Abstract

Symmetry: Culture and Science
Volume 31, Number 3, pages 231-260 (2020)
https://doi.org/10.26830/symmetry_2020_3_231

SYMMETRY GIVES MEANING TO ARCHITECTURE

Nikos A. Salingaros^*

^* Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249, U.S.A.
E-mail: salingar@gmail.com; http://zeta.math.utsa.edu/~yxk833
ORCID: 0000-0002-8856-9175

Abstract: Coherent structure affects us viscerally. Human perception relies upon combined symmetries to reduce information overload but random (disorganized) information is too much for us to process. Our brain automatically compares and groups architectural elements into larger wholes. We unconsciously analyze and process the information in any composition using mathematical relations that endow meaning to our environment. Design elements of the same size and shape can be aligned, reflected, or rotated. Their repetitions are regularly spaced; otherwise there is no symmetry. Scaling symmetry links components visually through magnified or reduced versions of the same element. Self-similarity at different magnifications is a basic feature of a ‘fractal’, and is a dominant feature in traditional and vernacular architectures. This is one reason why different architectural form languages have meaning for us. Mathematics also relates components of a whole via their relative number and size. In a stable complex system, there are few large objects, more intermediate-size objects, and many smaller objects, roughly in an inverse-power relationship.

Keywords: symmetry, composition, architecture, design, fractal, information compression, inverse-power scaling, coherence, systems theory, plane transformations

References:
Adams, G. and Ferrante, F. (2007) Markov Modeling Application to a Redundant Safety System, Proceedings of PWR2007 ASME Power Conference, [17-19 July 2007, San Antonio, Texas, USA], 1-7; https://www.nrc.gov/docs/ML0715/ML071570040.pdf. https://doi.org/10.1115/POWER2007-22119

Alexander, C. (2001) The Nature of Order, Book 1: The Phenomenon of Life, Berkeley, California: Center for Environmental Structure.

Alexander, C. (2009) Harmony-Seeking Computations: a Science of Non-Classical Dynamics based on the Progressive Evolution of the Larger Whole, [Keynote Speech at the International Workshop “The Grand Challenge in Non-Classical Computation”, University of York, UK, April 2005]. https://www.livingneighborhoods.org/library/harmony-seeking-computations.pdf

Berman, D., Golomb, J. and Walther, D. (2017) Scene content is predominantly conveyed by high spatial frequencies in scene-selective visual cortex, PLoS ONE, 12, 12, [22 December 2017]; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0189828. https://doi.org/10.1371/journal.pone.0189828

Biederman, I. and Vessel, E. A. (2006) Perceptual Pleasure and the Brain, American Scientist, 94, 3, 247-253. https://doi.org/10.1511/2006.59.247

Chang, L. and Tsao, D.Y. (2017) The Code for Facial Identity in the Primate Brain, Cell, 169, 6, 1013-1028; https://www.cell.com/cell/pdf/S0092-8674(17)30538-X.pdf. https://doi.org/10.1016/j.cell.2017.05.011

Coburn, A., Kardan, O., Kotabe, H., Steinberg, J., Hout, M., Robbins, A., MacDonald, J., Hayn-Leichsenring, G. and Berman, M. G. (2019) Psychological responses to natural patterns in architecture, Journal of Environmental Psychology, 62, 133-145; https://www.sciencedirect.com/science/article/pii/S0272494418305280. https://doi.org/10.1016/j.jenvp.2019.02.007

Coburn, A., Vartanian, O. and Chatterjee, A. (2017) Buildings, Beauty, and the Brain: A Neuroscience of Architectural Experience, Journal of Cognitive Neuroscience, 29, 9, 1521-1531; https://repository.upenn.edu/cgi/viewcontent.cgi?article=1161&context=neuroethics_pubs. https://doi.org/10.1162/jocn_a_01146

Collier, J. (1996) Information originates in symmetry breaking, Symmetry: Culture & Science, 7, 3, 247-256. https://www.researchgate.net/publication/250825786

Córdova-Ramírez, M. (2020) A False Promise of Progress, Inference, 5, 2, [4 May 2020]. https://inference-review.com/letter/a-false-promise-of-progress

Crompton, A. (2002) Fractals and Picturesque Composition, Environment and Planning B, 29, 451-459; https://www.cromp.com/download/pdfdocs/E&PB2002.pdf. https://doi.org/10.1068/b12822

Curl, J. S. (2018) Loss of Meaning, In: Curl, J. S., Making Dystopia: The Strange Rise and Survival of Architectural Barbarism, Oxford: Oxford University Press, 361-364.

