This introduction to the concept of biological complexity demystifies and debunks the argument of Paley that a complex watch is compelling evidence requiring a (complex) watchmaker (designer or creator). It employs a mathematical exercise to demonstrate this, involving a randomizing component (a die), and a simple mathematical rule (the non-random component), resulting in the repeated plotting of points. Repeated cycles eventually produce an orderly pattern. Students will learn that simple rules, acting on random events can easily produce complex, seemingly designed patterns.
GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus. As an interactive geometry system, GeoGebra can help you do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. Equations and coordinates can also be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.
The geo-coding of information for specific point locations and for regional boundaries is of fundamental importance to the ability of researchers to map spatial patterns and to explore relationships among phenomena across geographical space.
This chapter continues the examination and clarification of concepts relating to point objects, for which as argued in Chapter 1, appropriate, complex/ second order, concepts relate to words like ‘distribution’, ‘dispersion’, ‘density’, ‘pattern’ and ‘scale’ and, at higher level still, third order concepts relating to point process models, stationarity and isotropy/anisotropy.