I have in fact used powerlifters as the basis of the comparison in an effort to weight the picture as heavily as possible against my own case, i.e. to present a best possible case scenario from the point of view of the dinosaurs.
Photos courtesy of Chaillet's Gym, Suitland, Md. Dale Jacobson photographer.
My demonstration that sauropod dinosaurs could not exist in our present world is simple, logical, and reproducable. You scale any lifting event by dividing through by 2/3 power of weight. This inverts the effect of weight rising with the cube (with volume) of an increase in dimension while strength rises only with the square, being proportional to cross-section. This is called isometric scaling, and is the only true method of scaling.
For athletes built along very similar lines, typically champion lifters from around 150 lbs to around 220, championship lift numbers all but entirely line up (become the same number) when divided through by 2/3 power of weight. This form of scaling allows you to see who, amongst the champions of the various weight divisions, has actually done the "best" lift, regardless of size.
Thomas A. McMahon and John Tyler Bonner (On Size and Life, ISBN 0-7167-5000-7) describe this phenomena:
"Weight lifted in body weight classes up to 198 lbs. is precisely proportional to the .67 power of body weight, that is the 2/3 power of body weight in animals scaled by isometry."
Past 200 lbs. or thereabouts, the athletes begin to get thicker and more heavily muscled without getting much taller, and the system breaks down somewhat. It is obvious, however, that for determining lifting capabilities for the same man scaled to different sizes, the system is perfect since symmetry would always pertain.
This says that you can solve for the point at which any particular athlete would experience as much difficulty just standing as with a max squat or dead-lift effort simply by adding the man's weight to the bar and dividing through by 2/3 power of weight, and equate that to a number divided by 2/3 power of itself, e.g. for Kazmaier doing a 1000 lb squat or deadlift,
1340/340^.6666 = x/x^.6666
or just under 21,000 lbs becomes the point at which just standing becomes murderously hard.
Mr. Kazmaier tries his hand at the Scottish passtime of stone lifting. If you have to ask how much it weighs, you probably shouldn't try to lift it.
Like all top lifting athletes, his legs amount to roughly 50% of bodyweight. The same could never come close to being true for a sauropod, which needed much of its body weight for the digestive apparatus for handling leaves and low-value foods:
The sauropod shown is Wayne Throop's favorite rendition of a brachiosaur, or what I would call a sword-and-sorcery (fancifully muscular) brachiosaur. Even so, the sauropod's body is seen to be a joke compared to Mr. Kazmaier's as far as musculature is concerned, its legs not even as large or strong as Mr. Kazmaier's arms, much less his legs.
A sauropod dinosaur standing next to Mr. Kazmaier at the same weight, is seen to have something like a third of the available musculature, if that. Kaz lives at the top of the food chain, and is mostly muscle; the saur lives at the bottom, and his body is mostly gut and digestive system for processing leaves and other low-value foods. And, while structural differences conceivably could make standing slightly easier for the saur than it would be for a version of Kaz with equal musculature, there isn't enough structural difference in the world to compensate for the difference in musculature which would actually be seen. Again, it is known that muscle tissue is nearly identical for all vertibrates and there is no way to believe that the saur could be close to as strong as a version of Kazmaier at the same weight.
If Mr. Kazmaier could not stand over 21000 lbs., than neither could the saur. Again, even adding a near maximal bench-press figure into the bargain (adding 600 lbs to the numerator on the left in the equation above) and solving for:
1940/340^.6666 = x/x^.6666
does not allow Mr. Kazmaier to stand at any more than 70,000 lbs for a one-second effort, and since sauropods actually did get to sizes which would work out to 180 tons in our world (ultrasaur), they could not possibly have experienced gravity the way we do.
Again, beginning with 360-lb. versions of both Mr. Kazmaier and the sauropod and scaling to the 21,000 lb. size at which only a near maximal effort would allow Mr. Kazmaier to stand is entirely the same thing as simply putting the two on a planet with sufficient gravity to make standing a maximum effort for Mr. Kazmaier. Is the Sauropod, with only a small fraction the musculature, then going to walk around comfortably? Is he going to walk around comfortably at 17 times that weight, the 180-ton figure which Christopher McGowan gives for the ultrasaur, while Mr. Kazmaier would be crushed and suffocate at that same weight?
Note well: I have not demonstrated that sauropod dinosaurs would be impossible in our world by some small margin; I have demonstrated that they would be many times heavier than what is possible in our world. The only shot which Wayne Throop, Hokkanen, or anybody else has at disproving this thesis is to demonstrate some difference in structure which would allow the sauropod, with a small fraction the musculature of Mr. Kazmaier, to walk around comfortably at an order of magnitude greater size than that at which Mr. Kazmaier could even stand for a one-second effort. That is ludicrous.
