Why you can't juggle a 4 ball cascade
Haavard
Since I started juggling about three years ago, I have done both four and
five balls and their respective patterns; fountain and cascade, although
there are site-swap patterns that will make it look like you are juggling
four balls in a cascade pattern.
Moreover, I have read a fair bit on the mathematics of juggling, and the
site-swap notation makes things a lot more interesting, doubly so as I am
a physics undergrad.
Now, just recently I started thinking about why exactly it is that you
cannot juggle four balls in a cascade pattern. And it just seems a lot
trickier to explain, than I had though.
Sure, you can put up juggling diagrams of left and right hand and and note
that with four beats, the ball is going to land in the same hand.
But it just doesn't seem to cut it. I want an intuitive explanation. I
will try to juggle four balls in a cascade pattern, but even then, it is
not entirely clear why it won't work.
By the way, if you threw the balls at different heights, I think one
should be able to get it work. I suppose there is a site-swap for that too.
So if anyone has paid attention to the same question, I would be happy to
hear from you.
--
----== posted via www.jugglingdb.com ==----
Boppo
There is indeed the 53, which is cascadey in that all the throws that
cross, and it's four balls, but they go to different heights. There's
also (4x,4x) which is kind of cascadey as well, except that it's
synchronous. There are also tricks like 5551 and 55550 which have
asynchronous throws and which cross, but they have gaps. Then of
course there are 3 and 5, which are very cascadey indeed, and
asynchronous, and all throws to the same height and everything, except
that they aren't four ball tricks. What there seems to be missing, is
a trick in which all the throws cross, and all the throws are to the
same height, and it's asynchronous, and it's four balls - the mythical
Four Ball Cascade.
Does this trick exist, or does it not? We'll just have to wait for an
upcoming video from me to see ... a video in which I attempt the
mythical four cascade, as well as the equally mythical five ball
fountain.
Stay tuned.
-boppo
edward
What's the definition of a cascade?
_HanS
I've been rewatching the siteswap dvd and reading a lot of articles lately
and to answer this question I think we have to let go of one of the basic
assumptions that are used where siteswap starts..
I was thinking about it just today while I was trying to come up with some
new squeeze-patterns. Multiplex notation was made possible by letting go
of the assumption or rule that two balls can't end up at the same place.
Squeeze-patterns are just a way to make this significantly more difficult
(instead of holding a 2 and let the second ball fall in, why not throw
them there so that they land at the same time).
And so I looked at the other assumption which is the timing of the throws.
For siteswap to work , the hands have to throw alternately
(right-left-right-left). Or exactly at the same time, for the synchronous
notation. But what if this rhythm was slightly different? There is
probably an amount of tricks that can be done with perfect timing of the
hands (off-beat as it will probably be). There is a part of the siteswap
dvd about this, but I think it can be explored more.
By example, if you would juggle 64 (it wouldn't be exactly 64, but now you
know what I'm talking about) with the 4's at the same height as the 6's
(by changing the rhythm of your left hand) wouldn't that be something like
a 5 ball fountain? It makes me wonder if a same principle can be used to
create the illusive 4 ball cascade. Hands would probably have to change
rhythm after every throw? I think getting it right would probably be very
difficult (and may be possible to translate back to siteswap with 2's and
0's)
Sorry this text is so long, I was just trying to recreate the thinking
process for myself.
What do you think about this (for now, let's call it Timeswap)
HanS
Dave Altman
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
You are over-thinking the problem. No amount of siteswap trickery can
explain it or make it possible. By definition, a cascade can only be done
with an odd number of objects, each hand doing the same motion, but in an
alternating timing. That is as intuitive of an explanation I can make.
Dave Altman
^Tom_
> By example, if you would juggle 64 (it wouldn't be exactly 64, but now you
> know what I'm talking about) with the 4's at the same height as the 6's
> (by changing the rhythm of your left hand) wouldn't that be something like
> a 5 ball fountain? It makes me wonder if a same principle can be used to
> create the illusive 4 ball cascade. Hands would probably have to change
> rhythm after every throw? I think getting it right would probably be very
> difficult (and may be possible to translate back to siteswap with 2's and
> 0's)
Wouldn't that be almost like calling 552 a 4 ball cascade?
