From: throopw@sheol.UUCP (Wayne Throop)
: From: email@example.com (Michael Agney)
: Message-ID: <1lq21gINNfhg@gap.caltech.edu>
: While a lot of what Ted has to say (of what I've seen) seems unscien-
: tific (at best), I don't know what the current ideas about sauropods
: are. Were they land or sea creatures? If either, what of the problems
: posed by Ted?
They were land creatures. Some of the most convincining evidence of
this is the trackway evidence from the American Midwest. I recommend
glancing at the recent collection of papers
_Dinosaur_Tracks_and_Traces_, edited by Gillette if I recall, and which
seems available in most university libraries.
For readings on the general area of sauropod limits and adaptations, see
Alexanders' _Dynamics_of_Dinosaurs_and_Other_Extinct_Giants_. Ted's
favored reference, McGowan's _Dinosaurs_Spitfires_and_Sea_Dragons, also
provides good background (though apparently you have to read it more
carefully than Ted to see this, since many of Ted's favorite puzzles,
such as how sauropods could eat enough, and how they could hold their
necks out straight, are explained in that book. Note also that Ted
can't seem to get the spelling of McGowan's name right for two postings
in a row, even after having this pointed out to him numberless times.
He gets it right in his recent "sauropods" posting, but gets it wrong in
his recent "rationale" posting.).
Also consider Bakker's _Dinosayr_Heresies_. Ted often takes the
lifestyle points and metabolic rate arguments from Bakker's work, and
combines them with criticisims from McGowan's work to try to make it
seem as if there is some contradiction or problem in the field. This is
just mixing and matching points from conservative and radical camps in
dinosaur studies, and the apparent contradictions Ted comes up with
this way are essentially quotes out of context.
And finally, Daltons and Waldens tend to have several recent books
on hand, especially those that go along with recent PBS and cable
presentations on dinosaurs, that give very good overviews, including
some of the reconstruction work on the musculature and skeleton
of brachiosaurs, as well as the family tree of the sauropods,
explaining the differences between braciosaurids and diplodocids
that Ted has had so much trouble with in the past.
So much for reading material. For the rest of this post, I'll
repost my own analysis of "Holden Numbering", as Holden's
inaccurate use of square-cube scaling is often called in talk.origins,
as well as a repost of some information about the largest
dinosaur finds that shows they are all well within reasonable
limits for strength, no attenuated gravity needed.
( Of course, Ted has already "refuted" this material. For comments
on these refutations, see the companion posting on "Holden refutes
his critics", coming to a talk.origins-carrying node near you. )
Subject: Holden Numbering
Summary: explanation of the Holden Number, and why Ted gets it wrong
Previous-Postings: 920727 920816 920928 921213
First, just what is the Holden Number? It is the weight in pounds-force
over the square of the cube root of the mass in pounds-mass
of any given creature. So
cat | 10 2.15
human | 200 5.85
elephant | 10000 21.5
brachiosaur | 150000 53.1
What does this calculation mean? It is a measure of force (the lbs
weight) per available cross section (the lbs mass ^(2/3)). The
lbs mass cube-rooted and then squared because the mass is a rough
indicator of volume, and hence the ^2/3 power of mass is a rough
indicator of cross section.
Whence then the Holden Limit of 27? Well, if an animal is lifing more
than its own weight, we can add the additional force to the top of the
ratio, yielding a Holden Number which characterizes that lift. (This
addition of weight plus load is invalid in detail, but arguably works
moderately well as an adequate approximation.) Holden claims that
Kazmaier's 1000 lb squat represents a limit of performance for animals
Kazmaier's size or larger, and that the squat in general accurately
models the act of standing up, and thus he calculates
(1000 + 350) / 350^(2/3) ~= 27
to get a figure for the maximum possible Holden Number of any creature.
Since this is pretty close to the actual Holden Number for the largest
elephants, Ted then jumped to the conclusion that elephants are the
largest creatures that can exist.
There are many side issues, such as
- other primates can sustain weights far larger
- I've found references to three elephants larger than
the one Ted uses for comparison
- elephants in circuses have been reported doing acts with
HN larger than 30
Ted has explanations for all of these points, but showing why he is
wrong on all of them would be prohibitively tedious. Let's just address
Ted's frequent claim that efficiency tends to go up with larger sizes.
