Good Math/Bad Math

Monday, June 05, 2006

More AiG lying with statistics: John Woodmorappe and Noah's Ark

Today's sample of bad math is something I talked about way back in my talk.origin days in usenet; and which has also been discussed by lots of other people. I thought it was too old, too well covered to be worth taking time and space here, but I keep having people forward it to me, suggesting I post something on it here. So who am I to stand in the way of the desires of the readers of this blog?

Back in 1996, a guy publishing under the pseudonym of "John Woodmorappe" wrote a book called "Noah's Ark: A Feasibility Study." AIG has an article discussing the basic ideas of the book here, and it is this article that I'll be using as the focus of my post.

Woodmorappe's text purports to be a details study of whether or not it was technically feasible for the biblical story of the ark to be true. He tries to demonstrate the possibility of truth by purportedly showing how all of the animals could fit on the ark, and proposing mechanisms by which they could be fed, wastes could be disposed of, etc.

The AiG article focuses on that first issue: is it possible that the ark, as described in the bible, have enough room to fit all of the animals? They admit that the answer to this comes down to two questions:
  1. How many animals needed to be on the ark?
  2. How much space was needed for each animal?
They play a few games to try to reduce the number of animals that they need to make space for, ending up with 16000 individual animals. The reasoning to get that number of pretty questionable, but it's not worth quibbling over, because of what comes next.

Woodmorappe wants to figure out how much space is needed by 16000 animals. How does he do that? Easy. He figures out an average amount of space needed by each animal, and multiplies it by the number of animals. Doesn't sound bad as a way of making an estimate, right?

Except... How does he figure out how much space is needed by each animal?

He figures out the median size of the animals in the ark; and determines that the median-sized animal would need a space of .5 by .5 by .3 meters - that is less than 1/10th of a cubic meter per animal. Multiply that by the number of animals, and you come up with 1200 cubic meters. Not terribly much space at all - which would mean that there would be plenty of room for food for the animals.

So what's wrong?

There are two different figures in statistics that can be used as an 'average' value, the mean, and the median. The mean is what we normally mean by average: take all of the values, add them up, and divide by the number of values. The median is a way of selecting a "typical" individual to represent the average: take all of the values, lay them out in order, and pick the value in the middle.

Woodmorappe uses the median. The median represents a "typical" individual; it's the value in the center. The nice thing about the median is that it gives you an idea of what a typical individual is like, without having it shifted by outliers in your data. But it's useless for trying to extrapolate to things about the population - because the outliers are part of the population; you can't eliminate them from your calculations about the population.

For example, I've had 7 pets in my lifetime. Their weights were 18lbs (a big fat cat), 15 lbs (a tiny poodle), 20 lbs (a smallish mutt), 20 lbs (another mutt), 10 lbs (a normal sized cat), 18 lbs (another poodle), and 78lbs (a golden retriever).

The median size of my pets? Well, in order they were (10, 15, 18, 18, 20, 20, 78); so the median was 18 lbs.

The mean size of my pets? (10+15+18+18+20+20+78)/7 = 25.5lbs.

If I use the median to reason about the group of pets, I'd conclude that all of my pets together would weight 126 lbs. But that's not true: they would weigh 179lbs! I'd be off by 54 lbs! Because by using the median instead of the mean, I've ignored the outlier.

That's exactly what Woodmorappe does. He concludes that the median animal is the size of a rat, and a rat, 1/10th of a cubic meter is more than enough space. But he's very deliberately eliminated the effects of elephants, dinosaurs (which Woodmorappe claims were on the ark!), horses, cows, antelope. They're all outliers in his data. By using the median, he's been able to reduce the space requirement by a huge factor - by at least something between one and two orders of magnitude!

This isn't sloppiness. No one would reasonably even compute a median size for something like this. This is a deliberate attempt to lie with numbers: by taking advantage of the fact that most of his readers aren't going to notice that he uses the median rather than the mean for an average (or in fact by relying on the fact that most don't even know the difference), he's lying to them to help them reach the conclusion that they really want.

Quite simply, Woodmorappe deliberately makes a mathematical error, and then uses that error to lie.


  • As far as I know, the median can also be larger than the mean, in which case an even smaller ark would suffice. What makes you think that in this case the median is one or several orders of magnitude smaller than the mean?
    I mean (no pun intended), to me this part of the ludicrous scam is less significant than the 16000 individuals that allegedly sufficed to re-populate the earth. If you take all known bird species, you already end up with 16000 individuals (males and females). Or did they take the eggs? Or could the birds keep flying or sit on mountain tops until the flood was over? There are just so many absurdities involved with the ark story that the mean vs median problem almost pales in comparison.

    By Anonymous The Reverent Bayes, at 3:19 PM  

  • 16000 animals? In two by two formation that would amount to only 8000 species. And that includes dinosaurs? And Noah took more than two of some animals, if I remember correctly. The math falls apart right there.

