A little piece of patternist analytical philosophy to brighten up your weekend.... I was thinking this stuff through today while going about in Tai Po running errands. Most notably, the back bumper of my car fell off yesterday, and I was trying to find someone to repair it. A friendly auto repair shop ended up reattaching the bumper with duct tape. A real repair is pending them finding a replacement for the broken plastic connector between the bumper and the car, in some semi-local junkyard. Egads! Well, anyway....
The concept of "representation" is commonly taken as critical to theories of cognition. In my own work on the foundations of cognition, I have taken the concept of "pattern" as foundational, and have characterized "pattern" as meaning "representation as something simpler."
But what is representation? What is simplicity?
In this (rather abstract, theoretical) post, I will suggest a way of grounding the concepts of representation and simplicity (and hence, indirectly, pattern) in terms of consciousness -- or more specifically, in terms of the concept of attention in cognitive systems.
I'll speak relatively informally here, but I'm confident these ideas can be formalized mathematically or philosophically if one wishes...
Suppose one has an intelligent system containing a large amount of contents; and each item of contents has a certain amount of attention associated with it at a given point in time.
(One can characterize attention either energetically or informationally, as pointed out in Section 2.6 of my recent review paper on consciousness. Given the close connection between energy and information in physics, these two characterizations may ultimately be the same thing.)
In real-world cognitive systems, attention is not distributed evenly across cognitive contents. Rather, it seems to generally be distributed in such a way that a few items have a lot of attention, and most items have very little attention, and there is a steep but continuous slope between the former and latter categories. In this case, we can speak about the Focus of consciousness as (a fuzzy set) consisting of those items that have a lot of attention during a certain interval; and the Fringe of consciousness as (a fuzzy set) consisting of those items that have more attention than average during a certain interval, but not as much as the items in the Focus do. (The general idea that human consciousness has a Focus and a Fringe goes back at least to William James.)
It seems to me one can ground the notion of representation in the structure of consciousness, specifically in the relation between the Focus and the Fringe.
Namely, one can say that ... R represents E, to system S, if: In the mind of system S, when R is in the Focus, this generally implies E is likely to be in the Fringe at around the same time (perhaps at the same time, perhaps a little earlier, or perhaps a little later).
As a single example, consider the typical simplifying model of the visual cortex as a processing hierarchy. In this case, we may say that when we are visually remembering the tree
I'd like to say that R is a pattern in E if: R represents E, and R is simpler than E. But this obviously begs the question of what constitutes simplicity....
In prior writings, I have tended to take simplicity as an assumptive prior concept. That is, I have assumed that each mind has its own measure of simplicity, and that measurement of pattern is relative to what measure of simplicity one chooses.
I still think this is a good way to look at it -- but now I'm going to dig a little deeper into the cognitive underpinnings of how each mind generates its own measure of simplicity.
Basically, I propose we can consider E as simpler than F, if it's generally possible to fit more stuff in the Focus along with E, than along with F.
Note that both E and F may be considered as extending over time, in this definition. Sometimes they may be roughly considered as instantaneous, but this isn't the general case.
One technical difficulty with this proposal is how to define "more." There are many ways to do that; one is as follows....
Define simple_1 as follows: E is simpler_1 than F if it's generally possible to fit a greater number of other coherent cognitive items in the Focus along with E, than with F. (This relies on the concept of "coherence" of a cognitive item as a primitive -- or in other words, it assumes that the sense or notion of what is a "coherent whole" is available to use to help define simplicity.)
Then define simple_2 as: E is simpler_2 than F if it's generally possible to fit a set of cognitive items with less simplicity_1 in the Focus along with E, as compared to with F.
One can extend this to simple_3, simple_4, etc., recursively.
According to this approach, we would find a detailed image of a tree is less simple than a rough, approximate image. When visualizing a detailed image, we keep more different samples of portions of the detailed image in Focus, leaving less room for anything else.
Similarly, the concept of the function x^2, once we understand it, takes up much less space in Focus than the procedure "take a number and multiply it by itself", and much less than a large table of pairs of numbers and their squares. Once an abstraction is learned (meaning that holding it in Focus causes appropriate knowledge to appear in Focus), and mastered (meaning that modifying it while it's in Focus causes the contents of Fringe to change appropriately), then it can provide tremendous simplification over less abstract formulations of the same content.
