<m>A</m>: An agent.
<m>C_A</m>: A cognitive controller (architecture) of agent <m>A</m>.
<m>P_A</m>: A perception process of agent <m>A</m> produces percepts.
<m>#</m>: A pattern, at any level of detail.
Given a pattern <m>'#'</m> and a perception <m>P</m> process of agent <m>A</m>, then
<m>P_A</m><m>('#'_n)</m>
is the percept produced by <m>A</m>'s <m>P</m> from pattern <m>'#'_n</m>.
<m>p_{i,A}</m>: A cognitive process of agent <m>A</m>; <m>p_{i,A}subset{C_A}</m>.
<m>G_A</m>: A set of top-level goals of agent <m>A</m>.
<m>g_A</m>: A subgoal of agent <m>A</m>; <m>{g_A} subset G_{A}</m>.
<m>B_A</m>: A set of actions or behaviors of agent <m>A</m> resulting from committing to one or more <m>g_A</m>.
Common sense tells us that if we were born with no sensory organs – at all – then we would be unlikely to develop a normal, healthy, fully-capable mind. The idea that perception is a necessary prerequisite for thought and intelligence has been at the center of epistemology for centuries. In the 1600s René Descartes, thinking about thinking, and about what reality really is, as well as his own place and existence in it, came up with the phrase Cogito ergo sum – I think, therefore I am. This was not just a phrase, it was a philosophical stance and conclusion that still permeates all deep thinking about thinking. A unique idea was that knowledge was constructed by the mind: If the wax that a candle is made from can so radically change shape and appearance, yet still be understood as “the same stuff”, then that had to be a process of thinking – since the perceptions were not enough to inform of this. And so thinking moved to the center stage, in the form of reasoning.
Descartes proposed a dualist theory, of mind and physical reality, where the mind is “immaterial” and interacts with the physical world through a particular part of the brain. One problem with this theory is that if the mind is immaterial, then how does it interact with the material body that it obviously controls? Descartes proposed that the mind interacts with the body through the pineal gland in the brain. He was right about the brain being important for thought. George “Bishop” Berkeley took this one step further and said that we – and in fact, all of existence – is nothing more than our sensations, since sensations are the only information we have about this thing we call “reality”. One problem with this view, pointed out by his critics, is that if something is not being observed it essentially does not exist, since all reality would then be created by the minds that perceive it. Berkeley did not despair but came up with an ingenious answer (but which most folks would now call silly), and this became the heart of his proof for the existence of God. The concept is nicely captured in this funny limerick:
God in the Quad by Ronald Knox ---- There was a young man who said, "God Must think it exceedingly odd If he finds that this tree Continues to be When there's no one about in the Quad." ---- REPLY Dear Sir: Your astonishment's odd: I am always about in the Quad. And that's why the tree Will continue to be, Since observed by Yours faithfully, GOD.
In spite of the absurdity to which philosophical musings have gone in the past few hundred years, the creation of the world by a perceiver is nevertheless a surviving idea which formed the basis for the school of cybernetics and the psychological theories of Jean Piaget. Piaget observed that children have very different ideas of what certain concepts mean than grownups – for example, the concepts of “more” and “less” seem to be interpreted by most youngsters in more simplistic ways than these concepts are intended to mean (saying, for example, that a thin tall glass has “more” water than a less tall but much wider container, which to a grownup obviously has more water than the thin glass). He conjectured that a human mind develops in stages, being lead through various developmental stages each of which is necessary for the next one, by interaction with the physical world and social beings.
This idea has been explored in the educational program of Seymour Papert, who has shown how educational results can be improved by organizing classes, educational material, etc. around the idea that children construct their own understanding. One obvious result from this thinking is that forcing every child into learning at the same pace is a good way to decrease the effectiveness of the education, since, if a child does not have proper preparation of a prior cognitive stage, efforts to build on this stage by presenting material which requires that stage to be reached beforehand, are likely to be a waste of time, or be inefficient at best.
Around the same time as Piaget was working on his theories the field of cybernetics adopted the idea of a “constructed” reality as well, contending that knowledge is not “handed down” or imparted to minds in some sort of direct way, but rather that the minds take an active part in constructing the knowledge they acquire. There are numerous reasons for taking this proposition seriously, as results in psychology, sociology, developmental robotics and artificial life seem to lend support for it in many ways.
Cybernetics developed along the same lines as computer science in that it emphasizes the transmission of information, and the operation of information transformation, abstracted from the medium in which it is implemented. This deflation of the importance of implementation stems in large part from this and the work of Alan Turing, who proposed a model for computation that we now refer to as “a Turing machine”, which abstracts away time and energy in computation, considering instead a “timeless” computation with infinite storage space. In spite of this “denouncement” of physics and “practical details” of any computational or intelligent process, some (tiny amount of) work in AI has nevertheless been done under the influence of constructivist theories in psychology, in particular the work of Drescher, whose thesis at the Massachusetts Institute of Technology described one of the first attempts at building an AI system that could, via interaction with the world, create concepts for things in its surroundings.
