Python syntax in Lisp and Scheme

[Kenny Tilton]

Andrew Dalke wrote:
> Me:
> 
>>>2 of 6 is better than random, so Jones' work can't be
>>>complete bunkum.
> 
> 
> Jon S. Anthony:
> 
>>2 of 6 is worse than flipping a coin.
> 
> 
> Since I said "Of the 6 languages there are two major misorderings"
> I suspect this discussion has reached the point of weariness.
> 
> Nevertheless, the ordering is 1 3 5 6 2 4
> 
> Assume a cost metric based on simple transpositions, where
> neighbors can be exchanged.  This is the familiar interchange
> (or Shell, or bubble, or ..) sort.  The degree of disorder is
> the number of exchanges needed to sort the list.  For the
> above it is ||{2-6, 2-5, 2-3, 4-6, 4-5}|| = 5
> 
> The average number of exchanges needed to sort a randomly
> arranged list with the Shell sort is N*(N-1)/4 == 7.5 for
> this list of size 6, so it's already better than average.
> 
>  From Knuth, Searching and Sorting, 5.1.1, Table 1, the
> distribution of the number of permutations with k inversions
> of a list of length 6 is
>    1 way to be ordered
>    5 to have one transpositions to be ordered
>  14 to be off by 2 transpositions
>  29
>  49
>  71
>  90
> 101
> 101
>  90
>  71
>  49
>  29
>  14
>    5
>    1 to be completely reversed
> 
> Thus there are 720 possible random orderings of a list of
> size 6 and only 169 ways to be off by 5 or fewer transpositions.
> meaning that there is only a 24% chance of being this good
> randomly.
> 
> If I understand 5.1.1(13) well enough, the variance is
> sqrt(6*(2*6+5)*(6-1)/72) == 2.66 which means we're
> right on the 1 sigma threshold, or about a 75% chance
> that his table was not randomly generated.
> 
> Again, this suggests Jones' work can't be complete
> bunkum.

I can see why you like studies. They are so much more malleable than 
peoples' reports of their experience. With numbers you can say things 
like "there is only a 25% chance I got this off a ouija (sp?) board" and 
it sounds good! I think the tobacco companies can use you, they're 
losing ground fast. Your research bureau can have the tag line "Our Data 
Guaranteed Not /Completely/ Random!"


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