Numbers do not exist in nature. That we invented a number system for use in the natural world in which countable items may be found is surely non-momentous. Morbidly numerous objects like grains of sand and difficult-to-count objects by the nebulosity like clouds are no reason to throw non-momentousness into doubt.
This brings me to Richard's original objection to Mandelbrot and fractals. Surely Richard doesn't believe that mathematicians have confused the map for the territory (that Borgesian story I referred to.) Mathematicians are aware that mathematical propositions only map onto each other exactly/ axiomatically; they are approximations when mapped onto the real world. Moreover, a mathematician would never make a stronger claim than “The coastline of Britain can be scaled up and down” or “The branching pattern in trees seems fractal”; the business of mathematics is looking for numerical patterns not explaining them.
About Kant I say nothing. The mere mention of his name gives me a headache.
David Savory
Vancouver
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