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2.1: World-model

Intelligence is an evolutionary advantage because it enables us to model, predict, and manipulate reality.  This includes not only Joe Caveman (or rather, Pat Hunter-Gatherer) inventing the bow and arrow, but Chris Tribal-Chief outwitting his (1) political rivals and Sandy Spear-Maker realizing that the reason her spears keep breaking is that she's being too impatient while making them.  That is, the "reality" we model includes not just things, but other humans, and the self.  (2).

A chain of reasoning is important because it ends with a conclusion about how the world works, or about how the world can be altered.  The "world", for these purposes, includes the internal world of the AI; when designing a bicycle, the hypothesis "a round object can traverse ground without bumping" is a statement about the external world.  The hypotheses "it'd be a good idea to think about round objects", or "the key problem is to figure out how to interface with the ground", or even "I feel like designing a bicycle", are statements about the internal world.

From an external perspective, cognitive events matter only insofar as they affect external behavior.  Just so, from an internal perspective, the effect on the world-model is the punchline, the substance.  This is not to say that every line of code must make a change to the world-model, or that the world-model is composed exclusively of high-level beliefs about the real world.  The thought sequences that construct a what-if scenario - a subjunctive fantasy world - are altering a world-model, even if it's not the model of the world.  A "vague feeling that there's some kind of as-yet unnamed similarity between two pictures" is part of the content of the AI's beliefs about the world.  The code that produces that intuition may undergo many internal iterations, acting on data structures with no obvious correspondence to the world-model, before producing an understandable output.

What makes a pattern of bytes - or neurons - a "model"?  And what makes a particular statement in that model "true" or "false"?  (3).  The best definition I've found is derived from looking at the cause of our intelligence:  "Intelligence is an evolutionary advantage because it enables us to model, predict, and manipulate reality."  Models are useful because they correspond to external reality.

I distinguish four levels of binding:

• A sensory binding occurs when there is a mapping between the model's data structures and characteristics of external reality.
• A predictive binding occurs when the model can be used to correctly predict future sensory inputs.  (This presumes some kind of sensory device targeted on external reality.)
• A decisive binding occurs when the model can predict the effects of several possible actions on external reality, and choose whichever action gives the best result (according to some goal system).  By modeling the future given each of several possible actions, it becomes possible to choose between futures - that is, between future sensory inputs.  (If the model is sufficiently accurate.)
• A manipulative binding occurs when a future can be hypothesized, and a sequence of actions invented which results in that future.  Given a desirable future - that is, a high-level property of the model which is defined by the goal system as an end in itself ("supergoal"), or which is a means to an end ("subgoal") - it is possible to invent the actions required to bring the model into correspondence with that future.  If the model is correct, taking the specified external actions will actually result in the desired external reality.
• Qualitative actions are selected from a finite set.  If this set is small enough that all possible actions can be modeled - and are modeled - then there is no fundamental distinction between a "decisive binding", and a manipulative binding that uses qualitative actions.
• Quantitative actions have one or more real (i.e., floating-point) parameters.  Since this will usually make an exhaustive, "blind" search either theoretically or practically impossible - particularly if the fit must be exact - some conscious heuristic, or a reversible feature of a sensory modality, must be used to derive the numerical action required from the numerical outcome specified.  (Note that adding a continuous time parameter to a simple on-or-off qualitative action makes it a quantitative action.)
• Structural actions have multiple elements (quantitative or qualitative), possibly with links or interactions (quantitative or qualitative).  Emitting a string of characters - "foobar" - would be an example of a structural action.  To deduce a required structural action without an exhaustive or impossible search requires either (A) a known rule linking actions and results, simple enough to be reversible, or (B) deliberate analysis of the simpler elements making up the structure.

The "world-model" for an AI living in that microworld consists of everything the AI knows about that world - the positions, velocities, radii, and masses of the billiard balls.  More abstract perceptions, such as "a group of three billiard balls", are also part of the world-model.  The prediction that "billiard ball A and billiard ball B will collide" is part of the world-model.  If the AI imagines a situation where four billiard balls are arranged in a square, then that imaginary world has its own, subjunctive world-model.  If the AI believes "'imagining four billiard balls in a square' will prove useful in solving problem X", then that belief is part of the world-model.  In short, the world-model is not necessarily a programmatic concept - a unified set of data structures with a common format and API.  (Although it would be wonderfully convenient, if we could pull it off.)  The "world-model" is a cognitive concept; it refers to the content of all beliefs, the substance of all mental imagery.

Returning to the billiard-ball world, what is necessary for an AI to have a "model" of this world?

• A sensory binding occurs when there is covariance between internal data structures of the AI and external properties of the billiard-ball world.  For example, when the floating-point number representing the position of the billiard ball varies with the actual position of the billiard ball.  We would also require that the same mapping - the same rules of interpretation - suffice to establish a binding between the modeled positions and actual positions of all the other billiard balls.  (5).
• A predictive binding occurs when the model is accurate enough to predict the future positions of billiard balls.  Assume a sensory device that reveals the positions of billiard balls to the AI, with a sensory binding (correspondence) between the data output by the sensory device and the actual positions.  When the AI can establish a sensory binding (correspondence) between predicted data and actual data, a predictive binding has occurred.
• A decisive binding requires that some limited set of actions be available to the AI - for example, choosing whether to subtract some fixed increment of momentum each time a billiard ball bounces off a wall.  (This action has been chosen so as to introduce no quantitative elements.)  It requires a goal state, such as "three balls halted on the north side of the board".  It requires that the AI be able to project the results of actions - to predict the world-state given the current world-model plus the fact of the action.  It requires that the AI be able to recognize, internally, whether a given imagined result meets the criteria of the goal-state.  Given these cognitive capabilities in a perfect world (6), a blind search through possible actions, combined with the programmatic rule "When an imagined situation meets the goal criteria, implement the action-list leading to that situation", would create the "atomic" case of decisive binding.  (Of course, in accordance with the Law of Pragmatism, simplifying the design down to the level where it's easy to visualize the code has stripped it of all useful intelligence.  Real minds are vastly more complex.)
• A manipulative binding would occur if, for example, the AI could control a cue ball, and knew how to use this cue ball to "create two symmetrical groups of three billiard balls".  In this particular example, a structural result (two groups of three) is obtained through a series of quantitative actions (forces applied to the cue ball at particular times).