Norbi
>
> By example, if you would juggle 64 (it wouldn't be exactly 64, but now you
> know what I'm talking about) with the 4's at the same height as the 6's
> (by changing the rhythm of your left hand) wouldn't that be something like
> a 5 ball fountain? It makes me wonder if a same principle can be used to
> create the illusive 4 ball cascade. Hands would probably have to change
> rhythm after every throw? I think getting it right would probably be very
> difficult (and may be possible to translate back to siteswap with 2's and
> 0's)
>
>
I think it's already called multi/poly-rhythmic.
My thoughts on the cascade 'problem'.
If you juggle 53 with the 5s thrown at 3 height and a 0 dwell time in the
left hand so you just hit it
back (or something like this...i'm not in the position to test my theory
now... i'm tangled up on a sofa
watching a movie) it should keep a reasonable cascade shape. No?
Norbi
Dave Altman
Still, nothing is going to be a four ball cascade. It is totally
impossible, really! By definition, all the balls of a cascade are thrown
at the same height. Any changing or bending of the timing to make four
balls look like a cascade might be a nice pattern, but it will never be a
cascade. A cascade can only be done with an odd number of objects, end of
story.
Dave Altman
Will Helm
> cascade. A cascade can only be done with an odd number of objects, end of story.
DAVE: "end of story" is so contrary to what juggling has always been,
that it sounds like a satyrical troll.
Whether BruceT or Norbi or somebody else gets it out on video first,
we'll want to see it. Whether the tactic is called variable dwell or
polyrhythmic is not going to be as interesting to me as there being a
waiting list of jugglers going for this stunt: a next "challenge",
yay! I like the consternation over the definition of what must be
done to do it: why isn't an async 53 a four-ball cascade? Why isn't a
synchopated (4x,4x) just as good? If you can do it, and an audience
likes it, or you like it, what difference does someone else's
"definition" make?
Who's going to troll, and who's going to throw?
WillH
Boppo
Well, I certainly hope to scoop the competition, so to speak.
(Hint: look in the r.j. archives. But I want to film it anyway. It's
easy - even though it IS impossible.)
-boppo
jimb...@aol.com
wrote:
Good point!
Why not juggle 4X with a near 0 dwell time?
Conventional fountains and cascades each have their respective
constant dwell times.
Shorting the dwell time would distort those patterns. Such juggling
is not 'natural.' Within the definition of a cascade surely is
written a reference to the proportional dwell time. [1]
but..
Is it possible - to shorten the dwell times AND to shorten the 5
throws to 4X in a 55550 enough to exclude that 0? [2]
If it is possible, by definition it would not be a cascade, but it
would be alternating hands tossing or hitting back crossing throws.
Anyone ever try to cascade 4 ping pong balls using 2 paddles?
Later,
Jim
[1] Claude Shannon's Juggling Theorem
[2] A siteswap zero is just time, isn't it?
_HanS
Yesterday I remembered seeing Matthew Tiffany do patterns like this that I
just couldn't get my head around until now. After searching 'polyrhythms
juggling' in Google I found this thread about 'multi-frequency juggling':
http://www.jugglingdb.com/news/thread.php?group=1&id=128146&highlight=polyrhythmic
Didn't have the time to read it all in full, but I guess they base it on
Beatmap? I'll have fun figuring it out later. There is also this article
in the archives with a chapter on it, here called 'polyrhythmic' again:
http://www.jugglingdb.com/compendium/geek/notation/siteswap/tweaked.html?lang=nl
Have fun with it
HanS
Dbjuggler
You throw right-left-right-left. Now the next throw would be right, but
the first throw was a right throw(this ball is in the left hand now) , so
the next throw comes from the left hand. There is no more detailed
explanation than this.
Dave Altman
Who is trolling who, WILLh:? "If...an audience likes it..." is funny, like
they care what jugglers call their patterns. Cascade is hardly a term I
made up and it isn't "MY" definition, at least not one that don't share
with other jugglers. It's been around for quite a while. I have no idea
how long, though. I doubt that it could be pin-pointed to any one person,
but that is a different story...
The only way anyone will ever do a cascade with four objects, isn't by
doing anything physical, it will be by changing the definition of the
term. While this is possible, why do it?
Asking how you can do a four ball cascade is like asking how do you do a
360 without spinning. In my satyrical trolling way, it can't be done. A
360 is defined by spinning around a full rotation. Anything else that
isn't that, isn't a 360, "end of story."
