Math and Paleontology

Cat and Bowl

This is from a book on dinosaur evolution – they’re invoking the square-cube law in discussion of warm-blooded dinosaurs.  Trying, anyhow.

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61 Responses to Math and Paleontology

  1. Toad says:

    Is warm bloodedness superior to cold bloodedness?

    Yes. When the cat’s body temperature cools from getting wet, it can recover faster with internally generated heat. A cold-blooded animal would have to bask in the sun for a longer period to recover its original temperature.

  2. A Fan says:

    A frightening example of what I’ve noticed in many of my less intelligent students: They can parrot a principle but are utterly unable to apply it, In this case, the captioner doesn’t even really state the principle properly; or, to be kind, fails to define “size” in a useful manner. How can this have gotten past any kind of decent editing process?

  3. MawBTS says:

    Ever since I learned of the square/cube law I keep applying it to monsters in movies, like Godzilla. We see Godzilla walking around bipedally, so the inference is that it must have bones, skin, and tissue made of some incredibly strong material.

    This means that the “realistic” Godzilla in the 1998 Roland Emmerich movie (which bleeds, gets hurt by gunfire, etc) is actually less realistic. If Godzilla was to exist, it really would need to be an indestructible behemoth.

  4. amac78 says:

    whereas the volume of the large bowl is three times that of the smaller bowl.

    Five times? Seven times? 3.14 times?
    Or perhaps the captioner has calculated the surface area of the radius correctly!

  5. Is it this blog’s position that the square/cube law has nothing to do with warm blooded creatures? Or is this just a weak book?

    • Kamran says:

      2^2 = 3 apparently according to the authors.

      • doombuggy says:

        They must be using modular algebra.

      • The fourth doorman of the apocalypse says:

        Umm, the caption was actually comparing the difference in radius’ to the difference in volumes.

        Perhaps the author of the caption was working in logarithms, and got 3 from 2^3.

        • kai says:

          yes. It also show a common problem in many science vulgarisation: The author assumes that their reader are so allergic to math that all equations are to be banned, even simple ones. Then they write stuff like square-function, cubic-function and then makes fool of themselves lol. Write simple equations like S~r^2, V~r^3 and it will be simpler for everyone…

        • kai says:

          Yeah, that and the fact that for this poor fish, the increased water pollution, cramped space and killer cat of the smaller bowl is much more of a problem than any Volume/Surface effect on the water temperature (small bowl will be less stable)….
          Living in a small unfiltered unplanted spherical aquarium indeed has important consequences for the fish – strongly decreased life expectancy for example 😉
          I wonder why he choose this poor example – probably he do not like fishes and like cats, what a crazy author!

        • Kamran says:

          I was wrong actually, they’re saying that 2^3 = 3!!! which is might be even worse.

    • IC says:

      Just think about how hot the center earth is, how cold the center of meterorite; and surface area vs volume.

      It is math question.

      • IC says:

        Certainly, a failed high school math calculation.

      • A Fan says:

        Why the center of the earth is hot is a complicated problem in physics. The explanation includes the production of heat by nuclear processes and the interaction of tidal forces and magnetic forces on the iron core of the earth. Mars is not that much smaller than earth and is cold all the way through. The moon is also cold all the way through. If the issue were purely one of conduction and convection of heat from the interior of a body to its surface and radiation of heat away from the surface then the square-cube principle would be sufficient to explain different temperatures in different sized bodies radiating heat at different rates. But in the particular case that you cite it isn’t. The most important factor by many orders of magnitude in this case is the generation of heat within the earth by a variety of mechanisms that do not exist in asteroids or indeed in most known planets and moons.

        • IC says:

          Well, it is analogy intended for some people with only high school education. Animal bodies have different internal temperature too and different sizes. The different organies have different heat production potential and conidtions. Nothing is simple.

          But if people even do not have high school graduate level of mental ability, it is hopeless.

          That is reason I do not like universal suffrage. Let mob to make important decision is really worrisome. Who knows how many galileo have they killed with jury trial.

          Imagine let mob decide wether you have cancer or not.

  6. Jaim Jota says:

    Erratum – it happens. But the dynosaur looks like a cat.

    • Jan Banan says:

      Not just erratum. The point of trying to illustrate the square-cube law ought to be showing the relationship of surface area to volume, since that’s what the square-cube law is, especially if you are trying to argue its relation to heat loss, which I assume is the whole point.

      Also, if you look carefully at the dinosaur you’ll see those are actually feathers.

  7. Jim W says:

    It reminds me of a goof in Asimov’s “Understanding Physics” book (page 15, volume II), where he claims that mirrors reverse left and right (as when you look into a mirror) but do not reverse up and down. I guess he never considered what happens when you look into a mirror while lying down.

