Math, Einstein and Modes of Human Thought
Before Relativity
In approaching mathematical thinking from a philosophical standpoint, many historical incidents lend themselves to examination. Perhaps most fascinating, and relevant, to the modern-day mind, however, is the topic of Albert Einstein and his theory of relativity. EinsteinŐs theory ranks not only as one of the most important scientific discoveries of the twentieth century, but as one of the most influential ones in terms of its impact on non-scientific thinking. Challenging mathematical and scientific models that were centuries old -- the absolutism of Euclidean geometry and Newtonian physics -- relativity was a concept which represented a new, and comprehensive worldview. As such, its influence extended to political, religious and philosophical realms previously oblivious to problems of geometry and physics. Relativity meant not only that different physical frames of reference were equally valid, but that intellectual ones were as well.
The Euclidean and Newtonian views which relativity necessarily questioned were equally radical in their own time. Alfred W. Crosby, in his book The Measure of Reality, argues that such theories resulted in "the quantification of western society," (Crosby, 3). Prior to 1400 A.D. the more spiritual, qualitative view of the world reliant on anecdotal, non-mathematical observation, ruled as a guide to the world. Existence was as it was perceived through human senses, distorted as they were.
But with a rediscovery of Euclidean geometry, and the eventual proliferation of Newtonian views as well, this "venerable" model, as Crosby refers to it, began to disappear. In its place arose an understanding of the world more abstractly expressed through definite numbers, or quanta. It was a change which shook the foundations of western EuropeŐs philosophical, as well as mathematical, institutions. As the astronomer and physicist Keppler stated in 1599,
"What else can the human mind hold besides numbers and magnitudes? These alone we apprehend correctly, and if piety permits to say so, our comprehension is in this case of the same kind as GodŐs, at least insofar as we are able to understand it in this mortal life," (Crosby, 126).
This tension -- between the rational and the spiritual -- was one that cut to the core of the rise of quantification. If the physical world could now be measured in exact, precise, absolute quantities, then the spiritual world must also resemble that. God's work was the world, and the world now had definitive rules. As the mathematician Blaise Pascal noted, the developments of classical physics filled a "terrifying" void (Crosby, 108).
The extension of quantification into formerly qualitative areas such as bookkeeping, art and cartography satisfied this new sense that absolute truth could be extended towards all areas of life. The premier historian of Renaissance art, Erwin Panofsky, noted that perspectival drawing -- the ability to precisely relate three dimensional objects in two dimensional images -- "satisfied the new craving for exactness and predictability" (Crosby, 197). The effect of this new paradigm was aptly summed up by Galileo in saying,
"Philosophy is written in this grand book, the universe, which stands continually open to our gaze, but the book cannot be understood unless one learns to first comprehend the language and read the letters in which it is composed. It is written in the language of mathematics...without [it], one wanders around in a dark labyrinth," (Crosby, 240).
There was one, and only one, way of viewing the world.