You asked, "what difference does someone else's "definition" make?" Well,
it is the basis for communication. If everyone called the same objects
totally different things, it would be quite confusing. You could a car an
"apple", a tree a "chair," and a store a "bathtub." So, instead of saying
you were going to get into your car to drive to the store to get some
apples, you'd say that you got into your apple, drove to the bathtub, and
you saw a bird in a chair. If you tell someone that, it doesn't change the
fact that you went to the store in your car and bought some apples, but it
will get you some funny looks if you tell people what you did, by not
using the same terms as everyone else, so, that is the difference it makes
if you don't use someone else's definition.
Janion
Surely if one hand threw ss5 normally with the scooping etc and the other
just batted the ball back the timing would be right. no?
For example in this video. http://www.youtube.com/watch?v=naU_5w85w5Q#
the batting immitates a cascade timing quite well.
Although its a bit confusing to make both hands work in a different way.
MichaelB
>
> Imagine you try to juggle a 4 ball cascade.
> You throw right-left-right-left. Now the next throw would be right, but
> the first throw was a right throw(this ball is in the left hand now) , so
> the next throw comes from the left hand. There is no more detailed
> explanation than this.
>
This is exactly the way I explain it when I'm teaching someone 4 ball
patterns. I don't know how you can make it any clearer.
edward
If nobody defines cascade then it's pretty much impossible to argue one
way or another, unless the whole question is about defining cascade such
that there isn't a 4 ball one?
Aymeric
80 with every other throw as inside throw?
A.
Boppo
Throw!!
Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
Please note the category I put the video in.
As an added bonus, I also do the 5 wimpy pattern as well as the
mythical 4 cascade and the 5 fountains. I am perhaps the first person
in the world to attempt the 5 wimpy pattern, and with any luck, also
the last.
-boppo
MichaelB
>
>
> Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
>
> Please note the category I put the video in.
>
> As an added bonus, I also do the 5 wimpy pattern as well as the
> mythical 4 cascade and the 5 fountains. I am perhaps the first person
> in the world to attempt the 5 wimpy pattern, and with any luck, also
> the last.
>
> -boppo
>
>
Nice. Especially liked the 4 ball "cascade like" looking pattern.
Norbi
>
> Still, nothing is going to be a four ball cascade. It is totally
> impossible, really!
Really? Nothing?
But you said.
> By definition, all the balls of a cascade are thrown
> at the same height.
Although said nothing about crossing or straight (not to mention I didn't
know there was a 100% universally recorded definition of cascade
anyway...) just the fact they are the same height.
SO...Boppo wins?
I personally think yes.
nOrbi
Dave Altman
>
> Dave Altman wrote:
> >
> > Still, nothing is going to be a four ball cascade. It is totally
> > impossible, really!
>
> Really? Nothing?
> But you said.
>
> > By definition, all the balls of a cascade are thrown
> > at the same height.
>
> Although said nothing about crossing or straight (not to mention I didn't
> know there was a 100% universally recorded definition of cascade
> anyway...) just the fact they are the same height.
>
> SO...Boppo wins?
>
> I personally think yes.
Well, sort of but not really, because, from what I understood in the
video, Boppo agrees with me that it is impossible to do a true four ball
cascade. He definitely did the best fake four ball cascade I've ever seen,
as well as the best fake five ball fountain.
Dave Altman
Boppo
wrote:
Geez, it's not "fake" it's "mythical." It's more like unicorns than
professional wrestling.
There's just no pleasing some people.
-boppo
Lloyd Ramsey
>....I am perhaps the first person
> in the world to attempt the 5 wimpy pattern, and with any luck, also
> the last.
B-po, was that some of the supposed "comedy"? I mean, (4x,6x) is just
an obvious siteswap, also done as a Half-shower, a 6 and 4 can be
done in every logical combination.
As for 4 with crossed toss positions, a fellow showed me that one
about, oh, let's say, less than ten years ago. Fooled me at the time,
and I still consider it to be enough of a Cascade form to call it
that. The best part about yours was so effectively hiding your hands,
as smooth as a magician.
I wish you had done a skewed version of (4x,4x) also, as it approaches
53 it gets as Cascadey. The question above about 552 is interesting
for the inquiry: no matter how little dwell there is for the 2, you
will still have non-alternating tosses. And alternating tosses are to
me more important in the question than path height. It is more likely
to match cross-positioned 4 for a Cascade form with 55550 than any of
the others, imo, the 0 "gap" can be almost unnoticed, along with the
right-right and then left-left hitch, with enough other proper
alternations to slide by unnoticed.
