## Thursday, March 7, 2013

### Organisms are built in four dimensions

Here is, I think, one observation, expressed in various and complementary ways:
• All species exhibit an average relative fitness, w, of approximately $w = 1$.
• On average, all organisms leave approximately one descendent.
• Over its lifetime, an organism does the work (joules) required to leave approximately one descendent.
• Over its lifetime, an organism must do the work required to build another organism of the same size.
Let
• A be the total amount of work required to produce a descendent.
• R be the rate of that work, and
• T be the time over which the work is done, then
RT = A

My "observation" above implies that A depends strongly on body size: It takes longer to build a large organism.

A 3-D organism has to propagate itself through time, at a velocity sufficient to maintain and replicate itself. The 4-D integral of that mass-time event is directly proportional to the mass of the organism. The rate or velocity measured at any instant in time, $t$, will be a 3-D slice of the 4-D mass-time event. As the event is proportional to the size (mass or volume) of the organism, the 3-D slice will scale to the 3/4 power of the 4-D event or size of the organism.