A densely wrought exploration of Mandelbrot equations, the Droste effect, the Barnsley theorem, and other thorny problems of mathematics.
“How long is the coastline of Cornwall, UK?” That’s a question that would have sent Newton and even Einstein into the depths of despair. It’s owing to an insight by Polish-born mathematician Benoit B. Mandelbrot that we can map out the three-dimensional world in which we live to some degree of certainty thanks to fractals, which, in nature, reveal themselves to be miniature images of the larger whole: “the magnified detail,” writes Cambridge econometrician Linton, “is exactly the same as the whole thing.” The attendant conceptual difficulty is that any map that is sufficiently detailed to reveal the whole accurately will be the size of the whole thing itself: A map of the universe would be the size of the universe, a thought that would have pleased Jorge Luis Borges. Lacking room and the wherewithal to prove the point with that map, mathematicians have come to develop numerical shortcuts—but those shortcuts are extraordinarily demanding of data, such that the GPS in your car relies on billions of numbers even as “nature…uses fractals for reasons of economy.” This is not a book for the mathematically weak of heart. Although it’s admirably short, certainly as compared to what might have happened to the discussion in the hands of a Douglas Hofstadter, each page bristles with equations and heady prose: “The pattern is clear; if you need l unit objects to make it m times larger then the number of dimensions the object has is d where l = md.” If that sort of writing is your cup of pi, then Linton’s compact explication of fractals will be child’s play; others will be flummoxed.
A small treasure for those who enjoy brain teasers and mathematical formulas.