You've been for me before only a vague reference in juggling history.
Now, you are a real cool real guy, thanks!
WH
Dave Altman
Oops! I meant to type "mythical," it must have been a typo. You know how
it is, my fingers slipped and something got in my eye...
Boppo
Yes, indeed some of the comedy is calling the third pattern "not
impossible, but highly inadvisable." Whether my sense of humor works
for everyone is another question ... well, I guess we'll see what
Sondre thinks of my other recent film.
If someone could juggle with a dwell ratio of zero in one hand and one
in the other hand, with four balls, the result would look exactly like
the 3 cascade, except there would always be the fourth ball in the
high-dwell hand. I just tried to do this but can't make it convincing
enough to be worth filming. In any case, the pattern will necessarily
be asymmetric, either with the extra ball on one side only as a result
of the ideal dwells, or as a result of slightly skewed timing as a
result of imperfect dwells (like, 0.1 and 0.9 dwell ratios) in
addition to the extra ball. Worse, at best it would look just like
the three cascade - and I *can* juggle three while also holding a
fourth ball in one hand that I never throw. But that pattern wouldn't
look like 4, while the high-scoop version that I filmed does look like
four, and the point was to do the 4 cascade - not the 3 cascade while
holding another.
The bottom line is that, since we have two hands, there really is an
enormous gulf between even patterns and odd patterns. 0 mod 2 and 1
mod 2 have really, really different properties.
-boppo
Matthew Tiffany
by making one hand have loads of dwell time and the other as little as
possible a 4b cascade is very possible. as is a sync 3b cascasde.
tiff
xx
Haavard
> Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
>
> Please note the category I put the video in.
>
> As an added bonus, I also do the 5 wimpy pattern as well as the
> mythical 4 cascade and the 5 fountains. I am perhaps the first person
> in the world to attempt the 5 wimpy pattern, and with any luck, also
> the last.
>
> -boppo
Boppo,
That 4 ball cascade is smooth. Whenever I try to do it, I just end up
doing 552. So it seems I have to reprogram my motor memory.
GuyHeathcote
figure-of-eight path, around which the balls travel at regular intervals.
Likewise, with five balls, a similar (but usually larger) path is also
achieved, again with the objects stationed at regular intervals. So, I
don't see why this can't apply to four balls also.
It would be straightforward to simulate the pattern on a computer, would
it not? The problem in real life is surely not that it's impossible, just
that the timing would be so pointlessly hard that it's not really worth
bothering with.
Sure, this doesn't really work in siteswap, but as the term 'cascade' was
coined long before siteswap was defined, I don't see why there's any
reason to restrict the term's meaning to patterns that only work within
siteswap's limitations.
Boppo
A figure 8 pattern, you say?
But lo! There are people who draw the figure 8 in a continuous
motion, like an infinity sign sideways, and others who draw the figure
8 sign as two circles, touching or even slightly interpenetrating.
The 3 cascade is for those who draw the figure 8 sign in one curve,
and my mythical four cascade is for those who draw two circles.
-boppo
crazy hippy
> Hello,
> Since I started juggling about three years ago, I have done both four and
> five balls and their respective patterns; fountain and cascade, although
> there are site-swap patterns that will make it look like you are juggling
> four balls in a cascade pattern.
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
> Sure, you can put up juggling diagrams of left and right hand and and note
> that with four beats, the ball is going to land in the same hand.
>
> But it just doesn't seem to cut it. I want an intuitive explanation. I
> will try to juggle four balls in a cascade pattern, but even then, it is
> not entirely clear why it won't work.
>
> By the way, if you threw the balls at different heights, I think one
> should be able to get it work. I suppose there is a site-swap for that too.
>
> So if anyone has paid attention to the same question, I would be happy to
> hear from you.
>
> ----== posted viawww.jugglingdb.com==----
I think the single most important characteristic of both the cascade
and fountain patterns is that they enable you to juggle in such a way
that both hands perform exactly the same action for every throw. That
is to say that the rhythm, heights and trajectory of the objects
within these two patterns have a perfect symmetry to them.
All even-numbered crossing patterns must in some way depart from this
symmetry, making them merely approximations of a true cascade. This
is because a cascade, by its very nature, is a pattern which allows an
odd number of objects to be juggled with perfect symmetry. This is
possible because there is a point during the cascade where the "extra"
or odd ball is suspended in the air and belongs to neither hand.
