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Infinity, Impossibility, and Art

What is infinity?. The quality or state of being. unbounded or unlimited endless not finite. Random House College Dict., 1992.. . A Historiographic Look at Infinity. Greek apeironconnotation was negative and pejorativeunorderedundefined. A Historiographic Look at Infinity beginning with the Greeks.

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Infinity, Impossibility, and Art

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    1. Infinity, Impossibility, and Art Michael Davis 4 April 2003 Hons 183: Mind, Art & the Brain

    2. What is infinity?

    3. A Historiographic Look at Infinity Greek apeiron connotation was negative and pejorative unordered undefined (Ahp ay rown)(Ahp ay rown)

    4. A Historiographic Look at Infinity beginning with the Greeks Pythagoras (582 507 BCE) natural numbers Plato (427? 347 BCE) concept of the Good Aristotle (384 322 BCE) actual vs. potential

    5. A Historiographic Look at Infinity on to the Middle Ages General attitudes St. Augustine (354 - 430)

    6. A Historiographic Look at Infinity in the Modern Age Galileo Galilei (1564 1642) Georg Cantor (1845 1918) Kurt Gdel (1906 1978)

    7. The Background of the Symbol Lemniscate - 1700s conic sections [(x-a)2 + y2][(x+a)2 + y2] = a4 The appropriateness of the symbol lies in the fact that one can travel endlessly around the curve demolition style, if you will (R. Rucker)

    8. The Background of the Symbol The symbol caught on popularly and was used on the Tarot card of the Magician (Juggler). Qualities: The Magician strides the webs of time, the bridges of our years; He sees the past and future, knows our hopes and fears. Source: http://www.tarot-card-meaning.co.uk

    9. Types of Infinity Temporal Infinities (music) Spatial Infinities (art) of the large in the small Infinity of the Mindscape (Rucker, 1995)

    10. How we first perceive infinity Successive Theory (Lakoff) Unconsciousness Theory (Baldwin) Cause and Effect Theory (refutation: Hume)

    11. Questions Raised by M. C. Escher in his Approaches to Infinity How can a composer succeed in evoking a suggestion of something that does not end? Music is not there either before it begins or after it ends.

    12. Gdel, Escher, and Bach: An Eternal Golden Braid Douglas Hofstadter (1979) Strange Loops artists can exploit our perceptions the artist will make the medium appear to be increasing but, eventually the audience member will find her/himself in the same place that she/he began

    13. Strange Loops: Visual Art

    14. Strange Loops: Visual Art II

    15. Strange Loops: Visual Art III

    16. Strange Loops: Music

    17. Strange Loops: Math

    18. Types of Impossible Figures The Necker (Rib) Cube The Tribar The Mbius Strip

    19. Necker Cube

    20. Cuboid (Necker Cube)

    21. Cuboid (Necker Cube) II

    22. Cuboid (Necker Cube) III

    23. Tribar

    24. Tribar II

    25. Tribar II

    26. Tribar III

    27. The Mbius Strip

    28. The Mbius Strip II

    29. The Mbius Strip III

    30. Bibliography and Further Reading Berbaum, K., Tharp, D., & Mroczek, K. (1983). Depth perception of surfaces in pictures: Looking for conventions of depiction in Pandora's box. Perception, 12, 5-20. Biederman, I. (1987). Scene Perception. Scientific American. Bloomer, Carolyn M. (1976). Principles of Visual Perception. New York: Litton Educational Publishing, Inc. Carterette, Edward C. (1975). Handbook of Perception. Volume V. New York: Academic Press, Inc. Coren, Stanley. (1978). Seeing is Deceiving: The Psychology of Visual Illusions. Hillsdale, New Jersey: Lawrence Erlbaum Associates, Escher, M. C. (1986). Escher on Escher. New York: Harry N. Abrams, Inc. Escher, M. C. (1967). The Graphic Work of M. C. Escher. New York: Meredith Press. Escher, M. C. (1971). The Work of M. C. Escher. New York: Harry N. Abrams, Inc. Fineman, Mark B. (1981). The Inquisitive Eye. Oxford: Oxford University Press. Gregory, R. L. (1973). Illusion in Nature and Art. London: Gerald Duckworth & Company, Limited.

    31. Bibliography and Further Reading Koffka, K. (1935). Principles of Gestalt Psychology. New York: Harcourt Brace. Matlin, Margaret W. (1988). Sensation and Perception. Boston: Allyn and Bacon, Inc. Peterson, Ivars (2001). Fragments of Infinity: A kaleidoscope of Math and Art. New York: John Wiley & Sons. Rainey, Patricia Ann. (1973). Illusions: A Journey into Perception. Connecticut: The Shoe String Press, Inc. Ramachadran, V. S. (1973). Utilitarian theory of perception. Washington, D.C.: American Psychological Association. Rucker, Rudy (1995). Infinity and the Mind. Princeton: Princeton University Press. Schattscneider, Doris (1990). Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M. C. Escher. New York: W. H. Freeman and Company. Wade, Nicholas. (1980). Visual Allusions: Pictures of Perception. Hove, UK: Lawrence Erlbaum Associates Ltd.

    32. Visual Images http://noordnet.net/optical_illusion/triangle.html http://www.worldofescher.com/gallery http://www.aspecialplace.net/illusions/necker_cube.htm http://www.public.asu.edu/~sbroder/Escher/figure4.html http://ccat.sas.upenn.edu/jod/augustine.html

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