Beauty and Aesthetics


"Beauty is in the eye of the beholder” .

Aesthetics, The Golden Proportion Ethnicity and  Illusion. Part III

The beauty about discussions in relation to beauty is that everyone is interested everyone has an opinion and in general no one is completely right. In recently a considerable amount of furore was created in the media over Samantha Bricks statements that she considered herself to be beautiful and another particular face was considered to be the absolute measure of beauty. (Florence Colgate)  Psychosocial publications abound in the popular press as well as scholarly works. Good facial aesthetics and beauty are not synonymous. The term beauty is used for everything from faces to sunsets and music. If asked “What did you eat last night?”  responding by saying “food.”  is as uninformative as using the term beautiful in any given phrase. It remains as firmly in the eye of the beholder in 2012 as it did in 1878, when Margaret Wolfe Hungerford included this simple phrase in her novel 'Molly Bawn'

From an Orthodontic perspective identifying a measurement of “beauty” remains another holy grail similar to that of  identifying a Cephalometric line of “stability”.


Even if point A were the target for beauty Orthodontic treatment cannot prevent aging and so even if point A were achieved during Orthodontic treatment for example the success would be transitory and the effect of the treatment short lived. Fortunately the preeminent work of Shaw and Richmond has avoided this quagmire by introducing both IOTN and PAR which now hold almost universal authority and identify firstly if someone “needs” treatment and secondly if they have been “improved” by it.


Keats wrote that "Beauty is truth, truth beauty" in the poem Ode on a Grecian UrnImmanuel Kant, writing in 1790, observed  "If a man says that canary wine is agreeable he is quite content if someone else corrects his terms and reminds him to say instead: It is agreeable to me," because "Everyone has his own (sense of) taste". Then the case of "beauty" is different from mere "agreeableness" because, "If  he proclaims something to be beautiful, then he requires the same liking from others; he then judges not just for himself but for everyone, and speaks of beauty as if it were a property of things."  Many a partner can declare the beauty of their true love to be met only by the silence of the ensemble.


Aesthetic judgments seem often to be at least partly emotional, intellectual and interpretative. Preference and choice have also seemed important in relation to aesthetics to some 20th century thinkers. Mary Mothersill, "Beauty and the Critic’s Judgment", describes aesthetic judgments as be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behaviour, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.[i]




Use of the Golden proportion in Dentistry and Orthodontics.


Facial recognition is thought to take place in the region of the brain called the fusiform gyrus in the temporal lobe. It is also thought to be involved in perception of emotions in facial stimuli, colour, word and number recognition. It is associated with synesthesia which covers a variety of conditions such as seeing letters in different colours normally, hallucinations drug induced or otherwise and Charles Bonnet syndrome. Trauma or lesions in this area can lead to a condition known as face blindness or Prosopagnosia. Patients suffering from this disorder are unable to identify celebrities, close relatives and even themselves in the mirror. Even without this disorder normal individuals can be subject to a variety of illusions and biases in face perception. Sexual dimorphism, emotional expression and recognition can all be affected by illusionary tricks that can fool our “face senses”.

The “illusion of sex” is a set of images created by the psychologist Richard Russell. In one particular illusion, sexual difference is perceived from the same photograph by simply using variation in the contrast of the images.

There is also a concept that humans find distortion of the “real human form” more aesthetic than a genuine reproduction of the “real human form ”. This stems from a study of very early sculptures from ancient nomadic peoples around 30,000 years BC  such as the Venus of Willendorf .

It is known that the Egyptians sculptures were created using a grid pattern and they continued this portrayal of the human form in profile using this method for three millenia. The Riace bronzes from 450BC are thought to have only been possible because Greece and Egypt began trading with each other. The skills required to create large sculptures being transmitted from Egypt to Greece. Despite the acclaimed artistic beauty of these sculptures some claim that the actual physical form is unattainable by humans.  A drive to produce realistic sculptures took place and resulted in such creations as “the Sicilian boy”. Once achieved these realistic types of sculpture were abandoned and sculptures designed along the lines that Polycleitus suggested were motion was introduced and mathematical formula were used to produce more aesthetically appealing sculptures.

The Golden proportion 1.618.

The discovery of the Golden proportion and it’s widespread use or discovery in the universe have lead it to being used in facial and dental assessments. Most discussions on facial aesthetics hinge on the discussion of the Golden proportion or Golden ratio. The relationship of the Golden proportion and its usefulness to mankind must be understood against the backdrop of Popperian scientific philosophy.


Whether the use or its occurrence in nature is real or fancied at some point the theory of its application will break down. Various discoveries and uses have been made of this proportion. The proportion is then rediscovered and reapplied in very different fields. A recent report suggested that women with mathematically perfect wombs are the most fertile this was Based on the 'golden ratio' of 1.618,

Read more:

Dentists will be most familiar with its use with respect to tooth size. Levin (1978) attributed his interest in the Golden proportion to Winston Senior. Marquardt reported that " The height of the central incisor is in the Golden Proportion to the width of the two central incisors." Even in this respect it cannot be used as a Panacea for all eventualities. Things such as varied crown emergence profile, very large incisors, asymmetric size in incisors or Talon teeth can confound the principle.

In 1982 Ricketts reported on the proportion’s significance in Orthodontics. In 1989 Kawakami et al investigated the Golden Proportion balance between eyes, nose and mouth in the facial appearance of Japanese individuals and, comparing the ratios to Caucasians, each ratio was then used for pre and post-operative aesthetic analysis using Moire' topography.

The Timeline for use or discovery of the Golden proportion is reported as shown:-

Timeline according to Priya Hemenway.[16]

  • Phidias (490–430 BC) made the Parthenon statues that seem to embody the golden ratio.
  • Plato (427–347 BC), in his Timaeus, describes five possible regular solids (the Platonic solids: the tetrahedroncubeoctahedron,dodecahedron and icosahedron), some of which are related to the golden ratio.[17]
  • Euclid of Alexandria  (c. 325–c. 265 BC), in his Elements, gave the first recorded definition of the golden ratio, which he called, as translated into English, "extreme and mean ratio" (Greek: ἄκρος καὶ μέσος λόγος).[5]
  • Fibonacci (1170–1250) mentioned the numerical series now named after him in his Liber Abaci; the ratio of sequential elements of the Fibonacci sequence approaches the golden ratio asymptotically.
  • Luca Pacioli (1445–1517) defines the golden ratio as the "divine proportion" in his Divina Proportione.
  • Michael Maestlin (1550-1631) publishes the first known approximation of the (inverse) golden ratio as a decimal fraction.
  • Johannes Kepler (1571–1630) proves that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers,[18] and describes the golden ratio as a "precious jewel": "Geometry has two great treasures: one is the Theorem of Pythagoras, and the other the division of a line into extreme and mean ratio; the first we may compare to a measure of gold, the second we may name a precious jewel." These two treasures are combined in the Kepler triangle.
  • Charles Bonnet (1720–1793) points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series.
  • Martin Ohm (1792–1872) is believed to be the first to use the term goldener Schnitt (golden section) to describe this ratio, in 1835.[19]
  • Édouard Lucas (1842–1891) gives the numerical sequence now known as the Fibonacci sequence its present name.
  • Mark Barr (20th century) suggests the Greek letter phi (φ), the initial letter of Greek sculptor Phidias's name, as a symbol for the golden ratio.[20]
  • Roger Penrose (b.1931) discovered a symmetrical pattern that uses the golden ratio in the field of aperiodic tilings, which led to new discoveries about quasicrystals.
  • ^ Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New


In the Elements, the most influential mathematics textbook ever written, Euclid of Alexandria (ca. 300 BC) defined a proportion derived from a division of a line into what he calls its "extreme and mean ratio." Euclid's definition reads:


A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

In other words, in the diagram below, point C divides the line in such a way that the ratio of AC to CB is equal to the ratio of AB to AC. Some elementary algebra shows that in this case the ratio of AC to CB is equal to the irrational number 1.618 (precisely half the sum of 1 and the square root of 5).


