Re: Cnidaria versus ctenophora


"Lorentz" <drosen0000@xxxxxxxxx> wrote in message news:f5pb3b$2u95$1@xxxxxxxxxxxxxxxxxxxxxx
Also, as I understand it, there is a difference between bilateral symmetry
and 'bi-radial' symmetry as seen in the ctenophores.
I agree. I am just thinking as a physicist who has studied
molecules. Molecules are classified by group theory. I haven't seen
evolutionary biologist refer to the group theory very often. Maybe
they should.

I ought to know something about the crystalographic point groups, but
I don't.

The ctenophores, as you say, have a biradial two-fold symmetry.
However, they also have a reflection symmetry. Symmetry groups are
determined by the group operations that leave the system unchanged.
Bilateral symmetry, to me, refers to systems that are invariant to a
reflection. However, there is no reason that other group operations
can't leave the system invariant.

Lets look at your diagrams, allowing only in-plane rotations and
reflections.

This diagram has bilateral symmetry:

O O
XXX
I agree that it has bilateral symmetry because there is a
reflection axis down the middle. The system is invariant to that
reflection. I also agree that it is not biradially symmetric because
the is no two-fold rotation that leaves the system invariant.I would
designate this system as invariant to the simple point group
C_2.

This diagram has bi-radial symmetry

O
XXX
O

I agree because it is invariant to the two-fold rotation. However,
it is also invariant to reflection. There is a reflection axis that
extends from O to O. A reflection through that axis leaves the system
invariant. ITo some biologists, the reflection axis would make it
bilateral. ...

I have to disagree. Implicit in the diagrams so far has been the assumption
that there is a distinction between top and bottom (i.e. between into the
paper and out from the paper). So a reflection in the plane you suggest
would alter the chirality. Not bilateral.

You get this:
OX
X
XO
which rotates to this
O
XXX
O
You can't superimpose.

But, as it happens, I think that the ctenophores may lack a top/bottom
distinction - at least Dawkins' photo of the "Venus's girdle" looks that
way. So you get bilateral symmetry anyways. After you do the reflection,
just turn it over to see that you haven't changed the chirality.


.

Relevant Pages

  • Re: Cnidaria versus ctenophora
    ... The ctenophores, as you say, have a biradial two-fold symmetry. ... they also have a reflection symmetry. ... can't leave the system invariant. ... This diagram has bilateral symmetry: ...
    (sci.bio.evolution)
  • Re: A question about the phase difference of the beam splitter.
    ... If one beam entered at ... then symmetry about the surface would imply constructive ... avoid violating conservation of energy, ... reflection or microwaves with a mesh ...
    (sci.optics)
  • Re: Chez Watt: Re: Granite, Symmetry, and ID - Summary
    ... There is no reflective symmetry, rotational symmetry, point ... There is no point about which David is symmetrical in any way. ... symmetries to get this point across (i.e., glide, reflection, glide ... the right eye is not ...
    (talk.origins)
  • Re: Symmetry of "Improper Rotations"
    ... Of course it's a mirror image of what you started with. ... Rotation of a plane ... symmetry - i.e., reflective rotational symmetry. ... symmetry, and _no_ reflection symmetry. ...
    (talk.origins)
  • Re: Cnidaria versus ctenophora
    ... they also have a reflection symmetry. ... can't leave the system invariant. ... I looke at the diagram and realized that I may have made ...
    (sci.bio.evolution)
Loading