By Ian Stewart
The well known writer of the "Mathematical Recreations" column in medical American explains the major techniques in math and their implications, mentioning that even if arithmetic is completely unreal--an solely psychological construct--it is the simplest device to be had for describing and figuring out the true international. Illustrations.
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Additional info for Nature's Numbers: The Unreal Reality of Mathematics (Science Masters Series)
Their equispaced alignment is an accident, depending on the position from which they are being viewed. Indeed, the very word "constellation" is a misnomer for an arbitrary accident of viewpoint. The numerical relation between the periods of revolution of 10, Europa, and Ganymede could also be an accident of viewpoint. How can we be sure that "period of revolution" has any significant meaning for nature? However, that numerical relation fits into a dynamical framework in a very significant manner indeed.
The pursuance of safe research will impoverish us all. The really important breakthroughs are always unpredictable. It is their very unpredictability that makes them important: they change our world in ways we didn't see coming. Moreover, goal-oriented research often runs up against a brick wall, and not only in mathematics. For example, it took approximately eighty years of intense engineering effort to develop the photocopying machine after the basic principle of xerography had been discovered by scientists.
Ancient human civilizations organized the stars in the sky in terms of pictures of animals and mythic heroes. In these terms, the alignment of the three stars in Orion appears significant, for otherwise the hero would have no belt from which to hang his sword. However, if we use three-dimensional geometry as an organizing principle and place the three stars in their correct positions in the heavens, then we find that they are at very different distances from the Earth. Their equispaced alignment is an accident, depending on the position from which they are being viewed.