The facial proportions of beautiful peopleWe consider Saira Mohan again; this time with funky lines drawn on her face. The lines are part of a unisex beauty mask/archetype that allegedly depicts the facial proportions of the most beautiful face, irrespective of race.
Figure 1: Saira Mohan with a superimposed beauty mask that is the brainchild of Stephen Marquardt of Marquardt Beauty Analysis.
The beauty mask appears to fit Saira Mohan reasonably well. If the mask proportions apply to beautiful faces irrespective of sex or race, then the mask likely has some interesting biological significance. Let us examine this issue.
Firstly, I would like to thank Cevan for bringing Figure 1 to my attention. Next, we consider the basics of the beauty mask. Stephen Marquardt, a surgeon, has worked on human beauty for decades and claims to have described facial beauty in an elegant manner by assembling several decagonal matrixes formed of golden-ratio sections to form a beauty mask. The golden ratio is the ratio that divides a line segment into two parts having a ratio that is equal to the ratio of the larger part to the entire line segment, i.e., a 1:1.618 ratio.
Many proportions in nature are compliant with the golden ratio, which is also known as phi or the divine proportion (Figure 2).
Figure 2: The golden ratio in nature; adapted from Gary Meisner/Yosh Jefferson. 
Marquardt claims that whereas nobody fits the mask perfectly, women fit it better than men and the most attractive people fit it the best; see a compilation by Yosh Jefferson in Figure 3.
Figure 3: Stephen Marquardt’s beauty mask applied to attractive women; it fits well the Asian woman, the African woman and the white women. 
Figure 3 shows something interesting. Among black-skinned Africans, many Somalis/Ethiopians are among the least Negroid-looking people, but the black woman shown in Figure 3 is even farther removed from the typical Negro, and I would bet that she has substantial European ancestry. Similarly, the Asian woman has many facial proportions more typical of whites and less typical of Asians. Are Marquardt and Jefferson arguing that the most attractive non-whites are those that are closest to the basic facial proportions of whites?
Jefferson has noted golden-ratio proportions in a classic drawing (Figure 4).
Figure 4: Golden-ratio proportions in a drawing by Leonardo DaVinci. 
On the other hand, the arm length of the Igbo woman, a typical example, shown in Figure 5, is surely not in compliance with the golden ratios in Figure 4; an Igbo man would be even less compliant since for the same height, men have longer arms than women.
Figure 5. Igbo woman.
Jefferson has also described the golden-ratio proportions of the ideal face (Figure 6).
Figure 6: The golden-ratio proportions of the ideal face. 
Next, we turn our attention to images of various individuals, each roughly typical of the population that they descend from (Figure 7). Note how compliant the facial features of these individuals are with Marquardt’s beauty mask (Figure 1, Figure 15) or Jefferson’s golden-ratio proportions (Figure 6).
Figure 7: Some examples of human facial biodiversity.
An examination of Figure 7 suggests that if Marquardt and Jefferson are correct, then some human populations have few individuals who could be considered very attractive and a few populations likely do not have a single such individual.
Next, we turn to some formal analyses, starting with laser-measured facial variation across four populations: white British, Inuit/Eskimo, Australian aboriginals, and West African Negroes; the landmarks compared are shown in Figure 8. 
Figure 8: Facial landmarks compared across populations. 
Discriminant analysis largely separated the four groups; the percentage misclassifications being: white British (23.5%), Negro (22.8%), Australian aboriginal (22.9%) and Inuit/Eskimo (6.9%); the discrimination would obviously have been better if more landmarks had been used. Figures 9-11 visually depict the discriminant functions; in each figure, the front view is shown at the top and the side view at the bottom. The dotted lines connect the average of the landmarks shown in Figure 8 for the entire sample, and the solid lines connect the shifted landmarks, which are shifted in the direction that distinguishes one specified group from other specified groups; Figures 9-11 depict shape variation, not size variation.
Figure 9 depicts discriminant function one, which largely separated the Inuit from the others.
Figure 9: Depiction of discriminant function 1. Compared to others, the Inuit have flattened faces and more prominent cheekbones. 
Figure 10 depicts discriminant function two, which largely separated the white British from the Australian aboriginals and the Negroes.
Figure 10: Depiction of discriminant function 2. Compared to Australian aboriginals and Negroes, whites have narrower faces, longer noses, closer-set eyes, cheekbones that are smaller when seen from front and regressed backward when seen from side, and flatter teeth; other differences are shown in the figure. 