C divides the line segment AB according to the Golden Ratio.


Who could have guessed that this innocent-looking line division would have implications for numerous natural phenomena ranging from the leaf and seed arrangements of plants to the structure of the crystals, some aluminium alloys and  the movements of the planets appearing in  fields as varied as the arts and the stock market?


In fact, realisation of the astonishing properties of this number since Euclid's definition is was has given it the honorifics "Divine Proportion" and "Golden Ratio."


Here I shall concentrate only on one of the surprising (claimed) attributes of the Golden Ratio its presumed association with aesthetics, since it provides a wonderful example of an attempt to mingle mathematics with art.


The Golden ratio in the arts


Many books claim that if you draw a rectangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of the height to width of that rectangle is equal to the Golden Ratio. No documentation exists to indicate that Leonardo consciously used the Golden Ratio in the Mona Lisa's composition, nor to where precisely the rectangle should be drawn. Nevertheless, one has to acknowledge the fact that Leonardo was a close personal friend of Luca Pacioli, who published a three-volume treatise on the Golden Ratio in 1509 (entitled Divina Proportione).


In The Sacrament of the Last Supper, by Salvador Dali there is very little doubt that he actually did deliberately include the Golden Ratio in his art. The ratio of the dimensions of Dali's painting Sacrament of the Last Supper is equal to the Golden Ratio. Dali also incorporated in the painting a huge dodecahedron (a twelve-faced Platonic solid) in which each side is a pentagon engulfs the supper table. The dodecahedron, which according to Plato is the solid "which the gods used for embroidering the constellations on the whole heaven," is intimately related to the Golden Ratio - both the surface area and the volume of a dodecahedron of unit edge length are simple functions of the Golden Ratio. Dodecahedral objects have found some practical applications, and have also played a role in the visual arts and in philosophy. Plato's dialogue Timaeus (c. 360 B.C.) associates the other four platonic solids with the four classical elements, adding that "there is a fifth figure (which is made out of twelve pentagons), the dodecahedron—this God used as a model for the twelvefold division of the Zodiac."  Aristotle postulated that the heavens were made of a fifth element, aithêr (aether in Latin, ether in English), but he had no interest in matching it with Plato's fifth solid. The Babylonians/Persians used the duodecimal system based on 12 rather than a decimal system based on 10. 12 months of the year 12 hours in a day ( later changed to 24) still used in the signs of the Zodiac and seconds in an hour. For older members of the readership they will recall 12 pennies in a shilling, 12 inches in a foot and 12 ounces in a pound and a dozen reasons to learn their 12 x table. The Romans also used a fraction system based on 12 from unica English derives the words ounce and inch. Digit counting in 12’s using 4 fingers of 3 phalanges each is also known in parts of Asia.




Magic dodecahedronsmagic triangles magic stars, and magic hexagons.

Magic squares were known to Chinese mathematicians, as early as 650 BCE. and Arab mathematicians, possibly as early as the 7th century, when the Arabs conquered north western parts of the Indian subcontinent and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics. The first magic squares or Yantras of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 CE, the Encyclopedia of the Brethren of Purity (Rasa'il Ihkwan al-Safa); simpler magic squares were also known to several earlier Arab mathematicians. Some of these squares were later used in conjunction with magic letters as in (Shams Al-ma'arif) to assist Arab illusionists and magicians.

A submission to Dr. Livio stated the following:


“Thank you for the page with the wealth of information on the Golden Section.

I am a researcher in music cognition. My explanation of a space of music includes calling the Pythagorean intervals the melodic reference elements or artistic universals in music. The sharing of the "strong" spectral information between tones of the Pythagorean intervals is most likely the origin of their auditory pleasantness. From a perspective of neurophysiology, it is possible that the sharing (and the supposed relative ease in processing of these intervals) is related to the lesser cost of neural processing as compared to non-consonant compounds. Most likely, these neuropsychological properties were the foundation for a paleo-scale; they were of importance for the musician’s ear just 400 years ago. Yet today we listen to the slightly mistuned intervals which lost their sonic purity with the introduction of tempered scale.

I am an admirer of Matyla Ghyka and I really like his ideas of "built-into" geometrical universals (for example, log relations) which, I believe, affect our perception of the world.

It is possible that some ratios of natural growth are inherent for our perception.”


The use of the  Fibonacci series and Golden proportion were used in India and the Far East to produce Magic squares using the 9 Hindu numerals.


The Magic 8-Ball 1950, was invented by Albert C. Carter, who was inspired by a "spirit writing" device used by his mother, Mary, a Cincinnati clairvoyant. In 1944, Carter filed a patent for his device, assigning it to Bookman, Levinson, and another partner in what came to be Alabe Crafts in 1946. They sold the device as The Syco-Seer. Carter, who, according to Bookman, was an alcoholic, died sometime before the patent was granted in 1948. In 1950 a version in the form of a traditional black & white Pool 8-ball. Inside is a cylindrical reservoir containing a white, plastic, icosahedral die ( platonic shape.) floating appropriately in alcohol with dissolved dark blue dye.


Each of the 20 faces of the die has an affirmative, negative, or non-committal statement printed on it in raised letters. There is a transparent window on the bottom of the Magic 8 Ball through which these messages can be read.

To use the ball, it must be held with the window initially facing down. After "asking the ball" a yes-no question (and shaking the ball), the user then turns the ball so that the window faces up, setting in motion the liquid and die inside. When the die floats to the top and one of its faces is pressed against the window, the raised letters displace the blue liquid to reveal the message as white letters on a blue background.


Possible answers

The 20 answers inside a Magic 8-Ball are:

● It is certain                ● Reply hazy, try again                        ● Don't count on it

● It is decidedly so      ● Ask again later                      ● My reply is no

● Without a doubt        ● Better not tell you now         ● My sources say no

● Yes – definitely        ● Cannot predict now              ● Outlook not so good

● You may rely on it   ● Concentrate and ask again    ● Very doubtful

● As I see it, yes

● Most likely

● Outlook good

● Signs point to yes

● Yes

10 of the possible answers are affirmative (●), 5 are negative (●), and 5 are non-committal (●).

Using the Coupon collector's problem in probability theory, it can be shown that it takes, on average, 72  questions of the Magic Eight Ball for all 20 of its answers to appear at least once.

Perhaps Orthodontic diagnosis could be simplified by changing the questions asked so that PCT’s could undertake the diagnosis and treatment therefore reducing costs.


This type of device also has ancient cousins at the British museum where instead of using the random wanderings of a Platonic shape the stars can be asked for answers to specific questions. The parallel today with daily horoscopes are obvious.


Whether use of magic squares is an absolute proof of identification of the Golden proportion is debatable. Bearing in mind that the Golden proportion has been found in many areas of science and mathematics it also has universal applications it may be that the use of magic squares is more to do with combinatorics or the fact that the mathematicians of the East were more advanced at an earlier stage than the ancient Greeks.


Combinatorics  in this context is a branch omathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include:-

“ counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designsand matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).”

Combinatorial problems arise in many areas of pure mathematics, notably in algebraprobability theorytopology, and geometry, and combinatorics also has many applications in optimizationcomputer scienceergodic theory and statistical physics. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which also has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms.



