Measuring Fractal Dimension ?

Robin Becker robin at
Thu Jun 25 05:01:53 EDT 2009

pdpi wrote:
> But yeah, Log2 and LogE are the only two bases that make "natural"
> sense except in specialized contexts. Base 10 (and, therefore, Log10)
> is an artifact of having that 10 fingers (in fact, whatever base you
> use, you always refer to it as base 10).

someone once explained to me that the set of systems that are continuous in the 
calculus sense was of measure zero in the set of all systems I think it was a 
fairly formal discussion, but my understanding was of the hand waving sort.

If true that makes calculus (and hence all of our understanding of such 
"natural" concepts) pretty small and perhaps non-applicable.

On the other hand R Kalman (of Bucy and Kalman filter fame) likened study of 
continuous linear dynamical systems to "a man searching for a lost ring under 
the only light in a dark street" ie we search where we can see. Because such 
systems are tractable doesn't make them natural or essential or applicable in a 
generic sense.
Robin Becker

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