Imagine you start a five-ball cascade. You begin the pattern out of
symmetry -- three in one hand, two in another. The first throw
corrects that imbalance, placing the odd ball in "no hand's land" as
it were. After that point, the symmetry of the pattern is self-
sustaining.
Fountains are much simpler. As we have an even number of hands,
juggling an even number of objects has an inherent symmetry.
Personally, I love experimenting with the syncopations and distortions
which result from this fundamental difference between odd-numbered and
even-numbered juggling. There is a world of possibility in the
disparity, but no odd-numbered "fountain" or even-numbered "cascade"
can ever have the perfect symmetry of a true fountain or cascade,
simply owing to the inherent nature of these patterns. It would be
akin to playing a musical score in the wrong tempo -- 4/4 instead of
6/8 (or something like that, my two years of middle-school band
haven't really equipped me to fully grasp musical theory). It might
work, but it's gonna be funky.
Adam Rowney
But its not a 4 ball cascade, Boppo said that. Its just a 4 ball fountain
with a lot of scoop.
Boppo
You can do that, but if you do, you will find that the throws become
synchronous - you will converge to (4x,4x), which is maybe as cascadey
as 4 ever gets. (At least, in the realm of reality and not myth.)
-boppo
Ameron Rosvall
>
> Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
>
> Please note the category I put the video in.
>
> As an added bonus, I also do the 5 wimpy pattern as well as the
> mythical 4 cascade and the 5 fountains. I am perhaps the first person
> in the world to attempt the 5 wimpy pattern, and with any luck, also
> the last.
>
> -boppo
>
>
Ok, so I was thinking about this and I decided to film my own take at a "4
ball cascade". I'm uploading a video response at writing moment, and I'd
like to get a bit more insight in what happens in the pattern I'm doing.
It's really simple to juggle, and it really feels a bit like a real 4 ball
cascade (not that I really know how a real 4 ball cascade would feel...),
but it is still very confusing to look at for me.
-Ameron
Ameron Rosvall
Haavard
> But its not a 4 ball cascade, Boppo said that. Its just a 4 ball fountain
> with a lot of scoop.
You are right -- my eyes deceiving me! I thought by scoop he meant that
he would spent more dwell time on some of the throws. But seeing it again
now, he just make it look like the balls cross, when they in fact don't.
It is almost too good though.
Jay Linn
<snip>
> The bottom line is that, since we have two hands, there really is an
> enormous gulf between even patterns and odd patterns. 0 mod 2 and 1
> mod 2 have really, really different properties.
Check, check, checkity-check. This is the nub of it - it's to do with
fundamental and immutable properties of numbers, and no amount of
jiggery-pokery will alter those properties. You can only change the
outcomes by altering the assumptions in the first place (or axioms, or
premises, or whatever you choose to call them). That's why Dave was right
to point out that attempting to alter definitions was futile, because you
render the original question meaningless by so doing.
I'd also like to add that there has been rather a lot of eyewash written
about bending siteswap numbers to help resolve the problem (jimbren1 was
triflingly guilty of this, and I daresay others have been too), but that's
putting the cart before the horse : Siteswap is a descriptive notation; if
you change the thing you do, you change the siteswap into the bargain,
because what you do defines the siteswap, and siteswap describes what you
do.
--
Jay Linn
Semper eadem.
GuyHeathcote
>
> You can do that, but if you do, you will find that the throws become
> synchronous - you will converge to (4x,4x), which is maybe as cascadey
> as 4 ever gets. (At least, in the realm of reality and not myth.)
>
> -boppo
Yes, I see what you mean. Except(4x,4x) implies a collision to me, so
some sort of non-siteswap-friendly tweak to the timing and/or positioning
is still needed to make it work.
TheGreatApe
Well put.
...JAG
Very clever, and nearly a solution. However, while the siteswap is 4, if
you look closely at the sequence of throw *positions*, what you have is:
RLRLLRLRRLRLLRLR
Note that every 4 throws you are throwing 2 in a row from the same
position, so it does not have the simple alternating pattern of a cascade.
It's fast enough to fool the eye and the untrained observer though.
..JAG
Boppo
Yes, and this is part of the reason why it's the wimpy pattern - you
just can't do it symmetrically or anti-symmetrically. It's more like
(4.1x,3.9x), the throws not quite being coincident and not quite going
to the same height.
