A note on

1
A note on functional space
2
A note on the use of a matrix to represent space
the functional space argument

• What we are looking for is a format to represent
  spatial layouts that inherently meets the
  requirements listed earlier
• We want a formalism that captures or has those
  properties, not one that describes or states them
  any language can do that!
• A matrix data-structure can be used to represent
  space, but it does not have spatial properties
  (magnitudes, continuity). The user has to
  stipulate what properties the matrix must have
  when it is used to represent space. For example,
• Cells in a matrix do not have to be accessed in
  any particular order if one insists that they
  must be accessed in some specified (listed) order
  this is not part of the matrix format.
• Cells in a matrix do not represent magnitudes
  except when their names are interpreted as
  numeral pairs
• Cells in a matrix do not represent configurations
  any more than a language does
• A matrix only seems to be a natural
  representation of (2D) space because we usually
  depict it as a NxN table

3
Functional space?

• There is no such thing as a functional space
  it is whatever we specify it to be, so it cant
  be used to explain how we represent space
• What seems confusing about this is that we can
  use a matrix to model space, just as we can use a
  diagram, but we do not want to claim that the
  system we are explaining (i.e., the brain) uses
  this matrix model since it does not have the
  right architecture (i.e., a memory addressable by
  numerals)
• In every case of a proposal for a format for
  spatial representation a useful heuristic is to
  ask what it assumes beyond what you could get
  with a description in natural language i.e.,
  beyond the content of what is represented.