p.4, 5 Although model building is not usually considered critical in the construction of scientific
theory, I would claim that it is... If the model is well conceived, it makes possible prediction and planning and
it reveals new possibilities.
p.11, 12 models, above all, make anticipation and prediction possible... In one sense,
all of science is based on model construction.
p.13-14 The program for studying emergence set forth here depends on reduction. Complicated systems
are described in terms of interactions of simpler systems.
p.14 For emergence, the whole is indeed more than the sum of the parts. To see this, let
us look again at chess. We cannot get a representative picture of a game in progress by simply adding the values
of the pieces on the board. The pieces interact to support one another and to control various parts of the
board. This interlocking power structure, when well conceived, can easily overwhelm an opponent with higher-valued pieces
that are poorly arrayed. A valid analysis of the game's setting must provide a direct way of describing these interactions.
p.23 Board games are a simple example of the emergence of great complexity from simple rules or
laws... Chess and Go have enough emergent properties that they continue to intrigue us and offer new discoveries
after centuries of study.
p.28 As we search for deeper understanding of the relation between numbers and models, maps are an appropriate
starting point. Maps eliminate detail in a straightforward way and, like games, they are among the earliest model-artifacts.
Moreover, our longer-range objective, a general setting for emergent processes, is a kind of map, so a better understanding
of maps will help define that objective.
p.38 In any game that is at all complex, a game plan or strategy is vital for effective play.
Roughly, a strategy is a prescription that tells us what to do as the game unfolds; it specifies a sequence of decisions.
p.41 the [recent chess-playing computer] programs are highly selective in the way they search the tree [of
possible game continuations]... we define strategies in much the same way we define games, via a set of rules. The
rules in the case of strategies are usually rules of thumb... Such rules pick out game features that... are relevant
to decisions at various points in the game... In this way we obtain an effective reduction of the enormous size of
the game tree and make possible an overall prescription that controls play throughout the game... Even if the strategy
has some components that are not easily described in terms of building blocks, it is a valuable starting point for modeling
the strategy.
p.42 all players are simultaneously trying to build models of what the other players are doing.
p.43 the computer is continually getting into parts of the move tree not previously observed... What, if
anything, shows the regularity and predictability we expect of emergent patterns?
Though prediction is difficult in these circumstances, it is not a hopeless task... weather models
do not yield exact predictions... Nevertheless, modern weather prediction is very helpful... It does forecast the likelihood
of rain... it does give the likely temperature ranges
p.44 The key to effective weather prediction, then, is the discovery and use of the mechanisms (building
blocks) that generate weather... The key to deeper understanding, as with weather prediction, is
to determine the level of detail and the relevant mechanisms... Using mechanisms as building blocks, we can
construct models that exhibit emergent phenomena in much the same way that interacting strategies in a game produce patterns
of interaction... perpetual novelty renders it difficult to make predictions, even when the mechanisms
(rules) and the initial state are specified.
p.45,46,48 To build a dynamic model we have to select a level of detail that is useful, and then
we have to capture the laws of change at that level of detail... There is, of course, no guarantee that we can find
simple laws of change for the level of detail selected. Indeed, the art of model building turns on selecting a level
of detail that admits simple laws... If the transition function (law) is "faithful", we can make predictions into
the indefinite future. Knowing the current state and input, we can determine the next state.... by simply iterating the use
of the transition function, we can explore future possibilities... The (usually simple) specification of a model - the transition
function - can yield a limitless array of consequences and predictions. A well-conceived model can, like chess, yield organized
complexities that repay decades and centuries of study. Moreover, these complexities may involve possibilities not conceived
by the modeler
p.54 just what is it that [Art] Samuel [creator of an early checkers-playing computer program]
was modeling? He was not attempting a detailed model of the thought processes of humans playing checkers. Rather, he was working
at the level of strategies. He selected building blocks describing features of the game relevant to good play, and
then provided ways of weighting and combining these building blocks to define strategies... The principles and rules
of thumb uncovered - clarifying the exploration of options (lookahead), subgoals, modeling the actions of other players, and
learning in the absence of reinforcement... have a central role in agent-based models of emergence and innovation.
p.55 The [Art Samuel computer-based] checkersplayer had to learn about early "stage-setting" moves that
make possible later obviously good moves. Stage-setting is the very essence of winning game play... human
players can usually acquire and use such knowledge... The checkersplayer must be able to emulate such performance.
p.65 A primate, for instance, ...can only react to things it can detect. Similarly, Samuel's checkersplayer
can only react to situations its features {vi} can distinguish.
p.75 It was a stroke of genius on the part of [Art] Samuel [creator of an early checkers-playing computer
program] to use his sum of weighted features, V, as an internal model of the opponent. With this one stroke he (a) greatly
amplifies V's power as a predictor, (b) makes possible rapid, sophisticated learning in the absence of reinforcement, (c)
uses model-based anticipation (lookahead) as a basis for learning, and (d) nicely implements [Hans] Berliner's exhortation
to avoid big mistakes.
p.76 Learning in complex environments requires a defined procedure for discerning early actions
that set up later, obviously good responses... In multiagent environments, emergent phenomena often arise from anticipation
of the actions of other agents.
p.78, 79 Credit to Stage Setting
Good play in a board game comes from subtle, stage-setting moves... that make possible later, obviously
good moves... The trick is to provide appropriate weights to features [JLJ or structures] that influence the choices
that set the stage... In effect, these features define subgoals to be sought in the absence of an obvious direction.
Their weights must come to favor choices leading to later, obvious advantage [JLJ or, in effect, positions that are deemed promising
and only later determined to be of obvious advantage].
p.122, 123, 124 what can we say about a general setting for the discussion of emergence? What form should
it take? ... By now it's clear that the setting must take modeling as its central concern: the setting must provide a way
to model a wide range of real systems that exhibit emergence ... the setting must capture the organized perpetual novelty
that we expect from games and other rule-based models... one recurring theme is essential to emergence: in each case
there is a procedure for freely generating possibilities, coupled to a set of constraints that limit those possibilities...
It is the thesis of this book that the study of emergence is closely tied to this ability to specify a large, complicated
domain via a small set of "laws." ...Agents [the components that make up our system of interest] are all described in terms
of rules or laws that determine their behavior in a larger context... The input state is determined by the immediate environment
of the agent, and the output state determines the agent's effect on its immediate environment... we are ready to start laying
out a general setting for the study of emergence via constrained generating procedures.
p.148 The very essence of an agent-based model is that individual agents are in direct contact with
only a limited number of other agents (often only one other) at any given time.
p.215, 216 When we play a game regularly, we begin to see certain kinds of patterns... that serve as building
blocks for longer-term, more subtle strategies. We use these patterns to select parts of the game tree, ignoring the overwhelming
range of nonproductive or uninteresting possibilities that make up most of the tree... Constrained by feasibility,
both human and program must find promising sequences in a vast space of combinations. Anticipation-based salient
features and sequences, in the manner of directed saccades [ A rapid intermittent eye movement, as that which occurs when
the eyes fix on one point after another in the visual field], offer great advantages over exhaustive search
