Chapter
1 A glance at the method
Cooperation
Mathematical metaphors
Natural
complexity
Can
you reverse this?
Order
out of disorder
This
is far from linear
Science
versus belief
Other links and comments
· Physics has been engaging in
a systematic study of inanimate matter from the point of view of what its basic
elements are like and how they interact. The success of this method is such
that very few now question —at least as a working hypothesis— that cooperation
between the parts of an object can determine its structure and functions,
something that has propitiated making incursions into other fields. This idea is
further developed from different standpoints in
® The Nonlinear Universe – Chaos, Emergence, Life, Alwyn C. Scott
(Springer-Verlag, Berlin 2007);
® Complexity. A Guided Tour, Melanie Mitchell (Oxford Univ. Press, NY
2009);
® Information, Physics, and Computation, Marc Mézard and Andre
Montanari (Oxford Univ. Press, NY 2009);
® More And Different - Notes from a Thoughtful Curmudgeon, Philip W.
Anderson (World Scientific 2011).
In line with the view we describe,
one may find useful the paper
® "Resource Letter CS-1:
Complex Systems" by Mark E.J. Newman, American
Journal of Physics 79, 800 (2011),
which describes much of the
related literature (some of it mentioned here in the proper chapters), and for
its classifications and commentaries on the subject.
· On orders of magnitude:
www.falstad.com/scale/, http://scaleofuniverse.com/ and www.wordwizz.com/pwrsof10.htm,
for example.
· The direct simulation of
fluids is a vigorous and useful discipline, as described in
® “Tackling turbulence with
supercomputers“, Parviz Moin and John Kim
(www.stanford.edu/group/ctr/articles/tackle.html, originally published in Scientific American), and
® “A numerical laboratory”,
Karl-Heiz A. Winkler, Jay W. Chalmers, Stephen W. Hodson, Paul R. Woodward and
Norman J. Zabusky, Physics Today 40,
28 (Octubre 1987; static.msi.umn.edu/rreports/1987/89.pdf).
Internet offers many good
collections of graphs and videos from simulations as, for instance, in www.efluids.com/efluids/pages/gallery.htm
and ctr.stanford.edu/ gallery.html. See also some very simple simulations at www.myphysicslab.com/
index.html.
· Sometimes one relates levels
of description other than the microscopic with the macroscopic, generally descriptions
that are closer to each other. Nowadays this is the case, for example, of
weather predictions were, for want of microscopic information (where are all
the molecules in the atmosphere and how are they moving at this precise
moment?) and computing power, one starts from an elemental phenomenological
description (for instance, what local currents are there?) to predict —quite
successfully— the large-scale phenomenological behaviour that matters to us.
See
® Weather by the numbers: The genesis of modern meteorology, K. C.
Harper (MIT Press, Cambridge, MA, 2012).
· For the hypothesis of
punctuated equilibrium, see
“Is a new and general theory
of evolution emerging?”, Stephen J. Gould, Paleobiology 6, 119 (1980).
This hypothesis, enunciated
in 1972, is not compared here with other, more popular ones (see next comment)
but just serves to motivate a model which illustrates the method. Nevertheless,
Michael R. Rampino has emphasized (in Historical
Biology, 8 November 2010) that Patrick Matthew, 20 years prior to Darwin’s On the Origin of Species, already pointed
out how geological records could indicate that “relatively long intervals of
environmental stability were episodically punctuated by catastrophic mass
extinctions of life”.
The model described in our
book and classes, which was introduced by
® Per Bak and Kim Sneppen in
"Puntuated equilibrium and criticality in a simple model of
evolution", Physical Review Letters
71, 4083 (1993) (see also the book How
Nature Works, by Per Bak (Springer-Verlag, Nueva York 1996 for a
non-technical description, and a code to perform your own interactive
simulation in http://www.jmu.edu/geology/evolutionarysystems/programs/baksneppen.shtml),
does not support a gradualist
view but is consistent with Darwin’s hypothesis. That is, that periods of
smooth change were interrupted by large events involving the extinction of many
species and the emergence of new ones. There is no need of external cataclysms
(meteorite collisions, climactic changes or volcanic eruptions) to explain
massive mutations or extinctions such as, for instance, the disappearance of
the dinosaurs —along with nearly 70% of species— dozens of millions of years
ago. For a recent breakthrough on this topic, however, see
® “The Chicxulub Asteroid
Impact and Mass Extinction at the Cretaceous-Paleogene Boundary”, by Peter
Schulte et al., Science 327, 5970 (2010).
