• Tag Archives math
  • New paper says dinosaurs were endomorphs.

    From left to right: Endomorphic Jay Cutler, Mesomorphic Arnold Schwarzenegger, and Ectomorphic poster-child Frank Zane
    From left to right: Endomorphic Jay Cutler, Mesomorphic Arnold Schwarzenegger and Ectomorphic poster-child Frank Zane

    Endo-what now? Allow me to explain.

    If one studies physical fitness (academically, or practically), then one is bound to come across the three main human body types. The endomorph, mesomorph and ectomorph.

    Endomorphs are characterized by their ability to easily gain weight (be it fat, or muscle).

    Ectomorphs are characterized by their ability to easily lose weight (fat, or muscle)

    Mesomorphs are the middle ground group that appear to have the most malleable bodies.

    In general, endomorphs have lower metabolisms than the other two, while ectomorphs tend to “run hot” all the time. Few people are all one way, or the other, but a notable dominance of one type, or another is usually prevalent.

    The endo/ecto part can get confusing; especially if one is used to these prefixes in the context of endotherm/ectotherm. The names seem to be reversed from what one might normally hear (ectomorphs being more “warm-blooded” than endomorphs etc). The names have nothing to do with thermophysiology. They were coined after the germinative layers of the body during embryonic development. Endoderm forms the digestive tract, and endomorphs are usually stereotyped as fat. Ectotoderm forms the skin, and ectomorphs are usually stereotyped as being “all skin and bones.”

    The reason I went with these specific bodybuilders (Jay Cutler, Arnold Schwarzenegger and Frank Zane) was partly to buck these stereotypes, but also to point out something that the news outlets are missing. Namely that having a lower metabolic state, does not mean one is a “couch potato” or has “forgone exercise.” Bigger, means more massive. That may mean fat, but as one can see above, it also can mean muscle and bone. Dinosaurs were not fatter than mammals. They were bigger.

    So what am I rambling on about?

    Grab a calculator and come along for the ride.

    Continue reading  Post ID 384

  • New study finds that numbers are inherent to humans…and…

    I came across this study today from The New Yorker.

    It’s a long (for the internet) read, so I’ll only do a few verbatim copies here. The gist of the study, by French scientist Stanislas Dehaene, is that the concept of integers (1,2,3 etc) is something that is hard wired in our brains. We have a natural ability to do rudimentary addition, and we can tell when one number is larger than another. Well, as long as the gap is large enough.

    According to the article:

    If you are asked to choose which of a pair of Arabic numerals?4 and 7, say?stands for the bigger number, you respond ?seven? in a split second, and one might think that any two digits could be compared in the same very brief period of time. Yet in Dehaene?s experiments, while subjects answered quickly and accurately when the digits were far apart, like 2 and 9, they slowed down when the digits were closer together, like 5 and 6. Performance also got worse as the digits grew larger: 2 and 3 were much easier to compare than 7 and 8. When Dehaene tested some of the best mathematics students at the ?cole Normale, the students were amazed to find themselves slowing down and making errors when asked whether 8 or 9 was the larger number.

    Dehaene conjectured that, when we see numerals or hear number words, our brains automatically map them onto a number line that grows increasingly fuzzy above 3 or 4. He found that no amount of training can change this. ?It is a basic structural property of how our brains represent number, not just a lack of facility,? he told me.

    This is fascinating. Especially the discovery of a “hard wired” number line (which goes right to left, apparently. See the article), which works really well up to about 4. The fascination comes not from the discovery of this in humans, but the fact that this degree of rudimentary math has been found in a wide variety of animals. The most recent being fish.

    In that study, scientist found mosquito fish (Gambusia affinis) females were able to count up to four (right at the end of the number line). Also, like in human studies, the fish were able to tell which group of fish was larger, as long as the discrepancy was big enough (approximately 2:1).

    Keeping with the theme of my site, the most famous example of reptilian counting would be that of varanids. Studies on the white throated monitor (Varanus albigularis), found that they can reliably count to six (King & Greene, 1999).

    So it seems that the concept of math is so important that it has been hard wired in our genes for at least 400 million years.

    Think about that the next time you ignore a mathematical equation.

    Also, give the article a read through. It is very intriguing. It’s the closest that psychology has ever come to being a hard science, and the ramifications for education cannot be understated.


    King, D. & Green, B. 1999. Goannas: The Biology of Varanid Lizards. University of New South Wales Press. ISBN 0-86840-456-X, p. 43.