Symmetry bilateral

Tliis passage is in French in both the German original and English translation of Mann s The Magic Mountain (see, References). 

Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed., 

Earlier, Mann discusses the symmetry of the human body in more detail, stressing the harmony between its external appearance and internal organization [3]  

It leaned thus, turning to smile, the gleaming elbows akimbo, in the paired symmetry of its limbs and trunk. The acrid, steaming shadows of the armpits corresponded in a mystic triangle to the pubic darkness, just as the eyes did to the red, epithelial mouth-opening, and the red blossoms of the breast to the navel lying perpendicularly below... 

Already Kepler noted in connection with the shape of the animals that the 

The three diameters of Kepler suggest a Cartesian coordinate system [2-3). 

Bilateral symmetry is indeed very common in the animal kingdom. It always appears when up and down as well as forward and backward are different, whereas leftbound and rightbound motion have the same probability. As translational motion along a straight line is the most characteristic for the vast majority of animals on Earth, their bilateral symmetry is trivial. This symmetry is characterized by a reflection plane, or mirror plane, hence its usual label m. 

The origin and meaning of the deviations from bilateral symmetry of the human face have generated considerable research interest (see, e.g., Ref. [2-4]). It may even be that the two sides of our face differ in expressing emotions, and one may be more private and the other may be more public.  

Differences between the left and right hemispheres of the brain have been the subject of intensive studies, and several monographs have appeared (see, e.g,. Refs. [2-5] and (2-6j). Hemispheric asymmetry has received so much attention that recently it was suggested that the time has come to put the brain back together again [2-6]. 

Bilateral symmetry has outstanding importance in man-made objects. It has a functional purpose. The bilateral symmetry of various vehicles, for example, is determined by their translational motion. On the other hand, the cylindrical symmetry of the Lunar Module is consistent with its function of vertical motion with respect to the moon s surface. It has been noted [2-7] that 

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The next qualitative change that occurs is the breakdown of the bilateral symmetry of the flow — the counterclockwise (left) eddy begins to grow at the expense of the clockwise (right) eddy, the latter effectively disappearing at t 300 psec. The symmetry is restored by / 370 psec, but at t 470 psec only the... 

Figure 6. Regression analyses of the relationship between male bilateral symmetry and five measures of male sexual performance in the Manchester whole-ejaculate and Calahonda field studies.

Figure 5.5 Horseshoe crabs and various species of their extinct ancestors (trilo-bites), all exhibiting bilateral symmetry. 

Most enzymes possess an infallible ability to recognize the difference between the right side and the left side of an organic substrate even when the latter has perfect bilateral symmetry. In fact, this ability is limited to prochiral centers of molecules and is a natural consequence of their reaction with the chiral... 

McBeath, M. K., Schiano, D. J., and Tversky, B. (1997). Three-dimensional bilateral symmetry bias in judgments of figural identity and orientation. Psychological Science, 8, 217-223. 

The bilateral symmetry of the human body is emphasized by the static character of many Egyptian sculptures (Figure 2-1). Mobility and dynamism, however, do not diminish the impression of bilateralness of the human body (Figure 2-2). 

Figure 2-2. Bilateral symmetry of the human body Sculptures at the top of a building at Piccadilly Circus, London (photograph by the authors).

Bilateral symmetry is found in some flowers, conspicuously, in orchids (Figure 2-4). Also, leaves often have bilateral symmetry, but it may be only accidental for a tree. Generally, trees and many other... 

Figure 2-3. Animals of bilateral symmetry (photographs by Zoltan Bagosi, Budapest Zoo, used with permission).

Both folk music and music by master composers are rich in symmetries. Figure 2-10 shows two examples with bilateral symmetry. The first example is from Bartok s Microcosmos series written specifi-... 

Weyl calls bilateral symmetry also heraldic symmetry as it is so common in coats of arms [6], Characteristically, the eagles of the Habsburgs (Figure 2-1 la and b) and the Russian Romanovs (Figure 2-1 lc) were double headed. 

Variations of RPE disturbances can occur but most often appear as well-circumscribed areas of RPE atrophy in the macular area, which may resemble a macular hole (Figure 35-9). A high degree of bilateral symmetry between eyes is generally noted, but occasionally the toxicity can affect one eye more than the other. 

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