Suppose that a cue ball travelling south at 4 meters/second, bumping into a billiard ball travelling south at 2 meters/second, results in the cue ball and the billiard ball travelling south at 3 meters/second.  Suppose, furthermore, that these rules are contained within the AI's internal model of the environment, so that if the AI visualizes a cue ball at {8.2, 6} of radius 1 travelling south at 4 m/s, and a ball at {8.2, 10} of radius 1 going south at 2 m/s, the AI will visualize the balls bumping one second later at {8.2, 11}, and the two balls then travelling south at 3 m/s.  It's a long way from there to knowing - consciously, declaratively - that two balls in general bumping at 4 m/s and 2 m/s while going in the same direction will travel on together at 3 m/s.  It's an even longer way to knowing that "if billiard ball X bumps into billiard ball Y, then they will continue on together with the average of their velocities".  And it's a still longer way to reversing the rule and knowing that "to get a group of two balls travelling together with velocity X, given billiard ball A with velocity Y, bump it with billiard ball B having velocity (2X - Y)".  Finally, to close the loop, this last high-level rule must be applied to create a particular hypothesized action in the world-model, and the hypothesized action needs to be taken as a real action in external reality.

Without jumping too far ahead, there are a number of properties that a world-model needs to support high-level thought.  It needs to support time - multiple frames or a temporal visualization - with accompanying extraction of temporal features.  It needs to support predictions and expectations (and an expectation isn't real unless the AI notices when the expectation is fulfilled, and especially when it is violated).  The world-model needs to support hypotheses, subjunctive frames of visualization, which are distinct from "real reality" and can be manipulated freely by high-level thought.  (By "freely manipulated", I mean a direct manipulative binding; choosing to think about a billiard ball at position {2, 3} should cause a billiard ball to materialize directly within the representation at {2, 3}, with no careful sequence of actions required.)  And for the visualization to be useful once it exists, the high-level thought which created the billiard-ball image must refer to the particular image visualized... and the reference must run both ways, a two-way linkage.

Time, expectation, comparision, subjunctivity, visualization, introspection, and reference.  I haven't defined any of these terms yet.  (Most are discussed in 3: Cognition, although you can jump ahead to Appendix A: Glossary if you're impatient.)  Nonetheless, these are some of the basic attributes that are present in human world-models, and which are Necessary (But Not Sufficient) for the existence of high-level features such as causality, intentionality, goals, memory, learning, association, focus, abstraction, categorization, and symbolization.

NOTE:

I mention that list of features to illustrate what will probably be one of the major headaches for AI designers:  If you design a system and forget to allow for the possibility of expectation, comparision, subjunctivity, visualization, or whatever, then you'll either have to go back and redesign every single component to open up space for the new possibilities, or start all over from scratch. Actualities can always be written in later, but the potential has to be there from the beginning, and that means a designer who knows the requirements spec in advance.

• 1:  After some soul-searching, I decided to use "his" instead of "vis", since (a) hunter-gatherer societies are often blatantly sexist; (b1) I'd have no qualms about using "his" or "her" if we were talking about Alice and Bob in cryptography; (b2) from a cosmic perspective, one occupation has no greater significance than the other.
• 2:  It is very likely that human intelligence derives not from the need to outwit tigers, but the need to outwit other humans.  (See conspecifics, and sexual selection in the glossary.)  Hopefully, none of this will hold true of AIs.  It's just an important thing to know about humans.
• 3:  Philosophers have been wrestling with this problem, "the meaning of meaning", for ages.  Attempts to create a mathematical definition are probably doomed; there are no selection pressures in favor of reasoning processes which are precisely definable and provably correct.  Evolution favors the creation of useful models - that is, models whose use promotes inclusive reproductive fitness.  In some cases, such as tribal politics, selection pressures may have favored inaccurate, observer-biased models, with consequent problems for modern-day humanity.  See also Interlude: The Consensus and the Veil of Maya.
• 4:  This may sound like the setup for one of those jokes that ends with the physicist saying "First, assume a spherical chicken...", but the billiard-ball domain is complex enough to pose nearly every problem that would be faced by a real-world AI, including uncertainty.  Even if sensory information is perfect and complete, the internal model is still uncertain - will spending 30 CPU-seconds on a problem-solving strategy yield results, or just another blind alley?
• 5:  Since a mapping inherently requires a mapper, I do not believe that there is any way to mathematically define a sensory binding in an observer-independent fashion.  In fact, I do not believe there is any way to define any binding in an observer-independent way.  I do not believe there is any mathematical way to define when Turing-computable process A instantiates Turing-computable process B.  I've tried.
• 6:  In an uncertain world, the AI would need to be able to recognize if a plan had worked, and re-plan if the actions did not have the predicted results.  Smart minds design plans that bear in mind the possibility of error.

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