Symmetry Circle in Budapest

SYMMETRY CIRCLE in Budapest (a monthly forum of ISIS)

Venue:  Artkatakomba,  Budapest, Szt. István krt. 2  (at the Pest side of the Margaret-bridge / Margit-híd)

March 12, 2011 (Saturday), 1 p.m.


the host of our last congress-festival Symmetry: Art and Science (Artists’ City Gmünd, Austria, August 23-29, 2010) will be the guest speaker.

Werner is a distinguished professor and composer, who was a pupil of Jenő Takács, Béla Bartók’s friend; see in German:

Werner made many surprises for the congress-festival of ISIS. There were two-three concerts or performances each day. Perhaps the greatest surprises for the members of ISIS were the following two:

– Werner’s own composition ISIS: Mandalas for String Quartet, op. 24 (2010), which was presented by the Graffe Quartet (Brno, Czech Republic)

– Aleksandr Skryabin’s Promethée: Le Poème du feu, op. 60 (1909/10), which was presented by a group of artists and scholars led by Werner using a real fire-organ.

It was dedicated to the outstanding scientist and artist, theorist and expert in light-music, Bulat Makhmudovich GALEYEV (1940-2009), founder of the Prometheus Institute in Kazan’, Tatarstan (Russia); see in Russian and English:

The group led by Bulat made various presentation of the same work by Skryabin. Their artistic and scientific achievements were summarized in many papers and a comprehensive book (1981). ISIS kept connections with Bulat and we hoped that we may invite him for the congress-festival. His sudden death was a shock for us.

Werner’s lecture in Budapest is again dedicated to him. This would be also the first presentation outside Russia of a new 2nd revised and extended edition of the mentioned book

Irina Venechkina and Bulat Galeyev

Poema ognya: Kontseptsiya svetomuzikal’nogo sinteza

(Poem of Fire: Conception of Light-Musical Synthesis, in Russian with English abstract and contents),

Kazan’: Kazan’skaya Gos. Konservatoriya, 2010, 351 pp.

Dénes Nagy will speak about Bulat and about the new book. Special thanks to Irina for sending some copies of this book to ISIS. We never will forget Bulat and his contributions.

The meeting of the Symmetry Circle will be followed by a joint event with NET (Folk Architecture Society):


(Professor of History of Architecture,  Technical University of Budapest):

The architectural traditions of the villages.

This will be followed, as usual, by a symmetric round table.

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Meanings of Symmetry

The meaning-family of symmetry was developed  through the ages in an interestic way. The main steps were made in both science  and art. Some meanings also appeared “between”: these are associated with both sides of culture.




common measure
– geometry
mirror sym.
– crystallogr.
periodic sym.
– physics

(Based on a slide that I presented at the first congress of ISIS,Budapest , 1989)