Figure 11 depicts discriminant function three, which largely separated the Australian aboriginals from the Negroes.
Figure 11: Depiction of discriminant function 3. Compared to Negroes, Australian aboriginals have smaller cheekbones (front view) and teeth that jut out more; other differences are shown in the figure. 
Given notable between-races central tendency differences with respect to shape as depicted in Figures 9-11, in addition to many additional differences concerning the lower jaw and the cranium (the part of the skull minus the face), it is clear that if Marquardt and Jefferson are correct, then the percentage of people that are highly attractive considerably varies by race, with the highest percentage found among whites. I don’t believe that this is what the authors are trying to convey, but this is what they come across as conveying.
Let us also address a study that evaluated racial cranial variation.  It should be obvious that physical variation involves both shape and size differences concerning the same structures, and then there are different kinds of shape differences, too. Therefore, with respect to the traits examined, it is desirable to separate shape from size and also separate the different aspects of shape. The statistical tool that does this is known as principal components analysis, which divides the variability of the traits measured into principal components that do not covary with each other. The first principal component (PC1) explains the largest amount of the variance, and subsequent PCs such as PC2, PC3, and so on, explain successively smaller proportions of the variance in the traits examined.
In this study, “the first six PCs individually account[ed] for 26.1%, 9.7%, 7.2%, 6.6%, 6.45%, and 5.3% of the variance, respectively,” and cumulatively accounted for 61.3% of the variance.  PC1 and PC2 are of special interest to us because both concern the shape of the region of the skull where the nose meets the forehead, which is notably different across the races.
“PC1 mainly reflects upper nasal projection but also breadth.” Compared to flat-faced Asians, whites have projecting and wide upper nasal bridges, with other races in between. “PC2 mainly reflects an inverse relationship between upper nasal breadth and projection.” The upper nasal bones are wide and flat in Negroes.
Figure 12 shows a plot of PC2 against PC1. The abbreviations mean: EU = European, AM = American Indian, AU = Australian aboriginal, PO = Polynesian, FE = East Asian and SS = sub-Saharan African. Each of these abbreviations lies at the center of the ellipse it represents.
Figure 12: PC2 vs. PC1. 
As seen in Fig 12, there is an overlap between within-population and between-populations variation. It is useful to know what proportion of trait variation in a species is due to its population structure, i.e., what proportion of the variance is between populations. This is measured by a statistic known as Fst; Fst values are listed in Table 1. The h-squared value = 0.55 in Table 1 means that the Fst values are calculated for a heritability of 55%, i.e., the proportion of the between-individuals variance accounted for by genetic factors is 55%, which is a reasonable value for cranial development. [4, 5]
Table 1: Fst values for the principal components.
Thus, Table 1 shows that 24% of the variance is between populations for PC1, 33% of the variance is between populations for PC2, and so on. Fst values are used in genetics for labeling extent of population differences; the magnitude of Fst being classified by Sewall Wright as follows: little genetic differentiation (0—0.05), moderate genetic differentiation (0—0.15), great genetic differentiation (0.15—0.25), and very great genetic differentiation (0.25 and above).  Overall Fst values in the 0.10—0.15 range are sufficient for racial classification, which the craniometric data in this study as well as genetic data elsewhere are compliant with. Although the Fst values in Table 1 are not based on genetics, they represent the same idea, and it is noteworthy that the Fst values for PC1 and PC2 are two- to three-fold higher than necessary for racial classification, i.e., the upper nasal region is considerably different across the races. Additionally, the analysis in Figure 12 was done after removing some cranial traits that were so different across the races that they dominated all analyses and the first few principal components. The authors of this study have cautioned against using the Fst data to support the existence of human races, but this caution is based on an article by Templeton, and this article has been debunked; see the “Fst follies” section here.
Anyway, why have I bothered to address the upper nasal region at length? Consider Marquardt’s beauty mask again (Figure 13). The shaded nasal region is unambiguously European, especially in the upper nasal region, and most non-whites and a number of whites don’t possess this type of nose.
Figure 13: Note nasal region (shaded).
Most non-whites—and some whites, too—have no hope of producing offspring with the fine nasal bones, especially upper nasal region, of the woman shown in Figure 14, even if they bred with her like.
Figure 14: A woman with fine nasal bones. Her facial proportions are more appealing for a European than some of the allegedly ideal proportions depicted by Yosh Jefferson in Figure 6; for instance, the eyes in Figure 6 are farther apart than the European norm and thereby more like that in non-Europeans.
