Principles of holistic control

Followup to: Where map meets the territory, Levels of structure, Keeping the target in sight, Vague questions and precise answers, Causal rules and unpredictable actions.

When mind is supporting a picture of environment, it is not being passive. Some of the future events in the environment are determined by this picture, they happen because they are in the picture. The chain of events flows from representation in the mind to the outcome through the actions, which lie on the both sides, in the mind and in the environment at the same time.

It is trivial that whatever state the low-level output event assumes in the mind, the same state will appear in reality, because it is the same event on both sides. For other events in the mind, it is not necessarily so; changing such events in the mind will make them represent environment incorrectly, rather than making them determine corresponding state of environment. On the other hand, every change that does leave representation correct, leads to the environment complying with it.

This perspective can be turned around: if representation is restricted to only assume correct states, it can be freely varied within that bound, and whatever picture of environment it chooses to draw will automatically come true.

One way of constructing an accurate picture of environment is through following the rules of thumb, filling the gaps in the picture based on known elements of any kind. When it is known that there is a chair in a room, it is possible to infer that the chair is likely to stand there, instead of flying in the midair, even though original description doesn’t include information about how the room floor relates to the chair.

Since this picture is centered around the actions of the agent that supports it, rules of thumb need to be sufficiently strong (if not individually then cumulatively) not to break down under the surprising changes of context that may result from the actions.

Each element of the representation asks a question, adds a constraint on the set of possible causal patterns that satisfy it. Additional elements help filling the gaps in the model of environment, initiating inference that weaves the structure. Not all details of the environment can be supported in the mind at once, even if they can be inferred from known facts. A tiniest hint may bring to attention many precise details, reconstructing intermediate elements of structure. Inferred from robust rules of thumb, state of mind would indirectly correspond to the state of environment, and giving different hints will lead to the state of mind corresponding to different aspects of environment.

The uncertainty about the future state of environment that is determined by the state of mind may be resolved in many ways, by assuming one of the allowed states of mind. On the side of the mind, the process of resolution of this uncertainty starts from making a decision, from introducing a fact in the model that doesn’t otherwise follow, and checking if the model assembles to a coherent state, if this element leaves the picture in the mind corresponding to environment, thus causing the environment to assume the state corresponding to the decision. If the decision consists in a relatively vague hint about the future, there are good chances that there is in fact a state of environment that satisfies the hint.

Much like drawing the attention to an aspect of environment, asserting a certain vague property in the future state of environment leads to construction of the detailed representation of the state of environment that has that property, driven by a multitude of specific inferred facts about the state of environment (both in the past and in the future) and general direction specified by the property. Where attention draws the details of representation from available factual information, model of the future may make up some of the details when they can be determined by the model. Thus constructed model will include events in the past and the future, but also the present, in particular low-level action events. Choosing a certain property in the future leads to construction of the model of environment that has that property, and the model of environment includes specific state of low-level actions in the present, which causes these actions to be carried out, which in turn determines the future to have required property, to be in accordance with the model.

The plan formed by the model of the future chosen to lead to a certain outcome doesn’t need to be very detailed, for example it doesn’t need to contain the whole sequence of low-level actions from the current point on. Plan gets refined as it unwinds, as more accurate factual information becomes available about events in the environment that were only modeled based on the goal at the start. At each moment, low-level action is chosen according to the best current guess included in the current model.

This approach allows to view the process of control in intelligent agent as a result of two cognitive pressures acting on representation of environment supported by its mind. The first pressure compels the representation in the mind to be correct, to depict the state of environment (past, future and present) as accurately as possible. The second pressure biases the representation to see the future state of environment that is as close as possible to the goal.

I call this perspective on how control algorithm could operate “holistic control”, to reflect the way plans get constructed. Inference operates across the levels of representation and in both directions in time, it is neither bottom-up nor top-down, it is not forward chaining or backward chaining. Control algorithm doesn’t contain clear-cut feedback loops, processing doesn’t happen in feed-forward fashion. The model of environment is held together by heuristic rules that aren’t organized in any kind of hierarchy, the model itself is “flat”, not modular except for the structure inherited from environment it represents. The operation of control algorithm is focused on the support of model of environment, not on action and perception. Action and perception are only peripheral (although indispensable) aspects of control, with low-level input binding the model of environment to reality at one tiny point, supplying new facts and showing the mistakes, and low-level output giving the model ability to participate in the causal web of environment.

Where map meets the territory

Followup to: Levels of structure, The dynamics of mind.

Events in the mind of intelligent agent indicate events in the environment. A configuration of events in the mind represents the current context, knowledge about which events are known to be present. Given a context, some additional events can be inferred according to known rules of thumb, supplementing the context with events on different levels of representation and resolving uncertain events.

The breakup of the current knowledge about environment on separate general events is a property of data structure, knowledge representation, designed for the purpose of being manipulated by inference algorithm. General events that don’t change (don’t become irrelevant or invalidated), and therefore don’t need to be manipulated by inference, don’t need to be separately represented in the mind. Events in the mind show what is different in the current knowledge about environment, they are active elements resulting from inference, starting from sensory input and trains of deliberative computation.

Most of the events in the mind are separate from events in the environment they represent. The property of representing (indicating) events in the environment results from using inference process that, through many intermediate steps, creates events in the mind in the right way. Some of the events, on the other hand, may be thought of as lying both in the mind and in the environment, and representing themselves. These are events of low-level input and output, boundary of the mind, where map meets the territory.

