WORLDS, EMPIRICISM & DATA

The Physical World

What it is	A set of constraints that determine what is and isn't possible. We call it “the laws of physics” (even though we don't know if they are immutable 'laws'). Animals and robots perceive the physical world through sensors.
Interaction	We think of the 'world' and 'intelligent beings' as separate processes. It is the interaction between intelligence and the world that is the focus of study in artificial intelligence. To be capable of adaptation requires measuring (some part of) the world. This is done via sensors.
Sensors are physical	Our sensors are made from the same stuff that they perceive and are subject to the same laws of physics.
“The real world”	…is a hypothesized phenomenon based on our collective experience of it and the apparent coordination this experience has with the apparent (experienced) experience of other similar beings. René Descartes, the French philosopher, famously claimed that “I think, therefore I am.” He recognized that the only certainty we have of anything is that we perceive in the here-and-now.
Artificial Worlds	We may conceive of any “world” which follows different rules than our own. These worlds are potential worlds for AI systems, just as the physical world is.
However …	Any implemented world, whether abstract or otherwise, must bow to the nature of the physical universe, because implementation means physically incarnated.
Hence	The nature of our physical universe is fundamental in AI.
A Question of (Un)certainty	The physical world, and in fact many artificial ones also, are uncertain, meaning that there is a lot about them that we don't know.
Reliable Regularity	To do anything reliably means depending on reliable regularity which is conducive to prediction.
AI Boils Down To	Building machines that can figure out what can be reliably achieved in uncertain worlds.
Abstract Worlds	We may of course define any kind of “world” of our choosing. However, if it is to be implemented it must run using some physical properties, be it an abacus, transistors, light, or something else, and if uses physical properties these must obey physical laws, which means that 1. an abstract AI that cannot be implemented is not intelligent (it is a blueprint for something else), and 2. any AI must be able to address - using intelligence - physical properties.

Worlds: How it Hangs Together

W: A World	W = { V,F,S₀,R }
V: Variables	V = { v₁, v₂, . . . , v{\|\|V\|\|} }
F: Transition Functions	F is a set of transition functions / rules describing how the variables can change. The dynamics can intuitively be thought of as the world’s “laws of nature”, continually transforming the world’s current state into the next: S{t+δ} = F(S_t).
C: A World Clock	The clock updates the Transition Functions. In the physical world C updates F (including energy transfer), irrespective of anything and everything else that may happen in the World, constraining how much can happen for any time unit.
S₀: Initial State	S₀ is the State that W started out in. In any complex world this is unlikely to be known; for artificial worlds this may be defined.
R: Relations	R are the relations between variables in the world. These may be unknown or partially known to an Agent in the world.
	Static World	Changes State only through Agent Action.
	Dynamic World	Changes State through Agent Action and through other means.
State	s_t in V_t. A set of variables x with a set of values, specified to some particular precision (with constraints, e.g. error bounds), for relevant to a World. For all practical purposes, in any complex World “State” refers by default to a sub-state, since it is a practical impossibility to know its full state (values of the complete set of variables) of a world; there will always be a vastly higher number of “don't care” variables than the variables listed for e.g. a Goal State (a State associated with a Goal).
	State definition	s_t in V_t where { x_l, x_u } \| {x_l =< x =< x_u} defines lower (x_l) and upper (x_u) bounds on acceptable range for each x to count towards the State, respectively.
Exposable Variables	Variables in V that are measurable and/or manipulatable in principle.
Observable Variables	Variables in V that can be measured for a particular interval in time are observable during that interval.
Manipulatable Variables	Variables in V whose value can be affected, either directly or indirectly (by an Agent or something else).
Measurement	The only way to “capture the world”, e.g. for the purposes of getting something done, is by sampling some of the physical properties of the world's variables at a particular time and place. This is what we call a 'measurement'.
Data	The outcome and record of a (stored) measurement that has been committed to at a particular time and place.

Laplace's Daemon


Concept	If a world is deterministic, and everything in it is caused from the ground up, from the smallest parts, then everything in that world is pre-determined based on its starting state.
Laplace	“In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism, by Pierre-Simon Laplace in 1814. According to determinism, if someone (the demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics.” source: Wikipedia
Hume	David Hume's theory of causation states that cause and effect relationships are not a product of natural law or universal truth, but are instead based on the necessity that we associate events based on experience.

Determinism vs. Non-Determinism

Is our universe deterministic?	This is a major question for physics, but ultimately is not of much consequence for those building GMI (general machine intelligence). This is because any agent situated in the physical world will never know the precise position, direction and momentum of all its smallest particles, and thus must always deal with uncertainty.
Regularity	A world with no regularity is pure noise. In such a world intelligence is useless.
Pure Determinism	A world that is completely deterministic is pre-determined at all levels for all eternity; in such a world there is no concept of choice, and hence there can be no relevance for intelligence.
“Axiomatic AI”	Some mathematicians believe the universe to be fundamentally mathematical, and see the role of science (and mathematics) to find its “ultimate formula”. Many AI folks seem to subscribe to such a view. We'll come back to that in a bit.

Time Scales of the Physical World Relevant to AI

From Card, Moran & Newell et al. The Psychology of Human-Computer Interaction (1983) & K. R. Thórisson PhD Thesis, MIT, 1996.

