it seems that until now in this discussion an important issue is the representation of the space and its rules.
On the space representation and mathematics here a short text by Michele Emmer. Michele can't directly participate to the discussion but gave us this contribute. It is the abstract of a paper for a congress on architecture which will take place next July. The title is: "The Idea of Space: from Topology to Virtual Architecture" and you can find it here: http://www.noemalab.org/download/emmer.pdf
Michele Emmer is full professor of mathematics at the University of Rome "La Sapienza". Filmmaker, his movies in the series "Art and Math" have been broadcasted by the State Italian television and distributed in many countries in english, french, spanish. He organized several events on "Art and Mathematics", including the annual conference on "Mathematics and Culture" at the University of Venice, the exhibitions and conferences on M.C. Escher (1985 and 1998) at the University of Rome and the section on Space at the Venice Biennale (1986). He has been responsible for the math section at the Science Center in Naples and for many other travelling exhibitions on math.
http://www.mat.uniroma1.it/people/emmer/
Some more examples. I remember, in 1995, a very expensive project in Italy devoted to reproduce Giotto's spaces - in particular the Basilica superiore of San Francesco di Assisi's frescos - in Virtual Reality (here one of the rare images of that experience: http://www.mediamente.rai.it/mediamentetv/learning/ed_multimediale/lezioni/05/immagini/giotto.jpg ). The claim was "to enter Giotto's spaces" (sorry, in Italian: http://www.mediamente.rai.it/home/bibliote/intervis/a/antinucc.htm#link008 )
Unfortunately Giotto's frescos are painted more than 130 years before the invention of the perspective (1435-36 by Filippo Brunelleschi and Leon Battista Alberti), hence his space is not regular nor unitary, it still has some of the discontinuities, disseminations and multiplicities of the medieval space. So, since Virtual Reality representation is instead based on the perspective, all the irregularities of Giotto's space simply disappear, his representation space translated into VR becomes regular, geometric, unitary. And totally misinterpreted! I think this is a clear example about the "normalization" and the regulatory effects of the perspective.
BTW a good book about the perspective as a "mediation" form is Erwin Panofsky, "Perspective as Symbolic Form".
Best,
Pier Luigi
--
Pier Luigi Capucci
e-mail: plc@noemalab.org
web: http://www.noemalab.org/plc/plc.html
skype: plcapucci
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