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# 2. Prolegomenon II

Our intention is to rise to the challenge set by Chaitin and as quoted in Prolegomenon I. We shall produce a fundamental mathematical theory for biology that is fully general and fully precise. Our intention is also to rise to the challenge set by Murray and as again quoted in Prolegomenon I. We shall produce universal laws and principles, as well as fully predictive theories, in ecology, evolution, and biology. Our intention is then to go well beyond these challenges and to produce the long-sought-for theory of a quantum biology, as well as to incorporate the special and the general theories of relativity.

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In order to achieve the above four purposes, we must first define our subject. We therefore offer the following. We define biology as:

dU = Mdt = δQ - dH; M > 0.

BIOLOGY: is the study of those systems that can replace their internal energy.

Explanation of Terms and Variables: dU is an infinitesimal increment in the population's total bodily matériel—i.e. in its biological matter of chemical components retained—in kilogrammes; M is the total dynamical mass flux, expressed in kilogrammes per second, of the chemical components passing through the population at each infinitesimal moment, dt, comprising its entire stock of biological matter, and where M = dU/dt, or where ΔU = ∫M dt; δQ is the infinitesimal increment in heat the population uses over the course of the transaction; dH is the infinitesimal increment of energy used to help form the chemical bonds that bind the population's relevant body material or stock of biological matter.

We also define ecology as follows:

pdt + mdt = dh + du = δq; m > 0.

ECOLOGY: is the study of the processes systems use to replace their internal energy.

Explanation of Terms and Variables: p is an individual biological entity's energy flux used, in watts, to form its varied chemical bonds at each infinitesimal moment, dt; m is that individual entity's mass flux, per that same dt, of its chemical components and biological matter bound in kilogrammes per second; dh (where p = dh/dt, or Δh = ∫p dt) is the infinitesimal increment in the stock of chemical bond energy used to bind the chemical components being retained; du (where m = du/dt, or Δu = ∫m dt) is the infinitesimal increment in the stock of chemical components or the mass of biological material being retained; δq is the infinitesimal increment in heat the organism uses over the course of the transaction.

The purport of our proposed definition for ecology can be seen in Figure 1.