Hands For The Mind
Models, Imagination, and Our Human Nature
Kenneth Haase
Draft, not for citation or circulation
Copyright (C) 1997, 1998 by Kenneth Haase
Preface
- Chapter I: Hands For The
Mind
As hands are to our motions, models are to our
thoughts. The nature of our models affects our thoughts just as the
nature of our limbs affects our motions. But unlike our limbs, we
have choices about the models we use, choose, devise, or share.
Because of this, it is helpful to think about the models we are using.
- Chapter II: Models as
Interfaces
Models are natural interfaces between systems in
the world. Just as a cell membrane is an interface between the
structures and operations of the cell and a complex environment,
models are interfaces between the complexity of the world and the
structure of our understanding.
- The Case of the Year 2000
describes some problems with a common model of dates which connects
the structures and operations of many computer programs to an
organization of events used by humans and their organizations. The
problem with this model is that it reflects purposes and assumptions
which have changed with the progress of time, so that the old model no
longer fits the context of its application.
- The Case of the Frog's Eyedescribes the
specialized way in which the frog's eye acts as a specialized interface for its own
particular --- frogly --- purposes. Vision involves models but these
models are usually so effective that they are never noticed until we understand
the context in which they are defined.
- The Case of the Missing
Calendar describes the strangely consistent forgetfulness of young children
about the order of events in the past. The rich and vivid memories of children have a
consistent pattern of gaps which reveals some of the purposes of
children's memories. Looking closer, we see that our adult memories
have similar gaps but that we use a sophisticated model of events ---
the calendar --- to cover them.
- The Case of the Inertial
Frame describes a long-enduring model of
space, time, and motion in the physical world which systematically
loses certain relations and highlights others. This story illustrates
how models in science, like models elsewhere, are interfaces which
select and discard aspects of the systems they connect. Science uses
use this selectivity and isolation to gain tremendous descriptive,
predictive, and manipulative power. The inertial frame, first
formalized by Isaac Newton, links the fall of an apple to the dance of
the planets to the path of a rocket flying through the air.
- The Case of the Special
Theory describes a subtle but profound change to
Newton's powerful model. To reconcile Newton's model with newly
formulated physical laws and with the growing scale and precision of
actual experiments, Albert Einstein replaced several of Newton's
assumptions with others, while keeping its essence intact. Einstein's
innovation sustained the power and applicability of the model of the
inertial frame, which remains central to our modern understanding the
physical world.
- Chapter III: Reference,
Imagination, and Convenience
- We learn a lot about our models by asking some
particular sorts of questions: Reference: what is the
model describing? Convenience: how is the model
used? Imagination: what does the model add? We can
look for answers to these questions by looking for a certain kind of
systematicity in our models. This chapter introduces these
ways of opening up models to see how they work while the subsequent cases
demonstrates them.
- The Case of the Alien World
reveals how many of our assumptions built into our models of the natural
world break down when we move into the alien world of undersea life.
In this world, we see the complications in the apparently simple acts
of naming organisms or of distinguishing plants from animals.
- The Case of the Lively Desert
shows how difficult it may be to have good models of wholes without
having good models of parts.
- The Case of Being Digital
focuses on questions of convenience by describing different numbering
systems, which are all different models for describing the same thing:
the profound notion of number itself.
- The Case of Signs &
Symbols looks at symbols in the natural world, discussing
animals which use symbols and the idea that some natural signs are in
fact symbols from the point of view of evolution.
- The Case of the Imaginary
Islands describes a rich set of models used by sailors in
Micronesia to successfully navigate hundreds of miles of open ocean
without instruments based on references to imaginary islands beyond
the horizon.
- The Case of the Missing
Numbers describes the extension of the idea of number to
negative numbers.
- The Case of the Imaginary
Numbers describes a further extension of number to the really
useful notion of imaginary numbers.
- Chapter IV: Consciousness: The Awareness of
Models
Where we look at how multiple models act and
interact in our minds, illuminating questions of awareness,
consciousness, and emotion in the context of a multiplicity of
models.
- Chapter V: Creativity: The
Origin of Models
Where we look at where models come
from, distinguishing natural models from mental models and describing
some the ways in which mental models evolve or are developed.
- Chapter VII: Odds & Beginnings
[Draft!]
Where we begin a dozen converstations based
on thinking about thinking with models.