Foreword to the Symmetry
Symmetry Festivals are multidisciplinary events
with a wide scope of scientific and artistic-cultural programs. The aim of such
Festivals is to provide a forum for discussing phenomena, principles, and
methods which cross boundaries between disciplines. Although most emerging
ideas begin in an individual discipline, at these Festivals the emphasis is
laid on the extension of those ideas — including applications — to other
disciplines. For example, symmetry and symmetry breaking (a synthesis of
constancy and change) stimulate dialogue between disciplines.
Our fundamental knowledge of the structure and
interactions of matter is based on the Standard Model (SM) of physics. The
Standard Model of the particles and fundamental interactions was elaborated in
the nineteen sixties by a unification of the theories of the electromagnetic
and the weak interactions, and was extended in the seventies to also cover the
strong interactions (electroweak and quantum chromodynamic theories). Although
the Higgs mechanism — which gives an account for the origin of mass — has been
incorporated, the fourth fundamental interaction, gravity, is still to be
integrated to form a more unified theory. Nevertheless, breakthroughs are
expected from experiments taking place at the Large Hadron Collider (LHC), in
Geneva. This machine, which recently
began operating, will achieve unprecedented high energies in order to test
theories at the cutting edge.
The history of the discovery of the electroweak
unification (by Glashow, Salam, and Weinberg; Nobel prize, 1979) will be
covered at the Symmetry Festival 2009 by one of the discoverers, S. Weinberg.
The contribution of A. Salam will be discussed by T. Toró. And the LHC experiments, along with the
results expected, will be presented by D. Horváth.
The history of the past sixty to seventy years
contains major discoveries pertaining to the fundamental structure of matter
and its interactions. Such findings were based on a consecutive sequence of discoveries
of new symmetries and how they were then broken. The Standard Model is a result
of that process. Although the SM (like any scientific theory) is not closed, at
our present stage of knowledge it appears to be the most complete such theory.
Attempts to elaborate more precise theories are usually based on more
fundamental symmetries (e.g., so called “supersymmetries”, combined
symmetries), and would incorporate the SM as a special case. All of those
theories aim at a unification of physical interactions by trying to find a common
reason for their functioning.
A discussion of the sequence of symmetries and
symmetry breakings also includes the investigation of asymmetries that tend to
destroy our preferred image regarding the “perfection” of nature. Among others,
chiral asymmetries related to the neutrino bear far-reaching consequences at
higher organizational levels; as can be seen through the history of the
evolution of matter.
Just as the baton of symmetry was passed, at the
turn of the 20th century, from crystallography to physics, so was it
also passed, at the turn of the 21st century, to the life sciences.
What role did symmetry breaking play in the emergence of life and in living
matter? These are hot topics of the day.
One of the main questions concerning asymmetry
is: Why do the macromolecules (amino acids, nucleic acids – like RNA and DNA –,
proteins) that compose biological matter, appear dominantly in one chiral form
in living beings? And why do the amino acids composing the proteins twist to
the left, while DNA twists to the right?
Research of the last 3 to 4 years enables us to obtain answers to those
questions. And the audience of Symmetry Festival 2009 will have an advantageous
opportunity to learn about some of the latest discoveries from the discoverers.
As a brief introduction to topics: Life emerges
in an aqueous environment built on asymmetric molecules (cf. lecture by G.
Pollack). Asymmetry of the water
molecule can be reduced to a spin distribution of the electrons of the H atoms
in the molecule. Results of experiments on the violation of symmetry in aqueous
solutions of chiral substances will be shown by Y. Scolnik. This basic physical
asymmetry determines the formation of the macromolecules; e.g., the intrinsic
asymmetries of amino acid enantiomers and their peptides
that possibly led to the biochirality. As a consequence of the latest
experiments, a quantitative correlation
between symmetry, negative entropy and information capacity in chiral
solutions will be presented (cf. keynote lecture by M. Shinitzky).
