mathematics in sociology
Holli Niesner
relevence of geometry to sociology or basically anything. Well, I've already
written an 8 page paper on the applications of geometry, but I was
specifically interested in those of geometry and sociology. I found a few
places on the web dealing with graph drawing and network theory, but any
extra help on other topics that I could use would be helpful. As a math
major, I feel I must defend my position :)
-Holli
Guy F. Brandenburg
people live physically clustered closely together in either tight little towns
(like, for example, French peasants) or in apartment buildings is no different
sociologically that a society where people live scattered all over the landscape
(like, for example, the Navajo)?
Does urban sprawl, which to a great extent is a geometrical problem, mean
nothing to this teacher?
If so, then it seems like this teacher is ignoring a fairly simple geometrical
application.
And the Chinese traditionally believe that the feng shui, or geography [read:
geometry], of a place determines whether it has good "luck" or bad. I really
don't know enough about feng shui to say whether it's a crock of manure or not,
but there might be something to it.
There must be lots of other applications.
Guy Brandenburg
Walter Whiteley
geometry course do a project on 'place theory' a theory in economic
geography about how cities, towns, villages will be arranged in
a flat plane, based on the costs of transportation, the size of
population needed to support an industry or business etc.
What was remarkable was how much of that 'geometric' pattern
one could see in distincly non-flat places (like
parts of Ontario where I live). Not quite sociology but
certainly a factor in how society is constructed.
If your teacher accepts that statistics is usefull in Sociology,
then the entire issue of putting data into visual (geometric) forms,
transforming it, and reasoning with it, has a substantial geometric
basis. I regularly discuss issues of ellisoids etc. with the
statisticians who work with psychologists, sociologists etc.
The visual might NOT be essential to how a computer churns out
calculations. It is essential to how many statisticians DECIDE
what calculations to instruct the computer to do!
Of course geometry is central to a large number of jobs these days
(CAD/CAM, design, computer animation, medical imaging, robotics,
... ) Since these, in turn, have a sociological impact, there
is an indirect connection.
The idea of using nets, graphs, concept maps, etc. is pretty common
in any area of creative work these days. Is this geometry?
I say yes - to me topology is a preliminary form of geometry.
[In fact Piaget reminds us that topology - what is connected to what -
is the earliest form of geometry that a child learns.
The fact that it is typically the last form of geometry we teach in
schools is a real educational problem!]
Geometry is one of two or three basic areas in which people learn
to reason visually. Reasoning visually is a KEY skill in many areas.
The use of the web (very visual) simply builds on that.
I am in the process of developing a course on 'reasoning with
visual information' and am amazed at the number of good resources
out there. It is also interesting to find materials about HOW
to improve your capacity to work with visual information.
Finally, it might be interesting to see if your teacher
sees a sociological impact to language - in particular
sign language and the Deaf culture. Sign language actually
involves substantial use of geometric transformations
(what the same sentence looks like from the point of view of the
person expressing it and the person 'reading it' is a
geometric transformation). You don't have to STUDY geometry
to do this. You do have to DO geoemtry and people who are
native users of sign language (e.g. sign language was the first language
they learned) do have additional visual skills when compared to the average
oral language person! A nice book about that experience is
Oliver Sacks Seeing Voices (and some of the references he gives).
I suspect, in the end, your teachers comment is more like:
I don't see the relevance of taking a course in grammer to doing
sociology. That is not, of course, the same as saying there is
no relevance to USING correct grammer in sociology! In many
cases that is what people are saying about geometry.
I don't see the relevance of taking a standard course in
geometry to the way I will use all those experiences and skills
which happen to include, implicitly, geometry.
Walter Whiteley
Mathematics and Statistics
York University
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> Hi there. My sociology teacher told the class a few days ago that he sees no
> relevence of geometry to sociology or basically anything. Well, I've already
> written an 8 page paper on the applications of geometry, but I was
> specifically interested in those of geometry and sociology. I found a few
> places on the web dealing with graph drawing and network theory, but any
> extra help on other topics that I could use would be helpful. As a math
> major, I feel I must defend my position :)
>
> -Holli
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