DeValois, R. and DeValois, K. (1988) Spatial Vision, New York: Oxford University Press.

Ellard, C. and Condia, B. (2020) Place, Peripheral Vision, and Space Perception: a pilot study in VR, In: Condia, B., Arbib, M., Ellard, C., Chamberlain, B. and Rooney, K., Meaning in Architecture: Affordances, Atmosphere and Mood, Manhattan, Kansas: New Prairie Press eBooks, No. 33, 33-54. https://newprairiepress.org/ebooks/33

Forsythe, A. and Sheehy, N. (2011) Is it not beautiful?, The Psychologist, 24, 7, 504-507. https://thepsychologist.bps.org.uk/volume-24/edition-7/it-not-beautiful

Giurfa, M., Dafni, A. and Neal, P. R. (1999) Floral Symmetry and Its Role in Plant‐Pollinator Systems, International Journal of Plant Sciences, 160, Suppl. 6, S41–S50; https://www.researchgate.net/publication/12729261. https://doi.org/10.1086/314214

Goldberger, A. L. (1996) Fractals and the Birth of Gothic, Molecular Psychiatry, 1, 99-104. http://reylab.bidmc.harvard.edu/heartsongs/molpsy-1996-1-99.pdf

Hersey, G. L. (1988) The Lost Meaning of Classical Architecture: Speculations on Ornament from Vitruvius to Venturi, Cambridge, Massachusetts: MIT Press.

Hersey, G. L. (1999) The Monumental Impulse: Architecture’s Biological Roots, Cambridge, Massachusetts: MIT Press.

Hodgson, D. (2011) The First Appearance of Symmetry in the Human Lineage: Where Perception Meets Art, Symmetry, 3, 1, 37-53; https://www.mdpi.com/2073-8994/3/1/37. https://doi.org/10.3390/sym3010037

Hodne, L. (2016) Symmetry and Utopia: The Aesthetics of Early 20th Century Architecture, Symmetry: Culture and Science, 27, 4, 431-446. https://doi.org/10.26830/symmetry_2016_4_431

Horáèek, M. (2020) Architects as Physicians, Inference, 5, 2, [4 May 2020]. https://inference-review.com/letter/architects-as-physicians

Itti, L., Koch, C. and Niebur, E. (1998) A Model of Saliency-Based Visual Attention for Rapid Scene Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 11, 1254-1259. https://www.researchgate.net/publication/3192913; https://doi.org/10.1109/34.730558

Jencks, C. (1969) Semiology and architecture, In: Jencks, C. and Baird, G., eds. Meaning in architecture, London: Barrie & Jenkins, 11-25. https://www.atlasofplaces.com/essays/meaning-in-architecture

Jiang, B. (2015) Wholeness as a hierarchical graph to capture the nature of space, International Journal of Geographical Information Science, 29, 9, 1632-1648; https://www.tandfonline.com/doi/full/10.1080/13658816.2015.1038542. https://doi.org/10.1080/13658816.2015.1038542

Jiang, B. (2019) Living structure down to earth and up to heaven: Christopher Alexander, Urban Science, 3, 3, 96; https://www.mdpi.com/2413-8851/3/3/96/htm; https://doi.org/10.3390/urbansci3030096.