So, having grounded both representation and simplicity in terms of the structure of attention, we have grounded pattern in terms of the structure of attention. This is interesting in terms of the cognitive theory I outlined in my 2006 book The Hidden Pattern and elsewhere, which grounded various aspects of intelligence in terms of the "pattern" concept.
As I've previously grounded so much of cognition in terms of pattern, if one then grounds pattern in terms of consciousness, one is then in effect grounding the structure and dynamics of cognition in terms of simple aspects of the structure of consciousness. This can be viewed mathematically and formally, and/or phenomenologically.
Often when one hears about "representation", the topic at hand is some sort of formal, logical or linguistic representation. How does that kind of representation fit into the present framework?
Formal or semi-formal systems like (formal or natural) languages or mathematical theories may be viewed as systems for generating representations of cognitive items.
(What I mean by a semi-formal system is: A system for generating entities for which, for a variety of values of x less than 1, we have a situation where a fraction x of the system's activity can be explained by a set of n(x) formal rules. Of course n(x) will increase with x, and might sometimes increase extremely fast as x approaches 1. Natural languages tend to be like this.)
When we have a situation where
then we can say that E "grounds" R.
Grounding tends to be useful in the case of systems where
These criteria hold pretty well in the case of human languages, and most branches of mathematics (I suppose the jury's still out on, say, the theory of inaccessible cardinals....)
Note that one system may be grounded in another system. For instance, formal grammars of English are grounded in natural English language productions -- which in turn are grounded, for each language user, in sensorimotor experience.
If it is simple to generate new representations using a certain system, then this means the process of representation-generation is a pattern in a the set of representations generated -- i.e. it's simpler to hold that process in Focus over an interval of time, than to hold the totality of representations generated by it in Focus over an interval of time. The formal and semi-formal systems adopted by real-world minds, are generally adopted because grounding is useful for them, and their process of representation-generation is a pattern.
This is all quite abstract -- I'll try to make it a little more concrete now.
Suppose I tell you about a new kind of animal called a Fnorkblein, which much enjoys Fbljorking, especially in the season of YingYingYing. You can then produce sentences describing the actual or potential doings of these beings, e.g. "If Fnorkbleins get all their joyful Fbljorking done in YingYingYing, they may be less happy in other seasons."
These sentences will be representations of, and patterns in, your visual images of corresponding scenes (your mental movie of the Fnorkbleins romping and Fbljorking in the throes of their annual YingYingYing celebration, and so forth). They will ground these images.
Furthermore, the process of formulating this Fnorkblein-ful sentences, will take relatively little Focus for you, because you know grammar. If you didn't know grammar, then formulating linguistic patterns representing Fnorkblein-relevant images would require a lot more work, i.e. a lot more Focus spent on the particulars of Fnorkbelein-ness.
Of course, people can use grammar fairly effectively -- including about Fnorkbleins -- without any knowledge of any explicit formalization of grammar. However, if one wants people to stick close to a specific version of grammar, rather than ongoingly improvising in major ways, it does seem effective to teach them explicit formalized rules that capture much of everyday grammatical usage. That is, if the task at hand is not deploying the grammar one knows in practical contexts, but rather communicating or gaining knowledge regarding which sentences are considered grammatical in a certain community -- then formalizations of grammar become very useful. This is the main reason grammar is taught in middle school -- giving a bit of theory alongside the real-world examples a child hears in the course of their life, helps the child learn to reliably produce grammatical sentences according to recognized linguistic patterns, rather than improvising on the patterns they've heard as happens in informal communication. (And it may be that formal grammars are also useful for teaching AIs grammar, to help overcome their lack of the various aspects of human life and embodiment that human children learn to pick up grammar implicitly from examples -- but that's a whole other story.)
It seems the act of teaching/learning the rules of grammar of a language, constitutes a pattern in "the act of communicating/learning the set of sentences that are grammatical in that language", in the sense that: If one has to tell someone else how to reliably assess which sentences are grammatical in a certain language (as utilized within a certain specific community), a lot less Focus will be spent via telling them the rules of grammar alongside a list of examples, than by just giving them a long list of examples and leaving them to do induction. When teaching grammar, while a rule of grammar is in the Focus, the specific examples embodying that rule of grammar are in the Fringe. While passing the rules of grammar from teacher's Focus to student's Focus, the real point is what is being represented: the passage of sets of sentences judged as grammatical/ungrammatical from teacher's Fringe to student's Fringe.
