From: mlindholm@cc.helsinki.fi
Newsgroups: bit.listserv.ingrafx
Subject: Re: quantification of the data content of a map
Date: 31 Dec 92 11:48:09 GMT
Organization: University of Helsinki

In article <9212280030.AA08068@amazon.evsc.Virginia.EDU>,         Faustino Arao Daria <fad8t@AMAZON.EVSC.VIRGINIA.EDU> writes:
> This relates to a posting dated Dec 18, 1992 which invited comments
> on a proposal :
> 
> ==========================================================================
> 
> The Quantification of the Efficiency of Transmission of Cartographic Data.
> 
>              A proposal submitted for consideration in:
>           Department of Geography, University of Portsmouth.
> 
>                               by
> 
>                           PAUL DARLOW,
> 
>              Undergraduate, Department of Geography,
>                   University of Portsmouth.
>                      (December, 1992)
> 
> ==========================================================================
> 
> 
> Comments :
> 
> 
> One of the five aims of Paul's Proposed Research Project is the
> 
>      Construction of a methodology
>      to enable the quantification of the data content of a map.
> 
> Paul has considered two approaches in his METHOLOLOGY
> (text reformatted) :
> 
>           "The quantification of spatial relationships is
>      substantially more difficult than quantifying map features.
>      Two initial approaches are recognised at this moment in time,
>      although experimentation with various concepts may produce
>      a more satisfactory solution.
> 
>      The first approach is to make the assumption that the
>      blank areas of a map are just as important as those areas
>      containing feature data. It can be said that a feature
>      not appearing in one location is of no less importance
>      than that feature appearing in another location.
>      If this assumption is made, all locations on a map have
>      equal relationships with all other locations on that map.
>      Quantification of relationships is then relatively simple,
>      by calculating the area of the map, dividing by the area
>      of the smallest 'bit' of information on the map and then
>      relating the answer to the scale of the map.
> 
>      The second approach is to use a computerised analysis of the
>      distance between each feature and every other feature on the map.
>      If the computer is set-up to keep a total of the distances,
>      eventually a final total can be produced, which could be used
>      to quantify the geographical relationship."
> 
> 
> Be it a raster-based or vector-based data, the information contained
> in a map file can be sent to a POSTSCRIPT printer as a PS/EPS file.
> Can the file size be used as an indication of the quantity of the
> data content of a map ?
> 
> By way of analogy, suppose the size of the postscript file of a
> "Where's Waldo" picture puzzle (vector-based) is
> 
>            1.1 Meg with    Waldo and
>            1.0 Meg without Waldo.
> 
> Assume that the Waldo cartoon character accounts for the 0.1 Meg
> difference.
> 
>     Can we conclude that the data content is higher in the
>     postscript file which includes Waldo ?
>     If yes, can we make the same inference in the case of a map ?
> 
> 
> 
> Consider the files in an ESRI graphics subdirectory.  Each file
> contains information on a particular feature of interest.
> The POSTSCRIPT command in ARC/INFO (v. 6.1) converts the files
> in such a subdirectory to one postscript file.
> 
> If there are more features of interest to a mapmaker or GIS programmer,
> then there will be more files in such a directory, and
> consequently, the Postscript file will be larger.
> 
>     Can we consider a POSTSCRIPT printer to be a dispassionate,
>     unbiased or objective map-percipient ?  If so, is there a need
>     to conduct experiments to determine the characteristics of an
>     'average' map-percipient ?


It is extremely important to distinguish between the 
different levels of information in a message (e.g. a map).  
In information theory, the concept of information can be 
understood in at least three different ways:
	- Syntactic information
	   = that what we usually call 'data', relates just
	   to the frequencies of the signs, without any 
	   interpretaion
	- Semantic information
	   = the meaning of the message in relation to
	   the things expressible in the language used
	- Pragmatic information
	   = the personal meaning of the message to the
	   sender and the receiver

I recommend that Paul Darlow (didn't get his email address)
reads an article written by me and my colleague where the 
applying of these three information levels to GIS user 
interfaces (and thus also to maps) is studied:

	Lindholm, M. & Sarjakoski, T. (1992).  User Models 
	and Information Theory in the Design of a Query 
	Interface for GIS.  In: A. U. Frank, I. Campari & U. 
	Formentini (eds.), Theories and Methods of Spatio-
	Temporal Reasoning in Geographic Space, Lecture 
	Notes in Computer Science 639, Springer Verlag, 
	Heidelberg.  pp. 324 - 347.

We can't measure on the same scale the number of 'bits' 
on  a map and the spatial relationships between features 
on the map.  In a sense, the spatial relationships do not 
exist on the map, rather they are our interpretation of 
the drawing.  The amount of syntactic information is 
often quite easy to measure.  The syntactic information 
amount in a raster map, for instance, is simply 

	the number of pixels * bits per pixel.

The size of a PostScript file is a similar measure.  
But, they do not tell us anything about the semantic or 
pragmatic information content of the map.  What does 
the map say to us?  How do we measure the meaning 
contained in the map?  Furthermore, the meaning and 
personal information amount of a map is different for 
different people.

The measures of syntactic information, such as the 
Shannon entropy, cannot tell us anything about the 
semantic and pragmatic information content.  
Unfortunately this is often not realized, which has 
caused many false conclusions and misunderstandings, 
e.g. the writings of Robinson and Petchenick.


Mikko Lindholm
Finnish Geodetic Institute
Department of Cartography and Geoinformatics
Ilmalankatu 1 A
SF-00240 Helsinki 
Finland

Internet:	mlindholm@cc.helsinki.fi
bitnet:		mlindhol@finuh.bitnet