  • Perhaps surprisingly to many people, the classical Greek term symmetria (summetria) did not refer to “bilateral symmetry” at all. Syn + metron is simply “common measure”. This concept, together with asymmetria, became important in geometry. following the discovery that two pairs of lengths could be both:
  • – commensurable, e.g., 1 unit-length and 2 unit-length
  • – incommensurable, e.g, the side and the diagonal of a square,                             i.e. 1 and Root(2).
  • We may believe that the proof of the latter led to modern mathematics (sic!). The fact that the ratio of the side and the diagonal of a square (or of a regular pentagon) cannot be expressed as  a/b, where a and b are integers was made by the method of indirect proof. First it was supposed that, to the contrary, there exist such a and b, but it led, after some logical steps, to contradiction. This fact meant that there are no such a and b. During this proof, logical operations were made with non-existing objects. Thus, this “new geometry” is not any more a practical field (geo + measure), but abstract science with a deductive system.
  • The expected good case was symmetria (commensurability), while the discovery of the new possibility of asymmetria (incommensurability) made some confusions. First of all, it “disturbed” the view of the Pythagoreans that everything can be expressed as ratios of integers, from musical harmonies to the motion of stars. This led very quickly to an aesthetical meaning of the same term:
  • symmetria refers to good ratios,
  • – asymmetria refers to bad ratios.
  • See the related algebraic terminology: rational vs. irrational (sic!) numbers.
  • The early works of the Pythagoreans (6th c. B.C.) do not survive. Thus, we should consider later sources. It is important that in the 5th and 4th cc., Plato and Aristotle used the term symmetria in both senses: as a geometrical term and as an aesthetical concept. In fact, Aristotle claimed that there are three species of beauty:
  • taxis (order – it is closer to the modern concept of symmetry than symmetria)
  • symmetria (proportion)
  • horismenon (definiteness).
  • In Latin the term symmetria had much less importance since different expressions were used:
  • – commensuratio (the geometrical meaning of symmeria)
  • – proportio (the aesthetical meaning of symmetria).
  • My view if that the term symmetria survived because of Vitruvius‘ terminology (De architectura libri decem, 1st c.). He used both symmetria and proportio, but in slightly different senses:
  • – symmetria refers to the theoretical aspects of proportions.
  • – proportio refers to the practical aspects.
  • I located many usages of the derivatives symmetria that are earlier than those ones which are given in major etymological dictionaries as the first usages outside Greek and Latin. All of these expressions are related to the modern translations of the Vitruvian text. In fact, the translators did not introduce the  deritaves of porportion in the case of symmetria, since Vitruvius made distinction between the two concepts.
  • However, this distinction was not relavent in later ages. The term symmetria became an “empty niche” for later usages …  and mathematician adopted it. A mirror symmetric (bilaterial-symmetric) object has two equal halves and such a half can be considered as the unit of “common measure” for the entire object. In the case of n-fold symmetry, we have n equal parts and one of them can be considered as unit of the “common measure”. Geometrical and crystallographic motivation helped the introduction of “crystallographic symmetries”, including translatary symmetries (periodic structures). In all above cases, symmetry can be interpreted as a transformation that moves the figure into itself, i.e., it reamains unchanged or, using another word, invariant.
  • The next generalization of the concept of symmetry was made in physics where not only the invariance of geometrical shape, but also physical proporties were considered. In fact invariances and conservation laws play a major role in physics, According to E. P. Wigner , who earned the Nobel-prize for his symmetry-related works,  there are three important levels:
  • – events
  • – physical laws
  • – symmetries, the laws of laws.
  • Symmetry, having roots in both art and science, may help the intersicsiplinary cooperation. In fact, symmetry may serve as a “bridge” between the two “hemispheres” of culture.
  • Let it be … symmetry…
  • References:
  • Nagy, D. (1995)  The 2500-year old term symmetry in science and art and its `missing link’ between the antiquity and the modern age, Symmetry: Culture and Science, 6, No. 1, 18-28.
  • Nagy, D. (1996)  Quasi-Symmetrien und dynamische Symmetrien: Über die Entwicklung der Symmetrie in der Natur und deren Wiederspigelung in menschlichen Begriffen,  [Quasi-symmetries and dynamic symmetries: On the development on symmetry in nature and its reflection in human concepts, in German], In: Hahn, W., and Weibel, P., eds., Evolutionäre Symmetrietheorie: Selborganisation und dynamische Systeme, Stuttgart: Hirzel, 219-228
  • Nagy, D. (1996)  The Western symmetry and the Japanese katachi shake hands: Interdisciplinary study of symmetry and morphological science (formology), In: Ogawa, T.,  Miura, K.,  Masunari, T., Nagy, D., eds., Katachi U Symmetry, Tokyo: Springer, 27-46.
  • Nagy, D. (1997)  Symmetry: From the birth of Greek mathematics and aesthetics to a modern bridge between science and art, In: Koptsik, V.  and  Riznichenko, G., eds., Mathematics and Art: International Conference, Proceedings, Moscow: Moscow State University, 64-69.
  • Nagy, D. (1998)  (Dis)symmetry: Mathematics and design, Euclidean vs. Vitruvian mathematics, In: Barallo, J., ed., Mathematics and Design 98: Proceedings of the Second International Conference, [June 1-4, 1998], San Sebastian: Universidad del Pais Vasco, 17-25.
  • Nagy, D. (2002)  Architecture, mathematics, and a “symmetric link” between them (From the Atomium building to the MatOmium project), Symmetry: Art and Science, 2002, Nos. 1-4, 31-62 [ = MatOmium Euro-Workshop, Brussels, April 9-13, 2002; Opening plenary talk of the workshop].
  • Nagy, D. (2007)  Forma, harmonia, and symmetria (With an appendix on sectio aurea), Symmetry: Art and Science, 2007, Nos. 2-4, 19-41 [Plenary talk at the Seventh Interdisciplinary Symmetry Congress and Exhibition, Buenos Aires, Argentina, November 11-17, 2007].
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Symmetry – Asymmetry – Dissymmetry

the lack of some possible elements of  symmetry,
a small violation of perfect symmetry