The rules of grammar, then, may be described as a "subpattern" in the act of communicating a natural grammar (a subpattern meaning they are part of the pattern of teaching the rules of grammar). This may seem a bit contorted, but it's not as complicated as the design of the computer I'm typing this on. Formal grammars, like Macbooks, are a complex technology that only emerged quite recently in human evolution.
And so, Bob's your uncle.... Starting from the basic structure of consciousness, it's not such a big leap to get to pattern -- which brings one the whole apparatus of mind as a system for recognizing patterns in itself and the world -- and to systems like languages and mathematics.
One can interpret this sort of of analysis multiple ways ... for instance:
Taking physical reality as the foundation, one can study the structure of consciousness corresponding to a certain physical system (e.g. a brain), and then look at the structure of the mind corresponding to that physical system as consequent from the structure of its consciousness.
Taking experience as the foundation, one can take entities like Unity and Attention as primary, and then derive concepts like Focus and Fringe, and from there get to Representation and Pattern and onwards -- thus conceptually grounding complex aspects of cognition in terms of phenomenological basics.
The concept of "representation" is commonly taken as critical to theories of cognition. In my own work on the foundations of cognition, I have taken the concept of "pattern" as foundational, and have characterized "pattern" as meaning "representation as something simpler."
But what is representation? What is simplicity?
In this (rather abstract, theoretical) post, I will suggest a way of grounding the concepts of representation and simplicity (and hence, indirectly, pattern) in terms of consciousness -- or more specifically, in terms of the concept of attention in cognitive systems.
I'll speak relatively informally here, but I'm confident these ideas can be formalized mathematically or philosophically if one wishes...
From Attention to Representation
Suppose one has an intelligent system containing a large amount of contents; and each item of contents has a certain amount of attention associated with it at a given point in time.
(One can characterize attention either energetically or informationally, as pointed out in Section 2.6 of my recent review paper on consciousness. Given the close connection between energy and information in physics, these two characterizations may ultimately be the same thing.)
In real-world cognitive systems, attention is not distributed evenly across cognitive contents. Rather, it seems to generally be distributed in such a way that a few items have a lot of attention, and most items have very little attention, and there is a steep but continuous slope between the former and latter categories. In this case, we can speak about the Focus of consciousness as (a fuzzy set) consisting of those items that have a lot of attention during a certain interval; and the Fringe of consciousness as (a fuzzy set) consisting of those items that have more attention than average during a certain interval, but not as much as the items in the Focus do. (The general idea that human consciousness has a Focus and a Fringe goes back at least to William James.)
It seems to me one can ground the notion of representation in the structure of consciousness, specifically in the relation between the Focus and the Fringe.
Namely, one can say that ... R represents E, to system S, if: In the mind of system S, when R is in the Focus, this generally implies E is likely to be in the Fringe at around the same time (perhaps at the same time, perhaps a little earlier, or perhaps a little later).
As a single example, consider the typical simplifying model of the visual cortex as a processing hierarchy. In this case, we may say that when we are visually remembering the tree
- the state of the upper levels of the visual hierarchy is in Focus, along with bits and pieces of the lower levels
- the full state of the whole visual hierarchy is mostly contained in Fringe
So the rough visual image we have of the tree in our "mind's eye" at a certain point in time, represents the richer visual image of the tree we have in our broader sensorimotor memory.
On the other hand, the phrase "the tree in the middle of my old backyard" may represent my stored visual images of that tree as well, if when that phrase occurs in my Focus (because I heard it, said it, or thought about it), my stored visual images rise into my Fringe (rising up from the deeper, even less attended parts of my memory).
From Attention to Simplicity
I'd like to say that R is a pattern in E if: R represents E, and R is simpler than E. But this obviously begs the question of what constitutes simplicity....
In prior writings, I have tended to take simplicity as an assumptive prior concept. That is, I have assumed that each mind has its own measure of simplicity, and that measurement of pattern is relative to what measure of simplicity one chooses.
I still think this is a good way to look at it -- but now I'm going to dig a little deeper into the cognitive underpinnings of how each mind generates its own measure of simplicity.
Basically, I propose we can consider E as simpler than F, if it's generally possible to fit more stuff in the Focus along with E, than along with F.
Note that both E and F may be considered as extending over time, in this definition. Sometimes they may be roughly considered as instantaneous, but this isn't the general case.
One technical difficulty with this proposal is how to define "more." There are many ways to do that; one is as follows....
