3. Introduction

In his book Proving Darwin: Making Biology Mathematical, Gregory Chaitin makes the valid point that:

If Darwin’s theory is as fundamental as biologists think, then there ought to be a general, abstract mathematical theory of evolution that captures the essence of Darwin’s theory and develops it mathematically.

And that is what we set out to do here (Chaitin, 2012, pp. 9-10).

As a part of his brief, Chaitin briefly examines theoretical physics with its powerful laws and comprehensive equations. He then—and surely somewhat surprisingly—goes on to say:

How can we do the same for biology, a very very different kind of science from physics?

Well, not by using the differential equations of theoretical physics! To develop a theoretical physics for biology, a fundamental mathematical theory for biology, we must use a different kind of mathematics. Differential equations will not do. Not at all (Chaitin, 2012, p. 10).

Chaitin realizes he cannot proceed without a clear statement of aims. Having made this robust but surprising rebuttal of the major method of contemporary theoretical science, he next asks the question:

What is biology really about? Well, it is about information (Chaitin, 2012, p. 10).

Chaitin's view of biology is expressed in his earlier 2007 paper:

So the idea is firstly that I regard life as software, biochemical software. In particular, I focus on the digital information contained in DNA. In my opinion, DNA is essentially a programming language for building an organism and then running that organism.

More precisely, my central metaphor is that DNA is a computer program, and its output is the organism. And how can we measure the complexity of an organism? How can we measure the amount of information that is contained in DNA? (Chaitin, 2007).

And once Chaitin has proposed his vision of biology, he proceeds to unveil his theory, which he calls ‘metabiology’.

We intend to unveil a completely contrary theory. Ours will be based upon the inherent scope and power of the very differential equations Chaitin has rejected. We must therefore begin differently. We shall instead try to understand ecology, the discipline very closely related to biology.

The Macmillan Dictionary of the History of Science defines ecology by saying it is:

The branch of biology dealing with interrelations between organisms and their environment. The term was coined in 1866 by Ernst Haeckel (1834–1919), but the idea of ecology is much older, having roots, for example, in the 18th century concept of the economy of nature. … After Darwin’s (1809-82) Origin of Species (1859), studies of plants and animals in Nature began to focus on how they are structurally and functionally adapted to the conditions of life (or habitat) and the struggle for existence [natural selection]. The key to understanding why certain organisms occur under particular conditions associated with other organisms was seen to lie in their physiological requirements (Bynum et al, 1983, p. 110).

Ecology therefore seems to be the scientific study of the interrelations amongst living organisms both with respect to each other and to their (natural) environment. It involves the abundance and distribution of organisms; the movement of materials and energy through their communities; the succession and development of the resulting ecosystems; and the more generalized abundance and distribution of biodiversity (Parker, 1998). Variables such as number, biomass, composition, and their rates of change—these last in particular being avowedly differential—would therefore seem a particular interest.

The above definition of ecology is rather longer than the differentially based one we gave earlier in Prolegomenon II. But it states the rather large methodological problem ecology has failed to resolve, and that stands at the heart of its difficulties when compared to the ‘hard’ sciences such as physics and chemistry. Biology and ecology show a complete lack of rigour in handling the most basic of scientific concepts.

The McGraw-Hill Concise Encyclopedia Of Science & Technology makes the essential problem clear by saying that ecology is “in more simple terms, environmental biology” (Parker, 1998, p. 663). So to know what ecology “really is” we must not only confront what the environment “really is”, but we must also confront what biology “really is”. This is not at all promising.

Biology and ecology as traditionally defined both face difficulties that are immediately apparent in the definition the 1971 Oxford English Dictionary gives to the former:

1. The science of human life and character.

2. The science of physical life; the division of physical science which deals with organized beings or animals and plants, their morphology, physiology, origin and distribution; … (Oxford, 1971).

The American Heritage Dictionary is little better:

the science of life or living matter in all its forms and phenomena, esp. with reference to origin, growth, reproduction, structure, and behaviour. (Heritage, 2004).

Philosophers and theologians, for example, are equally interested in “life”, so any designs biology and ecology might have on scientific respectability are promptly lost through this singular lack of linguistic specificity. Since biological work is often interpreted as an attempt to “define” life, philosophers, theologians, meditators, alternative health practitioners and many others rightly speak up, so taking most working biologists into areas they would much rather not concern themselves with, or else they would never get anything done. This is particularly so once Darwin enters the picture.

If, as Darwin said, ‘Natural Selection’ is a ‘power incessantly ready for action’, then it should be possible to measure it—specifically—as an ever-active force or potential whose value over an entire generation of biological entities is never—and can never—be zero (Darwin, 1859, p. 76). Furthermore, that force or potential should be unequivocally linked to variations in population numbers … but always so that its influence upon population size can be isolated and studied. There can then be no questioning its conclusions.

A clear definition of subject matter is obviously lacking here. Any proposed definition should surely do what the one we gave earlier successfully did, and avoid all references to contentious terms. What would surely be even better would be for biology to define itself as we have done, in avowedly scientific terms, avoiding all others. Our given definitions in Prolegomenon II are clear, concise, unambiguous, and are expressed in the strictest scientific and mathematical terms.

We now claim that with our proposed definitions, we can do what Chaitin says cannot be done. We can use differential equations to calculate the precise quantities of mass and energy any biological organism expends specifically upon natural selection and upon Darwinian competition and evolution. We can then use the same differential equations to prove that the said values cannot be zero for any organism or population.

We will then also justify our far more rigorous definitions for biology and ecology and demonstrate their usefulness, as differential equations, by unambiguously quantifying Darwin’s competition; his evolution; and his natural selection. We will further show that it is eminently possible to:

  1. specify the attributes and properties an organism must possess if free from Darwin’s competition and evolution;
  2. prove that an organism free from such competition and evolution is logically and practically impossible;
  3. calculate the precise quantities of mass and energy any given biological organism expends specifically—and only—upon Darwinian competition and evolution.
  4. show that biology and ecology are quantized.

Put clearly and simply, we will now create a rigorous mathematical model to accompany our definitions, and that will allow us to determine the joules of energy and kilogrammes of mass a chosen test species does in fact expend upon Darwinian competition and evolution; to calculate the values it would expend on survival and reproduction if free from these; to produce the equations that prove that those values are not only not zero for our test organism, but that they can never be zero for any organism, and that a population free from Darwinian competition and evolution is impossible; and to reveal the quantum nature of biology as a discipline.