, from which the arena of life emerged four billion years ago. Human culture, the third arena, started about 3 million years ago. We are now on the threshold of a fourth arena.

The second and third arenas each brought new kinds of beings into the world, and those beings brought with them new ways of being in time. Living beings, the second arena, use free energy – ultimately from the sun – to swim against the tide of entropy. Life has been getting ever more complex over the long run – something David Hays and I argued in A Note on Why Natural Selection Leads to Complexity.

The third arena has brought us, well, cultural beings – there is no one good word for them. Yes, we are talking about human culture and therefore about human beings. But in this scheme human beings are themselves creatures of the second arena, animals. But very special animals, but animals that that provide the arena in which cultural beings can live.

What do I mean by cultural beings? Things like songs, stories, works of visual art, buildings, machines, and so forth. All of these are cultural beings. Physically, they are constituted of matter in various ways, but they live in and through us.

And they have the potential to live as long as humans walk the earth. We know little of those protohumans who crafted those stone tools in Africa some two or three million years ago. They probably spoke some kind of proto-language, which is lost. Their clothing, lost, their songs and dances, lost, their food, what did they eat? But those stone tools persist, and specialists have spent hours upon hours trying to figure out how they made them.

What about the ancient Greeks? Some of their stories live on in the two poems by Home, Iliad and Odyssey. But many stories have been lost. We also have tools and implements, remnants of building, and so forth. We could ramble through all of human history like this, but you get the idea, no? Ancient texts, the Bible, the Bhagavad Gita, the Confucian Analects, and many others are still read today and used as guides to life. Cultural beings can, in the right circumstances, persist beyond the lives of the people who originally made them.

Sometimes an artifact – the material husk of a cultural being ¬– is brought to life after it has been dead. The manuscript for Sir Gawain and the Green Knight was lost in the 14th century, but brought back from the dead in the 19th. J.R.R. Tolkien produced an edition in the 20th century, it has become a staple of YouTube videos, and was recently made into a movie, for the third time, albeit with a story somewhat revised from the original.

These cultural beings have a different relationship with time and matter than life forms do. Lifeforms inevitably die and their matter disintegrates into dust. Cultural beings can migrate from one material matrix to another. As long as humans exist to animate them, cultural beings can persist.

What kind of beings will arise in the Fourth Arena? Do we see them now, if only in primitive form? It so, what and where are they? How do they differ from the cultural beings of the third arena? Perhaps they will be computational beings living in the cloud and producing, what? third arena cultural beings for human inhabitation?

More later.

The Fourth Arena: What’s Up in the world these days? We’re moving to a new, a new what?

About ten years of so ago I discovered object-oriented ontology (OOO) and Bruno Latour. That plunged me into a philosophy period during which I ended up taking a really Big Look at things. I ended up sketching a cosmology/ontology, Living with Abundance in a Pluralist Cosmos: Some Metaphysical Sketches. I ended up arguing that, to date, the universe has seen the emergence of three arenas of abundance. I’ve taken the term “abundance” from Paul Feryerabend: the universe is abundant, it just keeps generating lots and lots of stuff.

I’ve identified these three realms on this nice chart which I round in Wikipedia’s entry on Universe. Roughly speaking, the universe began 14 billion years ago, giving rise to the arena of Matter. Four billion years ago Life emerged. While animals do have culture – the higher primates, certainly, do beaver dams count as culture? I don’t know – it’s human culture that ushered in a new arena, that of Culture. Wikipedia dates Oldowan tools to about 2.6 million years ago. That’s when we can locate the origins of human culture. Whether it’s a million years later or earlier hardly matters on this time scale.

Just as the other areas exhibit internal differentiation, so does Culture. Over the years David Hays and I had developed an account of cultural evolution based on fundamental cognitive architecture which we cultural ranks. We’ve identified four cultural ranks. Rank 1 is based on speech and emerged we don’t really know how long ago. Let’s put it between 100,000 and a million years ago; I doubt that it’s younger and it may well be older. Rank 2 is based on writing and is 5000 to 7000 years old or so. Rank 3 began to emerge after Asian methods of calculation reached Europe by way of the Arabs. It is thus based on calculation and showed its face, say, 700 or so years ago. It gave us the scientific and industrial revolutions, but also the novel, coherent geometric perspective in drawing and painting, and harmony in music. We traced Rank 4 back to statistical mechanics and Darwinian evolution in the 19th century and flourished in the wake of Alan Turing’s conceptualization of computing and then, at mid-20th century, with the development and deployment of digital computers. At this point a large percentage of the earth’s peoples individually own one or more digital computers, whether in their phone or a laptop device, or some other device or devices.

Look at the time scales involved. Speech emerged millions of years ago. Writing only 1000s of years ago, 10,000 at the outside. Calculation is 100s of years, 1000 at the outside. And computation? Darwin published On the Origin of Species in 1859; Clausius formulated the idea of entropy in 1865. But the digital computer is a mere 70 years old or so. Cultural evolution is accelerating.

And what if we measure those intervals in generations, where a generation is 30 years? Let’s simplify things:

Speech = 1M years ago = 33,333 generations ago
Writing = 10K years ago = 333 generations ago
Computation = 1kya = 33 generations ago
Computing = 100 years ago = 3 generations ago

A mere three generations to remake the cognitive matrix from top to bottom; that’s compressing things quite a bit. Remember, culture is passed on through imitation and education between generations. But you can see where that evolution seems to be heading. It takes an individual 15 to 20 years to internalize the basic ideas and norms of their culture. Barring unforeseen advances in genetic engineering and pedagogy, that process cannot be compressed any more.

What’s happening now? Perhaps it is only the consolidation of Rank 4. Maybe it’s that, but also the emergence of a new rank. Hays and I talked about a fifth rank in private, but never published about it. Conceptualizing Rank 4 was difficult enough.

Still, the question must be asked: Are we witnessing the emergence of Rank 5 culture? And behind that lurks an even more radical question: Are we seeing the emergence of a new Arena of Abundance, the Fourth Arena?

We argued that Rank 4 was grounded in and driven by computing. At the moment it appears that machine learning, deep learning, artificial neural nets, all of them, are doing amazing things, things that are prompting apocalyptic fever in some quarters. Is AGI (artificial general intelligence) just around the corner? Will that yield a world of super-intelligence computers? What then?

I’m sure some of that is just hype and projection, tech-bros and others getting too far out over the edges of their skis. Here we have Holden Karnofsky breathlessly proclaiming we’re living in “the most important century” humankind has ever had. He’s projecting that, over the next 1.4 billion years humans and our intelligent machines are going to people the whole freakin’ galaxy. Really?

Karnofsky’s vision strikes me as something like Olaf Stapledon plus computers. It’s science fiction that’s escaped from the realm of imagination and into the real, not as actual, but as potential, as future. He senses that something Big is afoot and seeks to rationalize it.

Is that so very different from what I’m doing? I can’t help but wonder whether or not something of cosmic magnitude is in fact going on. However skeptical I am about all this AGI-is-coming hype, I am in fact deep into the process of drafting a paper arguing that machine minds are possible and that sketches out the broad requirements for them. Who knows?

More later.

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.