A note on “functional space”

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 can’t 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.