by means of relative selection
Using the Weyl and Ricci tensors to prove Darwin’s theories of competition and evolution
and to refute creationism and intelligent design
We base our perpetual but biological earth, as shown in Figure 6.1, on the real one around us. It has all the biotic and abiotic resources our populations and their circulations need.
Since this is the best of all possible worlds, this ideal earth provides all resources. It also absorbs all waste products without difficulty. There are no shortages. The environment never degrades. No adverse effects are imposed on any population. The entropy on our perpetual earth returns to the same value every generation for every population.
As in the accompanying Figure, our resource-rich and perpetual biological earth again abides by the Prévost theory of exchanges. It attains a suitable radiation balance.
All the biological forms on our perpetual earth can exploit the incoming solar radiation we have already provided. They can absorb whatever they need for their photosynthesis, metabolism, physiology, and other ancillary activities. And once they have used that radiation, they can also emit their low-grade wasted heat, down in the infrared regions, outwards into the surrounding free space. They can all do all this without any further degradation of the environment, and so without any net change in entropy.
An algebraic and geometric topology based proof.
A vector calculus based proof.
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