This is from a book on dinosaur evolution – they’re invoking the square-cube law in discussion of warm-blooded dinosaurs. Trying, anyhow.
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.
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?
Even rather simple mathematical ideas baffle 98% of the population….so we will be listening to this crap forever.
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.
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!
E) None of the above
Haha, I had to actually try some numbers on a calculator to be sure of the answer, that’s how lame my math skills are. The book’s editor should have just gone with “a lot bigger.”
Well, 3 is half of 8 if you slice 8 down the middle from top to bottom.
Volume = 4/3piR^3, if you have twice the radius then V = 4/3pi(2R)^3. Since 2^3 is 8, then doubling the radius yields 8 times the volume. Not 3.
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?
Read the caption.
2^2 = 3 apparently according to the authors.
They must be using modular algebra.
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.
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…
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!
I was wrong actually, they’re saying that 2^3 = 3!!! which is might be even worse.
Just think about how hot the center earth is, how cold the center of meterorite; and surface area vs volume.
It is math question.
Certainly, a failed high school math calculation.
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.
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.
Erratum – it happens. But the dynosaur looks like a cat.
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.
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.
He is not wrong. Thinking about it.
This is regarding different reference systems. One is applying to both. Other only is only for one.
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.
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.
What does Asimov getting HIV from a blood transfusion have to do with anything being discussed here?
Like I said.
Math is the rule how universe works (or laws of God if you are religious).
If God often reward the people who know rules of God, you should not be surprised.
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 …
Evidently the fish and cat live in an alternate, Sierpinski Triangle based universe.
Another example of mat ability at stake.
Unfortunately, math (or physics) ability deteriated after high school for a lot of people.
As foreigner writing in English, it is getting better. lol.
But seriously, I do not give a fuck to idiots who only good at grammar or spelling nazi. If you are long time reader here, you know how blog owner attitude toward these nazi.
“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.
BTW, the movie producer and director himself was once a soldier in Chinese army.
Good for him, patriotism is an admirable virtue. This pertains to the square cube law in what way?…
It is math question if you have not noticed.
Without putting words in IC’s mouth, I think his ‘BTW’ comment is explained by the fact that the film has an anti-war theme, which makes the fact that the highly successful producer/director of the film was once a PLA soldier somewhat poignant.
No desire whatever to turn the discussion into any kind of political debate, just trying to aid mutual understanding.
Thanks, mate – I’ll watch that film tonight, it looks good. If others are interested, they can find the plot etc. here: http://en.wikipedia.org/wiki/Assembly_(film)
M41 Walker Bulldog
Like being able to develop techniques to disarm land mines?
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?
It’s used as an undergraduate textbook. I picked it up at a book sale for ten bucks.
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.
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.
When I took geology in college we spent a lot of time on isotopic dating. I think the math was right …
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.
When I was in college, Calculus was required for a degree in Geology. Is this no longer the case?
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.
I think we’re talking hundreds of thousands of atmospheres, minimum.
Yerf, water is virtually incompressible.
Then how do black holes form?
Beats me. Are you sure that they do?
Enough gravity will compress anything.
Well those fish had better chew gum fast, then.
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.
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