searching, i found an excellent resource/example of mathematics/physics
and architecture... the webpage has the articles referenced below..
(going into www.architexturez.com 'research' category..)
bc
Nikos A. Salingaros: PAPERS ON ARCHITECTURE, PATTERNS, AND URBANISM.
http://sphere.math.utsa.edu/sphere/salingar/contr.arch.html
------------------------------------------------------------------------
1. Manifesto
2. Architecture
3. Urbanism
4. Biology and Computer Science
5. Oriental Carpets
6. Letters and Reviews
7. Some background
------------------------------------------------------------------------
MANIFESTO
The most exciting scientific developments of the past decade, such as
fractals, complexity theory, evolutionary biology, object-oriented
programming, and artificial intelligence, give us an idea of how human
beings interact with their environment. Organisms, computer programs,
buildings, neighborhoods, and cities all embody the same general type of
ordered, hierarchical system. All matter -- biological as well as inanimate
-- organizes itself into coherent structures. The human mind has evolved in
order to adapt to complex patterns in the natural world, so the patterns we
perceive around us influence our internal function as human beings.
A new, human-oriented architecture that the brilliant architectural
theorist Christopher Alexander proposes combines the best qualities of
traditional architecture while utilizing the latest technological and
scientific advances. The best architecture is complex and coherent, but
neither random, nor simplistic. New design rules derived by Alexander can
drastically improve buildings and cities. My contributions try to give
architecture and urbanism a scientific basis. Recent results concern visual
images, and applying pattern languages to grasp complexity in
organizational structures (for example, in a business or company).
The wonderfully rich complexity of the universe has been denied and
suppressed by twentieth-century architectural ideas. Society has been
robbed of its multidimensional structure ever since people have been
induced (or forced) to live in modernist planned cities. Our entire world
is now shaped by a simplistic anti-scientific philosophy, which is
supported by the architecture. This goes far beyond architecture itself,
because decades of teaching by our schools and media could be diminishing
people's capacity for scientific and mathematical thinking. It is time to
examine the effects -- possibly disastrous -- of design on mankind's
intellectual evolution.
ARCHITECTURE
The Laws of Architecture from a Physicist's Perspective
Physics Essays 8 (1995), pages 638-643.
Three architectural laws follow from how matter comes together to form
coherent structures; they are satisfied by most buildings in history up to
(but excluding) the twentieth century.
[Also available in LaTeX, DVI and Postscript formats]
Life and Complexity in Architecture From a Thermodynamic Analogy
Physics Essays 10 (1997), pages 165-173.
A visual model computes numerical estimates for the comparative degree of
organized complexity, or "life" of buildings, and contrasts this with the
disorganized complexity.
A Scientific Basis for Creating Architectural Forms
Journal of Architectural and Planning Research 15 (1998), pages 283-293.
A scaling rule is proposed for architectural elements based on the scaling
factor e = 2.718, the base for natural logarithms, and this is compared to
the Fibonacci sequence.
Architecture, Patterns, and Mathematics
Nexus Network Journal 1 No. 2 (1999), approximately 14 pages.
The elimination of visual patterns in twentieth century architecture could
be handicapping people's capacity for mathematical thinking, which works
strictly in terms of patterns.
Hierarchical Cooperation of Architectural Scales, and the Mathematical
Necessity for Ornament
Journal of Architectural and Planning Research (to appear)
Integrated structures follow the theory of hierarchical systems, developed
in computer science and biology, showing how architectural ornament on the
scales 1cm - 2m is necessary for coherence.
[The Journal of Architectural and Planning Research does not permit posting
before the Issue appears in print, so the link is to an early version]
An Absolute Measure of Design: the Architectural Temperature
Journal of Architectural Education (submitted)
The architectural temperature T measures the degree of detail, curvature,
and color in a design; we argue that human beings connect only to objects
that have a high value of T .
URBANISM
Theory of the Urban Web
Journal of Urban Design 3 (1998), pages 53-71.
Graph theory is used to show that a living city depends on an enormous
number of different paths, and how the evolution of an urban region from
"dead" to "alive" is sudden.
[Contact the author for a paper reprint. Link is to an earlier version
published electronically by Resource for Urban Design Information]
Urban Space and its Information Field
Journal of Urban Design 4 (1999), pages 29-49.
Urban space is characterized by the information field generated by
surrounding surfaces, and this in turn determines where paths and local
nodes develop in the open space.
Ecology and the Fractal Mind in the New Architecture: A Conversation
(co-authored with Victor Padrón)
Online Planning Journal 5 (to appear in 1999), approximately 12 pages.
