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SCALING_SIMILARITY

                                             May  6, 2008

                                             BLACK_SWAN

The roughness of terrain is invariant
with altitude only over some ranges
of altitude (and for some terrain).

Go up high enough and the earth seems
perfectly smooth (albeit, not quite a sphere).


And similarly (uh, no pun -- well, whatever),
fire may exhibit that celebrated bifurcating
fractal self-similarity at different
magnitudes, but there really is a noticeable
difference between large fires and small.

This is why a cheap special effect such as
burning a small model of a building never
looks quite right on film.



    "Some people ... have accepted the fractal 'up
    to a point.'  They argue that wealth, book
    sales, and market returns all have a certain
    level where things stop being fractal.
    'Truncation' is what they propose.  I agree that
    there is a level where fractality _might_stop,
    but where?  Saying that there is an upper limit
    _but I don't know how high it is_, and saying        This depends
    _there is no limit_ carry the same consequences      on what you're
    in practice."                                        trying to
                                                         practice.
                   -- p. 266, Nicolas Nassim Taleb,
                              _The Black Swan_


                      (April 17, 2008)

    And in a footnote, Taleb mentions there
    may be effective limits on the
    extremity of Extremistan, but he
    takes these limits as so high that
    we might as well call them infinite.

    Consider the possibility
    that there are actual limits
    to the effect of wild cards.

    If you can draw a probable
    boundary around the effects
    of even extreme events,
    that in itself might be
    useful



         The upper bound will never
         be found by someone who           There are places
         doesn't accept that it might      you can start:
         exist.
                                           It would seem that
            The style of scenario          the maximum number
            planning favored by            of book sales would
            Peter Schwartz                 be less than the
            encourages people to           world population.
            consider some extreme
            scenarios to get a
            sense of the range of
            things that can
            happen.






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