These examples are only the tip of the iceberg in terms of the appearances of the Golden Ratio in the arts. The famous Swiss-French architect and painter Le Corbusier, for example, designed an entire proportional system called the "Modulor," that was based on the Golden Ratio. The Modulor was supposed to provide a standardized system that would automatically confer harmonious proportions to everything, from door handles to high-rise buildings. But why would all of these artists (there are many more than mentioned above) even consider incorporating the Golden Ratio in their works? The attempts to answer this question have led to a long series of psychological experiments, designed to investigate a potential relationship between the human perception of "beauty" and mathematics.


The pioneering (rather crude) experiments in this field were conducted by the German physicist and psychologist Gustav Theodor Fechner in the 1860s. Fechner's experiment was simple: ten rectangles varying in their length-to-width ratios were placed in front of a subject, who was asked to select the most pleasing one. The results showed that 76% of all choices centered on the three rectangles having ratios of 1.75, 1.62, and 1.50, with a peak at the "Golden Rectangle" (with ratio 1.62). Fechner went further and measured the dimensions of thousands of rectangular-shaped objects (windows, picture frames in the museums, books in the library), and claimed (in his book Vorschule der Aesthetik) to have found the average ratio to be close to the Golden Ratio.


Many psychologists have repeated similar experiments since then, and obtained rather conflicting results. Michael Godkewitsch of the University of Toronto, for example, pointed out that average group preferences often do not reflect the most preferred choice. For example, the brand of tea that everybody ranks second-best may on the average be rated best, but nobody will ever buy it. Godkewitsch therefore noted that first choices provide a more meaningful measure of preference than averages. Godkewitsch concluded from a study conducted in 1974 that the preference for the Golden Rectangle reported in the earlier experiments was an artifact of the rectangle's position in the range of rectangles presented to the subjects. He noted: "The basic question whether there is or is not, in the Western world, a reliable verbally expressed aesthetic preference for a particular ratio between length and width of rectangular shapes can probably be answered negatively."


Other experiments, however, gave different results. In particular, British psychologist Chris McManus concluded in 1980 that: "There is moderately good evidence for the phenomenon which Fechner championed." Nevertheless, McManus acknowledged that "whether the Golden Section [another name for the Golden Ratio] per se is important, as opposed to similar ratios (e.g. 1.5, 1.6 or even 1.75), is very unclear."


Retired plastic surgeon Stephen Marquardt developed “facial masks” based on the golden proportion for clinical use. He stated on camera the presence of the golden proportion in a beautiful face predicted physical and mental health and invoked Darwin’s “Survival of the fittest.”  as the reason beauty and the Golden Proportion in particular was a desirable attribute in humans. (1990) The recent image published in the popular press as the most Beautiful in Britain of Florence Colgate actually demonstrates facial asymmetry. The eye width and nose width are not the same. The eye width or nose width divided by the mouth width does not generate the golden proportion. In order for the Golden proportion to be met the mouth must be narrower. Obviously measurements from photographs need to be interpreted with caution and Ms Colgate is smiling slightly so the mouth width could be smaller at rest. Clearly she is facially attractive but her image just demonstrates many of the themes explored in this paper.


The entire topic received a new twist with a flurry of psychological attempts to determine the origin of facial attractiveness. For example, psychologist Judith Langlois of the University of Texas at Austin and her collaborators tested the idea that a facial configuration that is close to the population average is fundamental to attractiveness. Langlois digitized the faces of male and female students and mathematically averaged them, creating two-, four-, eight-, sixteen-, and thirty-two-face composites. College students were then asked to rate the individual and composite faces for attractiveness. Langlois found that the 16- and 32-averaged faces were rated significantly higher than individual faces. Langlois explained her findings as being broadly based on natural selection (physical characteristics close to the mean having been selected during the course of evolution), and on "prototype theory" (prototypes being preferred over non-prototypes).


Science writer Eric Haseltine claimed (in an article in Discover magazine in September 2002) to have found that the distance from the chin to the eyebrows in Langlois's 32-composite faces divides the face in a Golden Ratio. Psychologist David Perret of the University of St. Andrews published in 1994 the results of a study that showed that individual attractive faces were preferred to the composites. Furthermore, when computers were used to exaggerate the shape differences away from the average, those too were preferred. Perret claimed to have found that his beautiful faces did have something in common: higher cheek bones, a thinner jaw, and larger eyes relative to the size of the face.



Livio considered that if you have the patience to juggle and manipulate the numbers in various ways, you are bound to come up with some ratios that are equal to the Golden Ratio.

Furthermore, he noted that the literature is bursting with false claims and misconceptions about the appearance of the Golden Ratio in the arts (e.g. in the works of Giotto, Seurat, Mondrian).


“The history of art has nevertheless shown that artists who have produced works of truly lasting value are precisely those who have departed from any formal canon for aesthetics. In spite of the Golden Ratio's truly amazing mathematical properties, and its propensity to pop up where least expected in natural phenomena, I believe that we should abandon its application as some sort of universal standard for "beauty," either in the human face or in the arts.”


Before the development of photography art was the only way of recording facial form. However art cannot be trusted in this respect because artistic licence means exactly that historic records may not reflect reality as these photographs from Rossetti’s paramour Jane Morris who had a complex relationship with the artist reveal. 


Disputed observations

Examples of disputed observations of the golden ratio include the following:

  • Historian John Man states that the pages of the Gutenberg Bible were "based on the golden section shape". However, according to Man's own measurements, the ratio of height to width was 1.45.
  • Some specific proportions in the bodies of many animals (including humans) and parts of the shells of molluscs and cephalopods are often claimed to be in the golden ratio. There is actually a large variation in the real measures of these elements in specific individuals, and the proportion in question is often significantly different from the golden ratio. The ratio of successive phalangeal bones of the digits and the metacarpal bone has been said to approximate the golden ratio. The nautilus shell, the construction of which proceeds in a logarithmic spiral, is often cited, usually with the idea that any logarithmic spiral is related to the golden ratio, but sometimes with the claim that each new chamber is proportioned by the golden ratio relative to the previous one; however, measurements of nautilus shells do not support this claim.
  • The proportions of different plant components (numbers of leaves to branches, diameters of geometrical figures inside flowers) are often claimed to show the golden ratio proportion in several species. In practice, there are significant variations between individuals, seasonal variations, and age variations in these species. While the golden ratio may be found in some proportions in some individuals at particular times in their life cycles, there is no consistent ratio in their proportions.Investing, some practitioners of technical analysis use the golden ratio to indicate support of a price level, or resistance to price increases, of a stock or commodity; after significant price changes up or down, new support and resistance levels are supposedly found at or near prices related to the starting price via the golden ratio. The use of the golden ratio in investing is also related to more complicated patterns described by Fibonacci numbers (e.g. Elliott wave principle and Fibonacci retracement). However, other market analysts have published analyses suggesting that these percentages and patterns are not supported by the data.


With respect to “Physical Attractiveness” there has been even more research. Subjetcs covered from hairiness to scent from height to skin colour are amply covered in numerous publications for those who enjoy a good read. All of this research does not mean however that facially unattractive people will be social failures, less intelligent or have had unsuccessful treatment. Cinderella did marry the Prince but Beauty also married the Beast.


Aesthetics in Orthodontics.

