RE: Ornithischia/Saurischia Ilium Mass Distribution Hypothesis

["Mike Milbocker" <mmilbocker@psdllc.com>]

Jaime A. Headden wrote:

>While acknowledging that this is a very neat theory, that one can
determine ornithischian from saurischian pelves under such criteria,
and/or that one can determine that such mass distribution is indicative of
which group an ilium falls under, one should have a few test ilia that
provide such a sound statement. As in, one can determine that the ilium of
*Alxasaurus* is saurischian (it is) despite it's arrangement of elements
resembles that of several ornithischians as well as advanced sauropods.

I first came on this idea when comparing a mount of Caudipteryx to a mount
of juvenile Psittacosaur Mon. and noticing that the shape and size of the
ilia were remarkably similar. To my horror, I noticed I had mounted the
Caudipteryx ilia backwards with respect to the psitt. mount(or the two halfs
on the wrong sides)so that the large lobe was pointed cephalo. I had done
this based on the ischium articulation and the direction I wanted it to
point w.r.t. the rest of the skeletal structure. Concerned, I turned my
attention to a well articulated specimen of P. Sinesis and found, like the
P. Mon., it had the large lobe of the ilium pointing caudal. After much
further research, looking especially at "miscellaneous" theropods and the
sauropods generally, I came to the reluctant conclusion that mass
distribution was quite powerfully indicative.

Although I don't have any Alxasaurus ilia at my disposal, the following link
http://the_dinosauria.tripod.com/alxasaurus.html clearly shows cephalo mass
distribution using the plane-view methodology described earlier. In my mind,
this is not a borderline case and strongly indicates Saurischia. Although, I
agree the arrangement of the pubis and ischium suggest Ornithischia. I also
concur with you fully on the need to study real ilia.

 >Where precisely on these primitive theropod ilia is the moment of
minimum inertia?

The moment of inertia is a measure of the work one must expend in rotating
an object about a chosen axis. For example, consider a pencil, it is far
easier to spin a pencil as if it were a wheel axil than to spin it at its
mid-point as if it were an airplane prop. The axis of minimum moment of
inertia is the axis of the pencil, and the axis of maximum moment of inertia
is the perpendicular at the midpoint of the pencil. Generalizing to all
geometries, one arrives at the Formal Hypothesis, which actually can be
stated in a number of equivalent ways. My point is that the line along which
the division of the ilium should be taken is along the axis giving the
minimum moment of inertia.

>And pardon me for asking such a
question, but I am curious as to the method by which one arrives at this
point with only ilia.

Of the three bones of interest, the pubis, ilium and ischium only the ilium
is connected to the synsacrum. However, if the pubis and ischium are
particularly heavy they may play a counter-balancing role as seen in modern
birds. In this case a compensating higher order term involving all three
bones may be required. However, I have not met with an example where this
was necessary. Parsimony compels me to remain with the hypothesis as stated.

You will notice the hypothesis as stated yields a binary answer, Saurischia
or Ornithischia. However, perhaps more can be extracted. I noticed predatory
saurischian tend to have very large cephalo bulges in the ilium. So, if I
may be so bold, perhaps a ratio, mass of cephalo region divided by mass of
caudal region would provide a useful metric for determination of predatory
behavior, i.e., vigourous upper body activity. A similar mechanism can be
seen to be at work in the modern bird, where the abrupt deceleration due to
landing has evolved the triad of pelvic bones into a single fused
ossification. If I may be even bolder, very large ratios may be indicative
of furcula.

Regards, and thank you for your kind comments, Mike Milbocker

-----Original Message-----
From: owner-dinosaur@usc.edu [mailto:owner-dinosaur@usc.edu]On Behalf Of
Jaime A. Headden
Sent: Monday, April 26, 2004 4:32 PM
To: dinosaur@usc.edu
Cc: mmilbocker@psdllc.com
Subject: Re: Ornithischia/Saurischia Ilium Mass Distribution Hypothesis


Mike Milbocker (mmilbocker@psdllc.com) wrote:

<Formal Hypothesis: For any ilium of the Dinosauria, find the line L for
which the moment of inertia is a minimum; find the point H on the line L
which is the most cephalo for which a plane perpendicular to L and
containing H intersects a point on the ilium; find the point T on line L
which is the most caudal for which a plane perpendicular to L and
containing T intersects a point on the ilium. Now, find the point M
equidistant from H and T on L. A plane drawn through M and perpendicular
to L divides the ilium into 2 regions. If the mass of the cephalo region
is greater than the mass of the caudal region, the ilium is Saurischian,
otherwise it is Ornithischian.>

  While acknowledging that this is a very neat theory, that one can
determine ornithischian from saurischian pelves under such criteria,
and/or that one can determine that such mass distribution is indicative of
which group an ilium falls under, one should have a few test ilia that
provide such a sound statement. As in, one can determine that the ilium of
*Alxasaurus* is saurischian (it is) despite it's arrangement of elements
resembles that of several ornithischians as well as advanced sauropods.

  Where precisely on these primitive theropod ilia is the moment of
minimum inertia? And pardon me for my dunce-itude for asking such a
question, but I am curious as to the method by which one arrives at this
point with only ilia.

  Cheers,

=====
Jaime A. Headden

  Little steps are often the hardest to take.  We are too used to making
leaps in the face of adversity, that a simple skip is so hard to do.  We
should all learn to walk soft, walk small, see the world around us rather
than zoom by it.

"Innocent, unbiased observation is a myth." --- P.B. Medawar (1969)




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