A good definition of magic would be: (1) the ability to discover
and predict the hidden powers of the cosmos. (2) The ability to harness such powers effectively for good
For such knowledge and ability was just what was sought
by the sorcerers, magicians, and numerologists of old. Since the time of Pythagoras numbers themselves contained a kind
of magic. However, even Pythagoras found numbers meaningful only when he substituted logic for magic, and thereby
discovered the hypotenuse of a right triangle, and also the system of harmonics (while trying to decipher the music of the
spheres.) Euclid went a step further when developing the axioms of basic geometry.
After the ancient Greeks, the use of numbers devolved down
through practical use to again return to the numerological magic, this time with alchemists, prognosticators, and Kabbalists.
No significant discoveries were made during that period. Then with the onset of thinkers like Roger Bacon the magic
of numbers again began to work fruitfully in the Western world. For now numbers were made to correspond to measurable
objects and events.
When observing and calculating heavenly bodies, Copernicus
found a sun centered theory more mathematically eloquent than the earth centered theory of old. Then Kepler's improved
math replaced Copernicus' unwieldy epicycles and discovered the true elliptical paths of the planets. (That's when he
exclaimed, "I write my equations after God!")
Then Newton invented calculus and developed an eloquent theory
of gravity useful to astronauts even today. In the 20th century, Einstein borrowed a ready made non Euclidian geometry
to discover four dimensional space/time. Meanwhile, quantum mathematics probed into the incredible mysteries of
the micro-cosmos. Today physicists and mathematicians are working together to find the grand unified "theory of everything"
encompassing all natures forces.
The logical/empirical numerology of science can also predict
future events, not only through the science of statistics, but also through the theories themselves.
The soundness of scientific theories is judged not only by how accurately they describe events but in how well they can
predict future discoveries and events.
Hence, numbers produce their true magic through rigorous logical
calculations, tested against empirically observable events.