Theory of Beauty

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  • After the time of the Pythagoreans, the Golden Ratio fades toobscurity in history until the Renaissance
  • the Golden Ratio resurfaces around the turn of the 16th century when Luca Pacioli publishes De DivinaProportione- which focused on what has come to be known as the Golden Ratio. Pacioli collaborated and lived with Leonardo Da Vinci,[11] who illustrated De DivinaProportioneLuca Pacioli's 1509 De DivinaProportione, ascribed "holy" or "magical" properties to the Golden Ratio
  • Some say the Golden Ratio was known as far back as 2500 BCE and used in the design of the Great Pyramid of Giza.the ratio of half the base to the pyramid's slant height is within 1% of the Golden Ratio.
  • Da Vinci is thought by some to have used the Golden Ratio in works such as The Vitruvian Man and The Mona Lisa, The Last Supper; but this is widely disputed and no obvious evidence to support it.another popular idea is that flowers have numbers of petals according to the Fibonacci numbers, which is true for some flowers, but also untrue for many others.some people say the human body exhibits Golden proportions.there is too much variance in body shape from person to person to imply that the human form conforms to a precise ratio, at least without concrete evidence
  • The dimensions of the Parthenon vary from source to source probably because different authors are measuring from different points. With so many numbers available, a golden ratio enthusiast could choose whatever numbers gave the best result. (Markowsky, 1992)overabundant hype and hoopla surrounding the Golden Ratio and Fibonacci SequenceTie in with our lecture: Much of this mystic beliefs stem from the Renaissance period, when the Ratio was labeled "Divine" and all things Greek were thought to be good.Remember how Pythagoras believed that all reality could be expressed mathematically and that numbers were sacred and eternal? It made sense that he would buy the idea of perfection of nature and the heavens, using a single ratio. We can see the appeal of such an idea. Even today, many remain fascinated by the Golden Ratio and its many forms of ‘manifestation’ in life.Remember before the Renaissance, people were in awe of the ancient Greeks and their achievements (eg. Parthenon in Athens)? It was fashionable to learn Greek and to learn the knowledge of the ancient Greeks. Renaissance manDa Vinci: keen interest in proportionIt was ‘observable’, and hence the idea can be easily passed on. However, we usually see what we would like to see. It is easy to claim that something has the golden proportion. Think of Aristotle's dual path of scientific reasoning: generalizing from particular observations into a universal law, and then back from universal laws to prediction of particulars.
  • Point out how it is not accurate. Just superimpose the golden spiral and everything can be claimed to fit. But do they really? Look at the stairs of Parthenon. Look closer at the twitterscreencap, does the spiral really fit nicely??
  • Not all plants, art pieces, buildings or faces fit the golden ratio proportions. Yet many of these ‘non-golden’ persons and objects are beautiful to others, nonetheless. Is it merely a coincidence then?There are thousands of websites claiming the Golden Ratio pervades everything in nature, but rarely are there credible academic sources that agreeConclusion: The Fibonacci Sequence and The Golden Ratio are interesting mathematical concepts with unique aesthetic properties. BUT. There exists an overabundance of mystical thinking, speculation and fiction about them appearing in art, ancient architecture and nature.
  • Symmetry was already an aspect well understood by the Greeks, Romans and even through the Renaissance period, by which buildings were all constructed based on sheer symmetry
  • Many other studies replicate similar results
  • I’m sure you must be excited to see what a complete research has shown
  • Much of their work evidently speaks volumes for th
  • Much of their work evidently speaks volumes for th
  • After the time of the Pythagoreans, the Golden Ratio fades toobscurity in history until the Renaissance
  • Theory of Beauty

    1. History of the Science of Beauty<br />Tan Kok Hong . Lim Kia Mian . Wong RuiXiong<br />
    2. 1<br />Defining Beauty<br />what is beauty? what are the theories of beauty?<br />
    3. DEFINITION OF BEAUTY<br />WHAT IS THE <br />DEFINITION <br />OF BEAUTY?<br />“No particular <br />definition”<br />
    4. DEFINITION OF BEAUTY<br />Definitions for reference<br />Beauty (according to Oxford Dictionary)Excelling in grace of form, charm of colouring, and other qualities, which delight the eye and call forth admiration: a) of the human face and figureb) of other objects<br />Beauty is a basic pleasure<br />Beauty can be something intrinsic to object (color, form, and other qualities )or simply the pleasure an object evokes<br />
    5. FROM ANCIENT TIMES<br />
    6. FROM ANCIENT TIMES<br /> < < <<br />
    7. FROM ANCIENT TO CONTEMPORARY<br />“Propertiesof beauty are the same, whether we are seeing a beautiful woman, flower, landscape or circle.”<br />
    8. 2<br />Golden Ratio<br />what is the golden proportion? why is it significant?<br />
    9. GOLDEN RATIO<br />Ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one<br />Ancient Greek mathematicians first studied it because of its frequent appearance in geometry<br />Irrational mathematical constant, <br /><ul><li>approximately 1.6180</li></ul>“Extreme and mean ratio" was the principal term used from the 3rd century BC until about the 18th century.<br />Denoted by the Greek lowercase letter phi<br />