    I heard a guy say once that Noah's Ark was really a spaceship and that the "animals" were just frozen embryos or some such.

    Frankly, I find that scenario more believeable than Woodmorappe's math. And I don't find it believable at all.

    By Blogger Rev. Joker Cross, KSC, at 3:24 PM  

  • bayes:

    Yes, you're absolutely right: the median can be larger or smaller than the mean. The median is a good measure in a population that is largely uniform, but which has outliers on either the upper or lower end which can distort the mean.

    In the case of Woodmorappe, there are two reasons that I stress the "high end" outliers:

    (1) In woodmorappe's presentation of things, he makes heavy use of the fact that the low-end outliers don't count. There are just too many insects, etc., so they're separated out.
    (2) Back when I first saw Woodmorappe's junk, several of us on looked at his list of species - and the list does wind up with a median between one and two orders of magnitude smaller than the mean.

    By Blogger MarkCC, at 3:46 PM  

  • reverent bayes,

    FWIW the analysis takes the Genus as matching the description of kind.
    (TalkOrgins describes it here:

    What is funny is that Woodmorappe then posits that the genuses (geni?) then rapidly mutated (i.e. evolved) after the flood to give us the current diversity of speciation.

    By Anonymous steve, at 3:56 PM  

  • The thought that came to mind when I read 16000 animals was "does that include all the insects?" I've heard that there are huge numbers of beetle species alone. Although, I suppose insects are pretty small. I wonder about the hundreds of different species of Cicadas, too - since they only come out once every x years.

    BTW, in many cases, God said that Noah should take seven pairs of each animal species: "From all the clean beasts take seven pairs, each with its mate, and from the beasts which are not clean take two, each with its mate. Also from the birds of heaven, seven pairs, male and female, so there will be seed on the face of all the land. Because in seven days I will make it rain upon the earth for forty days and forty nights, and I will wipe out all that lives that I have made from upon the face of the ground." I don't know what the proportion of clean species + bird species to unclean species is, but if we use the "16000 animals" number, then we are talking about between 8,000 and 1,142 different species (depending on the ratio of seven-pairs, single pair species). AND, Noah had to do it all in seven days.

    By Anonymous BC, at 4:06 PM  

  • BTW, I happened to find this page:

    They say that the Ark's capacity would allow for 273,120 animals - assuming you give each animal 5.5 cubit feet of space (they assume the average animal is about the size of a cat). They come up with some numbers for the number of species of mammals, birds, reptiles, etc. They assume that the animals hibernate (need little food and little cleaning). And say that they're below 273,120 animals.

    By Anonymous BC, at 4:34 PM  

  • Maybe the current earth is really a kind of jurassic park (except for the unlucky dinosaurs): the DNA of all species was stored and then injected in frog eggs at the appropriate time by god's scientist-angels. If true, the ark might have been really small. No wonder we can't find it back.

    By Anonymous The Reverent Bayes, at 4:46 PM  

  • The beauty of this method is that if it turned out that there isn't enough room on the ark, all Noah had to do was to reduce the median by throwing in a thimbleful of bacteria.

    By Anonymous arensb, at 4:57 PM  

  • Creationists like to say that they don't think the diversity of life could evolve on earth from a singled celled ancestor in a few billion years. I can confidently say that the diversity of life could not evolve from a few thousand individuals in a few thousand years.

    By Blogger Chris Hyland, at 6:08 PM  

  • > I can confidently say that the diversity of life could not evolve from a few thousand individuals in a few thousand years.

    I think some DNA comparisons would easily show that the different species did not arise from a "reduction in genetic information" as the creationists like to say. Each species as generated it's own information since divergence - a fact which is painfully obvious from genetic comparisons. (Of course, the creationists will, as usual, remain blissfully ignorant of the fact.)

    By Anonymous BC, at 6:16 PM  

  • Who cares if there was enough room? How did he gather them up, how did he know when he had them all, what did the carnavors eat???

    By Anonymous Anonymous, at 7:36 PM  

  • the problem Mr Noah has with his ark, neglecting all notion of a comfort zone for individual animals, is a bin packing problem. far more significant is the distribution of lengths of animals therein carried, that being defined as the critter's longest dimension. it's not like those 16000 beasties are all shape-shifters and occupy the same volume as their mass equivalent of dense fluid. indeed, the space density of tissue in the volume really occupied by an animal body is much less than that of water. so, i'd say Mr Woodmorappe has launched himself away from reality a lot sooner in the problem statement.

    even so, there are other amusing consequences of his hypothetical ark. if the 16000 are typical, the vast majority of them are small creatures and, being that, they consume far more food per unit mass than do large ones. like a rocket, then, Mr Woodmorappe needs to consider filling a substantial fraction of his ark with food, even if the time on board is 60 some odd days.

    naturally, being a Sunday school type of calculation, Mr Woodmorappe might skip the unpleasant but real consequences of 16000 critters consuming food. said ark would require very little ballast. said ark would also be incredibly cruel to its population, leaving them to wallow in each other feces after a couple of weeks.

    finally, Mr Woodmorappe would need to allocate space if not weight for extensive ventilation on board Mr Noah's ark, lest such a tightly packed population cook itself in its waste soup due to inadequate heat elimination.