    • IC says:

      He is not wrong. Thinking about it.

      This is regarding different reference systems. One is applying to both. Other only is only for one.

    • a very knowing American says:

      If you put a mirror on the floor and stand on it, or next to it, it will reverse your image up and down but not right and left.

    • peppermint says:

      that is not a goof. The meme “Why do mirrors reverse left and right, but not up and down” probably wasn’t first thought of by Asimov.

      Asimov was pretty smart, but he believed everything he was required to and died of AIDS.

  8. IC says:

    Like I said.

    Math is the rule how universe works (or laws of God if you are religious).

  9. Ursiform says:

    The key points appear to be that doubling the radius allows plants to grow in the bowl and prevents cats from climbing up on the bowl. The eight-fold increase in volume is too complicated to deal with …

    It is possible the author is not responsible for the figures or captions. I once read a science article in the LA Times (back when they bothered to have a science columnist) that had a picture with a ridiculous caption. I e-mailed the author and she responded that she had cringed when she saw the picture and caption they had attached to her column …

  10. Travis says:

    Evidently the fish and cat live in an alternate, Sierpinski Triangle based universe.

  11. IC says:

    “What tank is that 1:03:58?”
    Check that scene.

    This also illustrated simple math ability is critical for war effort. Facing one certain casualty, the consequance of who takes it makes a lot of difference in the outcome. In their debate, it becomes very clear. Next step is sense of duty which overcomes personal loss or fear.

    Intelligence matters in a most every thing.

  12. Patrick Boyle says:

    This is a strange book. It looks like it is a kiddie book and it is described as for ‘non-specialists’ yet it sells for $67. Who buys such a book?

    • gcochran9 says:

      It’s used as an undergraduate textbook. I picked it up at a book sale for ten bucks.

    • Sandgroper says:

      The comments say it fills a (very big) gap between the kiddies’ books and the heavy graduate palaeontology texts, and does a good job of it.

      And geologists can’t do math – everyone knows that. I’m semi-serious.

      • Sandgroper says:

        In their favour/defence, geologists and other earth scientists engage in less research fraud than anyone else. Psychologists engage in the most. Civil engineers like me come about half way between.

        And the illustrator for the book was a different guy from the book’s authors, so maybe he’s just a guy who can draw pictures of goldfish bowls, and the caption was the fault of the illustrator and editor, not the authors. Maybe.

      • ursiform says:

        When I took geology in college we spent a lot of time on isotopic dating. I think the math was right …

        • Sandgroper says:

          Yeah, various dating methods, and use of GIS, although those tend to be done by specialists, not field geologists – inevitably the earth sciences are developing a much higher math and programming content, like just about any other worthwhile field.

          Not that I’m dissing geologists, you understand; I work closely with them in order to do my job, and hold many of them in very high regard – they are more useful to me than a lot of other people, including a lot of my own profession.

          But you won’t see geologists routinely using a lot of calculus or algebra any time soon.

  13. Important consequences for the fish, yes. If 8 times the water is forced into a space only 3 times as big, the added pressure will likely kill the fish.

  14. Flemur says:

    Three times the volume is no problem because, when viewed from above, the fish bowls are elliptical and the bigger one has a higher eccentricity.

  15. Steven C. says:

    The law is misstated in the text; when an object is doubled dimensionally (regardless of its shape); the area increases by the square and the volume by the cube. So a fishbowl with twice the dimensions (height, width) has four times the surface area and eight times the volume of the smaller bowl. That applies to any structure, which is why giant humans suffer from physical disabilities. If my dimensions were doubled the same square-cube law would be obeyed. I would have eight times the volume, and mass, but only four times the cross-sectional area in my leg bones. I would also have eight times the volume of blood passing through blood vessels that have only four times the cross-sectional area and surface area of the vessels themselves, also four times the interior surface area in my heart. Similar problems with my kidneys and lungs. I’m also generating eight times the body heat, but have four times as much epidermis. It’s why elephants are not scaled up mice. A mouse could probably survive a fall thirty times its height, but an elephant would sustain serious injuries falling its own height. Scaling issues are very important in engineering as well. A building, made of the same materials and with the same dimensional ratios, that is ten times the size of a smaller building would have one-hundred times the surface area and one-thousand times the volume (and mass). So the weight on each square foot of foundation would be ten times as great as for the smaller building. Ants can run very quickly and carry a lot of weight, proportionate to their own, but scale them up to the size of a horse and their legs would snap trying to carry their own weight. Their simpler body organs would also not suffice for the demands placed upon them. Which is good because who wants to deal with horse-sized ants?

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