Moreover, I have shown and this WWW page documents the fact that this impossibility which sauropods would face standing in our present world is not an isolated phenomena, but is part of a big picture view, which is supported by many other observations.
Mr. Throop and others of the talk.origins regulars have never even attempted to address more than one of the several facets (torque) of the dilemma involving sauropod necks.
Again, scientists have noted the impossibility of sauropods holding their necks upwards due to blood-pressure problems. Nonethtless, holding their necks outwards in the manner now being put forth would entail at least four insoluble problems:
Further, the historical veracity of the solar-system configuration which would bring about attenuated gravity on Earth is now well documented, as one notes from several of the articles on this WWW page.
The most obvious characteristic of Mesozoic flora and fauna was the upper limit of size. Pangaea's forests contained giant lycopods, horsetails and pteridophytes, trees over 100m in height. Today the survivors of these primitive groups are mostly small plants; the tallest fern is only 20m high, and height is only achieved by the conifers and flowering plant trees with specially strengthened trunks and good root systems. The dinosaurs produced the largest terrestrial animals the world has ever known. Some weighed more than 80 tonnes, as much as 20 large elephants, but old views that they were slow, clumsy animals have been superseded by evidence that they were fast, active and probably warm-blooded,. The weight which a column can support varies as the cube of its linear dimensions and therefore the heavier the animal, the proportionally shorter and thicker the limb bones. The dimensions of an elephant's limb bones are approaching the maximum limits of size which physical forces permit and are already tending towards disproportionate thickness. Yet dinosaurs were of such a degree of magnitude heavier, that the larger herbivorous sauropods were traditionally thought of as wallowing permanently in swamps to take the weight off their feet. However, there is evidence that they were completely terrestrial and the large, bipedal carnosaurs, such as Tyrannosaurus, were manifestly built for running with hind limbs more slender in proportion to their bulk than those of an elephant. If gravity were less, then animals could be larger and still be active with relatively more slender limbs than an elephant. The Pterosaurs, or flying reptiles, are another case in point. Fossil specimens with wing spans up to 8m were once regarded to be at the limit of size for any airborne creature, even given that their bone structure was even lighter and stronger size for size than modern birds. Then Quetzalcoatlus specimens were found with wing spans up to 15.5m and pronounced at beyond the engineering limits for a living flying machine. Recent considerations of the circulatory systems of the larger dinosaurs suggest that the normal heart/lung construction would be insufficient to keep the brain supplied with oxygenated blood. The problem of explaining away the apparent defiance of physical laws by so many of the Mesozoic plants and animals is solved easily by an assumption of lowered gravity. Is it just coincidence that such forms of life should be abundant at the very period when all the continental areas were grouped into one land mass ?
1.Combing the world for high-ball weight estimates for elephants and low-ball estimates for sauropod dinosaurs. In particular, Throop cites what he takes for weight figures for several elephants which are in excess of the 21000 lb. figure which I claim is an outside limit for land animals today, claiming thus to show my own calculations to be fatally flawed.
2.Claiming that the degree of attenuation required to allow sauropods to feel about as heavy as elephants do now is not feasible or possible.
3.Citing a paper by H.E.I. Hokkanen of the Univ. of Helsinki published in the 1986 edition of the Journal of Theoretical Biology, claiming to demonstrate that an outside figure for weight for land animals would fall between 220,000 and 2,200,000 lbs., or possibly even be somewhat higher than that.
Monkey Business. Aside from the three serious objections, several non-serious objections have also been noted, most notably the claim that humans are somehow too weak to use in such a comparison because chimps have stronger arms than we do.
Item 1. can be shown to amount to guesswork and probably also boasting (the Guiness figures) in the case of elephants. In particular, it is shown that even if an elephant were to go slightly over the 21,000 lb. figure (there is no evidence that any have), it would not disprove my thesis. The low-ball weight estimates for dinosaurs are immediately seen to be irrelevant, since even they are far too high.
Item 2. would require a time machine for a complete answer to, and the most I can do by way of rebuttal is to note that the system being proposed by Talbott, Grubaugh, Bass, Cardona, Cochrane, and others would exert tidal pull, and that the evidence in support of this antique alignment is not imaginary or small. Beyond that, the people making the claim involved are assuming that only the tidal pull of the Saturn configuration was involved in the gravitational attenuation. Harold Tresman notes that the far more powerful Electro-magnetic fields of the Earth in prehistoric times were mainly responsible for the attenuation.
Item 3. can be shown to be massively in error, and to amount to an attempt to make a recognized problem go away by wishful thinking and by playing a lot of games with numbers and, in fact, could best be described as an exercise in numerology.