    10. GOLDEN RATIO<br />“VISUAL DEFINITION”<br />
    11. GOLDEN RATIO<br />Golden rectangle: side lengths are in golden ratio<br />When a square section is removed, we find another golden rectangle. This pattern can be repeated infinitely.<br />Corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property.<br />34<br />5<br />8<br />3<br />21<br />13<br />
    12. GOLDEN RATIO: A History<br />
    13. GOLDEN RATIO: A History<br />
    14. GOLDEN RATIO: Architecture<br />
    15. GOLDEN RATIO: Art and Nature<br />
    16. Middle Ages and Renaissance <br />GOLDEN RATIO: Analysis<br />Fits in with the idea of perfection and harmony<br />overabundance of mystical thinking, speculation and fiction<br />Food for Thought:<br />Why did ancient philosophers and so many others support this idea? Is the Golden perfection real?<br />
    17. GOLDEN RATIO: Analysis<br />
    18. GOLDEN RATIO: Analysis<br />
    19. GOLDEN RATIO: Analysis & Summary<br />Idea that the Golden Ratio was used in designing ancient architecture dubious<br />Interesting mathematical concepts<br />Influence from the ancient Greeks and Renaissance period<br />Unique aesthetic properties<br />Lack of academic sources<br />
    20. 3<br />Symmetry<br />symmetry as beauty? why is symmetry beautiful?<br />
    21. SYMMETRY BY GREEKS AND ROMANS<br />Symmetry is the foundation for numerous Greek and Roman architecture, continuing into the Renaissance <br />Victorian-style pillars<br />Trevi Fountain (Renaissance)<br />Pantheon of Rome (Roman Empire)<br />Parthenon of Acropolis (Ancient Greece)<br />
    22. SYMMETRY: FACIAL SYMMETRY<br />96%<br />
    23. SIR FRANCIS GALTON<br />Sir Francis Galton (1811-1911)<br />half-cousin of Charles’ Darwin<br />Polymath, numerous contributions to many scientific fields such asmeteorology, psychology, criminology<br />1876 - 1900: Composite Photography <br />projecting face photographs of many different individuals onto a single piece of photographic film<br />Galton’s colleagues noted that composites tended to be more attractive than the individual faces<br />
    24. COMPOSITE PHOTOGRAPHY<br />Case for Eugenics<br /><ul><li>Eugenics: Nature NOT Nurture determines a person’s eventual character and personality
    25. Identification of “typical criminal faces”</li></ul>Led to further studies of facial averageness!<br />
    26. FACIAL AVERAGENESS<br />Study of Facial Averageness<br />Numerous studies were conducted throughout the century BUT with advent of technology, greatly improved the studies<br />1886: Stoddard<br />1990: Psychologists Langlois and Roggman<br />2005: Imaging Researcher Pierre Tourigny<br />Computer algorithms revealed that symmetry plays a big role in human faces<br />
    27. FACIAL AVERAGENESS<br />Female celebrities<br />Caucasian males<br />Caucasian females<br />Caucasian females<br />
    28. FACIAL AVERAGENESS<br />Composite of 60 faces<br />consistently over 90%<br />
    29. DIFFERING INTEPRETATIONS<br />(1) symmetric individuals are attractive because they are particularly healthy<br />(2)averageness reflects optimal design of physical traits by nature<br />human visual system favours processing symmetric than asymmetric stimuli<br />
    30. Biological advances and knowledge<br />Symmetry: Analysis<br />Greek, Roman and Renaissance developments in architecture<br />Technological innovations (photography, computer algorithms)<br />study of non-scientific fields (eugenics)<br />
    31. LIMITATIONS OF EXPLANATION<br />still beautiful?<br />
    32. 4<br />Proportions<br />proportion as beauty? what proportions are significant?<br />
    33. PROPORTIONALITY<br />92%<br />
    34. PROPORTIONALITY<br />“What do we identify visuallyas human?”<br />Studying of proportions really took off during the Renaissance<br />Renaissance: the focus is back on HUMANS, THE HUMAN BODY<br />Focus on aesthetics brought about numerous developments in the study of proportions that define humans <br />
    35. ANCIENT GREEKS AND ROMANS<br />
    36. MICHELANGELO<br />
    37. LEONARDO DA VINCI<br />
    38. FACIAL PROPORTIONALITY<br />Renaissance Period<br />Leonardo Da Vinci and Michelangelo did extensive studies concerning the proportions of human face<br />Formed the basis of aesthetic knowledge on human faces<br />
    39. BODY PROPORTIONALITY<br />Renaissance period<br />Ideal height as having a head to body ratio of 1:8<br />V-shaped torso<br />Recent research<br />Men: a waist-to-shoulder ratio of 0.75 or lower are viewed as considerably more attractive<br />
    40. Proportionality<br />
    41. BEAUTIFICATION<br />Marquardt Beauty Mask<br />Dr. Stephen R. Marquardt<br />Retired oral and maxillofacial surgeon<br />Based on decagon structures<br />Female Mask<br />Male Mask<br />Side Profile<br />
    42. BEAUTY MASK<br />David Beckham<br />Megan Fox<br />Angelina Jolie<br />Marilyn Monroe<br />
    43. Artistic developments of Renaissance Man <br />Proportion: Analysis<br />Renaissance focus on Humans as SPECIAL CREATION of God<br />Architecture and Aestheticspropelling Humanistic studies<br />New Anatomical studies<br />
    44. 5<br />Evolutionary Beauty<br />what is the impact of evolution on beauty?<br />
    45. Darwinian Theory of Beauty<br />For nearly 2000 years, philosophers, artists and scientists have tried to explain beauty using mathematics. <br />WHY?<br /><ul><li>Mathematical idea fits in a general way with platonic or religious ideas about origin of the world
