Bigger is... more efficient!

                                                    <-- (Source 15)

...at least for an animal with a large body mass, because it has a more efficient use of food-energy than smaller animals.

Why do large animals need less food per gram of body mass?  Why do they use energy more efficiently when the animal is large, than when it is small?  This question deals with "universal scaling laws" (Source 7).

The Kleiber Law, illustrated in the chart above, says "Larger animals have relatively slower metabolisms than small ones. A mouse must eat about a third of its body mass every day not to starve whereas a human can survive on only 2%." (Source 13).

Why? Wherefore? Pourquoi? Warum?¿Por qué?

One possible answer is that the larger animal has a more complex and advanced, and therefore more efficient circulatory system, etc., perhaps because cells can only be so small?  Therefore they can survive on less because their large size allows for their internal workings to become richly branched, like a thick system of roots, whereas the mouse only has a few strands here and there, and so must eat more to get the energy it needs.

This could also be a reason why larger animals are known to live longer, like Galapagos tortoises, or large mammals like ourselves, whereas little hamsters can only expect 1-2 years (RIP Betty, beloved Mesocricetus auratus coconut-dweller! [Appendix A]).

Example of fractals (Source 6).

Quote from "Fractals" program by Nova.  This section I transcribed is about how these scientists figured out why the bigger animals were more efficient, somewhat with the help of the new way of looking at organic growth mathematically, through the use of fractals. 

The fractal idea is very similar to the Fibonacci sequence idea, and how it relates to nature, so I think it's odd this program didn't mention that...  For instance, they both can predict curves and organic growth patterns, like in a pineapple, or a seashell's spiral, but the Fibonacci idea definitely stays within the realms of the mathematical and geometric, while the fractal geometry is branching out into curves and branches and rugged teeth that are not used in high school geometry.  

And now, a selection of the transcript from this episode (Source 1):

"Narrator: It may take years before fractals can help doctor predict cancer, but they are already offering clues to one of biology's more tantalizing mysteries. An elephant, for example, is 200,000 times heavier than a mouse, but uses only about 100,000 times more energy, in the form of calories it consumes.

Geoffrey West, Santa Fe Institute: The bigger you are, you actually need less energy per gram of tissue to stay alive.  That is an amazing fact!

Narrator: And even more amazing is the fact that this relationship between the mass and energy use of any living thing, is governed by a strict mathematical formula [Image of E = M^3/4].

James Brown, University of New Mexico: So far as we know, that law is universal, or almost universal, across all of life.  So it operates from the tiniest bacteria, to whales and sequoia trees.

Narrator: But even though this law had been discovered back in the 1930s, no one had been able to explain it.

James Brown:  We had this idea that it probably had something to do with how resources are distributed within the bodies of organisms as they varied in size.

Geoffrey West: We took this big leap, and said: all of life, in some way, is sustained by these underlying networks that are transporting oxygen, resources, metabolites, that are feeding cells.  Circulatory systems, and respiratory systems, and renal systems, and neural systems.  It was obvious that fractals were staring us in the face.

Narrator:  If all these biological networks are fractal, it means they obey some simple, mathematical rules, which can lead to new insights into how they work.

James Brown:  If you think about it for a minute, it would be incredibly inefficient to have a set of blueprints for every single stage of increasing size.  But if you have a fractal code - a code that says when to branch, as you get bigger and bigger, then a very simple genetic code can produce what looks like a complicated organism.

Brian Enquist, University of Arizona:  Evolution by natural selection has hit upon a design that appears to give the most bang for the buck.

Narrator:  In 1997, West, Brown and Enquist announced their controversial theory: that fractals hold the key to the mysterious relationship between mass and energy use in animals.  Now they are putting their theory to a bold new test: an experiment to help determine if the fractal structure of a single tree can predict how an entire rain forest works.

[...] [Conclusion:]


Narrator: For generations, scientists believed that the wildness of nature could not be defined by mathematics.  But fractal geometry is leading to a whole new understanding, revealing an underlying order governed by simple mathematical rules.

Fern as an example of fractal structure (Source 8).

Geoffrey West:  What I thought of in my hikes through forests, is that you know it's just a bunch of trees of different sizes, big ones here, small ones there, looking like it's sort of some odd tree chaotic mess - actually has an extraordinary structure.

Narrator: --A structure that can be mapped out and measured using fractal geometry.

Brian Enquist: What's absolutely amazing is that you can translate what you see in the natural world into the language of mathematics, and I can't think of anything more beautiful than that." (Source 1, Time:  42:10- 52:06)

   Example of the fractal structure (Source 2)

So what is a fractal?  

