The foundations of conventional mathematics, both classical and modern, treat what can and can’t be counted or measured as mutually exclusive, i.e. as ‘something’(numerical or geometric presence) and ‘nothing’(numerical or geometric absence). The mutual inclusion of tangible and intangible presence in natural flow-form is hence precluded, by definition. Hence conventional mathematics is an irretrievably abstract idealization, which cannot and does not equate with reality, even as it is used as a tool to describe and predict natural structure and dynamics. At its root is the profound paradox that arises from treating 1 and 0 as static alternatives – as in the binary logic of digital computers.


What is truly needed for mathematics to correspond with reality is to recognise the natural inclusion of 0 as a local centre of intangible space within 1 as a dynamic inhabitant somewhere of infinite, intangible space everywhere. Only one serious attempt at such a formulation has been attempted, by Lere Shakunle in his development of ‘transfigural mathematics’. Meanwhile, even within conventional mathematical formulations the relatively recent development of non-linear dynamical systems theories (including what are known as chaos theory, complexity theory and fractal geometry) implicitly signal the need for fluidity and incorporation of infinite space.