Joye, J. (2006) An Interdisciplinary Argument for Natural Morphologies in Architectural Design, Environment and Planning B, 33, 2, 239-252. https://www.researchgate.net/publication/23541536; https://doi.org/10.1068/b31194

Joye, Y. (2007) Fractal Architecture Could be Good for You, Nexus Network Journal, 9, 2, 311-320; https://link.springer.com/content/pdf/10.1007/s00004-007-0045-y.pdf. https://doi.org/10.1007/s00004-007-0045-y

Kappraff, J. (2016) The Proportional System of the Parthenon, Symmetry: Culture and Science, 27, 4, 369-391.

Katona, V. (2019) Bauhaus 100: Symmetries and Proportions in Modern Architectural Composition, Symmetry: Culture and Science, 30, 4, 261-263. https://doi.org/10.26830/symmetry_2019_4_261

Kootstra, G., de Boer, B. and Schomaker L. (2011) Predicting Eye Fixations on Complex Visual Stimuli using Local Symmetry, Cognitive Computation, 3, 1, 223-240; https://link.springer.com/article/10.1007%2Fs12559-010-9089-5. https://doi.org/10.1007/s12559-010-9089-5

Kravitz, D., Peng, C. and Baker, C. (2011) Real-world scene representations in high-level visual cortex: it’s the spaces more than the places, Journal of Neuroscience, 31, 20, 7322-7333; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3115537. https://doi.org/10.1523/JNEUROSCI.4588-10.2011

Krishna, S. and Keasar, T. (2018) Morphological Complexity as a Floral Signal: From Perception by Insect Pollinators to Co-Evolutionary Implications, International Journal of Molecular Sciences, 19, 6, Article 1681; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6032408/pdf/ijms-19-01681.pdf. https://doi.org/10.3390/ijms19061681

Lakoff, G. and Nuñez, R. (2001) Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being, New York: Basic Books.

Li, R. and Bowerman, B. (2010) Symmetry Breaking in Biology, Cold Spring Harbor Perspectives in Biology, 2, 3, Article a003475; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2829966. https://doi.org/10.1101/cshperspect.a003475

Maas, H. (2008) Architectural Form Part 1: An introduction into understanding buildings, Lulu.com, 244 p.

Makin, A., Helmy, M. and Bertamini, M. (2018) Visual cortex activation predicts visual preference: Evidence from Britain and Egypt, Quarterly Journal of Experimental Psychology, 71, 8, 1771-1780; https://www.bertamini.org/lab/Publications/MakinHelmyBertamini2017.pdf. https://doi.org/10.1080/17470218.2017.1350870

Malcolm, G. L., Groen, I. and Baker, C. (2016) Making Sense of Real-World Scenes, Trends in Cognitive Sciences, 20, 11, 843-856. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5125545

Marijuán, P. C. (1996) Information and symmetry in the biological and social realm: New avenues of inquiry, Symmetry: Culture and Science, 7, 3, 281-294. http://symmetry-us.com/Journals/7-3/marijuan.pdf

Mattson, M. P. (2014) Superior pattern processing is the essence of the evolved human brain, Frontiers in Neuroscience, 8, Article 265, 1-16; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4141622/. https://doi.org/10.3389/fnins.2014.00265

Mehaffy, M. (2004a) Meaning and the Structure of Things, In: Steil, L., Hanson, B., Mehaffy, M. and Salingaros N. eds. Katarxis, No. 3, [September 2004]. http://katarxis3.com/Mehaffy_Meaning.htm

Mehaffy, M. (2004b) The New Modernity: The Architecture of Complexity and The Technology of Life, In: Steil, L., Hanson, B., Mehaffy, M. and Salingaros N. eds. Katarxis, No. 3, [September 2004] http://www.katarxis3.com/Mehaffy_New_Modernity.htm

Mehaffy, M. (2020) An Obsolete Ideology, Inference, 5, 2, [4 May 2020]. https://inference-review.com/letter/an-obsolete-ideology

Mehaffy, M. W. and Salingaros, N. A. (2011) Architectural Myopia: Designing for Industry, Not People, Shareable, 5 October 2011. https://www.shareable.net/architectural-myopia-designing-for-industry-not-people