The Festival also aims to satisfy the curiosity
of those who wonder whether symmetry principles play any role in the genetic
coding for protein synthesis. Bioinformatics, one discipline used in studying
the genetic code, proceeded at an accelerated pace in recent years. In
particular, there was the development of matrix genetics — matrix forms of
presentation of basic ensembles of molecular elements of this code. This new
mathematical approach has not only revealed surprisingly simple symmetries, but
also new evolutionary regularities, heuristic analogies, and algebraic tools
essential for understanding principles of formation of nucleotide (nitrogenous
bases) sequence and genetic triplets (codons) in DNA which determine sequences
of the twenty amino acids in proteins.
Bioinformatics of the genetic code applies not
only to geometric analogies with polyhedral and non-Euclidean space
symmetries. The revealed harmonic laws in the genetic matrices are also
associated with algebraic representations and generalized (hypercomplex)
numbers. Lectures (among others) by S.V. Petoukhov and J. Kappraff will
demonstrate that the genetic code conceals more symmetry principles than one
might have expected. These include analogies with further symmetry principles
that have been discovered in other disciplines.
and Interdisciplinarity in…
Synergetics — The philosophy behind many
fundamental investigations is the search for common principles based on
a common reason — as mentioned
above with regard to unification theories of physics and with regard to
bioinformatics. Common principles that govern nature are symmetry principles
and the principle of synergetics (cf. the lecture by H. Haken; e.g., from the
stability of the chemical molecules to the architectural structures). Those
principles hold far beyond physics.
Their treatment involves many disciplines
containing diverse approaches and methods. Investigation of symmetry breaking
phenomena and their explanation are tasks for scholars of the individual
disciplines. The role of the Symmetry Festivals is to provide a forum for the
discussion of the common principles.
Mathematics — Symmetry principles are
precisely formulated through the use of mathematics. The basic tool of
geometric and generalized symmetries (both of which have been met in physics)
is the theory of groups. A “group” is
a certain type of algebraic structure defined with its own axioms. Groups seem
appropriate to describe any kind of symmetry. These algebraic structures can be
represented in different ways, such as through the visually illustrative set of
symmetry transformations of polyhedra. Therefore, the study of symmetry
properties of polyhedra is a useful tool for all who apply generalized
symmetries in the different disciplines (cf. the lecture by Ch.
Goodman-Strauss). These symbolic representations are applicable not only in
education, but also in modeling and in the interpretation of experimental and
Crystallography — Polyhedral models and
their symmetries have been used in crystallography since the very beginning of
the modern study of the structure of matter. The basic notions of symmetrology
were elaborated in nineteenth-century crystallography (cf. the lecture by Th.
Hahn). Such notions were then borrowed first by physics and then by the other
disciplines (cf. the lecture by G. Náray-Szabó). Crystallography, even now,
plays a pioneering role in symmetry studies (cf. the lecture by A. Kálmán).
Mathematical tools of handling symmetries enter
not only in the sciences, but also in the
humanities. Examples will be
given in linguistics (by S. Marcus). And we shall also see the mathematical
connection of symmetries to the “letters/words” of the alphabet (letter
sequence) of the genetic code.
Symmetry in Science - Art Relations
Twentieth century arts tended to abstract the
geometrical forms from figurative depictions. This century-long process can be
traced from painting and graphics to sculpture, from photography to movies,
from music to literature, and from dance to the performing arts. Throughout this process one can observe the
application of more and more elements of symmetry.
From the end of the Renaissance to the nineteenth
century, science was considered to proceed primarily through the domain of
rationality and the arts primarily through the domain of the emotions. But in the twentieth century such barriers
between the sciences and arts were broken. The growing interaction between
science and art was two-way — each side influencing the other. The results of
these interactions will be presented, not only by certain papers, but more
viscerally through the art programs (exhibition vernissages, performances, and
concert) of the Festival.
The keynote and plenary lectures of the Festival
will provide a cross section of the connection among symmetry principles
prevailing in different disciplines. These principles — common to the different
spheres of phenomena in nature — will be featured in more detail in the
thematic sessions of the Festival. Our hope is to give attendees of Symmetry
Festival 2009 a unique forum for a novel and exciting experience that fosters
mutual understanding across disciplines.