    46. BUT, Measurement systems have failed to turn up a beauty formula!
    47. Another example how ideas of ancient philosophers have misguided later generations
    48. Darwin’s evolution theory led toparadigm shift from an emphasis on mathematics to biology</li></li></ul><li>EVOLUTIONARY PERSPECTIVE<br />Darwin: Evolution of Beauty <br />Natural Selection <br />Evolution or co-evolution of peculiar features give advantage to an organism, increasing chance of survival and reproduction<br />2) Sexual Selection<br />Some physical qualities lure the other sex<br /> e.g. Peacock’s tail that not only doesn’t helpwith but impedes survivability<br />Beauty is important in arousing and sustaining interest or even obsession to allow people to make decisions to enhance survival or reproduction<br />
    49. DARWINIAN APPROACH TO BEAUTY<br />Beauty is nature’s way of acting at a distance<br />Evolution’s trick is to make things beautiful, to make them exert a magnetism, and give one pleasuresimply by looking at them<br />The experience of beauty is a component of a series of Darwinian adaptations<br />Universality of our artistic and aesthetic taste can be explained by Darwinian theory of beauty<br />
    50. UNIVERSALITY OF BEAUTY<br />Is beauty a universal concept?<br />“Beauty lies in the eyes of the beholder?”<br />How about culture and media influences?<br />
    51. UNIVERSALITY OF BEAUTY<br />ACROSS AGE<br />Even 3 month old infants prefer to gaze at faces that adults find beautiful, including faces from races they have not seen before<br />7 year olds, 12 year olds, 17 year olds and adults do not differ significantly in their ratings of attractiveness of faces of children and adults<br />
    52. UNIVERSALITY OF BEAUTY<br />ACROSS CULTURE<br />Jones and Hill asked people from 5 cultures to rate a multiracial, multicultural set of faces<br />2 isolated tribes, Hiwi and Ache Indians<br />Russian<br />Brazil<br />United States<br />
    53. UNIVERSALITY OF BEAUTY<br />People tend to agree which faces are beautiful and find similar features attractive across ethnically diverse faces<br />All attracted to similar geometric proportions in the face<br /> Female faces with small lower faces (delicate jaws and relatively small chins) and eyes that were large in relation to the length of the face are preferred<br />
    54. UNIVERSALITY OF BEAUTY<br />“Is beauty a universal concept?”<br />Underlying universal mechanisms are responsible for beauty<br />Beauty is an engineered manifestation <br />Perception of beauty features may be governed by circuits shaped by natural selection in the human brain<br />
    55. UNIVERSALITY OF BEAUTY<br />But people still seem to be largely agreeable and consistent in ratings of beauty<br />People quote culture as being important BUT it still requires a basic premise that coheres with human intrinsic preferences of beauty and instinct<br />“Beauty lies in the eyes of the beholder?”<br />“How about culture and media influences?”<br />
    56. 6<br />Conclusion<br />thoughts on the history and theories of beauty <br />
    57. CONCLUSION<br />For thousands of years, philosophers, mathematicians and artists have tried to explain beauty using the language of mathematicsbut focus has been on details and intricacies<br />Darwin’s evolution theory provides a big picture: Experience of beauty, with its emotional intensity and pleasure, belongs to our evolved human psychology<br />Darwinian approach can be used to explain the universality and functionality of beauty <br />The answer to questions pertaining to beauty may lie in cognitive neuroscience and biology<br />
    58. History of the Science of Beauty<br />Tan Kok Hong . Lim Kia Mian . Wong RuiXiong<br />

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