Dialectic mathematics is a rigorously logical science, where statements are either true or false, and where objects with specified properties either do or do not exist. Algorithmic mathematics is a tool for solving problems. Here we are concerned not only with the existence of a mathematical object, but also with the credentials of its existence. Dialectic mathematics is an intellectual game played according to titles about which there is a high degree of consensus. The rules ol the game of algorithmic mathematics vary according to the urgency of the problem on hand. We never could have put a man on the moon if we had insisted that the trajectories should be computed with dialectic rigor. The rules may also vary according to the computing equipment available. Dialectic mathematics invites contemplation. Algorithmic mathematics invites action. Dialectic mathematics generates insight. Algorithmic mathematics generates results.
John Wilder Tukey, one of the greatest Statistician of the last century points to what the purpose of a graphic display should be:
- Graphics are for the qualitative/descriptive – conceivably the semi quantitative – never for the carefully quantitative (tables do that better).
- Graphics are for comparison – comparison of one kind or another – not for access to individual amounts.
- Graphics are for impact – interocular impact if possible, swinging-finger impact if that is the best one can do, or impact for the unexpected as a minimum – but almost never for something that has to be worked at hard to be perceived.
- Finally, graphics should report the results of careful data analysis – rather than be an attempt to replace it. (Exploration-to guide data analysis – can make essential interim use of graphics, but unless we are describing the exploration process rather than its results, the final graphic should build on the data analysis rather than the reverse.)
Tukey, J. W. (1993). Graphic comparisons of several linked aspects: Alternatives and suggested principles. Journal of Computational and Graphical Statistics, 2(1), 1-33.