       It's an irregularly shaped way that nature has of increasing its size.  An example is a tree - how as it branches out more and more it forms V's that are all basically the same pattern, but in different sizes.  This repetition is called a self-similar pattern (Source 9).  This idea was a breakthrough in science and mathematics because it shows that irregular growth patterns, as are the norm in nature, can be quantified, measured, predicted, and used for better technology.

For instance, the theory of fractals was used to come up with the idea to make cell phone antennae in a fractal design.  They found this not only picked up the signal better, but allowed it to pick up signals on multiple frequencies, allowing for multiple functions in one cell phone, without having to have dozens of different antennae sticking out of it.                           
Internal fractal-design cell phone antenna (Source 11).                Closer view of the design (Source 12).

Another interpretation of how the same shapes are repeated smaller and smaller ad infinitum, like Russian nesting dolls (Source 3).

(Source 10)




Video showing how the fractal smaller and smaller reproduction could potentially go on forever (Source 14).

Bibliography
1. "Fractals: Hunting the Hidden Dimension," NOVA, PBS TV program, aired 2008.  Viewed by DVD.  ISBN: 978-1-59375-852-3.
---------For more info on this program:
   You can find the complete transcript for, and other stuff related to this video at                      http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html, which by the way I didn't realize until after I transcribed all the above by hand, lol.

2.  Image 15, photo credit: Courtesy Art Matrix. From webpage related to NOVA PBS TV program, "Fractals: Hunting the Hidden Dimension."  WWW: http://www.pbs.org/wgbh/nova/physics/mandelbrot-fractal.html.

3. Image 12, photo credit: Courtesy Art Matrix.  From webpage related to NOVA PBS TV program, "Fractals: Hunting the Hidden Dimension."  WWW: http://www.pbs.org/wgbh/nova/physics/mandelbrot-fractal.html.

4. Image from "Friday Fluff," webpage post.  WWW: http://www.seekingelevation.com/2012/01/friday-fluff_27.html.

5.  Image from "How to Tell if my Teddy Bear Hamster is Pregnant," eHow article by Susan Grindstaff.  WWW: http://www.ehow.com/how_6374473_tell-teddy-bear-hamster-pregnant.html.

6. "Fractals everywhere" photograph by Hintersul, posted 2012.  WWW: http://hintursul.deviantart.com/art/Fractals-everywhere-288333753.

7. "Geoffrey West: Bio" webpage by Geoffrey West (I assume), 2012.  Santa Fe Institute faculty profile.  WWW: http://www.santafe.edu/about/people/profile/Geoffrey%20West.

8. Image from Minds, Brains & Catalysis:
A theory of cognition grounded in metabolism by Christopher J. Davia.  Chapter 10: "Scale invariance in biology," webpage.  Carnegie Mellon's Psychology Department, 2011.  WWW: http://www.psy.cmu.edu/~davia/mbc/10start.html.

9. "Fractal" Wikipedia article, 2012.  WWW: http://en.wikipedia.org/wiki/Fractal.

10. "Fractals: Hunting the Hidden Dimension" blog post by paul_mic, 2010.  WWW: http://monkeybuddha.blogspot.com/2010/12/fractals-hunting-hidden-dimension.html.

11. Image from "Fractal antenna constructions" webpage by ScienceProg.com: Electronics, 2007.  WWW: http://www.scienceprog.com/fractal-antenna-constructions/.

12. "Cell Phone Antenna or a Moth-Eaten Carpet?" image from "The Geometry of Nature" webpage.  WWW: http://www.mathgoody.com/4-4-Fractals/Fractals.html.

13. Image and text from "The Kleiber Law" blog post by ThePEG: the Equation of the Month blog, run by the Theoretical Population Ecology and Evolution Group, Biology Dept., Lund University, posted 2012.  WWW: http://equation-of-the-month.blogspot.com/2012_06_01_archive.html.

14. "Fractal Zoom Mandelbrot Corner" YouTube video uploaded by gooozz, 2006.  WWW: http://www.youtube.com/watch?v=G_GBwuYuOOs.

15. "Elephant and Mouse Friends" image from Puddle Jumpin' Cards by Sunny Rickards.  WWW: http://puddlejumpincards.bigcartel.com/product/elephant-and-mouse-friends.

Appendix A

She kind of looked like this (Source 5)!

Her coconut house kind of looked like that-ish (Source 4).  Yes, this is relevant to this topic because I'm still alive and she's dead.  See? - smaller animals die more quickly..... (pause)....Waaaaaahhhhhhhh  :'S

....Too cute!  Must abort!