Define simple_1 as follows: E is simpler_1 than F if it's generally possible to fit a greater number of other coherent cognitive items in the Focus along with E, than with F. (This relies on the concept of "coherence" of a cognitive item as a primitive -- or in other words, it assumes that the sense or notion of what is a "coherent whole" is available to use to help define simplicity.)
Then define simple_2 as: E is simpler_2 than F if it's generally possible to fit a set of cognitive items with less simplicity_1 in the Focus along with E, as compared to with F.
One can extend this to simple_3, simple_4, etc., recursively.
According to this approach, we would find a detailed image of a tree is less simple than a rough, approximate image. When visualizing a detailed image, we keep more different samples of portions of the detailed image in Focus, leaving less room for anything else.
Similarly, the concept of the function x^2, once we understand it, takes up much less space in Focus than the procedure "take a number and multiply it by itself", and much less than a large table of pairs of numbers and their squares. Once an abstraction is learned (meaning that holding it in Focus causes appropriate knowledge to appear in Focus), and mastered (meaning that modifying it while it's in Focus causes the contents of Fringe to change appropriately), then it can provide tremendous simplification over less abstract formulations of the same content.
From Attention to Pattern
So, having grounded both representation and simplicity in terms of the structure of attention, we have grounded pattern in terms of the structure of attention. This is interesting in terms of the cognitive theory I outlined in my 2006 book The Hidden Pattern and elsewhere, which grounded various aspects of intelligence in terms of the "pattern" concept.
As I've previously grounded so much of cognition in terms of pattern, if one then grounds pattern in terms of consciousness, one is then in effect grounding the structure and dynamics of cognition in terms of simple aspects of the structure of consciousness. This can be viewed mathematically and formally, and/or phenomenologically.
Logical and Linguistic Representation
Often when one hears about "representation", the topic at hand is some sort of formal, logical or linguistic representation. How does that kind of representation fit into the present framework?
Formal or semi-formal systems like (formal or natural) languages or mathematical theories may be viewed as systems for generating representations of cognitive items.
(What I mean by a semi-formal system is: A system for generating entities for which, for a variety of values of x less than 1, we have a situation where a fraction x of the system's activity can be explained by a set of n(x) formal rules. Of course n(x) will increase with x, and might sometimes increase extremely fast as x approaches 1. Natural languages tend to be like this.)
When we have a situation where
- R represents E
- R is a construct created in some formal or semi-formal system S
- E is not a construct in S; rather, E is connected via some chain of representations with sensory and/or motor data
then we can say that E "grounds" R.
Grounding tends to be useful in the case of systems where
- R is commonly simpler than E (or at least, there's some relatively easy way to tell what will be the situations in which R is going to be simpler than E)
- There is a methodology for going from E to the formal / semi-formal representation R, that doesn't take a huge amount of attention (once the mind is practiced at the methodology)
- Carrying out manipulations within the formal / semi-formal system commonly generates new formal / semi-formal constructs that represent useful things
These criteria hold pretty well in the case of human languages, and most branches of mathematics (I suppose the jury's still out on, say, the theory of inaccessible cardinals....)
Note that one system may be grounded in another system. For instance, formal grammars of English are grounded in natural English language productions -- which in turn are grounded, for each language user, in sensorimotor experience.
If it is simple to generate new representations using a certain system, then this means the process of representation-generation is a pattern in a the set of representations generated -- i.e. it's simpler to hold that process in Focus over an interval of time, than to hold the totality of representations generated by it in Focus over an interval of time. The formal and semi-formal systems adopted by real-world minds, are generally adopted because grounding is useful for them, and their process of representation-generation is a pattern.
This is all quite abstract -- I'll try to make it a little more concrete now.
Suppose I tell you about a new kind of animal called a Fnorkblein, which much enjoys Fbljorking, especially in the season of YingYingYing. You can then produce sentences describing the actual or potential doings of these beings, e.g. "If Fnorkbleins get all their joyful Fbljorking done in YingYingYing, they may be less happy in other seasons."
These sentences will be representations of, and patterns in, your visual images of corresponding scenes (your mental movie of the Fnorkbleins romping and Fbljorking in the throes of their annual YingYingYing celebration, and so forth). They will ground these images.
Furthermore, the process of formulating this Fnorkblein-ful sentences, will take relatively little Focus for you, because you know grammar. If you didn't know grammar, then formulating linguistic patterns representing Fnorkblein-relevant images would require a lot more work, i.e. a lot more Focus spent on the particulars of Fnorkbelein-ness.
