Aesthetics of Symmetry

1. Aesthetics of Symmetry

2. Aesthetics

3. Aesthetics comes from the Greek word aisthetike; coined by the philosopher Alexander Gottlieb Baumgarten to mean “The science of how things are known via the senses.” Aesthetics is defined by the Oxford English Dictionary as : 1. Concerned with beauty or the appreciation of beauty 2. Set of principles of good taste and the appreciation of beauty

4. Symmetry

5. Symmetry is defined by the Oxford English Dictionary as : 1. Correct or beautiful proportion of parts; balance; harmony. The word symmetry comes from the Greek word summetria,which is derived from the words sun meaning with or together, and metron meaning measure. 2. Repitition of exactly similar parts facing each other or a center.

6. Finding Symmetry

7. “Symmetry is encountered everywhere -- in nature, engineering, arts, and science. Note, for example, the symmetry of a butterfly and maple leaf, the symmetry of a car and plane, the symmetry of a verse and tune, the symmetry of patterns and borders, the symmetry of the atomic structure of molecules and crystals. The notion of symmetry can be traced down through the entire history of human creative endeavours. It has its beginnings in the well-springs of human knowledge and it has widely been used by all the modern sciences. So principles of symmetry dominate in physics and mathematics, chemistry, and biology, engineering, architecture, painting and sculpture, poetry, and music. The laws of nature, which govern the infinite variety of phenomena, in turn obey the principles of symmetry. Preface: This Amazingly Symmetrical World by L. Tarasov

8. Types of Symmetry

9. There are many types of symmetry such as Directional, Rotoreflectional, Glide reflectional, Helical, Scale symmetry and fractals. The most common types are reflection (bilateral or mirror symmetry), rotation, and translation. These symmetries may also be found in combinations of each other. We’ll be looking at examples of mirror symmetry, rotation, translation, and Helical. Symmetry is a property which figures in almost all serious efforts to explain esthetic responses and often is used as a synonym for harmony or proportion, but it is also susceptible of rigorous mathematical treatment and is in a strict sense a geometric concept.

10. Mirror Symmetry Reflection or mirror symmetry is most commonly found in nature. A mirror reproduces exactly what it “sees”, but reverses the spatial order: the mirror image of a right hand is a left hand, because the arrangement of fingers is reversed. Extending this analogy, we say that anything which can be thought of as divisible into two equivalent but mirror-image halves has mirror symmetry.

12. Rotational symmetry is defined as a pattern which “appears the same if rotated through a certain number of degrees about an axis passing through its center.” -- Patterns of Symmetry Rotational Symmetry This means that “an object coincides with itself exactly when turned about some axis through an angle of 360 degrees. – This Amazingly Symmetrical World

14. Translational Symmetry Translation symmetry refers to “any pattern that repeats indefinitely whether in one, two, or three dimensions” Strictly speaking, a body having a translational symmetry must be infinite in the direction of the translation. Day and Night by M C Escher

16. Helical Symmetry It can be thought of as rotational symmetry along with translation along the axis of rotation. The concept of helical symmetry can be visualized as the tracing in three-dimensional space that results from rotating an object at an even speed while simultaneously moving at another even speed along its axis of rotation (translation).

18. So . . . what is aesthetically pleasing or stimulating about Symmetry?

19. The Brain

20. Our perception seeks and enjoys order, and this quest seems to be a general principle which drives, in part, from the limited capacity of our brain to process information. Our short term memory seems to have the capacity to process 16 bits per second; less is perceived as boring, and more is stressful. Physiology Input = Involves the senses – the only way we can get information about the always changing environments in which we must function involves sensation and (at a more integral level) perception. “First, it has been found that perception is an active process of searching for order, categorizing, and interpreting.”

21. Aesthetic reasons for symmetry also may derive from a variety of sources. One is the aforesaid symmetry of the natural environment, whose properties often are reflected in constructed objects to appeal to the perceptual specializations that have developed in this environment. A second is a resonance with the inherent symmetries of the optics, retina and cortical projection of the visual system, which has circular symmetry overlaid with a mirror symmetry. *Designs such as those of Persian carpets may be particularly appealing because they harmonize with such symmetries. All images, artistic or scientific, whether they enter naively or self-consciously into our awareness, are abstractions from diverse phenomena. The abstraction of images occurs even during everyday perception, wherein the mind reduces the richness of sense data to orderly patterns.

23. What we consider as beautiful, or pleasing, may be a type of visual input that corresponds optimally to the processing rules of the central nervous system. These rules are, to some extent, genetically predetermined. However, the wealth of visual experiences, as well as the enduring learning processes, make aesthetic preferences subject to change. This adaptability is probably the reason why any static theory of aesthetics is unsatisfactory.

24. In 1790 Immanuel Kant published the Critique of Judgment, in which he dealt with the ultimately esthetic character of the presuppositions underlying man’s knowledge of the world. Man experiences beauty in certain aspects of nature, according to Kant, as a result of properties in his esthetic judgment, and not because beauty is an objective quality inherent in nature. Regularity in the object induces an experience of rhythm in its beholder. The pleasure we experience in contemplating a decorative design does not arise from its utility or our desire to own it but from the pleasurable play of our mental facilities in its presence.

25. Fitness and Reproduction Certain simple symmetries, and in particular bilateral symmetry, seem to be deeply ingrained in the inherent perception by humans of the likely health or fitness of other living creatures. . . Edler cited research supporting the claim that bilateral symmetry is an important indicator of freedom from disease, and worthiness for mating. In evolutionary psychology, symmetry especially facial symmetry is one of a number of traits, including averageness and youthfulness, associated with health, physical attractiveness and beauty of a person or animal. It is also hypothesized as a factor in both interpersonal attraction and interpersonal chemistry.