The major reason people seek orthodontic treatment is improvement of facial aesthetics (Birkeland et al., 1999Kiyak, 2000). Parents of young orthodontic patients expect that orthodontic treatment will improve the dental, dento-facial, and facial aesthetics of their children (McComb et al., 1996). Orthodontists also consider improvement of facial aesthetics as an important treatment goal, and therefore, it is an important issue in their decision-making process and their treatment plans (Bowman and Johnston, 2001Ackerman, 2004). The opinion of the general public, the consumers of orthodontic services, may have the most value in determining the appropriateness of aesthetic results (Bowman and Johnston, 2001). However, the question arises as to whether the public appreciate facial change brought about by orthodontic treatment (and growth) in the same way as orthodontists. Rosemie M. A. Kiekens, et al  explored this and concluded that:


“the expectations of parents of patients and of referring dentists are over-optimistic. Therefore, orthodontists should be aware of the fact that dentists expectations of patients and their parents can only be fulfilled to a certain degree. Especially for Class III patients, in which no significant improvement of facial aesthetics after treatment was found, orthodontists should be cautious with promises of aesthetic improvement. Professional background, age, gender, and geographical region of panel members have an influence on their evaluation of changes in facial aesthetics after orthodontic treatment.”


Reports often focus on facial aesthetics after orthodontic treatment using different treatment modalities often extolling the virtues of one method over another. In these studies, comparisons are made between extraction versus non-extraction (Bowman and Johnston, 2000), different types of functional appliances versus non-treatment (O'Neill et al., 2000), and orthognathic surgery versus non-surgical intervention (Phillips et al., 1992).


Skeletal II profiles have been considered the least attractive and are poorly tolerated in males (Cochrane et al., 1990; Knight and Keith, 1990). Extremely convex profiles or recessive chins and those with increased vertical proportions (De Smit and Dermaut, 1984; Czarnecki et al., 1993) have also been deemed least attractive. Sexual dimorphism is often a reason for seeking treatment. Larger mandibles are viewed as a male characteristic smaller mandibles as a female characteristic. Women will often seek Orthognathic surgery for a Class III mandible as it is viewed as masculine or perceived as more aggressive. Men will often grow beards to exaggerate a small mandible in Class II cases or soften the appearance of a larger Cl III mandible.


Facial appearance has an important influence on social well-being and others perception of one’s personal attributions (Albino et al., 1990). Some authors consider that there is national as well as international agreement on faces deemed most attractive (Ilife, 1960; Udry, 1965). Peck and Peck, 1970 considered that the more a particular facial type is observed, the more likely we are to perceive it as being correct. Alley and Cunningham, 1990; Langlois and Roggman, 1990 all considered that an attractive faces tend to be those of the average of that population.


The use of manipulated images has shown that horizontal mandibular changes are more accurately identified by professionals, while vertical changes are more readily recognized by lay people (Burcel et al., 1987; Romani et al., 1993. Facial symmetry is also considered an aesthetic requirement. Jenkins R et al (2011) found that when examiners considered different photographs of the same person, unfamiliar viewers perceived images of the same person as being different individuals. While familiar viewers perfectly identified the photos. Multiple photographs of any individual formed a continuum of good to bad likeness, which was highly sensitive to familiarity. They concluded  that their findings suggest that face photographs are unsuitable as proof of identity.


Kramer and Ward claimed that following on from earlier studies that people with different personality traits have different-looking faces. They investigated whether personality and health information are differently signalled by the two hemifaces. They concluded that Emotional stability and health were more accurately discriminated from the right hemiface, while extraversion showed higher accuracy from the left hemiface. They felt that they had found evidence that attractiveness differences between hemifaces depended upon the personality trait most clearly expressed.


Springer et al found  that individuals perceive their own beauty to be greater than that expressed in the opinions of others (p < 0.001). They felt that this observation provides insight into our basic behavioural patterns and suggested that there are strong psychological mechanisms in humans supporting self-identification and thereby encouraging the self-confidence. While the psychological basis of self-confidence is multifactorial, they felt that nothing more than the “beauty of the beholder is in the eyes of the latter”.


Naini et al considered Orthodontic- Orthognathic cases and concluded that, mandibular retrusion became noticeable at -4 mm and protrusion at 2 mm. The odds of desire for surgery were reduced by 85 per cent for those patients who had undergone bimaxillary surgery in relation to those with single jaw surgery. The lowest rated images demonstrated severe degrees of mandibular protrusion and retrusion. The highest rated images represented the idealized facial profile and minor variations thereof. Going through the process of orthognathic treatment did not appear from their results to have any significant effect on patients' perceptions of facial profile attractiveness or the limits of mandibular sagittal deviation at which they would desire surgery. The clinician's information provision during treatment did not seem to unduly influence orthognathic patients and did not make them more critical of jaw deformities. That is to say they were no coerced into treatment but desired it.

Does orthodontic treatment affect patients' quality of life? Was the question posed by Kiyak Concluding that: 

“the oral-facial region is usually an area of significant concern for the individual because it draws the most attention from other people in interpersonal interactions and is the primary source of vocal, physical, and emotional communication. As a result, patients who seek orthodontic treatment are concerned with improving their appearance and social acceptance, often more than they are with improving their oral function or health. Enhancing these aspects of quality of life is an important motive for undergoing orthodontic treatment. Regardless of age, patients' and their parents' or caregivers' expectations about improvements in oral function, aesthetics, social acceptance, and body image are important for both general dentists and orthodontists to consider when advising patients about these procedures and during the treatment process.”

 Wenfeng et al found that the presence of a task-irrelevant “attractive face” can induce a transient diversion of attention from a perceptual task. Observers were less efficient at detecting identity change among multiple “attractive faces” relative to “unattractive faces” when the target and distractor faces were not highly distinctive from one another. They also found that it was difficult to detect a change if the new face is similar to the old. Faces may have a special capacity to summon and recruit attention when they compete with other stimuli for attention. People tend to look longer at attractive than at unattractive faces. Facial beauty can be appraised automatically and rapidly. Beautiful faces may capture attention even when they are shown outside the foveal vision.


Aharon found that in particular, young heterosexual males rate pictures of beautiful males and females as attractive, but exert effort via a “keypress procedure” only to view pictures of attractive females. Functional magnetic resonance imaging showed that passive viewing of beautiful female faces activates reward circuitry, in particular in the nucleus accumbens.

Olsen reported on the fact that:

“ Those who are physically attractive reap many benefits, from higher average wages to a wider variety of mate choices. Recent studies have investigated what constitutes beauty and how beauty affects explicit social judgments, but little is known about the perceptual or cognitive processing that is affected by aesthetic judgments of faces and why beauty affects our behavior.”

 In this study, the authors show that beauty is perceived when information is minimized by masking or rapid presentation. Perceiving and processing beauty appear to require little attention and to bias subsequent cognitive processes. These facts may make beauty difficult to ignore, possibly leading to its importance in social evaluations.


Cellerino A. reported that averageness, symmetry and sex-specific traits have been associated with attractiveness. The effect of averageness is exemplified by blending a set of real faces into a chimeric face. The composite was considerd  more attractive than most of the faces used to create it. Beautiful faces are not simply average faces, however. If the female-specific features of a female composite face are enhanced, the resulting face is perceived as more attractive than the composite. In particular, smaller than average chin, smaller than average nose and higher than average forehead, all are traits associated with female's attractiveness. These traits have been interpreted as signs of high oestrogen/testosterone ratio and therefore cues of high fertility. However, these same traits are also a species-specific characteristic of Homo sapiens that differentiates it from other hominid species. Preference for caricature of human features could represent a relic of species recognition mechanisms. Female preferences for male faces proved to be more variable than male preferences for female faces.


 Rhodes considered averageness, symmetry, and sexual dimorphism as good candidates for biologically based standards of beauty. A critical review and meta-analyses indicated that all three are attractive in both male and female faces and across cultures. Theorists have proposed that face preferences may be adaptations for mate choice because attractive traits signal important aspects of mate quality, such as health. Others have argued that they may simply be by-products of the way brains process information. Although often presented as alternatives they argued that both kinds of selection pressures may have shaped our perceptions of facial beauty.

