ABSTRACT
Aids such as compasses and iron filings might provide the means by which such evidence is collected in the case of a magnetic field, but other techniques come to mind that we could use to identify information and computation in the synthetic worlds that interests us. Hermann Minkowski was a nineteenth-century German mathematician of Jewish and Polish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics and the theory of relativity. The solution of a general cubic equation may require intermediate calculations containing the square roots of negative numbers, even when the final solutions are real numbers, and the introduction of complex number provided a way around this. The polar coordinate system is useful in situations where the relationship between two points is easily expressed in terms of angles and distance; in the familiar rectangular coordinate system, such a relationship can be found through trigonometric formulation.