    By Anonymous ekzept, at 7:38 PM  

  • Of course there's a ton of stuff wrong with the whole ark thing.

    But what I wanted to get across with this post isn't that the whole ark story is completely impossible. What I was tying to focus on in this post is how dishonest these people are; and in particular, how they try to find ways to hide their lies behind mathematical distinctions that most people won't understand. What's remarkable about Woodmorappe isn't that he's yet another creationist who's trying to prop up biblical literalism; it's how blatant his is about his lying. This isn't like Dembski, who I think actually might believe his gibberish; there is simply no way that this is an accidental mistake: this is very clearly a deliberate lie.

    By Blogger MarkCC, at 8:03 PM  

  • One question that I put to Noahs-ark believers is this: if there was a worldwide flood, and the ark landed in the Middle-East, then how did cold-blooded animals get back to the Americas? There's an enormous biodiversity in the Americas - the species you find in the Americas are largely unique to the Americas. If there was a global flood, we should expect to find a derth of species in the Americas because they wouldn't be capable of swimming the oceans or crossing an ice-bridge near the Bering strait. This includes, most significantly, desert species (tarantulas, scorpions, snakes, lizards). It's implausible to suggest that they crossed an ice bridge across the Bering strait or swam the oceans. Further, the species are unique to the Americas. Rattlesnakes are found nowhere else in the world except in the Americas. How did they get to the Americas, and why did 100% of them die out in the Old World? Why aren't there a single species that exists in both the Middle East and in the North American deserts? The same holds true for species in the Jungles of South America - why isn't there a single species of animal which exists in both South American jungles and African jungles? Multiply this by thousands and thousands of different species.

    By Anonymous X, at 11:04 PM  

  • Although I of course read through all of this nodding my head and with no small amount of wry amusement, what strikes me most about this and similar disgressions is that here in the 21st century, trained mathematicians are compelled by the vagaries of society to offer earnest and detailed treatises on precisely why something as overtly implausible the ark fable could not, in fact, be true. From the standpoint of epistemology, taking the position that the ark story is even remotely plausible is tantamount claiming that a human being, given a sufficient amount of dietary fiber and cheap beer, could literally fart his way to Neptune, a proposition no one outside of locked institutions would offer. I think.

    By Blogger Beaming Visionary, at 3:00 AM  

  • "What's remarkable about Woodmorappe isn't that he's yet another creationist who's trying to prop up biblical literalism; it's how blatant his is about his lying."

    It's always useful to rememeber that the more honest creationists (ie Kurt Wise and Paul Nelson)will tell you there is no scientific evidence for a young Earth, but they believe it because that's what the bible tells them. Another common lie is that the movement started with Henry Morris, when Morris' work was actually based on the work of George McCeady Price. Price's books contain a great deal of arguments used by creationists today, and were based mainly on the assumption that geologists had misinterpreted their data. This assumption was due to the fact that otherwise geology contradicted his religious beliefs, which were based on the 'visions' of Seventh-Day Adventis founder Ellen White. I find this helps put creationists honesty and motives into perspective.

    By Blogger Chris Hyland, at 9:37 AM  

  • Look, the Ark story is silly. Damn silly. It's impossible in at least a half-dozen ways.

    The point here (I think) is the use of Mathematics to *lie*.

    By Anonymous SmellyTerror, at 9:47 AM  

  • To quote River from Firefly:

    River: Noah's Ark is a problem.

    Book: Really?

    River: We'll have to call it early quantum state phenomenon. Only way to fit 5000 species of mammal on the same boat!

    By Anonymous Anonymous, at 6:21 PM  

  • x:

    Don't forget the monotremes and marsupials!

    By Anonymous KeithB, at 7:12 PM  

  • But what does this tell us about PYGMYS and DWARVES?

    By Anonymous wamba, at 12:09 PM  

  • One could say that lots of miracles are needed to make the Ark work. Or just one. Clearly, the Ark itself was symbolic. The remaining miracle is that God saved the diversity of the animals on Earth. Interestingly, that includes the divirsity of humans.

    (from The Life of Brian:
    'Blessed are the cheesemakers?'
    'He doesn't mean that literally. He refers to all makers of dairy products.')

    By Blogger Stephen, at 9:21 AM  

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