Krzysztof’s main findings when analysing women of different ages and hormonal influence were as follows:

(1) Preference for sexy-looking faces was strongest in young, non pregnant women.

(2) Biologically more mature girls displayed more adult like preferences.

(3) The intra group consistency for postmenopausal women was relatively low.

(4) In terms of the preference pattern, pregnant women were more similar to perimenopausal women than they were to their non pregnant peers.

(5) Preference for youthful appearance decreased with the age of the women.


They argued that the life history of female preferences for male faces is, to a large extent, hormone-driven and underpinned by a set of evolutionary adaptations.


Langlois et al. 19871991) and Slater et al. 1998)  found that and even 3-day-old newborns preferentially look at the faces regarded by adults as attractive. Cooper et al. (2006) found that 4- and 9-year-old children preferred female faces with more childlike proportions than did 12-year-old children and adults.


Digitally masculinized male faces were preferred more strongly by reproductive-age women than by pubescent girls or postmenopausal women. Although use of hormonal contraceptives and stage of menstrual cycle were associated with sex hormone levels and were known to affect facial preferences (Jones et al. 2008; Penton-Voak and Perrett 2000), young, nonpregnant women have estradiol and progesterone levels many times higher than those of prepubertal girls and women 2 years or more after menopause but many times lower than women in the final trimester of pregnancy (Burger et al. 2002; Fleming et al. 1997; Winter 1978). Hormonal influences on facial preferences have been documented repeatedly (Jones et al. 2008; Roney and Simmons 2008; Theodoridou et al. 2009; Welling et al. 2007,2008) as having an effect.


Although the averageness hypothesis of facial attractiveness proposes that the attractiveness of faces is mostly a consequence of their averageness, 1 study has shown that caricaturing highly attractive faces makes them mathematically less average but more attractive. Here the authors systematically test the averageness hypothesis in 5 experiments using both rating and visual adaptation paradigms. Visual adaptation has previously been shown to increase both preferences for previously viewed face types (i.e., attractiveness) and their perceived normality (i.e., averageness). The authors used a visual adaptation procedure to test whether facial attractiveness is dependent upon faces' proximity to average (averageness hypothesis) or their location relative to average along an attractiveness dimension in face space (contrast hypothesis). The results of these 5 experiments supported  the proposal that there are specific nonaverage characteristics that are particularly attractive. The authors discussed the implications for the interpretation of studies using a visual adaptation paradigm to investigate attractiveness.

Buggio et al summarised that “Female beauty has always attracted human beings. In particular, beauty has been interpreted in terms of reproductive potential and advantage in selection of mates. They reviewed the literature on female facial and physical beauty with the objective of defining which parameters could influence female attractiveness.


Symmetry, averageness, and sexual dimorphism with regards to facial beauty, as well as waist-to-hip ratio (WHR), breast size, and body mass index (BMI) for physical beauty, have all been assessed. In current societies, it appears that facial attractiveness results from a mixture of symmetry and averageness of traits, high forehead and cheekbones, small nose and chin, full lips, thin eyebrows, and thick hair. A low WHR reliably characterized physical attractiveness, whereas inconsistencies have been observed in the evaluation of breast size and BMI. The importance of breast size appears to vary with time and sex of evaluators, whereas the impact of BMI is related to socio-economic conditions. The various hypotheses behind beauty and the role of attractiveness in mate choice and sexual selection were described in terms of continuation of human species. Intriguing associations emerged between features of attractiveness and some reproductive disorders, as both are substantially influenced by sex steroid hormones.”


The only studies which do not appear to have been undertaken at present are appraisals of “Beauty”  undertaken by either the unborn or the recently dead.



Depending on which authors you read having a symmetrical face is more attractive the individuals concerned with this desirable attribute will in general have more partners both before during and after marriage. They will start sexual activity earlier than their peers and earn more money. The increased earnings they may not however necessarily share. There is associated with this research the difficulty of preference versus choice. Most people may prefer something but that does not mean they would necessarily choose it.


Individuals with facial deformity have to work harder at their social skills to overcome social aversion to their physical appearance. The stories associated with the “Elephant man”,  observations with patients with CLAP and other facial deformaties  Simon West and the reports produced by “Changing faces” all enlighten us to the fact that facial aesthetics alone is not the end of the story. Many successful and famous individuals have malocclusion Bruce Forsyth, KenDodd, Esther Rantzen, Janet Street Porter. Transferred qualities onto beautiful people can be too much for the individuals concerned  “You are beautiful therefore, you must be happy and successful.”  

“If you consider yourself to be beautiful when you are young take lots of photographs as no one will believe you when you are older”.

The beautiful among us are the first to notice this charm fading with time. If an individual’s  personality is based on external appearance for  adoration the fear of this being lost can trigger depression. Self harm and depression and  facial dysmorphofobia are also linked to suicide. “Preference” to mean evaluative judgment in the sense of liking or disliking an object (e.g., Scherer, 2005) is the most typical definition employed in psychology. However, it does not mean that a preference is necessarily stable over time. Preference can be notably modified by decision-making processes, such as choices (Brehm, 1956; Sharot, De Martino, & Dolan, 2009), even in an unconscious way (see Coppin, Delplanque, Cayeux, Porcherot, & Sander, 2010). Choice consists of the mental process of judging the merits of  multiple options and selecting one of them.


Personal factors determine food choice.  These include preferenceassociationshabitsethnic heritagetraditionvaluessocial pressureemotional comfortavailabilityconvenience,economyimagemedical conditions, and nutrition.


Psychologists have developed a personality test that determines where an individual lies on the satisficer-maximizer spectrum. A maximizer is one who always seeks the very best option from a choice set, and may anguish after the choice is made as to whether it was indeed the best. Satisficers may set high standards but are content with a good choice, and place less priority on making the best choice. Due to this different approach to decision-making, maximizers are more likely to avoid making a choice when the choice set size is large, probably to avoid the anguish associated with not knowing whether their choice was optimal.


The term choice theory is the work of William GlasserMD, Glasser believes that "pleasure" and "happiness" are related but are far from synonymous. William Warren Bartley compared critical rationalism to the very general philosophical approach to knowledge which he called "justificationism". Confuisngly he stated that most justificationists do not know that they are justificationists.


Justificationism is what Popper called a "subjectivist" view of truth, in which the question of whether some statement is true, is confused with the question of whether it can be justified (established, proven, verified, warranted, made well-founded, made reliable, grounded, supported, legitimated, based on evidence) in some way.


Refutation/Falsification  of the Golden proportion, Symmetry and the “Average” as measures of Beauty.


Previously published work by Moss Linney and Lowey  (1995) set out deliberately to falsify the possibility that the 3D average face could be an aesthetic goal or measure of beauty and tried to identify if a sample of “Facially Aesthetic” individuals matched the “Average”  “Symmetry” and the “Golden Proportion”.

Using pooled 3D data from the UCH facial scanner an average 3D female face was constructed and an average 3D male face. A well known London Modelling agency was contacted and they were asked to provide 2 samples of 30 male and 30 female registered models for an investigation into “facial beauty”. This biased the sampling of the models specifically selected by the modelling agency for this purpose. They were however all subjectively considered to be facially aesthetic by at least one of the authors. 3D facial data, Cephalometric and Panoramic radiographs were undertaken as well as photographs and intraoral measurements. Mario Livio drew attention to this work in his book on the Golden proportion but misquoted the authors in one section and correctly quoted them in another.