26. Safety and Security Another more subtle appeal of symmetry is that of simplicity, which in turn has an implication of safety, security, and familiarity. A highly symmetrical room, for example, is unavoidably also a room in which anything out of place or potentially threatening can be identified easily and quickly. People who have, for example, grown up in houses full of exact right angles and precisely identical artifacts can find their first experience in staying in a room with no exact right angles and no exactly identical artifacts to be highly disquieting. Symmetry thus can be a source of comfort not only as an indicator of biological health, but also of a safe an well-understood living environment.

27. Symmetry expressed in other organisms which impact our own biological needs – threat, danger… . . . a tiger passing by may be of concern, but when it turns to exhibit its proverbial symmetry by facing you, it is time to take action!

28. Culture and Symbols Finally – Perceptions and appreciation of symmetries are also dependent on cultural background. -Symbols -Memes – cultural units of inheritence -Communication/ coding -(Art)

29. Bibliography The Oxford American Desk Dictionary and Thesaurus 2nd edition. Oxford University Press: Berkley Books, New York, 2001. Tyler, C.W., eds. Human Symmetry Perception and its Computational Analysis. Lawrence Erlbaum Associates, Publishers: Mahwah, New Jersey, 2002. Rentschler, Ingo, and Barbara Herzberger, eds. Beauty and the Brain. Birkhauser Verlag, Basel. 1988. Ritterbush, Philip C., The Art of Organic Forms. Smithosonian Institution Press: City of Washington, 1968. Hersey, George. The Monumental Impulse. MIT Press: Cambridge MA, 1999. Washburn, Dorothy K., and Donald W. Crow, eds. Symmetry Comes of Age. University of Washington Press: Seattle and London, 2004. Rosen, Joe. Symmetry Discovered. Cambridge University Press: Cambridge, 1975. L. Tarasov. This Amazingly Symmetrical World. Mir Publishers: Moscow, 1986. Lederman, Leon M., and Christopher T. Hill. Symmetry and the Beautiful Universe. Prometheus Books: Amherst, New York, 2004. Senechal, Marjorie, and George Fleck, eds. Patterns of Symmetry. University of Massachusetts Press, Amherst `977. Stokstad, Marilyn. “Art History Revised Second Edition Vol 1. Emerita The University of Kansas 2005.

30. *Edler, RJ. June 2001. "Background Considerations to Facial Aesthetics". "Sexual reproduction and parasite resistance" section retrieved 31 May2005. http://commons.wikimedia.org/wiki/Image:Singapore_Zoo_Tigers_cropped.jpg http://www.sculpturegallery.com/butterflies/bf_group14.jpg http://www.goldenmuseum.com/0501Symmetry_engl.html http://www.flickr.mud.yahoo.com/photos/pg-photography/sets/72057594059164372/?page=3 http://www.dartmouth.edu/~matc/math5.pattern/Hargittai.p49.gif http://en.wikipedia.org/wiki/Symmetry#Helical_symmetry http://www.wheelockweb.com/images/nautilus.jpg http://gallery.hd.org/_exhibits/natural-science/_more2001/_more10/galaxy-spiral-NGC628-Messier74-in-Pisces-taken-by-GMOS-telescope-in-Hawaii-ANON.jpg http://weathersavvy.com/hurricane_bonnie_OPT.jpg http://leadinganswers.typepad.com/photos/uncategorized/dna_strands.jpg http://blueblau.stumbleupon.com/tag/spirals/ http://www.lhup.edu/~dsimanek/eye2.jpg http://www.mprugs.com/images/large/large170a.JPG http://www.agoracosmopolitan.com/home/Frontpage/2007/01/09/01300.html http://en.wikipedia.org/wiki/Symmetry_%28physical_attractiveness%29 http://www.uclan.ac.uk/psychology/research/research.htm http://en.wikipedia.org/wiki/Symmetry http://www.mbari.org/staff/jones/images/meeting.jpg http://news.nationalgeographic.com/kids/2003/10/images/tiger-big.jpg http://strangepaths.com/wp-content/uploads/2006/10/neuron.jpg http://en.wikipedia.org/wiki/Image:Religious_syms.png https://notes.utk.edu/bio/greenberg.nsf/e972592203c877ef8525676b005ded2d/af3655dde24dd275852569b10065375c?OpenDocument https://notes.utk.edu/bio/greenberg.nsf

31. Abstract The aesthetical appeal for symmetry is a complex issue with many questions. Is symmetry aesthetically pleasing due to the structures of our eyes? Does the break down of visual forms into pattern sized bites for our brains to process influence aesthetics? Could symmetry be equated with beauty due to harmony, balance, and proportion? Does recognizing symmetry in our surroundings allow us to better function as organisms in relation to finding mates, identifying predators, or seeking security in our environments? Symmetry plays a serious role in art and symbol and we communicate between peoples and pass on cultural ideas. Are our aesthetical appeals to certain kinds of symmetries genetic or tied to evolutionary causes? There seem to be many developmental, evolutionary, ecological, and physiological causes for the aesthetic appeal for symmetry to meet some of our needs.

32. OutlineAesthetics of Symmetry • Explain symmetry • Types of symmetry • Brain – physiological – input • Health/Fitness/Beauty • Safety/security • Culture/ Symbols • Art/Communication