Good Math/Bad Math

Tuesday, March 21, 2006

Crackpot math: Velikovskians and Dinosaurs

As I always say, one of the best ways of recognizing a crackpot is through math. You can make nice arguments about all sorts of theories using words, but if the math doesn't back it up, the words are worthless.

One of my favorite examples of this comes from back in the days when I was active on the usenet newsgroup, where there were a bunch of Velikovskians. My personal favorite was a wacko named Ted Holden. Ted believes that gravity is not the dominant force in orbital mechanics, but that it's all electromagnetic. (But of course, there's nomath in that argument!)

Ted also beleives in a strange theory where Saturn used to be an "electromagnetic star" positioned very close to the earth, and that this created a zone of weakened gravity on earth. His argument for this is based, among other things, on the idea that dinosaurs couldn't possibly have stood in current earth gravity. Why not? Well, it's obvious! If we scale a human weightlifter up to the size of a dinosaur, he won't be able to stand up.

In Ted's own words:

Any animal has to be able to lift its own weight off the ground, i.e. stand up, with no more difficulty than Kazmaier experiences doing a 1000 lb. squat. Consider, however, what would happen to Mr. Kazmaier, were he to be scaled up to 70,000 lb., the weight commonly given for the brontosaur. Kazmaier's maximum effort at standing, fully warmed up, assuming the 1000 lb. squat, was 1340 lb. (1000 for the bar and 340 for himself). The scaled maximum lift would be a solution to:
1340/340^.667 = x/70,000^667 or 47,558 lb..
He'd not be able to lift his weight off the ground!
A sauropod dinosaur had four legs you might say; what happens if Mr. Kazmaier uses arms AND legs at 70,000 lb.. The truth is that the squat uses almost every muscle in the athlete's body very nearly to the limits, but in this case, it doesn't even matter. A near maximum benchpress effort for Mr. Kazmaier would fall around 600 lb.. This merely changes the 1340 to 1940 in the equation above, and the answer comes out as 68,853. Even using all muscles, some more than once, the strongest man who we know anything about would not be able to lift his own weight off the ground at 70,000 lb.!

Moreover, Kazmaier is using glutteal and lower back muscles in the squat, and pectorals in the benchpress, i.e. extra muscle groups which the sauropod he is being compared to would not be assisted by in standing. Any tiny advantage in leverage which a sauropod might have over the human lifter for any reason, would be overwhelmed by the huge edge in available musculature and the usage of the extra muscle groups on the part of the human in the comparison.

To believe then, that a brontosaur could stand at 70,000 lb., one has to believe that a creature whose weight was largely gut and the vast digestive mechanism involved in processing huge amounts of low-value foodstuffs, was somehow stronger than a creature its size which was almost entirely muscle, and that far better trained and conditioned than would ever be found amongst grazing animals. That is not only ludicrous in the case of the brontosaur, but the calculations only get worse when you begin trying to scale upwards to the supersaur and ultrasaur at their sizes.

How heavy can an animal still get to be in our world, then? How heavy would Mr. Kazmaier be at the point at which the square-cube problem made it as difficult for him just to stand up as it is for him to do 1000 lb. squats at his present size of 340 lb.? The answer is simply the solution to:

1340/340^.667 = x/x^.667

or just under 21,000 lb.. In reality, elephants do not appear to get quite to that point. McGowan (DINOSAURS, SPITFIRES, & SEA DRAGONS, p. 97) claims that a Toronto Zoo specimen was the largest in North America at 14,300 lb., and Smithsonian personnel once informed the author that the gigantic bush elephant specimen which appears at their Museum of Natural History weighed around 8 tons.
Again, in all cases, we are comparing the absolute max effort for a human weight lifter to lift and hold something for two seconds versus the sauropod's requirement to move around and walk all day long with scaled weight greater than these weights involved in the maximum, one-shot, two-second effort. That just can't happen.

Yes indeedy - because a scaled version of the weightlifter Bill Kazmaier couldn't bench press his scaled weight if he were the dinosaur, a dinosaur couldn't possibly have stood up.

That's the argument: if a human scaled up with perfect proportions to the weight of a dinosaur, he wouldn't be able to stand up. The only math is the multiplication needed to scale a human weightlifter to dinosaur size.

What's wrong with the math? Mainly the fact that it's totally invalid.

It's true that pretty much, muscle is muscle. There's no dramatic difference between the strength of muscles on different animals. But: there's a huge difference in anatomy.

The weight that a muscle can lift isn't just based on how much tension the muscle can create. It's based on the structure of the thing it's pulling against. Remember the lever principle: the torque that I can exert by pushing or pulling on a lever is proportional to how far I am from the fulcrum. Muscles act the same way: to know how much a muscle can lift, you need to know the pivot points and the attachment points, to work out the effective length of the lever arm.

