Friday, August 21, 2009

Weight stuff (again)

I've become fascinated by the mathematical gesticulations associated with metabolic rates and weight loss.

I've been playing with the Harris-Benedict equation

Then I watched a TV special on fractals and, lo and behold, there's yet another magic equation ... Kleiber's law connecting the Energy expended to maintain a certain body Mass:
E = k M3/4   where k is some constant

The interesting thing about this one?
It (supposedly) applies to everything from roaches to rhinos.

If by Energy we mean calories ingested, then when we apply the magic law to Homo Sapiens, it suggests that a reduction in caloric intake is associated with a weight loss like so:

See the blue dot?
It says that a 10% reduction in caloric intake should (eventually) result in a 13% reduction in mass weight.

.

I've memorized the numerical values involved with the chart and, at every opportunity, mumble in crowded elevators:
"Eat 10% less, weigh 13% less ..."
I might point out that Kleiber's law is NOT universally accepted.
Some suggest a 2/3 law instead, like: E = k M2/3
That's like saying that Energy requirements depend upon surface Area whereas Mass depends upon body Volume.
That is (dimensionally speaking):
E = C1 Length2   and   M = C2 Length3 ... so E = k M2/3

Anyway, using 2/3 gives the gray graph.

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