To build on Jim Fischer's post (and his notation), perhaps I misread the
Lusby/Housel article.  As I understood it, a "perfect Housel" switches
order in the middle and the center is always supposed to be down-facing.
Apologies if I am misrepresenting the article.

9 Frame version:
Frame Number                 1  2  3  4  5  6  7  8  9
A "perfect Housel"           YA YA YA YA AA AY AY AY AY
The 10 Frame version:
Frame Number                1  2  3  4  5  6  7  8  9 10
A "perfect Housel"         YA YA YA YA YA AY AY AY AY AY

As I read the article, there could be up to 10 errors in a ten frame set-up
and an "anti-Housel" would start with both centers up-facing but otherwise
alternate cleanly.

Frame Number                1  2  3  4  5  6  7  8  9 10
The "anti-Housel"          AY AY AY AY AY YA YA YA YA YA

1 in 1024 chance of a 10 frame "perfect Housel" and 1 in 1024 for an
"anti-Housel".  However, I could make an argument that the"anti-Housel" is
actually closer to a "perfect Housel" than a "random" because at least the
alternation is consistent.  Maximum disruption might follow this pattern.
Frame Number                1  2  3  4  5  6  7  8  9 10
worst?                     AY YA AY YA AY YA AY YA AY YA

(The article would appear to dispute this definition of worst since I think
they propose a reason why the Y orientation will always be found to the
outside.)  If we change Jim's definition of error to counting the
incidences of AY YA, we take a conservative position and get back to a
maximum of 5 errors.  That definition has an added benefit that it gets rid
of what might be expected to be trivial errors where the YA AY pattern just
happens not to fall in the middle of the hive (frames 5 and 6).

Based on that definition, the distribution of potential errors is
     0 errors     11
     1 errors     165
     2 errors     462
     3 errors     330
     4 errors     55
     5 errors     1

If the bees build randomly, "perfect Housels" would be expected to be
statistically rare, but near perfects might not be uncommon.  I'm not sure
what I've really proved here except that statistics is more interesting
than the work I was supposed to be doing tonight.  Interpretations or
suggestions for how to collect the data to prove or disprove the original
theory?

Mike Rossander














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