 In this “Facially Aesthetic” sample the authors tried to identify if the “Golden proportion” would appear when comparing mouth widths, nose widths and eye widths. Clearly the Pooled 3D images for the Average male and Average female are strikingly different from the Pooled 3D images for the average male and female M odels. The female model group had smaller mandibles. The male model group had more pronounced Gonion and chins. None of the images measured displayed the “Golden proportion” . There was a degree of facial asymmetry in both the male and female model samples.

The Cephalometric and Intraoral measurements were also revealing. If  IOTN were applied to this sample then a percentage would have to be considered “in need of treatment”. The extent to which the soft tissue profile matched the underlying dental malocclusion was also of interest as the 3D soft tissue facial appearance was not always matched by the hard tissues underlying them . The complete range of Cl III, Cl II div2 and Cl II div 1 malocclusions were found within the model sample.  The only photograph measured in this study which demonstrated the Golden proportion was one of the late Princess Grace of Monaco, Grace Kelly. Known as a screen “goddess” for her beauty. Deifying of the beautiful as a social exercise is not new. The same approach was used in ancient Greece. Antoninus was considered one of the most beautiful people in ancient Greece and was awarded the status of God. The ancient Greeks considered that Gods could appear in earthly form. This demonstrates that even today we are not so different socially from ancient peoples in our adoration of the beautiful.

The author responsible for the measurements, when the presence of the Golden proportion was discovered in this single photograph, then asked his two daughters aged 4 and 6 look at all the photographs displayed on the kitchen table and pick out the “prettiest lady”.

This was undertaken by each child separately and only the author knew which photograph each had chosen. They both chose the black and white photograph of Grace Kelly. There was no time constraint, there were numerous photographs of in colour, profile and various other images they could have chosen. While not exactly a clinically controlled random and prospective trial the findings did interest the author and are therefore reported here.

At 73, Brigitte Bardot, the greying goddess


 Because of the importance given to facial aesthetics in human communities vast amounts of money are used to enhance facial aesthetics and the concept of  “ beauty” has been endlessly explored throughout the millennia. Whether it can be measured or not is debateable. Whether the Golden proportion, Symmetry or Averageness are tools fit for this purpose is also debatable. Whatever measurement is used the occurrence of beauty is transient and has a direct analogy in orthodontic treatment with stability. The old adage appears to be true that if one considers oneself beautiful when young take lots of photographs as no one will believe you when you are old.   


Facial measurement and ethnicity.

There are obvious morphological and facial differences between different ethnic groups. This is part and parcel of the study of Anthropology and the study of human migration and development. Much has been written about what distinguishes the “races” and there origins. Yet from mitochondrial evidence it appears clear that all of the so called “races” around the world encompassing the Chinese and Japanese, the Australian Aboriginals, African Americans and Anglo Saxons are all descendents of a small group of individuals who migrated out of Africa between 165,000 and 60,000 years ago.


Historically Facial measurements have had a rather an inglorious past and have played their role in “separating” out members of a population for segregation, discrimination or genocide. (Lemkin). Following Darwins publication of the origin of species the now broadly discredited political and philosophical ideas expressed in Eugenics by Galton and others emerged. Within these philosophical concepts people were directly referred to as belonging to the "criminal races" "Scottish race" "cockney race" etc. The various genocides associated with the history of Colonial expansion during this period have also not helped in this matter.


Using Facial measurement it was considered possible not only to identify people within racial groups but also identify such things as criminal tendency. Facial measurements as well as other techniques were used by the Nazi party to identify groups for extermination. By using Facial measurement it was considered possible to identify people within different groups and it was a direct precursor to the use of facial measurement by the Nazi party to identify groups for extermination. One group of course being Jews but another was of course Gypsies. So this segregation was not confined to segregation on the basis of skin colour or religion but also on a way of life. Members of the Gypsy community have their origins associated with different population migrations at various times but they became known as Gypises during Henry VIII’s time as the original people fleeing violence had migrated out of India. Their speech was not recognised and they were named “Egyptienes” which became abbreviated later to Gypsies. (Firth)


Recent media attention focused on the “Dale Farm” and French evictions highlights the ongoing discrimination focused on Gypsies. What is less well known is that gypsies have been identified as a specific ethnic group by the United Nations and as such should be afforded the same legal protection as any other ethnic group from discriminatory behaviour. What is also less well known is that in the United Kingdom racist discrimination which can be successfully argued as genocide has been accepted practice against the Gypsy population throughout the centuries in Britain since the reign of Henry the VIII.


What is less easy to understand is that this would not be tolerated by the wider public or the courts if directed to any other ethnic or social group. For example presently alleged racist Footballers comments receive far less tolerance than similar comments made towards the Gypsy population. Also to describe the centuries old habit of attacking the Gypsies and Travellers of Britian as genocidal seems something of an overstatement. However by the very definitions introduced by Lemkin and who categorised genocide for the United Nations after the atrocities witnessed during the Second World War it cannot be denied that this is appears to be what is taking place. .



The former Nazi regime specifically targeted Gypsies for ethnic cleansing. Echoes of which were so similar to the recent expulsions undertaken by the Sarkosey regime in France that it generated international public condemnation. Some of the individuals targeted in that group even had French passports and had had been “French” for three generations at least. It also echoed the Muslim expulsions from Southern Spain who were as Iberian as their Northern Christian cousins. Either Gypsies are not an identifiable ethnic group in which case they should be treated equally under the law in all countries or they are an identifiable ethnic group and in which case they should be offered the same protection under the law as any other ethnic group. Defence against Public offences of racial encitement to violence and abuse being the least of these protections. Gypsy is currently used to cover a broad diverse group of people. In addition the direct implication is that anyone tagged and identified as belonging to this group is by definition genetically predetermined to be involved in criminal activity.


This is also not without historical precedent. When Eugenics emerged the philosophical concepts  were used in an attempt to ethnically cleanse the world of the Jewish race. It is less well known that these same ideas were used to civilise first nations during global imperialist expansion.


Racial difference as a reason for directing government policy is also neither new or unusual.

King Leopold II of belgium almost destroyed the native population of the Congo in Africa. In 1896 a German newspaper reported that 1308 hands had been collected in a single day for failure to meet rubber quotas. This number included children. One of Leopolds lieutenants wrote " only the whip can civilise the black".

In Tasmania the original 5000 inhabitants had lived in isolation for 10000 years.  in 1803 the island was settled by Europeans and these Aboriginal "godless " peoples required civilising. murder and conflict ensued until by the end of the 1820's. George Arthur the governor who knows Wilberforce and has already being warned that genocide would be unacceptable by the British government. Determined to the last few hundred Arthur turns to George Augustus Robinson a missionary to rescue the remaining aboriginals. They were transported to Flinders island and  in order for them to "learn" to settle down and become agriculturalist settled Christians. By the mid 1840's 260 of the original 300 were dead. Within one generation a complete civilisation which had survived for thousands of years as a Nomadic people was recorded and exterminated in an attempt to alter convert them into settled civilised agriculturalists.

In the mid 1990's Richard Herrnstein and Charles Murray "The Bell Curve" claimed that racial disparity in IQ tests proved the innate inferiority of black people.

Currently the use of terms associated with most ethnic identities are used cautiously. Terms such as "the Irish problem" or "the Jewish problem" would be impossible to print in a modern media context. This consideration seems to have escaped the use if the word "gypsy" in modern publications and reporting.

Some Gypsies do identify themselves as different ethic group yet they are not afforded equal rights when it comes to modern media coverage. The headlines of any of the above stories would be considered unprintable if the word gypsy were removed and black, irish, middle eastern, Chinese or any other ethnic group were substituted. Criminal activity is not separated from ethnic background in a considered way. The term Gypsy is being used in association with diverse crimes by diverse groups or individuals as a badge of guilt as blatant as a yellow star if david in order to confirm in the public arena stereotypical ideas. Gypsy equals criminal equals ethnic cleansing  and a requirement for government policy and policing behaviour to force gypsies to become civilised and settle down.