(Based on a slide at the first congress of ISIS, Budapest , 1989)

Added on February 19, 2011

  • Usually Louis Pasteur is credit for introducing this expression in French (1848). Note, however, that I know a slightly earlier usuage in English, but the context in that case is not very interesting (some ships are dissymmetric). In the same time, Pasteur solved a main problem of chemistry and the new expression is associated with the birth of stereochemistry (3D chemistry).
  • The problem was the following: how is it possible that molecules with the same chemical composition and the same geometric shape may have different physical properties, specifically turning the plane of the polarized light to the left or to the right? In his paper, Pasteur suggested that the left-handed molecules and the right-handed molecules are equiavalent in geometry by a mirror reflection, but still these are different physically. Indeed, we cannot move our left hand into the postion of our right hand. A practical problem: a left-handed glove cannot be transformed into a right handed one.
  • It is important to note that not all figures have left-handed and right-handed versions. Let us think, for example, about a cube. What are the requirements of having left-right versions.  The answer by Pasteur is that some elements of symmetry should be missing. Thus, mirror symmetrc objects have no left-right versions. However, there is no need for asymmetry, the total lack of elements of symmetry: the letters S and Z have two-fold rotational symmetry, but still have two versions. These two letters are often “mirrored” by small children and people with dyslexia also have problem with these. Using Pasteur’s terminology: dissymmetry is needed for having left-handed and right-handed molecules, not asymmetry. Of course, asymmetry can be considered as the extreme case of dissymmetry.
  • Later, Pierre Curie adopted the same term into physics (1894). He went so far that made a famour claim: “Dissymmetry makes the phonmenon”. Then Russian crystallographer adopted the expression (Shubnikov and Koptsik). Unfortunately, the term “dissymmetry” was sometimes translated into English as “asymmetry”, eliminating the important difference between the two expression. I also noticed that a book in Japanese translated the French term “dissymmetry” as “antisymmetry”. In fact, I suggested a new Japanese expression to make distinction (“fu-tai-shou”).
  • I believe that the concept “dissymmetry” is very useful in aesthetics, too:
  • – Symmetry: perfect order,
  • – Asymmetry: total chaos,
  • – Dissymmetry: its small level may have the aspect of beauty.
  • Here we see immediately that we should have (dis)symmetry measures. The topic of symmetry is not any more a yes/no question, but a quantity that should be measured. There are various methods for measuring symmetry.
  • Some experimental-aesthetical investigations made clear that we prefer a small level of dissymmetry much better than the perfect symmetry. I was told by a physical anthropologist that not only the very much asymmetric face may hint some mental disorder, but also the perfectly symmetric one.
  • A related topic is the often discussed topic of the right-brain / left-brain. In 1989, at the opening of the first congress of ISIS, I suggested to speak about art and science not as”two cultures” (Ch. P. Snow), but as about just one culture, which is a split culture (cf., split brain) with two “hemisphres” (art/humanties and science/technology). Obviously, the two “hemispheres” of culture should cooperate, similarly to the functioning of human brain.
  • I am eager to revitalize and popularize the concept dissymmetry not only in science, but also in art.
  • My related publications (the papers on “split culture” not listed here):
  • Nagy, D. (1984)  Szimmetria – aszimmetria – disszimmetria, [Symmetry-asymmetry-dissymmetry, in Hungarian], In: Természettudomány – világnézet – kultúra, Visegrád: ELTE TTK Filózófia Tanszék, 149-152.
  • Nagy, D. (1996)  (Dis)symmetry measures, Circular of the Society for Science on Form, Japan, 10, No. 3, 16-17.
  • Nagy, D. (1997)  (Dis)symmetry in art and science: East and West, [Abstract of a plenary talk, in English and Chinese], Abstracts of the Papers of the II East Asian International Semiotic Seminar, [Shanghai, October 19-25, 1997], Shanghai, China: East China Normal University, 95-96.  [The full version is also published.]
  • Nagy, D. (1998)  (Dis)symmetry: Mathematics and design, Euclidean vs. Vitruvian mathematics, In: Barallo, J., ed., Mathematics and Design 98: Proceedings of the Second International Conference, [June 1-4, 1998], San Sebastian: Universidad del Pais Vasco, 17-25.  [Paper version of an invited plenary talk].
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ISIS GENERAL ASSEMBLY (August 23 and 27, 2010)


