5
Inside Models

We are told that the universe may be finite but unbounded. What sense does this make? Measured by the simplest way of thinking through the idea, it seems to make no sense at all. Imagine yourself riding outward on the crest of a beam of light into this possibly finite universe. Travel long enough and what happens? It seems that if the universe if finite, there must be an end, you and your beam of light running into something that bottles the universe up, makes it finite. But when you imagine that, you have a boundary to what was supposed to be unbounded.

There is a second puzzle too: Running into a boundary seems contrary to the very concept of universe. Having ridden the beam of light to the limit, which feels perhaps rigid like steel or yielding like rubber, you naturally ask, "What's beyond the boundary?" The quick answer "nothing" seems nonsensical. How can there be nothing beyond a boundary? The answer "more space" tells you that you have not really travelled to the end of the universe, because that space should be included in the universe, even if there is nothing in it. So your light beam ride leads you not only to peculiar physical boundaries but peculiar limits of logic as well.

Perhaps standing back a bit from this effort to understand a finite unbounded universe would help. Your ride on the beam of light, the image constructed in an effort to make sense of a finite but unbounded universe, is a model. In conjuring that image, you

-124-

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Knowledge as Design
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Acknowledgments xi
  • Introduction: The Giving and Getting of Knowledge xiii
  • 1 - Knowledge as Design 1
  • 2 - Design Colored Glasses 35
  • 3 - Words by Design 64
  • 4 - Acts of Design 93
  • 5 - Inside Models 124
  • 6 - Inside Argument 155
  • 7 - The Art of Argument 183
  • 8 - Schooling Minds 210
  • Notes 233
  • Sources 242
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