Humans doing squat lifts or bench presses are terrible at this. Our joints are extremely skinny; the attachment points are set up with relatively small moment arm - which means that our joints do not lift well. Look at a human skeleton's knee joint - and compare it to a dinosaurs knee joint:

Look at the width of the bone at the knee joint! That's one serious lever. Measuring it with some screen ruler tools, I get human knee joints as around 2x the width of the knee bone, but that doubling is shared on both sides of the bone - it's close to symmetrical. The dinosaur bone is very assymetrical, and it projects forwards approximately 4x(!) the width of the lower leg bone. Ignoring any other factors, the dinosaur will have at least three times the lifting strength in its leg of the human. And the knee is a relatively strong joint for a human; our backs are terribly weak in an upright posture; comparatively, dinosaurs had very different vertebrae and hips from us, which sacrificed mobility in exchange for strength. (See, for example, here.)

So does it make any mathematical sense to extrapolate what a dinosaur could do based on comparison with a scaled human? Hell no. The math just doesn't support it.


  • I think somebody enjoyed those "Giant Amazon Women" cartoons a little bit too much.

    By Blogger Thomas Winwood, at 8:33 AM  

  • Is this really a problem with bad math? It looks more like bad anatomy. Math, per simpliciter, cannot deliver observable facts.

    By Blogger SOB2, at 10:05 AM  

  • It's a problem with incorrect application of math, which is bad.

    By Blogger Julia, at 10:28 AM  

  • I have to agree with sob2. Ted's problem wasn't math. We don't say that he used the wrong operations or plugged in the wrong numbers. You might say he used bad physics, since he didn't look carefully at the system he was claiming to model. And he certainly ignored anatomical differences. But the math itself? Eh.

    By Anonymous jackd, at 11:08 AM  

  • Ted's problem was indeed the math. Math is not just manipulation of numbers. Otherwise you're claiming that using the Drake Equation is not bad math; but since using the Drake Equation *is* bad math, we have found a contradiction! QED! #P

    By Anonymous Guy, at 11:49 AM  

  • I want to hear more about Ted's crazy Electromagnetic Star Saturn idea. It sounds positively loopy.


    By Anonymous Anonymous, at 11:58 AM  

  • Ted clearly used math to drive home his point. Many, many people think that math, like computers, is infallible. For math, they seem to think that 2 + 2 = 4: 3 or 5 is right out. It is certain. For computers, they don't really know how they work, but suspect that there is some math behind it, and computers don't make any mistakes. The quote from Babbage says it all:

    On two occasions I have been asked [by members of Parliament!], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

    By Blogger Stephen, at 12:01 PM  

  • Ted's argument may not be pure math, but it does mis-use math to draw an incredibly wrong conclusion. As I see it, the only way to say that the whole scaling-Kazmaier-up thing isn't bad math is just saying that it's so very bad that it doesn't count.

    The problem with that approach is: it doesn't work. The faux math of arguments like Ted's does convince people sometimes. They believe that math gives right answers, and they don't know enough to recognize that it's being misused. So they wind up accepting a thoroughly bad argument, because it contains what looks like math.

    But in the end, it's a bad argument supported by thoroughly awful math.

    By Blogger MarkCC, at 12:55 PM  

  • Ted Holden? There's a blast from the past. He used to hang around on the Ada (programming language) forums and drive us completely bats. Do you mean to say that he was annoying other people too? Hard to believe; I'd have thought he would have had to work full time to misunderstand Ada and the programming profession in general so completely. Where Is He Now?

    By Blogger Bob Munck, at 1:37 PM  

  • Bob:

    Ted is a multidimensional menace. He never limited himself to annoying one group of people. He was a nutso ant-Ada bigot (I never understood why, if he hated Ada so much, he spent so much time in a forum of Ada users); a nutso anti-evolutionist; a nutso velikovskian, and if I recall correctly, a nutso ultra-libertarian.

    I have no idea of what he's doing now; my one reservation about posting this critique was that it's likely to draw his attention!

    By Blogger MarkCC, at 1:56 PM  

  • Bob:

    Ted is a multidimensional menace. He never limited himself to annoying one group of people. He was a nutso ant-Ada bigot (I never understood why, if he hated Ada so much, he spent so much time in a forum of Ada users); a nutso anti-evolutionist; a nutso velikovskian, and if I recall correctly, a nutso ultra-libertarian.

    I have no idea of what he's doing now; my one reservation about posting this critique was that it's likely to draw his attention!

    By Blogger MarkCC, at 2:13 PM  

  • It's a little stale, but Ted may still be around.


    By Anonymous Anonymous, at 3:41 PM  

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