(One reason Ted often gives for this is the creature's "muscles binding
together". He has also said in this connection that "Ants probably
derive Holden numbers far above the 27 I mention".
But why bother with "probably"? Let's take a really large ant, and give
it tremendous strength: 1 gram of ant, lifing 100 times its weight.
This loads the dice in Ted's favor. Yet the HN of such an ant is less
than 15. Even such a goliath of an ant would have to lift 200 times
its weight or so before reaching HN 27. And more reasonably sized
ants would have to lift 500 or 1000 times their weight. Ted is
definitely mistaken here.
( Note: Guiness mentions some beetles that come close, but you will note
that those events don't involve lifting, but simply the point at which
their exoskeletons crush. )
Ted also frequently claims that "[...]layers of thick muscles will begin
to bind somewhat against each other" as size increases, and points to
the fall-off of square-cube-scaled performance in weightlifting in the
highest weight classes. Unfortunately, what Ted doesn't tell you is
that his theory of "muscles binding" can't explain the whole story,
because performance also falls off in the *lower* weight classes, and
that can't be due to Ted's "muscle binding" theory. Again, Ted is
So we can see that animals do NOT necessarily do worse on square-cube
corrected scales as they get larger. Now let's concentrate on just
why sauropod dinosaurs could do better than Kazmaier.
1) biped/quadruped differences
2) cross section differences due to non-proportional scaling
3) leverage differences due to non-proportional scaling
We can correct the Holden Limit to apply to quadrupeds by simply adding
the weight Kazmaier can lift with his arms to that he can lift with his
legs to get a rough idea. That modifies the formula to
(1660 + 350) / 350^(2/3) ~= 40
In the ballpark for a brontosaur, but still short of the HN for a
brachiosaur. But we can account for proportional scaling differences
between species by dividing by a more appropriate factor. We can't
really determine what that factor is easily, but we can get a ballpark
idea by using the bone thickness factor reported by Alexander and others
of (1/2.73). Ted calls this a "mysterioso, non-real-world" fudge
factor. Actually, it is based directly on observation, so it is, in
fact, a non-mysterioso real-world factor, despite Ted's claim. Ted also
says "bones don't lift weight, muscles do". Quite so, but I'm using
Alexander's numbers on bone thickness to scale the whole limb, muscles
and all. Note that this will give us a different scale completely, so
we have to do the figure for both Kazmaier and the brachiosaur:
(1660 + 350) / 350^(2/2.73) ~= 27.5
150000 / 150000^(2/2.73) ~= 24.2
( By coincidence, the limit number here turns out to be much the
same as the original Holden Limit. )
So, if we simply take nonproportional scaling into account, as Ted
refuses to do, we can see that at least the brachiosaur is within
the corrected limit.
Finally, we can add a factor correcting for leverage to our formula by
assuming that limb length scales as cube root of mass, while joint
radius scales as 2.73 root of mass. Working it out, we get this (note
that the limit this time is 22):
(1660 + 350) / (350^(2/2.73) * (350^(1/2.73)/350^(1/3))) ~= 22.6
600000 / (600000^(2/2.73) * (600000^(1/2.73)/600000^(1/3))) ~= 22.6
That is, a better estimate than Ted's of the limiting size of an animal
in 1G is about 600000 lbs. The largest plausible figures for sauropod
masses are half that. At large sauropod sizes, this means that limbs
only about 20 percent proportionally thicker than Kazmaier's are
required. And such legs would, indeed fit under a sauropod.
In fact, measurements made from human and dinosaur bones as reproduced
in library references shows sauropod bones *at* *least* that much
thicker (meaning that the leverage advantage is definitely there, and
that the cross section advantage is plausibly there.) A more detailed
posting of this fact was done some time ago.
