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T-720-ATAI-2016 Main


Lecture Notes F-7 02.02.2016


What Kind of System is Mind?

Simple system The human brain consists of <m>1011</m> neurons, each with around 1000 connections. A computer has a lot less components, but can hardly be appropriately described as a 'simple system'. Wherever we look, everything points to the mind not being “simple”.
Complex uniform system While the neurons in the human brain are one kind of cell, there are at least 2500 types of neurons in the human brain; the number of major groupings of these is 500, with each group containing 5 types of neurons, on average. Ref So at least when it comes to human “wetware”, it doesn't point in the direction of uniformity.
Complex heterogeneous system The best (some say only) example of a general intelligence, the human mind, is best described as a “large, heterogeneous, densely-coupled system – a HeLD. It is a hybrid system.

When studying a system composed of many parts, some identifiable structures can be seen to form hierarchies, for dynamic systems both in space (mantissa and abscissa) and time (interaction of parts). In the human brain the number of neurons is <m>1011</m> (<m>y´ = 10y</m>).


Complex Systems

Kind of SystemWhat it Consists ofTheoryMethodology
Static system Elements of the system do not interact, or interact slowly. Example: Mountains. Depends on the domain. Ditto
Dynamic system Elements of the system interact. Depends on the domain. Ditto
Simple system Few interacting parts Mechanics Observation of operation, experimentation, parts analysis. Analytic analysis.
Complex uniform system Vast amounts of identical elements interacting Thermodynamics Statistics. Mathematical models and simulation.
Complex heterogeneous system Multiple unique elements interacting –missing!– Agent-based models and simulation

Properties of HeLDs

Emergence Properties of a system that are not inherent in the description of its parts. The wetness of multiple water molecules. The pressure of a gas when heated.
Two types of emergent properties Locally emergent; globally emergent.
Local emergence Property belongs uniformly to all the system's parts. If we can take a small part of the system away, and the rest still retains the emergent property, the property is called local. Atoms in a gas.
Global emergence Property belongs to sub-parts of the system. If the emergent property disappears when we take away a part of it, the property is globally emergent. Spark plugs in an automobile.
Brains Human brains exhibit both globally and locally emergent properties, along several dimensions.

How to Study HeLDs Scientifically

Reductionism The method of isolating parts of a complex phenomenon or system in order to simplify and speed up our understanding of it. See also Reductionism on Wikipedia.
Occam's Razor Key principle of reductionism. See also Occam's Razor.
HeLD Cannot be studied by the standard application of reductionism/Occam's Razor, because the emergent properties are lost. Instead, corollaries of the system – while ensuring some commonality to the original system in toto – must be studied to gain insights into the target system.
Agent & Environment We try to characterize the Agent and its Task-Environment as two interacting complex systems. If we keep the Task-Environment constant, the remaining system to study is the Agent and its controller.

How to tease apart HeLDs.

Relationship between system, its task-environment, and the world.

What Kind of Worlds?

Balance The Worlds we are interested in strike a balance between completely dynamic and completely static.
They also strike a balance between completely deterministic and completely random; some regularity must exist at a level that is observable initially by a learning agent.
Completely static No (or little) need for learning.
Completely random Learning is of no use.
Limited time No Task, no matter how small, takes zero time.
“Any task worth doing takes time.”
All implemented intelligences will be subject to the laws of physics.
Limited energy “Any task worth doing takes energy.”
All implemented intelligences will be subject to the laws of physics.
No task takes no time or energy If <m>te</m> is a function that returns time and energy, an act of perception
<m>te(p in P) > 0</m>
a decision <m>d</m> in
<m>{te({d in D}) > 0}</m>,
and an action
<m>te(a in A) > 0</m>.
It follows deductively that since any Task requires at the very least one of each of these, in the minimum case to decide whether the Goal of a Task <m>T</m> is achieved, then
<m>te(T) > 0</m>.
Anything that takes zero time or zero energy is by definition not a Task.

What Kind of Task-Environments?

Environment Large number of potentially relevant variables.
Task Ditto.
Medium number of Solutions.
Instructions: possibly.

Characterizing a World

World A set of variables with constraints and relationships.
<m>W = {lbrace V,F rbrace}</m>
where <m>V</m> is a set of variables and <m>F</m> is a set of transition functions / rules describing how the variables can change.
Static World Changes State only through Agent Action.
Dynamic World Changes State through Agent Action and through other means.
Physical World In a physical world
<m>W = {lbrace}x_1, x_2, … x_n, f_1, f_2, … f_m {rbrace}</m>
<m>x</m> are real-valued variables,
<m>V_{t+delta} = F(V_{t})</m>
<m>{lbrace}{x}over{.}_1, {x}over{.}_2, … {x}over{.}_n {rbrace}</m>
represent the first derivative of the variables during continuous change.
State A set of values (with constraints, e.g. error bounds) for a set of variables <m>x</m> relevant to a World.
For all practical purposes, in any complex World we will speak of “State” even for sub-states, as most useful States will be sub-states, since there will always be a vastly higher number of “don't care” variables than the variables listed for e.g. a Goal State.
State definition <m> S = V </m>
<m> lbrace_x_l_x_u_rbrace {
} x_l_x_x_u </m>

define lower and upper bounds on acceptable range for each <m>x</m> to count towards the State, respectively.
Environment <m>{E = {lbrace V_E, F_E rbrace} + C delim{} V_E subset V & F_E subset F }</m>

where <m>C</m> are additional constraints on
<m>V, F</m>
and some values for <m>V</m> are fixed.
Task A Problem that can be assigned in an Environment. Typically comes with Instructions (guide to Solutions, partial Solution or full Solution - at some level of maximum detail).
“Task” definition An assigned Problem.
Task-Environment An Environment in which one or more Tasks may be assigned.
Problem A Goal with (all) relevant constraints imposed by a Task-Environment.
Goal A (future) (sub-) State to be attained, plus optional constraints on the Goal.
“Goal” definition <m>G subset S </m>

attached to a Problem.

Family A set whose members share one or more common trait within some sensible (defined) allowed variability, defined as one or more of the types of variables, number of variables, the ranges of these variables.
Problem Family A set of problems that are similar in important ways; a Problem and its variations.
Domain A Family of Environments.
Constraint A set of factors that limit the flexibility of that which it constrains.
Solution The set of (atomic) actions that can achieve a Goal in a Task-Environment.
Action The changes an Agent can make to variables relevant to a Task-Environment.
Plan A partial way to accomplish a Task.
Instructions Partial Plan for accomplishing a Task, typically given to an Agent along with a Task by a Teacher.
Teacher The Agent assigning a Task to another Agent (student).


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