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    Re: Lunars using Bennett
    From: Peter Fogg
    Date: 2008 Apr 4, 19:29 +1100

     Alexandre you wrote:
    
    >  The tables in Bennett do not have sufficient
    >  accuracy ... because they are
    >  rounded to 1'.
    >  ... and the errors will accumulate).
    
    Firstly; these are not 'errors', which implies inaccuracy, but rather
    a limitation in precision.
    
    Secondly; the amounts by which the values are rounded up or down, when
    added together (as they are in Bennett) will NOT tend to accumulate,
    but will tend to cancel each other out, and trend towards accuracy,
    rather than inaccuracy.
    
    In Jan 05 I tested this and presented the results here:
    http://www.fer3.com/arc/m2.aspx?i=021346&y=200501
    
    and then, in:
    http://www.fer3.com/arc/m2.aspx?i=021372&y=200501
    
    summed up the chances of all 6 rounded values accumulating towards
    inaccuracy, rather than tending to cancel each other out, as:
    "... the chance of that most unlikely event is one in six to the power
    of six, or 0.00002, or [happening, on average, in] 0.002% [of cases
    where there are 6 rounded values added together]".
    
    Finally, the issue I take exception to here should be clear enough -
    it is limited to this strange yet persistent notion that the amounts
    by which values are rounded will tend to accumulate in series.  I have
    no opinion about using Bennett for lunars, other than to congratulate
    d walden on the ingenuity of the idea.
    
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