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Wikipedia defines bilateria as :

animals with bilateral symmetry, i.e., they have a head ("anterior") and a tail ("posterior") as well as a back ("dorsal") and a belly ("ventral"); therefore they also have a left side and a right side.

By symmetry, I understand that divisions of the body along some plane be similar. Now, if you have a head and tail, isn't the horizontal symmetry lost (head and tail look different) ? Similarly, for a vertical division, a different looking belly and back also destroys symmetry along this axis.

An organism whose head and tail are exactly the same (you can't even make out if something is head, and the other, tail), is perhaps "actually" bilaterally symmetrical (along the horizontal axis).

What am I missing here ?

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You are missing that "bilateral symmetry" does not mean "the divisions are the same on some arbitrary plane" it means "the divisions are the same on one specific plane".

That specific plane for animals with bilateral symmetry is on the mid-saggittal plane that divides the body into left and right. You won't get symmetry if you bisect in any other plane. If you do get symmetry in a different plane, then you are no longer talking about bilateral symmetry but rather some other type of symmetry, such as radial symmetry, spherical symmetry, or biradial symmetry.

Note also that although many animals do not have perfect bilateral symmetry in their internal organs (humans, for one), they are still considered to be bilateral symmetrical, because the bilateral symmetry is the main organizing feature of the whole animal.

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Horizontal axis is a meaningless term.

Bilateral literally means bi=two Lateral=side, so one plane (two halves) of symmetry comparing sides, the symmetry is in comparing right to left.

having a front and back create alone (no top and bottom or left and right) would create something like radial symmetry. add a diffrence in top and bottom and you get bilateral, in which left and right are the only plane in which one side mirrors the other. Consider this image. An organism where you can't tell one end form the other would be a sponge things with no symmetry or spherical symmetry, symmetric across all possible planes.

Horizontal axis could mean anything, it could mean three different things(symmetrical top to bottom, symmetrical front to back, or symmetrical left to right) that's why we use terms like bilateral. So you need to qualify what you mean by horizontal. Horizontal is not an axis it is a plane, and I know of nothing symmetrical along that plane (top vs bottom).

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