Covers topics such as how our fractal mind influences fractal qualities in
man-made structures such as buildings and artworks. Touches on Jungian
archetypes, and analyzes how the Modernist anti-fractal attitude is
antithetical to ecological thinking.
A Universal Rule for the Distribution of Sizes (co-authored with Bruce J. West)
Environment and Planning B, submitted for publication.
Most pleasing objects and designs obey an inverse power-law distribution in
their subdivisions, which is a widely-observed relationship in both the
natural and social sciences. Modernist design grossly violates this rule.
Complexity and Urban Coherence
Journal of Urban Design (submitted)
The theory of complex interacting systems, developed in biology and
computer science, is applied to urban design. Coherence results from
intense local couplings, and long-range connections that reduce disorder.
The Geometry of Urban Boundaries
(in preparation)
Urban boundaries in living cities have fractal dimension ranging between
0.5 for arcades, up to 1.5 for undulating walls that accommodate activity
nodes. Contemporary cities limit their boundaries to fractal dimension
exactly one.
BIOLOGY AND COMPUTER SCIENCE
*Please note that, since these topics lie outside my specialty, I welcome
offers from possible co-authors.
The Structure of Pattern Languages
(submitted for publication)
Patterns encapsulate information about recurring solutions; here we discuss
techniques for linking observed patterns to create a language that brings
all the patterns together.
[Link is to an earlier version]
A Pattern Measure for Arrays (co-authored with Allen Klinger)
Submitted for publication.
A quantitative model for computing a measure of organized complexity is
developed, and is applied to distinguish between 6X6 arrays with four
different types of entries.
Pattern Languages: Connecting Design Patterns to form Solutions
(co-authored with Clinton L. Jeffery)
(in preparation)
Describes how to connect software patterns to generate coherent large-scale
objects; this procedure is illustrated by examples in C++.
Complexity Measures in Computing (co-authored with Thomas W. Lynch)
(in preparation)
Discusses how both software and hardware complexity can be better
understood by a new measure, and applies it to a ripple carry adder.
ORIENTAL CARPETS
In Defense of Alexander
HALI: The International Magazine of Antique Carpet and Textile Art 78
(1995), pages 67-69.
Proposes that a quantitative analysis based on interlocking elements, and
the similarity of designs on different scales, can predict the emotional
appeal of a carpet.
The "Life" of a Carpet: an Application of the Alexander Rules
Oriental Carpet and Textile Studies V (1999), edited by M. Eiland, Jr. and
R. Pinner (Danville, California: International Conference on Oriental
Carpets), pages 189-196.
Derives a checklist of design criteria, including the correct use of local
contrast, scaling, similarity, detail, and randomness, that distinguish a
carpet with "life".
LETTERS AND REVIEWS
An interview entitled "Mathematician Sums Up Laws of Architecture" appeared
in the Road Runner magazine, November 1995.
Letter to the AIA Newsletter, entitled "Mathematics and 21st Century
Architecture", June 1997.
Book review of Christopher Alexander's "A Pattern Language" for amazon.com,
May 1998.
Letter to the Editor of D Magazine summarizes how Dallas has been destroyed
by Modernist architecture, October 1998.
------------------------------------------------------------------------
SOME BACKGROUND
Reading Christopher Alexander's Notes on the Synthesis of Form and the
Pattern Language as a student convinced me that contemporary design is
driven by irrelevant fashions and opinions. Twentieth century architectural
thought is confused, and is embracing an increasingly nebulous vocabulary
in an effort to shield itself from scrutiny. Architecture at present lacks
any connection to other disciplines that define structured human thought,
relating only to an anti-scientific de-constructivist philosophy.
The necessity of introducing logical analysis and scientific thinking into
architecture has become increasingly clear to both of us. Not only is the
world being covered by ugly buildings, but their underlying structural
order may be adversely affecting the way people live and think. Cities are
shaped on whims, which have irreversible negative consequences on society
for decades afterwards. The ideas behind contemporary architecture could be
damaging the thought processes that allow us to understand the physical
world through science and mathematics.
For the past decade or more, I have been learning from Alexander in the
process of helping him finish his monumental book The Nature of Order. I
have advised him on the presentation and flow of ideas. The publication of
his book on Oriental Carpets (see my article In Defense of Alexander) led
me into the fascinating world of textile designs. Countless discussions on
this material has taught me the profound meaning of geometry in the built
environment, and how man is willfully damaging it.
------------------------------------------------------------------------
This site was included in the Guest Section of Internet Architecture Zone
for April 1997, and by Web Architecture Magazine for January 1998.