Let us also address Marquardt’s beauty mask from the side (Figure 15). Marquardt’s beauty mask is clearly that of a European and also that of a masculinized woman; some of the clearly observable masculinized traits [7, 8] include a nasoglabellar region (where the nose meets the forehead) that is curved in a masculine manner, a nose that projects in a masculine manner, a masculine chin region and a sharp gonial angle.
Figure 15: The beauty mask of Stephen Marquardt from the side. Note arrows pointing to the masculinized regions.
Other than using the golden ratio, Marquardt has used a large database of attractive individuals of different races to come up with his beauty mask, yet claims that white women, on average, have a face that is somewhat broader than the beauty mask, which should not be the case given the finds seen in Figures 9 and 10. Now, a quick examination of Marquardt’s website reveals the pictures of mostly high-fashion models, which he apparently has used to come up with his mask, and which in turn explains the masculinization in his mask proportions since high-fashion models tend to have masculinized faces, reflecting the fact that most top fashion designers are gay men.
I have previously pointed out that beautiful people tend to possess multiple population-typical traits, and this has biological significance. Therefore, given the finds in Figures 8-12, which should be mostly known to keen observers anyway, it is unlikely that one could come up with a beauty mask/archetype that describes the facial proportions of the most beautiful people in all races. There are additional problems with Marquardt’s beauty mask since he claims that his mask applies to the most beautiful people. As I have alluded to previously, the most beautiful people tend to somewhat deviate from the average with respect to some traits, and there are at least two such types of deviation that are relevant to us: one related to sex hormone profiles and another related to gracility of facial features (details to be posted later). Obviously, different sex hormone profiles in men and women and racial variation in central tendency/gracilization make it impossible to come up with a unisex and cross-racial beauty mask that describes the facial proportions of the most beautiful. Marquardt’s beauty mask doesn’t do justice to white beauty and it is clearly unfair to non-whites, which I do not believe to be deliberate on his part but it is something that has apparently resulted from his over-eagerness to describe beauty in simple terms. Beauty has a complex nature. The association of beauty with having multiple population-typical traits, sex hormone profiles, and gracilization suggests that it is not completely subjective, i.e., something that can be dismissed as simply lying in the eye of the beholder, but aesthetic preferences nevertheless vary by race and species, reflecting the fact that population-typical traits vary by race and species; there is also individual variation, but most individuals within a race assess facial beauty in a similar manner.
Marquardt and Jefferson could make a powerful case for their work if they came up with beauty masks for various animal species and showed how masks for ancestral species could be transformed to that of their different-looking present descendents without seriously undermining the alleged biological significance of the mask among the intermediate types, but I don’t believe they would be able to do this.
Further, a great many proportions/patterns in nature undoubtedly have nothing to do with the golden ratio, i.e., in many cases, it is surely futile to attempt to reduce visual appeal to patterns derived from the golden ratio.
Returning back to Saira Mohan, even though she is able to fit Marquardt’s beauty mask reasonably well, she still doesn’t qualify as a great beauty by European standards. Finally, the racial differences talked about in this post strengthen my previous argument that the beauty of the most attractive whites cannot be enhanced—but will be undermined, instead—via the absorption of non-whites among whites.
[Note: My previous post attracted close to 250 comments, most of them off-topic. If you feel like commenting, please note that there will be plenty of future opportunities for you to discuss immigration, Jews, free speech and Roman history at MR, i.e., please avoid off-topic comments.]
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3. Roseman CC, Weaver TD: Multivariate apportionment of global human craniometric diversity. American Journal of Physical Anthropology, 2004, 125:257-263.
4. Devor EJ: Transmission of human craniofacial dimensions. Journal of Craniofacial Genetics and Developmental Biology, 1987, 7:95-106.
5. Sparks CS, Jantz R: A reassessment of human cranial plasticity: Boas revisited. Proceedings of the National Academy of Sciences—USA, 2002, 99:14636-14639.
6. Hartl D, Clark AG: Principles of population genetics. Sunderland, MA: Sinauer Associates; 1989: 118-119
7. Rosas A, Bastir M: Thin-plate spline analysis of allometry and sexual dimorphism in the human craniofacial complex. American Journal of Physical Anthropology, 2002, 117:236-245.
8. Walrath DE, Turner P, Bruzek J: Reliability test of the visual assessment of cranial traits for sex determination. American Journal of Physical Anthropology, 2004, 125:132-137.
Posted by J Richards on Friday, June 3, 2005 at 11:14 AM in Anthropology, Race realism
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