Christopher McGowan is curator of vertebrate paleontology at the Royal Ontario Museum, and notes (Dinosaurs, Spitfires, and Sea Dragons Pages 96 and 97) that African elephants are the larger of the two groups of elephants (African and Asian), weighing "up to five or six tons". He cites an elephant at the Toronto Zoo which was the largest specimen in North America and was weighed posthumously at 14,300 lbs.
The most serious and authoritative book which I've been able to find regarding elephants is "Elephants, Majestic Creatures of the wild, ISBN 0-87596-143-6, Consulting Editor Jeheskel Shoshani, PHD. The cover leaf reads in part:
"Here, assembled in one volume by a team of international experts, is the most authoritative, up-to-date account of this extraordinary creature... A team of internationally renowned authorities from all over the world has provided the text for this publication. The contributers are:
Dr. Larry D. Agenbroad Dr. Esmond Bradley Martin Mr. Anthony C. Beilenson Mr. Jeffrey A. McNeely Dr. Lucia Caloi Dr. Vil:tor M. Mjl:hels~n Dr. Edwin H. Colbert Ms. Cynthia Moss Mr. J. C. Daniel Dr. Ronald Orenstein Mr. Yang Dehua Ms. Mary Ann Owens Dr. lain Douglas-Hamilton Dr. Maria Rita Palombo Dr. P. S. Fasa Ms. Katherine B. Payne Dr. John F. Fisenberg Dr. Joyce H. Poole Dr. S. Keith Fltringham Mr. Ian M. Redmond Dr. Daniel C. Fisher Dr. Michael J. Scmidt Dr. Nicholas Georgiadis Mrs. Daphne Sheldrick Dr. Anthony J. Hall-Martin Dr. Jeheskel Shoshani Dr. DIrriti K. Lahiri- Mrs. Sandra Lee Shoshani Choudhury Dr. Sylvia K. Sikes Dr. William R. Dr. Kes Hilliman Smith Langbauer, Jr Mr. Bucky Steele Dr. Richard M. Laws Dr. Pascal Tassy Dr. Richard E. Leakey Mr. C. Dale Tuttle Mr. John Lehnhardt Dr. Philip J. Viljoen Dr. Jerold M. Lowenstein Dr. Kenneth C. Wylie
Page 40 provides a tabular rundown of elephant statistics and parameters, including:
MAJOR DIFFERENCES AMONG SUBSPECIES OF ELEPHANTS WITHIN THE AFRICAN ELEPHANTS, LOXODONTA AFRICANA Bush subspecies Forest subspecies (L.a. africana) (L. a. cyclotis) Weight 4,000-7,000 kilograms 2,000-4,500 kilograms (8,820-15,430 pounds) (4,410-10,000 pounds) Height at shoulder 3-4 meters (10-13 feet) 2-3 meters (6 feet 7 inches-10 feet).......
The 15,430 lb. figure obviously pertains to at least one 13' specimen, which is ballpark for the largest they ever get. Thus we see that there is a general concensus amongst experts that the largest elephants get to a size range of 14,000 - 16,000 lbs.
McGowan, cited above, notes the extreme difficulty of actually weighing elephants, alive or dead, and leaves one with the clear impression that most such weight figures are little better than guesses. The highball weight figures which Throop cites for elephants are a combination of guesswork and games with numbers. Nobody has ever weighed an elephant and gotten such numbers.
There is one more little consideration to note here. I have claimed that any animal has to be able to stand up (in case he should slip or fall or wish to lie down for whatever reason or whatever. That is certainly true if you consider an animals life as a whole; nonethtless, elephants never stop growing and it is conceivable that these very largest specimens of African bulls, the 14,000 - 16,000 lb. specimens, representing a tiny percentage of all elephants, may be spending the last ten years or so of their lives without coming off their feet, simply availing themselves of the graviportal structure of their bodies to sustain the weight until the end.
Thus, it is even conceivable (in theory if not in reality) that an elephant might reach a size slightly above that which I note as the maximum at which any animal could hope to stand, i.e. the weight figure you get by scaling Mr. Kazmaier to a size at which standing becomes a near maximal effort. It is possible that even at 15,000 lbs. or thereabouts, these largest specimens are in such a condition, i.e. if they ever fell or got off their feet, it would be all over.
A sauropod dinosaur, however, would be above that size from early childhood, and it is inconceivable that their entire existence depended on never sitting down, never falling, never laying down for any reason from early age, and that they thus dominated the Earth for tens of millions of years.
So much for item 1. Again, item two would require a time machine to altogether refute and I do not own one. I would refer readers to the text files containing evidence which David Talbott, Dwardu Cardona, and others have assembled.
