From: celarier@reed.edu (Stuart Celarier)
Newsgroups: rec.juggling
Subject: Re: half and quarter showers.
Keywords: Showers, quarters, site swap notation, problem set
Date: 18 Aug 92 18:18:26 GMT
Article-I.D.: reed.1992Aug18.181826.13715
Organization: Reed College, Portland, OR

In article <MAILQUEUE-99.920818123352.480@lucs-01.novell.leeds.ac.uk>  
STA5CW@lucs-01.novell.leeds.ac.uk (Chris Wright) writes:
>      On the subject of the half-shower:
> ...
>     Moving on to six balls, the possibilities are 9 3 and 7 5.
> Perhaps we could call 9 3 a half shower, and 7 5 a quarter shower?
                                                     ^^^^^^^^^^^^^^
I had a great shower for a quarter myself in upstate New York after the  
Montreal convention!  Good hot water and lots of soap.

>                                   Chris Wright, Leeds, England.

	I wouldn't worry myself silly trying to reconcile two different  
systems for describing juggling patterns.  Site swap notation only  
describes a small subset of all the possible juggling patterns; current  
jargon and lingo is not precise enough to describe the details in found in  
site swap speak.

	As Chris points out, looking at how half showers (or other tricks)  
are described in siteswapese does often lead one to whole families of  
related tricks, which is part of the power of the notation.

	Incautious Chris leads into the subject with

> We all know that a three ball HALF shower is just 3 in s-s, and would
> agree that a four-ball half shower is 5 3.

I would definitely *not* know that a three-ball half shower is 3.  The   
site swap pattern 3 describes the cascade.

Otherwise, thanks for the great posting, Chris!  It really got me thinking  
-- and now its your turn to think.  All responses welcome.


	*  *  *  *  *  Problem set  *  *  *  *  *

	Email your answers to celarier@reed.edu and I will be happy to  
summarize and post correct or thought provoking responses.

1.  What *is* the site swap notation for the three-ball half shower?

2.  Why doesn't the four-ball half shower notation, 5 3, distinguish  
between the right- and left-handed half shower?  Can you propose an  
extension to the basic site swap notation which could distinguish the  
orientation of these two tricks?

	Multiple hand site swap notation works like this:  if  H  is the  
number of hands, then number the hands 1, 2, ..., H; the hands throw in  
the repeating sequence, h = <1, 2, ..., H, 1, 2, ...>; and a throw of  
height  n  from hand  h lands in hand  h+n modulo H.  For example, with  
three hands (H=3) a throw of height  n=3  lands back in the same hand that  
threw it (h' = h);  n=4  lands in the hand one to the right of the one  
that threw it (h' = h+1 mod H).  

3.  Can you describe families of half shower patterns where the number of  
hands  H = 3, 4, 5, or an arbitrary value (H=K)?  Describe what makes  
these patterns like a half shower.
  
4. Extra credit.  What names would you select to describe individual  
multiple hand half shower tricks in keeping with Chris Wright's half-,  
quarter-, eighth-, sixteenth-, ..., or half-, third-, quarter-, fifth-,  
.. notation?
--
Stuart Celarier		"No Problem, Easy Pickup" Portland Jugglers
celarier@reed.edu	PO Box 82842
503/236-9386		Portland, Oregon 97282
Newsgroups: rec.juggling