July 19, 2007

The Ubiquitous Symmetry

Ever wondered why our bodies are so symmetrical? I mean, if you cut our (and also other animals') bodies in half (don't do a Jack the Ripper though!), through a line that passes through the nose, navel, the perineum (i.e., a sagittal section); you get two halves, left and right, which exhibit a near perfect mirror image symmetry. Not only are they found in the animal kingdom; in a molecular level (e.g. in crystal lattices), and subatomic level (electron spins) too they exist.

The question naturally arises why nature exhibits this mathematical expression. A complacent and plausible explanation would be that it was an act of the evolutionary selection process (in the case of animals). A symmetrical body would give us the advantage in standing upright, against gravity. Assymetricality would mean a 'couple' (the couple/torque of physics: and not husband and wife!) working on the body, thus making it fall.

We should not nevertheless, ignore the plants' own aptitude in mathematics too. They are expert in number theories, in that, they exhibit Fibonacci cauliflower showing fractal geometrysequence ( 0, 1, 1, 2, 3, 5, 8, 13, 21, 34......every number is the sum of the previous two numbers), fractal geometry (image to the left) and many others. Another interesting thing that amazes me about plants is the way the tree trunks so faithfully point towards the center of the earth, even on a sloping hill. In other words, the tree trunks could be considered as an extension of the earth's radius.

Lets discuss the point why and how we are symmetrical. When a sperm meets and combines an ovum, a zygote is formed. The cells in this zygote multiplies resulting in a ball kind of stuff, called the blastocyst. In this sphere like stuff, only the central portion remains, in the form of a disk, while the rest of the sphere disappears. This central disk then differentiates (=evolves into different kinds of tissues) into three layers: an outer ectoderm, an inner endoderm and an intervening mesoderm sandwiched between them. Now this three layered disk then folds in such a way so that the edges of the disks appose and merge. This merging point is the navel or umbilicus (and other midline structures), via which the fetus gets nutrition from the placenta, via the umbilical cord. The limbs like arms or legs form as an offshoot from this folded structure. No wonder then, that the growing fetus will be symmetric, since the left and the right halves including the limbs are forming almost identically from a single entity.

Dysmorphisms do occur though, despite all this. In the case of other animals too, this same kind of embryogenesis is seen (and expected too), as ontogeny repeats phylogeny.

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