Hands For The Mind
Models, Imagination, and Our Human Nature

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Kenneth Haase

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Draft, not for citation or circulation
Copyright (C) 1997, 1998 by Kenneth Haase
Preface

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• 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.