Hokkanen begins by claiming that a maximum weight limit for land animals is "suggested to lie" between 220,000 and 2,200,000 lbs., and that "a possibility for a still higher mass, in case of new adaptations, is not excluded". This number (the 220,000 - 2,200,000 lb. figure) is then derived via what I would regard as an exercise in numerology. He in fact ends up claiming that the same figure arises from consideration of stress on bones as well as from consideration of muscular stress and that has to raise immediate alarm bells for anybody familiar with any sort of realities involving lifting, since it is common knowledge that bones will generally support a much greater weight than the animal which owns them could lift or otherwise stand up with.
Hokkanen shows a disinclination for dealing with real things early on, beginning with an analysis of stress on a one-legged animal:
He also notes the nature of allometric scaling, i.e. Muscle-Mass = a * Body-Mass^b,
or in plain language, muscle mass equals some constant times body mass raised to the power of a second constant, in which the pair of constants, a and b, "are parameters to be determined from theory or measurements".
Very obviously, in the case of dinosaurs, these allometric scaling constants will amount to nothing more than a wild guess, although that does not stop Hokkanen from using them.
What is much worse is that, aside from being wild guesses, allometry numbers are all based on today's reality with respect to gravity and assume that. Thus, attempting to use a size limit for animals derived in this manner as an argument against the thesis of attenuated gravity in antique times (Throop is certainly guilty of this whether or not Hokkanen is) amounts to an exercise in circular reasoning.
Hokkanen proceeds into a discussion of stress on bones, which I view as largely irrelevant. Bones do not, in fact, lift weight; muscle lifts weight. If Hokkanen or others wish to demonstrate that a brachiosaur's bone structure might support 220,000 - 2,200,000 lbs, they can be my guests; the idea that one of them could LIFT such a weight or, equivalently, stand at such a weight in our world as it is now constituted, is preposterous as I have noted.
He then (pp 495 ff) begins a discussion of muscle strength, with the following diagram:
and proceeds to derive the figures noted by equating the torques shown, i.e.
Dp * Fm = L * Mg,
in which Dp is the short distance shown, Fm is muscular force, L is the long distance shown.
We note at once that the entire process will be very sensative to small changes in the short distance Dp and that estimates of Dp for sauropods could not be much more than guesswork. We also note that, depending on your point of view, Hokkanen may or may not be leaving out a trigonometric function since the tricep muscle shown is not pulling straight away on the bone attachment.
He then goes on to note that the muscle force required (Fm) is proportional to the square of the (unknown) muscle diameter, and proceeds to derive the muscle diameter using an estimate of muscle mass based on allometric tables, and the force Fm as
Fm = SIGMAm * Muscle-Mass / (RHOm * Lm)
in which RHOm is the theoretical maximum isometric stress which muscle tissue can produce, which he gives as 3*10^5 Newtons per meter squared, citing Wells, 1965 as a reference.
He then notes that, using allometry values for a 50 killogram animal, he derives a maximal size for land animals roughly the size of an African elephant and that, being somewhat less than happy with that result, he next proceeds, noting that the result is "very sensative to changes in [allometric] parameters i.e. that the system is ill-conditioned, to use the maximal values of allometric parameters within the 95% confidence limits noted, and derives the 220,000 - 2,200,000 lb. figure.
A minimal listing of things which Hokkanen has done wrong or overlooked would have to include the following:
1.He has not, as I have, included any consideration of anything known and real in his study of lifting capabilities.
2.The dependence upon the short distance Dp in his model is probably ill-conditioned. Certainly, this distance could not be known accurately in the case of sauropods.
3.Allometric parameters for a dinosaur are basically guesswork.
4.The dependency upon allometric parameters is admittedly ill-conditioned, yet Hokkanen use the maximum possible value in deriving his result.
5.Allometric parameters for known animals, the entire basis of the study, are based upon the assumption of today's gravity. If it were true (and it is) that the model of the antique system which I, David Talbott, Ev Cochrane, and others adhere to is the correct one, then an estimate of allometric parameters for a sauropod based on today's realities could not possibly be valid. This in fact amounts to another case of circular reasoning.
6.The use of a maximal stress per cross-section of muscle figure is a gross oversimplification. In particular, it leaves out the entire question of friction and muscle binding which have to increase as creatures become progressively more bulky and powerful. This is, in fact, the reason that 250 lb. athletes will scale out to a somewhat greater weight of barely standing than Kazmaier does, not that that helps the sauropod since, again, the situation does not get better as you get bigger.
7.Hokkanen claims to derive the same upper limit of size for land animals from considerations of bone as from considerations of muscle, a result which flies in the face of all common experience.
Hokkanen might could be forgiven overlooking the circularity involved in using allometry the way he does since the notion of attenuated gravity in prehistoric times is not yet common knowledge. Other than that, this paper is or should be an embarassment, and certainly does not amount to a rational case against my own thesis.