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From: william@hitl.vrnet.washington.edu (William Bricken)
Newsgroups: sci.virtual-worlds
Subject: "Space"
Message-ID: <9007250107.AA01311@hitl.vrnet.washington.edu>
Date: 24 Jul 90 17:07:59 GMT
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In reference to the nature of SPACE:

The mathematical theory of measurement provides a concise summary ofthe 
generic types of spaces.  Here they are, with slight elaboration.
This list is a hierarchy, each following type is an elaboration of the 
preceeding ones.  Note that each can be conceptualized as one-dimensional,
additional dimensions (2D, 3D, etc) are merely orthogonal products of
more than one space.  

For grounding, it is commonly assumed that our everyday living space is 
composed of three REAL spaces at right angles.  In fact, this idea was 
made up in the middle of the sixteenth century by Descartes. Cyberspace 
illustrates the notion that space is quite arbitrary, it provides an 
opportunity to retrain ourselves to perceive all the other types of space.  
TIME is just another space, one that we have forgotten how to travel freely 
in.  So is SCALE.  The technical challenge of cyberspace is how we will be 
able to *mix* types of space in the same perceptual environment.


          ***THE VARIETIES OF SPACE***

INDICATIVE:  the elementary domain of perception.  Where our mind is.
  This one is not taught in school.  See Spencer-Brown, Laws of Form.

NOMINAL:  a set, unordered collections of things.  EG:  the space of
  cyberspace novels, of fish in a pond, of items on a menu.

ORDINAL:  ordered, ranked things.  EG: your list of most to least
  favorite novels, pecking orders of fish, steps in an instruction.

INTERVAL:  order in which the distance between items is equal.  Integers.
  EG:  pages in a novel, age in days of fish,  cells on graph paper.

RATIONAL:  intervals which support ratios.  Numerical fractions.  EG:
  percentages of each letter in a novel, portions of a meal each fish eats,
  comparison of monetary wealth.

REAL:  continuous space.  Real numbers.  EG: our model of the space
  underlying words on a page, the weight and length of fish, physical
  space.

IMAGINARY:  contradictory spaces. Sqrt[-1].  Both True and False.  EG:
  our construction of mental images from words, wave propagation, inside a
  black hole.


Note how going down this hierarchy successively adds more mathematics and
less physical reality.  Note how cognitive spaces bound both the top and the
bottom.


William Bricken
HITL, UW

william@hitl.vrnet.washington.edu