Mehaffy, M. W. and Salingaros, N. A. (2013) How Modernism Got Square, Metropolis, 19 April 2013, [Reprinted as Chapter 3 of Design for a Living Planet (2015) Portland, Oregon: Sustasis Press, and Kathmandu, Nepal: Vajra Books]. https://www.metropolismag.com/architecture/toward-resilient-architectures-3-how-modernism-got-square

Millais, M. (2020) The Origins of Architectural Barbarism, Inference, 5, 2, [4 May 2020]. https://inference-review.com/letter/the-origins-of-architectural-barbarism

Miller, G. A. (1956) The Magical Number Seven Plus or Minus Two: Some Limits on Our Capacity for Processing Information, The Psychological Review, 63, 81-97. https://doi.org/10.1037/h0043158

Murray, S. O., Kersten, D., Olshausen, B., Schrater, P. and Woods, D. (2002) Shape perception reduces activity in human primary visual cortex, Proceedings of the National Academy of Sciences USA, 99, 23, 15164-15169. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC137561

Phillips, A. (2018) Why symmetry gets really interesting when it is broken, Aeon Magazine, 10 April 2018. https://aeon.co/ideas/why-symmetry-gets-really-interesting-to-physics-when-it-is-broken

Ram, M., Singh, S. B. and Varshney, R. G. (2013) Performance Improvement of a Parallel Redundant System With Coverage Factor, Journal of Engineering Science and Technology, 8, 3, 344-350. http://jestec.taylors.edu.my/Vol%208%20Issue%203%20June%2013/Volume%20(8)%20Issue%20(3)%20344-%20350.pdf

Ruggles, D. H. (2018) Beauty, Neuroscience, and Architecture: Timeless Patterns and Their Impact on Our Well-Being. Denver, Colorado: Fibonacci Press.

Salingaros, N. A. (1998) A Scientific Basis for Creating Architectural Forms, Journal of Architectural and Planning Research, 15, 4, 283-293, [Revised version is Chapter 2 of A Theory of Architecture, 2nd ed. (2014) Portland, Oregon: Sustasis Press].

Salingaros, N. A. (2006) A Theory of Architecture, Portland, Oregon: Sustasis Press, [2nd ed. 2014].

Salingaros, N. A. (2010) Algorithmic Sustainable Design: Twelve Lectures on Architecture, 2nd ed., Portland, Oregon: Sustasis Press.

Salingaros, N. A. (2011) Why Monotonous Repetition is Unsatisfying, Meandering Through Mathematics, 2 September 2011. https://arxiv.org/pdf/1109.1461v1.pdf

Salingaros, N. A. (2015) Alexander’s Fifteen Fundamental Properties, ArchDaily, 2 May 2015. https://www.archdaily.com/626429/unified-architectural-theory-chapter-11

Salingaros, N. A. (2018) Applications of the Golden Mean to Architecture, Symmetry: Culture and Science, 29, 3, 329-351, [Substantially revised version of an earlier article published in Meandering Through Mathematics, 21 February 2012]. https://doi.org/10.26830/symmetry_2018_3_329

Salingaros, N. A. (2019) How Mathematics Will Save the Built World!, Common Edge, 28 January 2019. https://commonedge.org/how-mathematics-will-save-the-built-world

Salingaros, N. A. and Sussman, A. (2020) Biometric pilot-studies reveal the arrangement and shape of windows on a traditional façade to be implicitly “engaging”, whereas contemporary façades are not, Urban Science, [submitted]. https://doi.org/10.3390/urbansci4020026

Salingaros, N. A. and West, B. J. (1999) A universal rule for the distribution of sizes, Environment and Planning B: Planning and Design, 26, 6, 909-923, [Condensed version (without equations) is Chapter 3 of Principles of Urban Structure (2005) Amsterdam, Holland: Techne Press. 2nd ed. (2014), Portland, Oregon: Sustasis Press]. https://doi.org/10.1068/b260909