Of course, people can use grammar fairly effectively -- including about Fnorkbleins -- without any knowledge of any explicit formalization of grammar. However, if one wants people to stick close to a specific version of grammar, rather than ongoingly improvising in major ways, it does seem effective to teach them explicit formalized rules that capture much of everyday grammatical usage. That is, if the task at hand is not deploying the grammar one knows in practical contexts, but rather communicating or gaining knowledge regarding which sentences are considered grammatical in a certain community -- then formalizations of grammar become very useful. This is the main reason grammar is taught in middle school -- giving a bit of theory alongside the real-world examples a child hears in the course of their life, helps the child learn to reliably produce grammatical sentences according to recognized linguistic patterns, rather than improvising on the patterns they've heard as happens in informal communication. (And it may be that formal grammars are also useful for teaching AIs grammar, to help overcome their lack of the various aspects of human life and embodiment that human children learn to pick up grammar implicitly from examples -- but that's a whole other story.)
It seems the act of teaching/learning the rules of grammar of a language, constitutes a pattern in "the act of communicating/learning the set of sentences that are grammatical in that language", in the sense that: If one has to tell someone else how to reliably assess which sentences are grammatical in a certain language (as utilized within a certain specific community), a lot less Focus will be spent via telling them the rules of grammar alongside a list of examples, than by just giving them a long list of examples and leaving them to do induction. When teaching grammar, while a rule of grammar is in the Focus, the specific examples embodying that rule of grammar are in the Fringe. While passing the rules of grammar from teacher's Focus to student's Focus, the real point is what is being represented: the passage of sets of sentences judged as grammatical/ungrammatical from teacher's Fringe to student's Fringe.
The rules of grammar, then, may be described as a "subpattern" in the act of communicating a natural grammar (a subpattern meaning they are part of the pattern of teaching the rules of grammar). This may seem a bit contorted, but it's not as complicated as the design of the computer I'm typing this on. Formal grammars, like Macbooks, are a complex technology that only emerged quite recently in human evolution.
Interpretations....
And so, Bob's your uncle.... Starting from the basic structure of consciousness, it's not such a big leap to get to pattern -- which brings one the whole apparatus of mind as a system for recognizing patterns in itself and the world -- and to systems like languages and mathematics.
One can interpret this sort of of analysis multiple ways ... for instance:
Taking physical reality as the foundation, one can study the structure of consciousness corresponding to a certain physical system (e.g. a brain), and then look at the structure of the mind corresponding to that physical system as consequent from the structure of its consciousness.
Taking experience as the foundation, one can take entities like Unity and Attention as primary, and then derive concepts like Focus and Fringe, and from there get to Representation and Pattern and onwards -- thus conceptually grounding complex aspects of cognition in terms of phenomenological basics.
3 comments:
Ok, some thoughts and questions...
1. "One can characterize attention as either Energy or Information." Is this in part because the many of the objects of attention have energy and momentum?
I recently awakened from the end of a dream into a deep meditative state while still being 'asleep'. From there "I" or my focus of attention was able to examine closely the percolation of 'patterns' (images, phrases, music fragments, snapshots of events from my planetside life. 'I' was able to watch and re-enter that chaotic substrate at will. I noticed that the arising patterns mostly related to personal experiences had charge and momentum. Interacting with them caused them to cluster to together and follow sequential transformations. And so I wonder if this experience had some external validity and provided further insight into some of the ecology of patterns within the focus of attention.
2. Are patterns linked in representation because they have a similarity of pattern? How are patterns linked into associative webs?
3. Do psychedelics like LSD and mushrooms increase the energy of the focus of attention or do they narrow the focus so patterns and their relationships seem to have greater, even fractal like complexity?
4. Do we construct stories or narrative sequences of patterns as a method of integrating and simplifying information? And does this have any implications for constructing Artificial General Intelligence?
5. Is the relationship between patterns itself a pattern? Can patterns become encapsulated as patterns or objects of attention?
6. How does fantasy work? An old psychedelic insight of mine was that objects of consciousness-attention had different qualities (patterns) which could be transferred to other objects. Can this work in your model of patterns within the focus attention?
I’m not that much of a internet reader to be honest but your blogs really nice, keep it up!
I’ll go ahead and bookmark your site to come back in the future. Many thanks|
Feel free to surf to my page - 대구오피
(jk)
Interesting post I enjoyed read this
Post a Comment