Maxwell's Demon

Source: Wikipedia By User: Htkym - Own work, CC BY 2.5, REF
A Thought Experiment	Imagine a container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. The average speed of the molecules in B will have increased while in A they will have slowed down. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics. A heat extractor operating between the thermal reservoirs A and B could extract energy from this temperature difference, creating a perpetual motion machine. [ Adapted from Wikipedia ]
The Error	The thought experiment is flawed because the demon must be part of the same system that the container is part of; thinking (or computation, if the demon is a robot) requires time and energy, and so whatever heat is saved in the container will be spent to run the demon's thinking processes. (This was first proposed in "On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings" \| 1929 by Leo Szilard.)

The Physical World & AI Research

Physical World	The field of physics has been systematically studying the physical world since the ancient Greeks. Over 2000 years later physics is now the most advanced scientific field of all of science. Any proper scientific theory of anything must ultimately rest on its shoulders.
What is it?	Physics seeks to uncover the “ultimate” rules which determine how the universe behaves, including life, intelligence and everything else. No (general or limited) intelligence in a complex environment such as the physical world can be granted access to a full set of axioms of the system it’s controlling, let alone the ⟨agent,environment⟩ tuple, and thus the behavior of a practical generally intelligent artificial agent as a whole simply cannot be captured formally. (see Steunebrink et al 2016)
Useful AI	To be useful, an AI must do something. Ultimately, to be of any use, it must do something in the physical world, be it building skyscrapers, auto-generating whole movies from scratch, doing experimental science or inventing the next AI.
What this means	A key target environment of the present work is the physical world.
Uncertainty	Since any agent in the physical universe will never know everything: Some things will always be uncertain.
Novelty	In such a world novelty abounds—most things that a learner encounters will contain some form of novelty.
Learning	Some unobservable exposable variables can be made observable (exposed) through manipulation. For any Agent with a set of Goals and limited knowledge but an ability to learn, which variables may be made observable and how is the subject of the Agent's learning.

Empiricism

What it is	The idea that all knowledge comes from experience – the senses. In AI it also means that this experience comes from the physical world, through physical sensors.
Why it matters	Before the emphasis on empirical knowledge, science did not have a chance to rise in any obvious way above “other sources of knowledge,” including old scriptures, intuition, religious beliefs, or information produced by oracles.
Empiricism & Science	The fundamental source of information in (empirical, i.e. experimental) science is experience, which eventually became the formalized comparative experiment.
Comparative Experiment	A method whereby two experimental conditions are compared, were they are identical except for one or a few strategic differences that the experimenters make. The outcome of the comparison is used to infer causal relations. Often called “the scientific method”, this is the most dependable method for creating reliable, sharable knowledge that humanity has come up with.
Logical Positivism	Philosophical school of thought closely related to empirical science.
Rationalism	Historically a philosophically opposing view to empiricism, contending that knowledge is produced through innate knowledge, not through experience.
Empirical Rationalism	Both pure empiricism and rationalism are exaggerated views on where knowledge comes from. The sensible happy medium is that knowledge is bootstrapped from innate bootstrapping processes on which knowledge is built through experience. This is the philosophical view that we take in this course.

Key Concepts in Empirical Science

Theory	A scientific (empirical) theory is a “story” about how certain phenomena relate to each other. The more details, the more accurately, and the larger scope the theory covers, the better it is.
Hypothesis	A statement about how the world works, derived from a theory.
Experimental design	A planned interference in the natural order of events.
Subject(s)	Subject of interest - that to be studied, whether people, technology, natural phenomena, or other
Sample	Typically you can't study all the individuals of a particular subject pool (set), so in your experiment you use a sample (subset) and hope that the results gathered using this subset generalize to the rest of the set (subject pool).
Between subjects vs. within subjects design	Between subjects: Two separate groups of subject/phenomena measured Within subjects: Same subjects/phenomena measured twice, on different occasions
Quasi-Experimental	When conditions do not permit an ideal design to be used (a properly controlled experiment is not possible), there may still be some way to control some of the variables. This is called quasi-experimental design.
Dependent variable	The measured variable(s) of the phenomenon which you are studying
Independent variable	The variable(s) that you manipulate in order to systematically affect (or avoid affecting) the dependent variable(s)
Internal validity	How likely is it that the manipulation of the independent variables caused the effect in dependent variables?
External validity	How likely is it that the results generalize to other instances of the phenomenon under study?

Controlled Experiment

What is it?	A fairly recent research method, historically speaking, for testing hypotheses / theories
When	When it is possible to control and select everything of importance to the subject of study
How	Select subjects freely, randomize samples, remove experimenter effect through double-blind procedure, use control groups, select independent and dependent variables as necessary to answer the questions raised.
Why randomize?	Given a complex phenomenon, it is impossible to know all potential causal chains that may exist between the various elements under study. Randomization lessens the probability that there is systematic bias in any factors that are not under study but could affect the results and thus imply different conclusions.
What is randomized?	The sample should be randomized; subjects should be randomly assigned to control group versus experimental group; Any independent variable identified which could affect the results but is not considered of interest to the research at hand.
Bottom line	The most powerful mechanism for generating reliable knowledge known to mankind.

Center for Analysis and Design of Intelligent Agents

Table of Contents

WORLDS, EMPIRICISM & DATA

The Physical World

Worlds: How it Hangs Together

Laplace's Daemon

Determinism vs. Non-Determinism

Time Scales of the Physical World Relevant to AI

Maxwell's Demon

The Physical World & AI Research

Empiricism

Key Concepts in Empirical Science

Controlled Experiment