(during the 8th congress of ISIS, Gmuend, Austria – August 23-28, 2010)

Venue: Gasthof Prunner: Patio (a congress hotel) – August 23 (M) at19:30

If there is no quorum in that time (the first day of the congress),

the new schedule is – August 27 (F) at 19:30

at the same place with the same Agenda


(1) Opening

(2) Report by Ted Goranson (Chairman, ISIS-US) about the new site

(3) Report by Dénes Nagy (President)

(4) Report by George Lugosi (Treasurer)

(5) The journals of ISIS and the Membership Fee

– (5.1) Printed journal

– (5.2) E-journal

(6) Proposal: The establishment of the Youth Organization of ISIS

(7) Deciding the location of the next congress of ISIS in 2013 and other events

(8) Revision of the Acts of ISIS

ISIS is registered in Hungary, which country became a member of EU, and thus the old Acts require some revisions accordingly

(9) Election of officers

(10) Others

Let me know if you suggest new items.

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Why ISIS? International Society for the Interdisciplinary Study of Symmetry

International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry / ISIS-S / ISIS)

Nomen est omen… The simple name “Symmetry Society” is also used, but the purpose of the long official name was very simple: the abbreviated form should also make some sense. We ended up with ISIS, since Isis can be associated not only with ancient learning (via a goddess), but also with various fields of art and science. The main purpose is to have more bridges (“symmetries”) between different fields of art and science, more cooperation among artists and scholar in an overspecialized world. Since the expressions “symmetria” is used in both art and science since ancient time, it could help us to have a common language (“symmetric language”).

We made a tradition to visit various regions in the framework of our triennial congresses and exhibitions: we started in Europe (Budapest, 1989), went to the Far East (Hiroshima, 1993), then to North America (Washington, D.C., 1995), which was followed by a trip to the Middle East (Haifa, 1998), then to the South hemisphere, specifically to Australia (Sydney, 2001), again to Europe (Tihany, 2004), then back to the South (Buenos Aires, 2007), and now we are heading to Central Europe:

Artists’ City Gmuend, August 23-28, 2010.
Until now, we had “congress-exhibitions”, but now our host Werner Schulze, a distinguished composer and professor of music transforms it into a “festival-congress”.

ISIS-Symmetry has a special interest in art-science connections or, in a broader sense:

art and the humanities – science and technology

The specialization in the last centuries led to various disciplines, while most problems are complex and require interdisciplinary approaches. At the opening of our first congress (1989), I suggested speaking about “split culture”, using a metaphor from brain research, instead of the widely used term “two cultures” (C. P. Snow). According to this interpretation, we have just one culture, but it has two “hemispheres” that should cooperate via some bridges (corpus callosum). My terminology was also introduced and discussed by T. Avital’s monograph (Art versus Nonart, Cambridge University Press, 2003, pp. 34-35; Chinese translation, Beijing, 2009, p. 53; Spanish translation, forthcoming). I am glad that my metaphor reached so many parts of the world by Avital’s help.
In an earlier lecture, I pointed out that art-science connections may appear at various levels:

(1) Strengthening interdisciplinary thinking in general.

(2) Helping education by presenting new connections (e.g., “beautifying” science education and giving new “outlooks” in art education).

(3) Presenting exact methods for artists and new fields of application for scientists.

(4) Giving new inspirations to artists and scientists by a broader scope.

(5) In some special cases, helping the solution of concrete problems (see, e.g., the reconstruction of Bach’s Kunst der Fuge by W. Graeser; the recognition of a mistake in the crystallographic tables by analyzing M. C. Escher’s periodic drawings).

Beyond “symmetry” (commensurability, proportion, harmony, bilateral symmetry, crystallographic symmetries, invariance, orderliness, etc.) and “asymmetry” (the opposite of symmetry), there is a third one between:


In fact, in nature we have just dissymmetry, a small violation of perfect symmetry, and it is usually more beautiful.

Let us have (dis)symmetry!

See you, hopefully, in Gmuend!

Special thanks to

Ted Goranson (U.S.), who made our society more “symmetric” with this new site

Patricia Muñoz (Argentina), who made Möbiusean logo for us (one may believe that a band has always two sides, but the Möbius strip has just one, similar to my view that we have just one culture of art and science).

Werner Schulze (Austria), who bridges art and science in each moment during our work towards the next festival-congress.

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