Now, Ted's resolution of this "problem" is different. Instead of taking
into consideration a more detailed model, Ted persists with the
oversimplified Holden Number, exploits his confusion between one of the
slimmest of sauropods (diplodocus) and a rather more stout sauropod
(apatosaurus, or brontosaurus), combines this with the mistaken
impression that some of the larger mass estimates are calculated by
force estimation instead of volume estimation, and comes up with the
curious formula (against the original Holden Number scale remember,
where the limit is 27, not 22):
150000 / 500000^(2/3) ~= 23.8
Both methods account for sauropods. Ted does it by assuming
that sauropods were subject to 150000/500000 G effective acceleration,
or about one-third gravity. Why Ted's attempts to supply a reduced
effective acceleration fail, of course, is material for several
As for me, I can't see that the .3 gravity is required to solve the
"problem", because the assumptions behind the Holden Limit at 10 tons or
so in 1G are simply incorrect.
Subject: Holden and the superhumongoreallybigosaurs
Summary: Ted is basing his arguments on very scant evidence
:: From: firstname.lastname@example.org (Stan Friesen)
:: Message-ID: <email@example.com.COM>
::: Again, McGowan and others give out the weight for an ultrasaur as
::: 360,000 lbs,
:: What others?
: From: news@fedfil.UUCP (news)
: Message-ID: <169@fedfil.UUCP>
: Articles I've seen in newspaper and magazine accounts which, due to space
: limitations, I cannot always keep... The Avon Field Guide to Dinosaurs.
It is always well to remember that McGowan and others give out the weight
for an ultrasaur as 180 or so tons based on the assumption that it is
close to 100 ft long. But that is only the upper limit of a range of
guesses at its length.
:: In particular its accuracy is limited to the accuracy of the model.
:: And just how accurate do you think a model based on *one* *leg* is going
:: to be? (At the time McGowan wrote his book, only one leg from the
:: ultrasaur has been exhumed, so that was all that was available for
: I remember reading that collar bones, ribs, and other bones were
: uncovered in the late 70's. McGowan's book is dated 1991. What exactly
: are you talking about?
Actually, the situation is worse than Stanley points out, though
Ted is right that more than "a single leg" is known of Ultrasaurus.
Let's look at a very recent book (published 1992), organized around the
major finds of currently active researchers, and containing interviews
with them. The book is _The_Kings_of_Creation_, by Don Lessem. Let's
see what there is to see about Ultrasaurus. From the chapter on
sauropods, "Land of Giants", we have these points:
In the summer of 1972, Jensen went to Dry Mesa on a headline-making
hunt. "I was an obsessed man. I was going to find the oldest,
biggest carnosaur [meat-eading dinosaur], the bigger the better,
even though scientifically that means little."
He struck upon the shoulder blade of an enormous dinosaur [...]
A little figuring, based on comparisons of this shoulder bone and
vertebrae found nearby with those of other giant sauropods, put
the length of the new animal at eighty-two to ninty-eight feet
(or even 140 feet, if it proved to be related to the long-tailed
Diplodocus, as Jensen believes) [...]
That was the discovery of Supersaurus.
In 1979, Jensen was again digging around the Dry Mesa site, [...]
when he and his crew came upon another shoulder blade. This one
was nearly nine feet long, and broader than that of Supersaurus.
If not from an animal longer than Supersaurus, it certainly belonged
to a far heavier animal.
That was Ultrasaurus. But...
Jensen did not get around to formally dubbing Supersaurus and
Ultrasaurus until October 1985 [...]
Jensen didn't base his new genus on the intriguing giant shoulder
blade evidence. Ranterh he used one of several vertebrae found nearby
as his holotype -- the distinctive bone upon which hangs new species
or genus identification.
Jensen called his own diagnostic skills into question in a 1987
paper. There he took the unusual step of withdrawing his assignment
of a neck vertebra to Ultrasaurus. He redubbed it [..presumably this
means the vertebra..] a diplodocid, in keeping with the backbone's
And Jensen noted, the biggest scapula from Dry Mesa should be the
holotype for identifying Ultrasaurus. Now, however, he has changed
his mind again: "That was wrong. I was pressured to publish a lot
quickly. I assumed incorrectly it was Ultrasaurus." Now Jensen
believes the shoulder blade belongs to an unidentified brachiosaur,
but not Ultrasaurus. By this latest analysis the quary at Dry Mesa
would contain at least four different giant sauropods.
