#19
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Re: Variance is Fractal
Let's see.. a few definitions for fractal:
[ QUOTE ] A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale. [/ QUOTE ] [ QUOTE ] A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. [/ QUOTE ] [ QUOTE ] A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. [/ QUOTE ] Ok, so you are talking about a concept as though it's a geometric shape. Marijooana is good, mmmm-kay? Let's list common properties of fractals: [ QUOTE ] A fractal often has the following features: It has a fine structure at arbitrarily small scales. [/ QUOTE ] Fail, poker actions are discrete. [ QUOTE ] It is too irregular to be easily described in traditional Euclidean geometric language. [/ QUOTE ] Fail, even if I give you the benefit of the doubt translating to a graph, since sample variance is hardly irregular. [ QUOTE ] It is self-similar (at least approximately or stochastically). [/ QUOTE ] Fail, sample variance curves aren't self-similar. [ QUOTE ] It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). [/ QUOTE ] Fail, obviously. [ QUOTE ] It has a simple and recursive definition. [/ QUOTE ] Fail, obviously. So I ask again, what the hell are you talking about when you say variance is fractal? |
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