[3rd edition] the work offers an explanation of nature and mathematics in terms of rectilinear algorithms. It starts by refuting the existence of transfinite numbers. It goes on to disprove irrational numbers, transcendental numbers, and even the literal existence of arcs. It explains arcs as appearances only, due to the small size of the underlying polygons that make up arcs. It explains diagonals and arcs in terms of rectilinear step ladder sequences and offers the reasons for this. A theorem is put forth that offers a method to prove the existence of commensurable units for the unit square and rectangles in general. It does not offer a means of determining their actual numeric value. The work ends with several suggestions as to where mathematics might go in light of a cubic world view.