For the plot showing the fraction
of genera that are observed in one temporal interval but not in the following
one as obtained from marine fossils, see
® Robert A. Rohde and Richard
A. Müller, in “Cycles in fossil diversity”, Nature
434, 208 (2005), which used data in
® A Compendium of Fossil Marine Animal Genera, J.J. Sepkoski, edited
by David Jablonski and Mike Foote, Bulletin
of the American Paleontology 363 (2002).
· Concerning the concept of
complexity, see
® “Simple lessons from
complexity”, Nigel Goldenfeld and Leo P. Kadanoff, Science 284, 87 (1999);
® “Computational
Irreducibility and the Predictability of Complex Physical Systems” Navot
Israeli and Nigel Goldenfeld, Physical
Review Letters 92, 074105 (2004);
® “Complexity Ideas from
Condensed Matter and Statistical Physics”, Luciano Pietronero, Europhysics News 39, 26 (2008);
® “Science of Chaos or Chaos
in Science?”, Jean Bricmont, Physicalia
Magazine 17, 159 (1995), also published in Annals of the New York Acad. of Sci. 775 (1996).
·
Ha de notarse con
firmeza que, aun cuando pueda decirse que la ciencia de la complejidad respira
cierto postmodernismo, intencionados excesos en esa línea —como la falacia de
que la ciencia es subjetiva— en absoluto son aceptables. Esto ha sido
ampliamente discutido en relación con el llamado “asunto Sokal”; véase www.physics.nyu.edu/faculty/sokal/
que contiene la bibliografía relevante.
· On the concept of
irreversibility and the apparent contradiction between the microscopic and
macroscopic descriptions of a physical systems, we recommend the clarifying
writings of physicist Joel L. Lebowitz (1930), analyst and spreader of
Boltzmann’s ideas. See
® “Boltzmann’s Entropy and
Time’s Arrow“, Joe L. Lebowitz, Physics
Today 46 (September 1993) and related correspondence in 47
(November 1994);
® “Microscopic Reversibility
and Macroscopic Behavior: Physical Explanations and Mathematical Derivations”,
in 25 Years of Non-Equilibrium
Statistical Mechanics, Javier J. Brey, Joaquín Marro, Miguel Rubi and Maxi
San Miguel, Lecture Notes in Physics 445
(Springer-Verlag, Berlin 1995).
A somewhat related reading
is
® A Brief History of Time — From the Big Bang to Black Holes, Stephen
Hawking (Bantam Books, 1988).
For new interesting views of
irreversibility in a microscopic, either classical or quantum setting, see:
http://prx.aps.org/abstract/PRX/v2/i1/e011001.
· The rigorous foundation of
an approach based on entropy trying to understand the observed natural order is
attempted in
® “Dynamical ensembles in
nonequilibrium statistical mechanics”, Giovanni Gallavotti and Eddie D.G.
Cohen, Physical Review Letters 74,
2694 (1995).
The first argument we
developed on the matter as a more phenomenological alternative is discussed in
the book
® Into the Cool: Energy Flow, Thermodynamics and Life, Eric D.
Scheneider and Dorion Sagan (University of Chicago Press 2005).
For related arguments see
also
® Nigel Goldenfeld and Leo P.
Kadanoff, already mentioned above;
® Pattern formation. An introduction to methods, Rebecca Hoyle
(Cambridge Univ. Press 2006);
® The Emperor's New Mind: Concerning Computers, Minds and Laws of Physics,
Roger Penrose (Oxford Univ. Press 1989), Chapter 7, and
® “Modeling the physics of
storm surges“, Donald Resio and Joannes J. Westerink, Physics Today (September 2008), page 33.
The study of phase
transitions in complex systems is an active field of research is described for
physicists in the book
® Nonequilibrium Phase Transition in Lattice Models, Joaquín Marro
and Ronald Dickman (Cambridge University Press 2005).