Salingaros Home Page Some Notes on Christopher Alexander
and architecture... the webpage has the articles referenced below..
(going into www.architexturez.com 'research' category..)
bc
Nikos A. Salingaros: PAPERS ON ARCHITECTURE, PATTERNS, AND URBANISM.
http://sphere.math.utsa.edu/sphere/salingar/contr.arch.html
------------------------------------------------------------------------
1. Manifesto
2. Architecture
3. Urbanism
4. Biology and Computer Science
5. Oriental Carpets
6. Letters and Reviews
7. Some background
------------------------------------------------------------------------
MANIFESTO
The most exciting scientific developments of the past decade, such as
fractals, complexity theory, evolutionary biology, object-oriented
programming, and artificial intelligence, give us an idea of how human
beings interact with their environment. Organisms, computer programs,
buildings, neighborhoods, and cities all embody the same general type of
ordered, hierarchical system. All matter -- biological as well as inanimate
-- organizes itself into coherent structures. The human mind has evolved in
order to adapt to complex patterns in the natural world, so the patterns we
perceive around us influence our internal function as human beings.
A new, human-oriented architecture that the brilliant architectural
theorist Christopher Alexander proposes combines the best qualities of
traditional architecture while utilizing the latest technological and
scientific advances. The best architecture is complex and coherent, but
neither random, nor simplistic. New design rules derived by Alexander can
drastically improve buildings and cities. My contributions try to give
architecture and urbanism a scientific basis. Recent results concern visual
images, and applying pattern languages to grasp complexity in
organizational structures (for example, in a business or company).
The wonderfully rich complexity of the universe has been denied and
suppressed by twentieth-century architectural ideas. Society has been
robbed of its multidimensional structure ever since people have been
induced (or forced) to live in modernist planned cities. Our entire world
is now shaped by a simplistic anti-scientific philosophy, which is
supported by the architecture. This goes far beyond architecture itself,
because decades of teaching by our schools and media could be diminishing
people's capacity for scientific and mathematical thinking. It is time to
examine the effects -- possibly disastrous -- of design on mankind's
intellectual evolution.
ARCHITECTURE
The Laws of Architecture from a Physicist's Perspective
Physics Essays 8 (1995), pages 638-643.
Three architectural laws follow from how matter comes together to form
coherent structures; they are satisfied by most buildings in history up to
(but excluding) the twentieth century.
[Also available in LaTeX, DVI and Postscript formats]
Life and Complexity in Architecture From a Thermodynamic Analogy
Physics Essays 10 (1997), pages 165-173.
A visual model computes numerical estimates for the comparative degree of
organized complexity, or "life" of buildings, and contrasts this with the
disorganized complexity.
A Scientific Basis for Creating Architectural Forms
Journal of Architectural and Planning Research 15 (1998), pages 283-293.
A scaling rule is proposed for architectural elements based on the scaling
factor e = 2.718, the base for natural logarithms, and this is compared to
the Fibonacci sequence.
Architecture, Patterns, and Mathematics
Nexus Network Journal 1 No. 2 (1999), approximately 14 pages.
The elimination of visual patterns in twentieth century architecture could
be handicapping people's capacity for mathematical thinking, which works
strictly in terms of patterns.
Hierarchical Cooperation of Architectural Scales, and the Mathematical
Necessity for Ornament
Journal of Architectural and Planning Research (to appear)
Integrated structures follow the theory of hierarchical systems, developed
in computer science and biology, showing how architectural ornament on the
scales 1cm - 2m is necessary for coherence.
[The Journal of Architectural and Planning Research does not permit posting
before the Issue appears in print, so the link is to an early version]
An Absolute Measure of Design: the Architectural Temperature
Journal of Architectural Education (submitted)
The architectural temperature T measures the degree of detail, curvature,
and color in a design; we argue that human beings connect only to objects
that have a high value of T .
URBANISM
Theory of the Urban Web
Journal of Urban Design 3 (1998), pages 53-71.
Graph theory is used to show that a living city depends on an enormous
number of different paths, and how the evolution of an urban region from
"dead" to "alive" is sudden.
[Contact the author for a paper reprint. Link is to an earlier version
published electronically by Resource for Urban Design Information]
Urban Space and its Information Field
Journal of Urban Design 4 (1999), pages 29-49.
Urban space is characterized by the information field generated by
surrounding surfaces, and this in turn determines where paths and local
nodes develop in the open space.
Ecology and the Fractal Mind in the New Architecture: A Conversation
(co-authored with Victor Padrón)
Online Planning Journal 5 (to appear in 1999), approximately 12 pages.
