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
Now that we have our earth, a sun, and some free space to put them all in, we need to establish a “typical” population of “typical” biological entities.
Our prototypical biological entity, shown in Figure 7.1, is a simple biological cell. It has the minimum DNA and other components it needs to survive, and to reproduce itself. It can engage in basic photosynthesis and other such metabolic and respiratory processes.
Our cell or biological entity has an entry orifice. When it needs material resources it can open this entry orifice. It then draws everything it needs into itself from the surroundings. Those resources attach themselves by forming single chemical bonds. Whenever the entry orifice is open, it means the amount of materials entering is greater than that leaving.
Once our cell or biological entity has absorbed all the resources it needs, it can close its entry orifice. We can call this Stage I.
But our cell also of course needs energy. So it has a separate entry aperture. It uses this to absorb all the radiant energy it might need.
As with the entry orifice, when the entry aperture is open then the amount of energy entering is greater than that departing. We can call this Stage II. And, in the same way, once our cell or biological entity has absorbed all the energy it requires, it can close its entry aperture.
When our entity closes its entry orifice and entry aperture, it can engage in its sundry metabolic, physiological—and also reproductive—processes. It can open or close either one or both at any time necessary, and for as long as necessary.
We also give our prototypical biological entity a separate exit orifice. When it has undertaken all its desired processes, it can open that exit orifice and disgorge any wastes. They are then absorbed back into the environment. When the exit orifice is open, the amount of materials leaving is greater than that entering. We can call this Stage III.
And in similar fashion, it also has an exit aperture through which it can transmit whatever low-grade radiant energy or heat it desires into the surrounding free space. Once again, when the exit aperture is open, then the amount of energy leaving is greater than that entering. We can call this Stage IV.
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And we are now done.
Our biological entity now has all the capabilities it needs to insert itself into the Prévost theory of exchanges, maintain a balance, and allow us to prove what is possible and not possible.
Although our prototypical biological entity is free to open and/or close its entry and exit orifices and apertures in any combination it pleases, our little model is easier to develop if we consider them one at a time.
Every population of such entities can now programme its members' DNA to open and close their orifices and apertures for its own distinctive periods of time. Each entity, and population, can thus take on and release its materials and energies, and all in its distinctive amounts, and at pertinent rates.
And now we have our prototypical biological entity and our matching population, we are ready to observe them go through the circulation of the generations, and reproduce.
An algebraic and geometric topology based proof.
A vector calculus based proof.
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