Acculturation meeting of cultures(wikipedia)


Cranial capacity has also been used as an indirect measurement of intelligence. Book about negroid intelligence




Sattarzadeh Ali Payam , Lee Robert T.****


Once again variation is the rule and using Cephalometric  normative data as a target for aesthetic results should not be considered as reliable Kenza Lahlou, et al concluded


“Differences in the dentofacial relationships of various ethnic groups have been observed by many investigators (Loutfy et al., 1970Chan, 1972Shalhoub et al., 1987Cooke and Wei, 1988Al-Jasser, 2000Hamdan and Rock, 2001Behbehani et al., 2006), and, as a result, a number of standards have been developed regarding various racial and ethnic groups. All these studies indicate that normal measurements for one group should not be considered normal for others. Different racial groups must be treated according to their own characteristics. Cephalometric norms taken from European-American means are useful diagnostic aids, but should not be used as treatment goals for individual patients”



The interesting thing from the more recent evidence regarding maternal mitochondrial inheritance is that all “races” are descendent from a single human homo sapiens migration from Africa around 70,000 years ago. So despite the obvious external morphological differences we are all part of the same original family.  as skin races in general for   m


It is clear that the use of a Caucasian standard set of Cephalometric landmarks cannot be applied universally If for example the average height in England was 160cm. It does not mean that everyone who is not 160cm is abnormal or that they should undertake treatment to become 160cm or if they have had treatment and are 159 or 170 cm that the treatment has failed. Equally if they are 180cm it does not automatically mean they are from a different ethnic background or that there is a particular height they should have been expected to reach either with or without treatment. I leave aside sexual dimorphism, asymmetry and any association with intelligence and height (cranial capacity) for the time being.





Despite all of the research and training we have only a partial insight into the problems our patients request help with. Therefore because our insight is only partial the unscrupulous or the malevolent can take advantage of this. Clinicians require protection.


Also if outside of the percentile of “beautiful” this does not mean that an individual is condemned to a life of misery. Equally projecting onto so called “beautiful people” direct associations such as  intelligence, happiness and wealth is a delusion.


An analogy can be drawn between weight and Cephalometric measurements or the “Golden proportion”.


If the following hypothesis were made that Everyone in the population must have the same weight/height ratio. Anyone who is not this weight/height must be treated until they are this weight/height and could be deemed disabled. This weight/height ratio confers beauty and is stable once achieved. Failure of treatment to this weight/height is negligent and any future change after completion of treatments to this weight/height is negligent relapse and the responsibility of the clinician regardless of signed treatment consents.  This applies regardless of presenting ethnic background original height/weight ratio of the patient, parent expectation, cost, duration of treatment, diet/training regime used, duration and type of post treatment diet/training advised and compliance.



[i] The Ancient Civilisations and the history of the Golden proportion.




When discussing facial aesthetics the most often quoted references relate to the various great ancient civilizations: Egypt, Greece and Rome.  MesopotamiaPersiaIndia, the Celtic peoples, China, and the Mayans for example are often not considered.


The most commonly referred to set of facial proportional tenets was introduced by the Greeks. Polycleitus (450-420 B.C.) was among the first to use artwork to portray the “ideal” facial proportions. Aristotle (384-322 B.C.) later recorded his subjective impressions of what specific measurements represented the “ideal” facial proportions. Marcus Vitruvius Pollio (31 B.C.-14 A.D.) later wrote about the exact dimensions that were deemed the aesthetic ideal by the ancient Greeks. The European Renaissance artists, most notably Leonardo da Vinci (1452-1519 A.D.), would later take the concepts of the Greeks and develop them into a system known as the “neoclassical canons”   Salvador Dali certainly used the Golden proportion in his work deliberately and the Golden ratio and aesthetics is discussed in detail in the book by Mario Livio.

There is considerable scholarly debate as to whether the ancient Egyptians used the Golden proportion in building the pyramids despite the fact that the building of the pyramids predates the written work of Phidias (480-430 BC) who along with Pericles was responsible for  much of the rebuilding of Athens including the Parthenon. False witness was brought against Phidias for embezzeling gold and he was imprisoned and died in jail. The letter Phi is named after him.

One Egyptian pyramid is remarkably close to a "golden pyramid"—the Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu). Its slope of 51° 52' is extremely close to the "golden" pyramid inclination of 51° 50' and the π-based pyramid inclination of 51° 51'; other pyramids at Giza (Chephren, 52° 20', and Mycerinus, 50° 47') are also quite close. Whether the relationship to the golden ratio in these pyramids is by design or by accident remains open to speculation.

 Adding fuel to controversy over the architectural authorship of the Great Pyramid, Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height, except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem nor any way to reason about irrationals such as π or φ.

Michael Rice asserts that principal authorities on the history of Egyptian architecture have argued that the Egyptians were well acquainted with the golden ratio and that it is part of mathematics of the Pyramids, citing Giedon (1957). Historians of science have always debated whether the Egyptians had any such knowledge or not, contending rather that its appearance in an Egyptian building is the result of chance.













Islamic Translation of Ancient texts.


According to Islam, human works of art are inherently flawed compared to the work of God; thus, it is believed by many that attempting to realistically depict the form of an animal or person is an insolence to God. In the Pan Indian philosophic thought the term 'Satyam Shivam Sundaram' is another name for the concept of  “the Supreme”. 'Sat' is the truth value, 'Shiv' is the good value & 'Sundaram' is the beauty value.


The fall of Alexandria led to a wealth of information falling into Arabic hands.

In the 9th century a translation movement took place in Bagdhad. Christians, Jews and Muslims studied and worked side by side translating all of the ancient texts in the “House of Wisdom”, records of this enterprise exist in the Bodlian library in Oxford today. The works of Galen, Ptolemy, Pythagorus and Zarathustra were all translated into Arabic and this cultural absorption was sponsored across the Arabic worlds by the Abbasid Kaliphs.


Universities sprang up across the Arabic world such as those in Damascus, the Al al Azhar in Cairo, Fez and elsewhere including of course Islamic Spain. 400 years after the fall of Alexandria  in 711AD the Islamic invasion of Spain took place by Tariq Ibn Ziyad and lead to the establishment of Al Andalus, (Andalusia).


From that date Islamic influence was present in Spain for almost 600 years. In 1086 Andalucia brought in Moroccan troops the Almoravids who were strict Islamists to support them in battle defending their Spanish domain. Despite these additional troops the Islamic Rachman dynasty collapsed in 1095.


The Reconkista of Spain.


By 1250 only Granada remained Islamic. At this time it is thought that up to 70,000 Muslims lived in North Castillo and East Aragon. Castillo was passed onto Isabella who then married Ferdinand age 18 and who was heir to Aragon in the East in1469.  United they started the Reconquest of Spain.


After the sacking of Rome in the 5th Century the so called “Dark ages” began and western culture was driven by Christian philosophical thought during the 9th-11th centuries. This was based more on divine revelation than rational thought. It should be remembered that the various inquisitions were introduced to suppress heresy during this time. The Papal medieval inquisitions against the Cathars in the Languedoc region of southern France took place between 1184-1230. The inquisition introduced during the reign of Isabella and Ferdinand famously known as the Spanish inquisition took place around 1480. Pope Urban II tried to remove Islam from the holy lands with the crusades of the 11 -13 Centuries. Galileo’s trial for heresy for supporting Copernicus and heliocentricity took place under Pope Urban VIII in 1632.


