Foreword to the Symmetry Festival 2009

György Darvas

Introduction

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.

Symmetry and Matter

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.

Symmetry and Life

Just as the baton of symmetry was passed, at the turn of the 20^th century, from crystallography to physics, so was it also passed, at the turn of the 21^st 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.

Symmetry 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 theoretical results.

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.

Final Remarks

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.