State of the environment is reflected in the mind, events outside the agent are warped around the border to fit inside its mind. These events include elements of future as well as past, elements independent on agent’s actions and determined by them. Two pictures of environment work by different laws: events in the environment itself are constrained by laws of physics and feature excruciating level of detail, while events in the mind are simple caricatures constrained by rules of thumb, mimicking the former. Both pictures meet at the identity of boundary events, at input and output. Events at the boundary are identical in both forms, and events further and further away from the boundary in both directions are traced through chains of relations holding in each of the pictures, reaching high-level events in the mind and events far away, both in space and time, in the environment. Captured in correspondence, pictures determine the elements in each other.

Causal rules and unpredictable actions

Followup to: Causation as robust indication, Unpredictability of actions.

Changes considered for causal rules to handle are usually brought up in the context of decision making. Decisions lead to actions, and actions can create radical changes in context. Being the most unpredictable, actions of intelligent agents serve as the hardest test for robustness of causal rules and filter out many rules of thumb that are not normally considered causal. The more significant changes are allowed to occur, the less rules of thumb are general enough to endure them.

Causal rules don’t need to be preserved for all physically possible contexts, since only contexts that follow from causal history of environment are actually realized, and only optimization processes that currently exist in the environment can change contexts in novel ways. Causal rules serve as a tool that works where the set of significantly different causal patterns remains approximately the same, but within that domain of applicability they allow to draw accurate conclusions. Thus, causal rules only need to persist during sufficiently insignificant changes in global context that preserve the semantics of events, through local changes in context that can be enacted by existing optimization processes.

For example, grass is usually wet when it’s raining. Wet grass is a good indicator of rain, it is a reliable rule of thumb in natural context. Yet if an intelligent agent creates a new context, by specifically pouring water on the grass, in this new context the rule will no longer hold, wet grass doesn’t cause rain. Colliding stones produce a sound in natural context, and if an intelligent agent collides stones in artificial context, there is still a sound, which shows that colliding stones cause a sound.

Causal rules are rarely infallible, the same principle that tests them and distinguishes them from mere correlations can break them as well. There usually is a way to create a contrived context in which a given causal rule will no longer hold. Colliding stones in vacuum or colliding specifically crafted elastic “stones” will produce no audible sound. Administering symptom relief medicine leads to disease not causing symptoms. Only causal rules that follow immediately from laws of physics or those guarded by limitations in available technology can withstand a directed attack. Thus, most of the causal rules have additional conditions, specifying the kinds of changes that they are able to withstand.

This places various correlations on the same scale with causal rules, distinguishing causal rules only by generality, applicability in wider context. Depending on the context, different strength is required from rules to carry out accurate inferences, and weaker rules can contribute considerably to determining the details not captured by stronger causal rules.

Causation as robust indication

Followup to: The flow of reality, Semantics of the rules of thumb.

There are multiple senses in which words causation and causality are used, and many historically accumulated complications. Basically, causality is a relationship between two events, cause and effect, that establishes the effect as reliably following (from) the cause. Causal relations are naturally used for describing functional structure of environment. In addition to enumeration of events (“button was pressed; light turned on”), causal relations establish the internal structure that binds these events (“button was pressed, which caused light to turn on”). Functional structure allows to model the dynamics of environment in different contexts, acting as an algorithm that computes state of environment given different initial conditions. This way, causal relations not just describe the structure of a fixed scene, but generalize to other scenes.

The sense in which effect follows from cause reliably is the subject of many disputes. Restricting the notion of causality only to relations that hold deterministically makes it almost useless for modeling real environment. Thus, effect should be allowed to sometimes not follow the cause, which contributes to the problem of connection between correlation and causation. Two events may be highly correlated, yet not causally dependent, and otherwise, two events may be causally dependent, but without overwhelming correlation. Apples often lie on the ground near the apple tree, but they don’t cause the apple tree to appear nearby. Smoking causes cancer, but only sometimes.

The difference that is usually pointed out between statistical properties and causal properties appears when studied scene is changed. One of the central problems in statistics is regression, inference of the whole distribution from limited number of observations. It can consist in e.g. finding the values of parameters that give a distribution from parameterized set that fits the data best. The distribution that describes the data is considered to be fixed and the same for all data points. Even when data points are taken from a process that changes its state over time, distribution that describes development of the process is still specific (even though it’s uncertain). Statistical properties of a single distribution describing static conditions are contrasted to causal properties that describe the behavior of the scene when conditions change. Statistical properties change with conditions, but causal properties are fixed, and can be used to regenerate statistical properties of the scene from changed conditions.

Yet if we consider the development of environment as a whole, there are no external changes to be applied to the dynamics of environment. Everything that happens, happens within the environment, every change is interaction between configurations within the dynamics of reality. From this perspective, causal properties may be regarded as statistical hypotheses that hold for considered part of the environment both before and after the change is applied to it through interaction with other parts of the environment. Statistical properties of a fixed distribution thus apply only to a limited part of the dynamics of the scene when it isn’t changed, while causal properties are more general statistical properties that persevere through “external” changes.

Let’s focus on a specific class of causal properties that describe rules of thumb which indicate events given other events. This way, a causality relationship between cause and effect becomes a rule of thumb that provides evidence for effect given the cause. The feature that distinguishes causal rules from other rules of thumb is that they provide evidence for effect given the cause in many contexts, even in contexts that were changed through interaction with various causal patterns. Causal rules are rules of thumb that are general enough not to break down as the dynamics of environment unfolds. In this sense, causal rules are the only reliable kind of rules of thumb.