In Spain, Christianity progressed South with a scorched earth policy and a protection racket culture with mercenaries fighting on both sides of the religious divide regardless of their own religious beliefs.  In 1085 Christians seized control of Toledo but the Muslims were allowed to remain there. Cordoba fell to the Christians in 1236 and Granada in 1492.  



During this period Alfonso VI’s march into Toledo in 1085 was a significant event in the promotion of the Golden proportion. Most western libraries contained few books when compared to Islamic libraries, perhaps a hundred or so compared with the 80,000 known to have existed in the Islamic library in Cordoba. During the “Reconquest of Spain” huge amounts of Arabic information as well as Arabic translations of Greek and Roman texts falls into Christian hands. 





The Hindu-Arabic numeral system and the Roman numeral system.


Two related key factors which governed the desire for scientific research in both the major religions of Christianity and Islam during this period came from the necessity to study time. Knowledge of time and the calendar was required to decide the time of prayer and periods of fasting and feast days in Islam and Christianity especially in calculating the date of Easter in Christianity.


Roman numerals were cumbersome to use and the perplexing state of affairs caused by the absence of the numeral Zero (from the Arabic “sifr” meaning empty)  in the Roman numeral system led to the Calendar beginning BC I and AD I. The actual Hindu numbers 1,4, and 6 appeared around 300 BC and the numbers 2,7, and 9 around 400BC. The Arabic numerals were being used between 500-800 AD, well before they became known in western culture.


Once discovered however Hindu-Arabic numerals were used in practice because of their simplicity. Evidence exists in the building of the great Cathedrals. Salisbury Cathedral has beams dating from 1240 carved with Arabic numerals to designate which beam is to be placed where. Other examples of words which come from direct Arabic translations are Arsenal, Alchemy, Algorithm, Alcohol, Alkali. In the field of medicine Avicenna’s medical texts became available to the new Christian occupiers in Spain along with Averroes’s comments on Aristotle.


Scholars travelled from England to Spain in the quest for knowledge. Daniel of Morley in late 1100 left from England and went to Toledo to hear philosophy. Daniel came to see the bishop of Oxford afterwards with his texts.  Alard of Bath also came back from Toledo and stated: "from the Arabs I have learnt one thing to lead by reason. I will detract nothing from God but very carefully listen to the limits of human knowledge only were this utterly breaks down should we refer things to God "


The relevance of the Reconquest of  Spain in considering the Golden Proportion


During the  “Reconkista” the Christians regained power in Spain. In Cordoba to reflect this a cathedral was built in the middle of the mosque there. The two buildings still stand there reflecting the turbulent religious struggles present during this period. In 1492 the Christians entered the Al Ambra mosque. Granada was under siege for 1 year until 1526. In Granada by 1609  all Muslims were either expelled or converted. The people living here at that time were not however Burbars or Arabs they were Spanish by blood or DNA and as Iberian as their Christian cousins in the North.  It is estimated that over a 10 year period 250,000 Muslims were expelled from Spain and most of these went to North Africa. Ironically the authors of the “Reconkista” Isabella and Ferdinand were later buried in the al Ambra mosque surrounded by Islamic texts  


During the reconquest of Spain, religious and ethnic divisions were not always clear. Guzman el Bueno established the Medina Sidonia line. His descendent the very Spanish Duchess of Medina Sidonia, when analysing her own family history discovered that her ancestor was in fact a Muslim Moor from Morroco and neither Spanish or Christian. In 1600 her family had “cleaned up” their family history to make it appear more Spanish and Christian.  Alliances were also made between  Christians and Muslims. El CID (from the Arabic Al Sidi or Sayyid: meaning Master or Lord)  was also known as Rodrigio Diaz de Vivar 1043-1099. He was a mercenary and fought first for a Moorish king then with a combined Moorish and Christian army created his own fiefdom in Valencia.


Many of the battles could be therefore described as a Civil war between Iberians of two different faiths but not always on religious grounds as these battles formed the basis of a 300 year land grab. Under Islamic rule conversion was not compulsory but Christians and Jews paid more tax.  Many examples of tolerance of the Christian and Jewish communities did exist. It can be speculated that earlier unforced conversion to Islam may have been as much about tax avoidance as being of religious importance. Conversion could be of significant financial benefit to a family. Forced conversions did take place however under Christian rule during the reconquest of Spain. By 1483 in Andalucia all Jews and Muslims had either been expelled or converted leading to a group of individuals being referred to as “Convertos”.



Two very influential characters at this time appear to have been Ibn Rushid known as Averroes and Ibn al Haitham known in the west as Alhazen. Proof that the Arabic translations were not simply that “translations” but that active research and development of ancient principles had taken place in the Arab world exist. Ibn al Haitham for example developed an accurate theory of Optics and described the function of the human eye as well as the Camera Obscura. Arabic preservation of Aristotle Euclidex  Plato were then all translated into Latin.


Averroes is considered to be the person responsible for the next great translation and is duly paid homage to in Rafael’s painting  the “School of Athens”. The first translation being that of the ancient texts from Greek and Latin into Arabic and the second being from Arabic into Latin. Without the preservation of the ancient texts in Arabic they would most likely have been lost to the world. Averroes certainly undertook the translations in Cordoba and wrote commentaries to express understanding of the translations alongside the texts. Aristotle in particular requires considerable assistance as the original Greek is considered complex. Averroes is often referred to simply as “the commentator” in many texts through the 12-14th Centuries.

Even the great work of Copernicus (1473-1543) can be mirrored by an almost exact replica in an earlier work by Sharaf Al din Al Tusi an astronomer working in Iran 1213.


Averroes philosophical arguments, rehearsed to allow secular investigation coexist with the Isalmic religion, were also used as a defence to heresy for those seeking out rational thought as opposed to divine revelation in Christianity during the Renaissance.


In relation to the Golden proportion parts of the Al Ambra mosque are thought to have been constructed using this proportion. Although Islamic architects also used the proportion 1:ü2 which is, 1: 1.414 and appears in some buildings. Evidence of the cross fertilisation of ideas can be seen elsewhere. King Peter of Seville 1248 a Christian king built an Arabic palace. Peter I of Castillo had arches built based arches on the golden proportion. So Islamic scholars translated applied and expanded upon Greek knowledge during this period before the Renaissance.


Roger  I and Roger  II of Sicily are also considered to have fostered and spread the knowledge from Southern Spain because of their knowledge of Arabic texts. Roger I was a Norman (circa 1030/40 to 1101) who conquered Sicily which contained Muslims and Greek speaking Christians. Along with Robert d'Hauteville they spread their conquest across Southern Italy and Malta.  Roger II 1095-1154 eventually inherited the throne and his mother Adelaide del Vasto was linked to the Aleramici on her father’s side who had lands throughout Italy.


Roger II drew round him distinguished men of various races, such as the famous Arab geographer Muhammad al-Idrisi and the Greek historian Nilus Doxopatrius. The king welcomed the learned, and he practised toleration towards the several creeds, races and languages of his realm. To administer his domain he hired many Greeks and Arabs, who were trained in long-established traditions of centralized government. This links the Norman, Arab, Greek, Italian, Spanish and English cultures in ways which are often oversimplified and were in fact much more fluid across these cultures.


By 1591 Phillip of Spain had established Gymnasia using Arabic numerals but Averroes also known as Abulcasin and other Arab intellectuals by then had been airbrushed out of history.  


It is interesting to speculate that the rebirth of culture, the arts, medicine and science known as the Renaissance following the fall of the Roman Empire and the dark ages may well have not occurred without Islamic influence.  




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