Not surprisingly, Jensen's reconsiderations of Ultrasaurus left
other paleontologists puzzled and displeased. Several doubt that
Ultrasaurus is an animal distinct from Brachiosaurus, and few think
Jensen's description and naming will stand the test of time. But
The Dry Mesa quarry is still producing new fuel for the dispute.
[.. a gargantual pelvis and other finds, some attributed to
Ultrasaurus by some, but nothing definitive..]
So. We see that the size was guessed based on a shoulder blade, and a
mismatched vertebra. Further, 100 feet long is only the longest of a
range of guesses, just as for Supersaurus. (It is typical of Ted to
take the longest of a broad and speculative range as definitive.
Perhaps this is because he is viewing things through accounts in the
popular press, which are in turn trying to make things sound as big and
amazing as possible.)
So, let's see what the best expert in the biz (after whom the
Ultrasaurus species, "Ultrasaurus macintoshi" was named) has to say.
McIntosh has examined all the bones in question. He was one
of the first outsiders at Dry Mesa after the giant pelvis was
found. He has worked with Gillette and has long been convinced
of the worthiness of Gillette's claim that Seismosaurus is a new
and singularly long animal. Of Ultrasaurus, he says, "It's known
from so few bones. I'm skeptical." McIntosh is not convinced that
Ultrasaurus is something new. Like other researchers, he thinks it
might be just a big Brachiosaurus. Its huge vertebra with a high
spike, used to name the animal, might belong to the rear end
of a diplodocid. Nor did the shoulder bones excavated at Dry Mesa
provide clear evidence for Ultrasaurus or Supersaurus in McIntosh's
mind. "But I thought all three were different." Still, it's
possible, says McIntosh, that "Supersaurus and Ultrasaurus might be
the same animal." As for Supersaurus, McIntosh is more confident
as to its identity, but not utterly convinced. "I'd say it's a
diplodocid with a two-thirds' chance of being new. But I hate
to speculate. [...]"
Of the Seismosaurus site, Lessem has this to say:
Unlike Jensen's Dry Mesa site, this one was not a jumble of bones
from many species, but rather the largely intact remains of one
Of the seismosaur, there is no doubt: it is a diplodocid sauropod
of 140 to 150 feet in length. It is by far the largest sauropod
for which complete a complete skeleton is available (and even it
isn't completely excavated, let alone prepared or mounted).
:: Try reading some actual journal articles on dinosaur weight estimates,
:: and you will see that they are generally considered to have about a 30%
:: (or higher) confidence bound. This is *very* crude, little more than
:: order of magnitude.
: 30% Off from 180 tones is still 120 tons and more. He still can't
: make it. Bill Kazmaier at that size would be able to lift less than
: half his weight off the ground, and Kaz is the most powerful creature
: his size or larger, lb. for lb. imaginable.
Ted has a limited imagination indeed. And, as I've already pointed out,
sauropods didn't have to be stronger "lb. for lb." (though Ted probably
means square cube scaled strength instead of lb. for lb. as he
actually says). But the main thing to note here is that Ted is missing
the ponit. The point is, WITH A SKELETON the weight estimates can be
off 30%. That's the best case, when a volumetric model made with full
information, and only guessing at the density. With no skeleton, as in
the case of Ultrasaurus, one is even guessing at the length. And the
guesses of length span 20%, corresponding to masses from under 100 tons
to 180 tons.
As more information is known about Ultrasaurus, the estimates are
tending towards the low end of the original range of guesses. Ted has
claimed that this re-evaluation was based on trying to get the weights
down under 132 tons, given by Guiness as a limit. But from above we can
clearly see that this is not the case. The re-evaluations are based on
featues of the bones themselves. So, far from interpreting the bones in
light of an attempt to get a known result, new results are being arrived
at because of newly noted features of the bones, or because of new finds
: Archimedes' technique could not be improved upon, assuming you have a
: good idea as to the general shape and size of the creature involved,
: which we do.
No, we do not, as I've amply demonstrated above.
The bottom line is, the largest example for which a full skeleton
is known is under 100 tons. Even the Ultrasaurus is plausibly
under 100 tons, based on the 20% range of sizes in the original
identification. Ted is basing his argument for masses over 100 tons
on very poor evidence indeed.
And, of course, Ted's unmodified square-cube scaling is invalid.
Wayne Throop firstname.lastname@example.org