Re: excited state - not
- From: Jack Boyce <jboyce@xxxxxxxxx>
- Date: Wed, 26 Aug 2009 11:11:02 -0700 (PDT)
On Aug 25, 4:08 pm, sjestme <sjes...@xxxxxxxxx> wrote:
cf.:http://www.jugglingdb.com/news/thread.php?id=216468
The term "excited state" was not derived from juggling, and would not
be derived from juggling. It has a place in juggling for no reasons
relevant to juggling, and to no good purpose for juggling. It is
confusing, discouraging, and false. It refers to patterns that are
not separable from similar patterns by anything that is or is about
excitement, nor by a peculiar condition that would be a state.
Some patterns cannot be started from a standard grip by single
alternating tosses ("vanilla" rules [1]), and also not directly from
the ball-number Cascade or Fountain. The reason is a high-beat toss
and consequent low-beat tosses. When a low-beat toss is positioned
too close to the start for there to be such an opportunity at the
start, another toss or tosses must be made to allow a vanilla start
for that code string. Once the pattern is started, it can continue as
usual, retaining no aspects different from another pattern with those
tosses. Terms suitable for juggling would refer only to the possible
use of starting tosses, not the emotional notion of "excited" nor the
general difference of a "state".
For all 3-ball independent patterns, a 1 is not before the third
position, a 0 is not before the fourth position. For all patterns
needing a single leading toss, there was a 1 in second position that
is thereby moved to third place, or a 0 in third position moved to
fourth; for all patterns needing two tosses, there was a 0 in second
place moved to fourth. For a vanilla start of four balls, a 1 must
be, or made to be, in fourth place and a 0 in fifth; a 2 can be in
third place, a 3 in second. For five balls, 0 in sixth place, 1 in
fifth, 2 in fourth, 3 in third, 4 in second. Etc.
Patterns of the same ball number with the same start (including none)
can be chained [2]; they are merely in that group, not in a "state",
and nothing else is true about them by sharing a start. Independent
patterns will become dependent, not "excited", by order rotation, as
with 441 needing a leading 4 as 414 and a leading 44 as 144 [3], in
both cases shifting the first occurrence of the 1 as noted above, and
then continuing as exactly the same pattern. The only need for a
closing sequence would be to chain to the ball-number pattern (and
that group), and it can be the completion of any independent pattern.
[4] An independent pattern is produced by the proper combination of
the start, the dependent pattern, and a completion of the start.
Grouping, and excluding, under the unfortunately entrenched jargon
"excited state" obscures those factual relationships. Many wonderful
patterns and potential routines are neglected because "excited state"
conveys mystery, difficulty, and undeserved credit, with no
information useful for juggling. You still don't know how to start
it, and for juggling, that is all there is to it -- however much more
has been and could be said about it.
-------------------------------
[1] Allen Knutson Oct 1993: "More precisely stated: with the usual
number balls in your hands (equal, or one more in the starting hand)."
[2] Bengt Magnusson, Feb 1991: "It seems like any excited tricks with
the same start up sequences should be able to follow each other. Maybe
each excited word length should be further subdivided into tricks with
identical start up sequences? This would define an equivalence class
of tricks, by the way."
- Jack Boyce, Aug 1994: "He was getting close to the correct
statement, which is that two tricks can be concatenated if and only if
they have the same starting sequences."
[3] Bengt Magnusson, Feb. 1991
[4] transitions between any two patterns of any nature apparently can
be calculated, links to generators in other topics.
.
Yes, the concept of a "state" is an abstraction; it isn't something
physical you can point to. The state of the pattern after a given
throw corresponds to the rhythm and timing of objects landing, if you
were to stop juggling after the throw in question. The state evolves
from throw to throw through the pattern.
The fact that it is an abstraction, however, says nothing about the
utility or "validity" of the idea. The question is: Does the
abstraction allow you to see things in a way you didn't before, or
yield some other benefit? With states the answer is clearly yes.
States, and in particular state diagrams, give you an easily-
understood, graphical way of figuring out transitions between siteswap
patterns. They allow you to quickly and reliably spot whether a given
pattern is composed of multiple, shorter patterns. Conversely, they
allow you to easily see which patterns can be composed together to
form longer valid patterns. (i.e., they form a more rigorous basis
for Bengt's comment [2] that you reference)
The specific terminology is due to Paul Klimek, a juggler from Santa
Cruz who was one of the independent inventors of siteswap notation.
It's a reference to atomic physics; Paul conceived of the balls as
electrons swirling around in orbitals, with quantized "states" of
excitation. He did not have a detailed description of what a state
is; this came later, in 1990. For Paul it was mostly just an
intuitive analogy. Whatever one thinks of his terminology, it seems
to be here to stay.
Bruce and Bengt conceptualized siteswaps somewhat differently: They
imagined the balls being permuted (swapped) between different
locations (sites) in the pattern. The term "siteswap" comes from
them. For example, you could think of the 64 in ...555555 64 55555...
as effectively swapping the locations of two balls within the five
ball cascade. Applying more involved permutations yields other
patterns, like 66661. This way of conceptualizing it only leads to
what we today call ground-state patterns. It was a while before they
accidentally happened across a nontrivial excited state pattern, and
saw they were missing this other class of patterns. Another missing
element was the zero throw, which Paul had invented. In Bengt's
earliest lists of siteswaps (he wrote the first siteswap generator),
you'll find there are no patterns containing zeros. The lesson I
suppose is that one's conceptual framework for a problem can be
important.
Jack
.
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- From: sjestme
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