· The interesting complex behaviour
of the physical pendulum is illustrated in:
www.elmer.unibas.ch/pendulum/index.html, www.myphysicslab.com/pendulum2 .html,
and
webphysics.davidson.edu/applets/pendulum/pendulum.html.
· Concerning the scientific
method, the existence of an underlying mathematical order, of laws governing
the behaviour of living beings and their environment, only began to become
accepted in the 17th century. Though we must cite Leonardo da Vinci who,
spelling out the future as with so many other issues, wrote, “Nothing exists…
but a unique knowledge that ensues from experimentation.” In fact, he embraced
the method before precursors such as the philosopher Francis Bacon (1561) and
the physicist Galileo Galilei (1564).
· Concerning the effects of
electromagnetic fields on biological and other media, we refer to the available
scientific reports on the subject. For example, the reports by the World Health Organization (http://www.who.int/peh-emf/about/WhatisEMF
/en/index.html), the European Union
(http://europa.eu/index_en.htm), and the American
Association of Physicists in Medicine (http://www.aapm.org/links/ medphys/).
· We avoid contexts in which
the distinction between “true” and “false” currently stem from criteria that
transcend natural experience and mathematical logic. For discussion on these
matters, see
® Voodoo Science: The Road from Foolishness to Fraud, Robert L. Park
(Oxford University Press, NY 2002);
® “Debate about science and
religion continues”, Physics Today,
February 2007, http://www.physicstoday.org/resource/1/phtoad/v60/i2/p10_s1?bypassSSO=1;
® Science, Evolution, and Creationism, Institute of Medicine of the
USA Academy of Sciences (The National Academy Press, Washington DC 2008);
® Beyond the Hoax: Science, Philosophy and Culture, Alan D. Sokal
(Oxford University Press 2008).
The site
http://physicsworld.com/cws/article/indepth/46661 shows some recent physicists
comments on philosophy, and you may find interesting reading (with arguments,
for instance, on why we prefer reading fiction and believe in myths despite a
complete lack of scientific evidence):
® The atheist's guide to reality: Enjoying life without illusions, by
Alex Rosenberg (Norton 2011); physicsworld.com/cws/article/print/2012/may/17/reality-bites.
·
Para este capítulo
introductorio, además de lo anterior, mencionamos:
·
Concerning
general physics, the sites www.physics.org and www.aip.org are good guides, and
sometimes they include physics popularization; look also at
® “The entangled dance of
physics: Physics so permeates today's world that we often can't even see it”, Physics Today 59, 51 (December
2006), by Stephen G. Benka.
Note that physicists
consider the journals Physics Today, by The American Institute of Physics
(AIP), and Physics World, of the British Institute of Physics (IoP), as two
main references to follow actuality in the field.
·
The
relation between physics and life is developed in many books and papers from
many different points of view, which rarely coincide with the one in our book
(P&L), so that they complement this. An example is
® ¿What is Life? by Erwin
Schrödinger (1887–1961), Nobel Prize in physics, published in Cambridge
University Press 1992. This is a classic that influenced the XX Century
biology.
·
Most
interesting because their value as popularizations of the modern scientific
knowledge, and also because they eventually deal with some of the topics of
interest in P&L are the books by physicist Roger Penrose (1931), including
those not yet mentioned above:
® Shadows of the Mind: A Search for the Missing Science of Consciousness,
1994;
® The Road to Reality: A Complete Guide to the Laws of Physics,
Jonathan Cape, London 2004.
·
On
the other , the book
® A Different Universe – Reinventing Physics from the Bottom Down, by
Robert B. Laughlin, 1998 Nobel Prize in physics, published in Perseus,
Cambridge MA 2005,
shares some of the thoughts
in P&L. For instance, Laughlin argues that physics is in the middle of a
crisis, an ideological battle, and that is time to focus on the physics
emerging from the most basic laws. (He also relates a “theory of everything”
with reductionism, a topic addressed above.)