Covers topics such as how our fractal mind influences fractal qualities in
man-made structures such as buildings and artworks. Touches on Jungian
archetypes, and analyzes how the Modernist anti-fractal attitude is
antithetical to ecological thinking.
A Universal Rule for the Distribution of Sizes (co-authored with Bruce J. West)
Environment and Planning B, submitted for publication.
Most pleasing objects and designs obey an inverse power-law distribution in
their subdivisions, which is a widely-observed relationship in both the
natural and social sciences. Modernist design grossly violates this rule.
Complexity and Urban Coherence
Journal of Urban Design (submitted)
The theory of complex interacting systems, developed in biology and
computer science, is applied to urban design. Coherence results from
intense local couplings, and long-range connections that reduce disorder.
The Geometry of Urban Boundaries
(in preparation)
Urban boundaries in living cities have fractal dimension ranging between
0.5 for arcades, up to 1.5 for undulating walls that accommodate activity
nodes. Contemporary cities limit their boundaries to fractal dimension
exactly one.
BIOLOGY AND COMPUTER SCIENCE
*Please note that, since these topics lie outside my specialty, I welcome
offers from possible co-authors.
The Structure of Pattern Languages
(submitted for publication)
Patterns encapsulate information about recurring solutions; here we discuss
techniques for linking observed patterns to create a language that brings
all the patterns together.
[Link is to an earlier version]
A Pattern Measure for Arrays (co-authored with Allen Klinger)
Submitted for publication.
A quantitative model for computing a measure of organized complexity is
developed, and is applied to distinguish between 6X6 arrays with four
different types of entries.
Pattern Languages: Connecting Design Patterns to form Solutions
(co-authored with Clinton L. Jeffery)
(in preparation)
Describes how to connect software patterns to generate coherent large-scale
objects; this procedure is illustrated by examples in C++.
Complexity Measures in Computing (co-authored with Thomas W. Lynch)
(in preparation)
Discusses how both software and hardware complexity can be better
understood by a new measure, and applies it to a ripple carry adder.
ORIENTAL CARPETS
In Defense of Alexander
HALI: The International Magazine of Antique Carpet and Textile Art 78
(1995), pages 67-69.
Proposes that a quantitative analysis based on interlocking elements, and
the similarity of designs on different scales, can predict the emotional
appeal of a carpet.
The "Life" of a Carpet: an Application of the Alexander Rules
Oriental Carpet and Textile Studies V (1999), edited by M. Eiland, Jr. and
R. Pinner (Danville, California: International Conference on Oriental
Carpets), pages 189-196.
Derives a checklist of design criteria, including the correct use of local
contrast, scaling, similarity, detail, and randomness, that distinguish a
carpet with "life".
LETTERS AND REVIEWS
An interview entitled "Mathematician Sums Up Laws of Architecture" appeared
in the Road Runner magazine, November 1995.
Letter to the AIA Newsletter, entitled "Mathematics and 21st Century
Architecture", June 1997.
Book review of Christopher Alexander's "A Pattern Language" for amazon.com,
May 1998.
Letter to the Editor of D Magazine summarizes how Dallas has been destroyed
by Modernist architecture, October 1998.
------------------------------------------------------------------------
SOME BACKGROUND
Reading Christopher Alexander's Notes on the Synthesis of Form and the
Pattern Language as a student convinced me that contemporary design is
driven by irrelevant fashions and opinions. Twentieth century architectural
thought is confused, and is embracing an increasingly nebulous vocabulary
in an effort to shield itself from scrutiny. Architecture at present lacks
any connection to other disciplines that define structured human thought,
relating only to an anti-scientific de-constructivist philosophy.
The necessity of introducing logical analysis and scientific thinking into
architecture has become increasingly clear to both of us. Not only is the
world being covered by ugly buildings, but their underlying structural
order may be adversely affecting the way people live and think. Cities are
shaped on whims, which have irreversible negative consequences on society
for decades afterwards. The ideas behind contemporary architecture could be
damaging the thought processes that allow us to understand the physical
world through science and mathematics.
For the past decade or more, I have been learning from Alexander in the
process of helping him finish his monumental book The Nature of Order. I
have advised him on the presentation and flow of ideas. The publication of
his book on Oriental Carpets (see my article In Defense of Alexander) led
me into the fascinating world of textile designs. Countless discussions on
this material has taught me the profound meaning of geometry in the built
environment, and how man is willfully damaging it.
------------------------------------------------------------------------
This site was included in the Guest Section of Internet Architecture Zone
for April 1997, and by Web Architecture Magazine for January 1998.
Salingaros Home Page Some Notes on Christopher Alexander