HOME | PAPER | Overview | Synopsis | Four Laws | Four Maxims | Three Constraints | Equations | Blog |
About Us
Kofi Busia, author of the material on this site, is a graduate of Oxford University. He gained a place with science credentials, but instead changed to do his undergraduate degree in Oxford's distinctive Philosophy, Politics and Economics. He was then able to combine his interests with a study of how diseases are contracted, transmitted, and treated socially, genetically, and medically in both traditional and more complex societies. He therefore followed with graduate studies in Medical Anthropology, which suitably brought together his studies to that point in both the sciences and the arts. His researches in Medical Anthropology required extensive studies in the history of both biology and energy, with a particular emphasis on thermodynamics. The unusual combination of skills needed to model and contrast such disparate societies and their disease processes ultimately led him to the first of the four models he was eventually able to construct for biology and ecology. That first thermodynamic model incorporated the three constraints that he discovered, and to which all biological organisms are subject. He noted that this model depended heavily on the constraint of constant equivalence, and this convinced him that other models based on each of the other two constraints must exist. He was eventually able to repeat his discoveries and to use each of the three constraints as the foundation for a distinct model. The constraint of constant propagation led to a dynamics-based model while the constraint of constant size led to a wave-based one. Still not satisfied with that, and in search of comprehensiveness and complete rigour, Kofi Busia set himself the task of constructing a fourth model circumscribing them all. That fourth model is the vector-based one presented on this site. It is certainly the most involved, but it is also far and away the most rigorous. Its foundations are two of the most demanding, and in their turn the most rigorous, of all theorems in the pantheon of science and physics: the Liouville theorem and the Helmholtz theorem. The former establishes the boundary conditions for a population's biological activities, while the decompositions of the latter establish the uniqueness of each species or population. All four models are supported and validated by the experiments conducted with Brassica rapa, and as detailed elsewhere on this site (description, and analysis).
Recent Posts
- Walls, energy, and a Centre for Biology
Let us consider the following apparently definitive declaration made by the Centre for Mathematical Biology, Oxford University: “You can’t compare a living organism to a heat pump”. But … is this really true?
Read more ...
- The more they remain the same the more they change
John Ray, the English naturalist and scientist, produced the first ever biologically-relevant definition of ‘species’. He was trying to classify plants and in 1686 wrote: In order that an inventory of plants may be begun and a classification (divisio) of them correctly established, we must try to discover criteria of some sort for distinguishing what [...]
Read more ...
- Can we escape evolution?
Although the word ‘constraint’ often has a negative connotation in ordinary language, it is how scientists and mathematicians operate. One of the first and most effective uses of a scientific-mathematical constraint came in the seventeenth centruy from the Frenchman Pierre de Fermat (of ‘Fermat’s last theorem’ fame). Natural philosophers of his day wondered what path [...]
Read more ...
- Geography and the Gibbs energy
The ‘Gibbs energy’ is invariably difficult to explain to those who don’t know what it is. And despite its importance, it was only at the end of the nineteenth century that Max Rubner, the German physicist and physiologist, at last convinced other scientists that the energy that biological organisms use in metabolic processes exactly equals [...]
Read more ...
- Circumambulations: what are they, and why are they relevant to biology?
So what is a circumambulation, and why is it relevant to biology and evolution? Brian Charlesworth wrote in his book Evolution in age-structured populations (Cambridge University Press, 1994) that: “… the concept of generation time is a rather arbitrary one”. He then lists several alternatives. It is surely rather strange that something so fundamental to [...]
Read more ...