·
A
complementary description to the one in P&L is presented in the book:
® Thinking in Complexity – The Computational Dynamics of Matter, Mind and
Mankind, by Klaus Mainzer, Springer–Verlag, Berlin 2004,
which deepens on the concept
of complexity, including a look to historic antecedents, and focuses on the
non-linear dynamic description that he takes as a common to all the relevant
phenomenology, including biology and sociology.
·
Concerning
complexity, it is also worth mentioning meetings such as the ones in the series
“International Conference on Complex Systems” and the book
® Unifying Themes in Complex Systems, edited by Ali A. Minai and
Yaneer Bar-Yam, Springer en 2007.
A comment to this book
remarks how scientists have been applying during the last years the principles
of the science of complex systems to a wider and more varied range of problems,
thus reaching answers to old problems in biology, ecology, physics,
engineering, computer science, economy, psychology and sociology. This is precisely the situation that we
describe in P&L in a way that may be useful to many.
· No es fácil (ni quizá necesario) definir el concepto
de complejidad. Por ejemplo, Wolfram (en su libro citado) identifica
complejidad con imposibilidad de predecir usando papel y lápiz. Pero puede
predecirse lo esencial, aunque no todos los detalles, en algunos de estos
supuestos casos imposibles. De hecho, la física estadística predice la
temperatura de un gas sin conocer la posición y velocidad de todas las
moléculas. Esto sugiere simplificar la regla local de un autómata para tratar
de obtener una especie de descripción de baja resolución, lo que es posible a
veces. Detalles
de esto, en
® “Computational
Irreducibility and the Predictability of Complex Physical Systems” por N.
Israeli and N. Goldenfeld, en Physical
Review Letters 92, 074105 (2004).
En este contexto, es notable la diferencia entre
“sistema complicado” y “sistema complejo” como hacen Luis Antonio N. Amaral y
Julio M. Ottino, en “Complex Networks”, The European Physical Journal B 38, 147
(2004). Un gran avión consta de muchas partes, pero diversas y con funciones
específicas, y es incapaz de organizarse o adaptarse por sí mismo, no
resultando más orden que el predeterminado en su diseño.
·
There
are several other books as, for example,
® Computer Simulations with Mathematica – Explorations in Complex
Physical and Biological Systems, Richard J. Gaylord and Paul R. Wellin,
TELOS (Springer-Verlag), New York 1995,
which may also serve as a
general reference here. In a relatively simple, interactive way, this one
teaches the reader to make simulations like the ones discussed in P&L, including
generation of random numbers, the game of life, traffic, forest fires, random
walks, percolation, avalanches and Ising model.
·
Some
Universities have developed interesting projects aimed at translating
scientific knowledge with sufficient rigor to students lacking motivation for
and information in physics and mathematics. A good example is a course on the
frontiers of science of the University of Columbia, USA, whose aim is to endow
the student of a rigorous preparation as an intelligent citizen in today’s
complex and changing world, so that the course illustrates how scientists think
and teaches some basics concerning brain and behavior, astronomy, climate and
evolution.
· Un cierto discurso quiere contraponer, digámoslo
brevemente, reduccionismo con holismo, entendiendo éste como defensa
de la imposibilidad de explicar propiedades y leyes de un sistema complejo en
términos de las de sistemas más sencillos. Es cierto que algunos científicos
han expresado una razonable precaución respecto de una confianza excesiva en el
reduccionismo. Se argumenta que no es posible imaginar cómo “reducir” emociones
humanas a leyes físicas fundamentales, y que el libre albedrío sería una
quimera si admitiésemos el reduccionismo hasta sus últimas consecuencias. No
creemos, por supuesto, que todo lo observable pueda relacionarse con
descripciones fundamentales. De hecho, no se tiene a veces indicación alguna de
cómo relacionar niveles, de cuál es el sistema o los constituyentes de éste que
determinan el fenómeno a explicar, el objeto no es homogéneo respecto de sus
partes o presenta otras características que hacen imposible un tratamiento
cooperativo, etc., etc. En cualquier caso, nos parece que todo científico puede
coincidir con las extraordinarias expectativas que hoy tiene la relación entre
niveles tal como es abordada en nuestro libro P&L.
·
Nota: véanse las
referencias y enlaces que se incluyen en las dispositivas del curso, que a
menudo completan las anteriores.