By the same token, my call for a new constructivist AI has at its center a focus is on the constructivist stance – that minds actively create their own knowledge via interaction with the world. But unlike prior work, it argues that the present methods developed, and loved, in traditional computer science will not suffice for achieving such systems, at least not in their ultimate form or promise of significant developmental autonomy. This is because these methodologies rely on traditions where manual creation of the detailed operations of the computing machinery is the only accepted method. The ability to create systems that can construct themselves, even to some small extent, is exceedingly difficult – if not impossible. And unlike prior efforts in cybernetics, a new constructivist AI must deal with the reality that computation takes time. Computing whether some statement is true, or whether some plan is better or worse than another, or whether we can find exceptions to some generalization about the physical world, is infinitely easier if we are given infinite time. Note that “infinite time” is even longer than “all the time in the world”. If we have infinite time we don't even have to hurry! We can just do our thing, for as long as we want, and look at all possibilities, even if there is an infinite number of them! Obviously that is not an option for the serious theoretician. In the context of intelligence assuming infinite time even creates an oxymoron, because if it weren't for finite time or finite resources, there would be no reason for intelligence to exist.
So the new constructivist AI must come to grips with how knowledge is temporally grounded. This creates a number of challenges, a primary one being that all cognitive processes must, more or less, be temporally grounded or temporally 'aware' – they must be relatable, in a reasonably easy way, to the progression of time in the physical world.
Our quest for systems that are more capable than those of yesteryear has brought us to the point of considering how such systems – that can adapt to a wide variety of contexts and learn a wide variety of tasks – should be architected. Since we cannot architect them by hand (we don't know what the wide variety of context and tasks may entail) we must impart some meta-principles to these systems, ways of having them “figure things out for themselves”. Since current methods of software development are not up to the task, how does the desire for such systems affect our toolset? What new tools and methods do we need?
If a system <m>A</m> increases autonomously the set of patterns <m>#</m> that it can recognize, and the set of states <m>S_o</m> that it can use as output to control the effects of the environment <m>E</m> on itself with respect to these patterns, the system is said to be growing its intelligence. Creation of models that describe <m>A</m>'s possible percepts <m>P</m>, without increasing the potential of <m>A</m> to control <m>E</m>, is growth of the knowledge of <m>A</m>, which is a subset and prerequisite of intelligence. Knowledge + available behavior to control the environment for the purposes of achieving <m>A</m>'s goals, is intelligence.
The distinction between knowing what and knowing how highlights the importance of unification of the two in producing intelligence: It is conceivable that a human will know a lot about a certain phenomenon <m>phi</m> without knowing much or anything about how to do something about or with <m>phi</m>; for that to happen the human must have actionable knowledge – an ability to to turn its knowledge of the various aspects of <m>phi</m> into actions that change or affect aspects of <m>phi</m>.
So far, intelligence in this new formulation is thus the ability of a system to autonomously increase its own ability to control states of its environment, to achieve its goals. But we need more than that, the system must be able to generate its own subgoals autonomously.
Any system capable of cognitive growth must be capable of some sort of self-evaluation, otherwise it will not be able to decide whether certain milestones in its growth are being reached, or whether changes made in light of experience have been for the better. The self evaluation must in fact be of a particularly powerful kind, compared to most constructionist approaches to such evaluation that we could cook up, because large parts of the system's knowledge, as well as the architecturo-cognitive mechanisms that produced them, must be able to serve as the subject of such an evaluation. In its most extreme case the whole architecture <m>Psi</m> evaluates its present state in light of past state(s):
<m>C~=~{f_m}~(C_{t-n})</m>
where <m>n</m> is some steps back in time. <m>f_m</m> is a meta-function that implements self-inspection. This is an example of a system-wide, transversal function: The system incorporates mechanisms that enable it to evaluate some significant part of itself, and use the outcome to decide what to do next. Whether the system inspects its own state to finish a particular immediate task, improve some subset of its own mechanisms, or evaluate its own growth, this is what is meant by transversal, pan-architectural functions. Such functions do not have to take the whole architecture as input, and they typically do not. It is more typical that some subset of the architecture <m>psi</m> is being evaluated:
<m>psi_{t+1}~=~{f_m}~(psi)~delim{|}~psi{subset}C_A</m>
Such self-inspection is a requirement for what has been called recursive self-improvement.
2022©K. R. Thórisson
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