Sasaki, Y., Vanduffel, W., Knutsen, T., Tyler, C. and Tootell, R. (2005) Symmetry activates extrastriate visual cortex in human and nonhuman primates, Proceedings of the National Academy of Sciences, 102, 8, 3159-3163; https://www.researchgate.net/publication/8022092. https://doi.org/10.1073/pnas.0500319102

Seresinhe, C. I., Preis, T. and Moat, H. S. (2017) Using deep learning to quantify the beauty of outdoor places, Royal Society Open Science, 4, 7, Article 170170, [19 July 2017]. https://doi.org/10.1098/rsos.170170

Sessions, R. and Salingaros, N. A. (2010) Urban and Enterprise Architectures: A Cross-Disciplinary Look at Complexity, Lecture Notes, International Association of Software Architects Webinar, 15 October 2010. http://zeta.math.utsa.edu/~yxk833/urbanandenterprisearchitectures.pdf

Sussman, A. and Hollander, J. B. (2015) Cognitive Architecture, New York: Routledge. https://doi.org/10.4324/9781315856964

Sussman, A. and Ward, J. M. (2017) Game-Changing Eye-Tracking Studies Reveal How We Actually See Architecture, Common Edge, 27 November 2017. http://commonedge.org/game-changing-eye-tracking-studies-reveal-how-we-actually-see-architecture/

Sussman, A. and Ward, J. M. (2019) Eye-tracking Boston City Hall to better understand human perception and the architectural experience, New Design Ideas, 3, 2, 53-59. http://jomardpublishing.com/UploadFiles/Files/journals/NDI/V3N1/SussmanA%20WardJ.pdf

Taylor, R. P. (2006) Reduction of Physiological Stress Using Fractal Art and Architecture, Leonardo, 39, 3, 245-251; http://citeseerx.ist.psu.edu/viewdoc/download. https://doi.org/10.1162/leon.2006.39.3.245

Taylor, R. P., Newell, B., Spehar, B. and Clifford, C. (2005) Fractals: A Resonance Between Art and Nature?, In: Michele Emmer, ed. Mathematics and Culture II: Visual Perfection, Berlin: Springer-Verlag, 53-63; https://www.researchgate.net/publication/226130687. https://doi.org/10.1007/3-540-26443-4_6

Taylor, R. P., Spehar, B., Van Donkelaar, P. and Hagerhall, C. (2011) Perceptual and physiological responses to Jackson Pollock’s fractals, Frontiers in Human Neuroscience, 5, 60, [22 June 2011]. https://doi.org/10.3389/fnhum.2011.00060

Tullett, A. M., Kay, A. C. and Inzlicht, M. (2015) Randomness increases self-reported anxiety and neurophysiological correlates of performance monitoring, Social Cognitive and Affective Neuroscience, 10, 5, 628-635; https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4420739. https://doi.org/10.1093/scan/nsu097

Tyler, C. W., Baseler, H., Kontsevich, L., Likova, L., Wade, A. and Wandell, B. (2005) Predominantly extra-retinotopic cortical response to pattern symmetry, Neuroimage, 15, 24, 306-314; https://christophertyler.org/CWTyler/TylerPDFs/TyleretalfMRISymmetryNI2005.pdf. https://doi.org/10.1016/j.neuroimage.2004.09.018

Whitehead, A. N. (1929) Process and Reality, New York: Free Press, [2nd ed. 1979].

Wilkins, A. J. (2016) A physiological basis for visual discomfort: Application in lighting design, Lighting Research & Technology, 48, 1, 44-54. https://doi.org/10.1177/1477153515612526

Wilkins, A. J. (2018) Looking at buildings can actually give people headaches. The Conversation, 5 July 2018. https://www.cnn.com/style/article/why-looking-at-buildings-can-give-people-headaches/index.html

Wilson, E. O. (1998) Consilience: The Unity of Knowledge, New York: Alfred A. Knopf.

Wolfram, S. (2002) A New Kind of Science, Champaign, Illinois: Wolfram Media.

Zeki, S. (2019) Beauty in Architecture, AD Architectural Design, 89, 5, 14-19. https://doi.org/10.1002/ad.2473