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> IT REVOLUTION BOOK SERIES


Michele
Emmer deals with several absolutely crucial arguments in this volume.
To recall them in order: a. space does not exist as an objective fact
but simply as a mental (and scientific) form; b. these mental and
scientific forms of representing space vary from era to era (for example
flat Euclidean space, threedimensional Cartesian space, Gauss' curvilinear
geometry, Riemann's 'ndimensional' geometry, etc.); c. these mental
and scientific forms have utilitarian value. We use them if they work,
we set them aside if they do not work. Euclidean geometry is more
than accurate when dividing up farmland but we must come up with another
one to measure the curvature of solar rays. (At times, the truth is
mathematicians first invent the scientific theory and then later,
occasionally much later, discover the physical phenomena to which
it could usefully be applied); d. these mental forms in any case have,
or can have, intrinsic beauty. This aspect of beauty cannot be ignored
because otherwise we could not explain either the total immersion
the work of the mathematician requires, or the intimate familiarity
between mathematician and architecture: even though from different
angles, they are both polysemic disciplines, they serve a practical
end, but they neither exhaust themselves nor become flat on this.
Setting aside the exceptional competency of the author, these arguments
are illustrated in Mathland with two rare qualities: first
of all, with exemplary clarity and secondly through a controlled,
subterranean passion that is still however transmitted to the reader.
I believe many, after the first reading, will want to return to the
pages to make drawings and notes, to attempt to read more on the same
material by the same scholar. I am also convinced that if this book
falls into the hands of an intelligent high school student or a student
of architecture or engineering that it would be a good way of understanding
the great framework in which to apply the necessary hard work of mathematics.
But naturally Mathland has even greater importance as part
of this book series for architects and researchers who give center
place to the relationship between computer technology, new scientific
discoveries and the central problem of architects: space. Emmer writes:
I would like to recount just a small part of the story that led to
profound changes in our idea of the space that surrounds us, and help
understand how in some sense we ourselves create and invent space,
modifying it according to changes in our ideas of the universe. Or
perhaps one could say it is the universe that is modified following
the mutations in our theories. The word mutation, the word transformation
are the keys to this understanding.
Space, as shown in this book, "mutates" and is strictly dependent
on our scientific concepts. The concept of mutation of these scientific
concepts is important because even architecture mutates over time
with the various periods and variations in the tools that allow its
realization. Now, we maintain the fundamental tools that give form
to architecture are not only materials, construction techniques and
functions but above all spatial and scientific concepts. As if mathematical,
geometric and scientific knowledge of space is transformed into physical
construction, into "things" through architecture. Look for example
at the Egyptian Pyramid. Is not the Pyramid (and I have already discussed
this theme in this series) the edification of several notions of geometry
and trigonometry? Indeed, without those notions, without those mental
forms, would the Pyramid even be conceivable? Is not the Pantheon
the fruit of a very sophisticated geometric calculation, of considering
space and calculations under the form of a "geometry" evidently possessed
by the Romans (who would have never been able to construct that type
of edifice with their abstruse numbers). And let us make the example
of all examples with the affirmation of a new architecture at the
beginning of the 15th century. Was not the invention of perspective
perhaps at the basis of the transformation of the architecture of
Humanism? Perspective became 'reified'. Indeed, the scientific concept
is precisely what finally makes space perceptibly "measurable" and
leads us to consider an architecture made in its image and likeness:
a modular, proportioned architecture, made up of repeatable elements
made to be "perspectiveable".
We can be certain of some of these relationships between the scientific
concepts of space and architecture, the relationship between perspective,
the architecture of Humanism and the Ptolemaic universe, or that of
Cartesian space, of the Mongian projection system and the progressive
birth of an architecture first aperspective and then more and more
abstract and analytical. But what is happening today? Where are we
going? Because if the concept of space has been mutated (and how it
has!) and if the computer technology of this mutation is an agent
to at least two or three different powers, then we are in a field
of research as rich as it is difficult.
To understand some of these territories and attitudes, it would be
useful to recall one point that moves throughout this book. This is
the figure of the leap or rather the act of the leap. Emmer explains
that in order to understand a space one cannot be immersed in it but
must make a leap outside it. Remember? In another circumstance we
spoke of fish: fish only know fluid as if it were air around them.
They know nothing either of what the sea or a lake or a river might
really be and know even less the space in which humans live. Only
a "leap" outside that aquatic surface can open up the sensation of
another space.
Now this book has made an indispensable contribution and enriched
research into new spaces. We begin to understand the laws and see
several possibilities. Above all we are in a "topological" concept
of space (we are not interested in the construction of geometric "absolutes"
but in systems of families and possible relationships between forms)
and are also working to give form in architecture and spaces actually
explorable in more dimensions with respect to the three Cartesian
ones, dimensions in which the spacetime geometry is actually something
different than what we have been accustomed to since Newton. How to
do that? How to imagine these spaces that are "absolutely" just as
real as those we are traditionally accustomed to considering? In reading
this book, you will see that asking these questions will seem natural
to you as well. Welcome to Mathland and just like dolphins
that take oxygen to leap out of the sea or like Abbott's Square
suddenly catapulted into three dimensions, you will think as well:
"An unspeakable horror seized me. There was a darkness; then a
dizzy, sickening sensation of sight that was not like seeing; I saw
a Line that was no Line; Space that was not Space: I was myself, and
not myself. [...] Either this is madness or it is Hell." But anguish
quickly gave way to wonder: "A new world!"
Antonino Saggio


[20dec2003] 