(Of course there is the manly way to do the wimpy pattern, arranging
perfect collisions every pair, so the balls don't cross sides but
their momentum does, transferred to the other ball.) The Saturn
trick is another way to perfect the wimpy pattern, but that of course
loses a different kind of symmetry, now the props aren't all
identical.
-boppo
Ameron Rosvall
Yep, and what I'm curious about is how this compares to 55550, which also
throws 2 from the same side every 4 throws. Since this is at an even tempo
it would be nice to see this pattern animated beside a 55550 to compare.
Boppo
What do you mean the balls don't cross? The arcs intersect by a lot!
-boppo
Kelhoon
[Stuff]
>
> Yes, indeed some of the comedy is calling the third pattern "not
> impossible, but highly inadvisable." Whether my sense of humor works
> for everyone is another question ... well, I guess we'll see what
> Sondre thinks of my other recent film.
Since when is Sondre the final arbiter of humour !?!??
>
> If someone could juggle with a dwell ratio of zero in one hand and one
> in the other hand, with four balls, the result would look exactly like
> the 3 cascade, except there would always be the fourth ball in the
> high-dwell hand. I just tried to do this but can't make it convincing
> enough to be worth filming. In any case, the pattern will necessarily
> be asymmetric, either with the extra ball on one side only as a result
> of the ideal dwells, or as a result of slightly skewed timing as a
> result of imperfect dwells (like, 0.1 and 0.9 dwell ratios) in
> addition to the extra ball. Worse, at best it would look just like
> the three cascade - and I *can* juggle three while also holding a
> fourth ball in one hand that I never throw. But that pattern wouldn't
> look like 4, while the high-scoop version that I filmed does look like
> four, and the point was to do the 4 cascade - not the 3 cascade while
> holding another.
>
> The bottom line is that, since we have two hands, there really is an
> enormous gulf between even patterns and odd patterns. 0 mod 2 and 1
> mod 2 have really, really different properties.
>
> -boppo
>
I was pondering this last night, could a 4 ball cascade be done with 3
hands ? Which led me to, if so, could it be juggled with 2 hands
throwing/catching from 3 different positions instead of the normal 2 ? A
bit like the right-middle-left pattern or 3 ball columns, maybe some
jiggery pokery with 4 ball columns/pistons.
It needs more pondering however,
juggle on,
Kelhoon
Boppo
> Boppo wrote:
>
> [Stuff]
>
>
>
> > Yes, indeed some of the comedy is calling the third pattern "not
> > impossible, but highly inadvisable." Whether my sense of humor works
> > for everyone is another question ... well, I guess we'll see what
> > Sondre thinks of my other recent film.
>
> Since when is Sondre the final arbiter of humour !?!??
>
Sorry, that was another joke.
> > If someone could juggle with a dwell ratio of zero in one hand and one
> > in the other hand, with four balls, the result would look exactly like
> > the 3 cascade, except there would always be the fourth ball in the
> > high-dwell hand. I just tried to do this but can't make it convincing
> > enough to be worth filming. In any case, the pattern will necessarily
> > be asymmetric, either with the extra ball on one side only as a result
> > of the ideal dwells, or as a result of slightly skewed timing as a
> > result of imperfect dwells (like, 0.1 and 0.9 dwell ratios) in
> > addition to the extra ball. Worse, at best it would look just like
> > the three cascade - and I *can* juggle three while also holding a
> > fourth ball in one hand that I never throw. But that pattern wouldn't
> > look like 4, while the high-scoop version that I filmed does look like
> > four, and the point was to do the 4 cascade - not the 3 cascade while
> > holding another.
>
> > The bottom line is that, since we have two hands, there really is an
> > enormous gulf between even patterns and odd patterns. 0 mod 2 and 1
> > mod 2 have really, really different properties.
>
> > -boppo
>
> I was pondering this last night, could a 4 ball cascade be done with 3
> hands ?
Well, you could do a symmetric pattern this way, if your hands were
120 degrees apart. One ball would kind of bounce continuously in a
ring around the three hands. If you know another juggler, or even a
half-juggler, you could try this. But then, that wouldn't be a
"cascade," it would be a "snorgleput" which is what the three-handed
Andromedans who juggle this pattern call it. The cascade is already
taken to mean a two-handed pattern with an odd number of balls. Those
Andromedans have found a slight difference between 1 mod 3 and 2 mod
3, which is like the difference between clockwise and
counterclockwise, but they are more similar to each other than they
are to 0 mod 3.
> Which led me to, if so, could it be juggled with 2 hands
> throwing/catching from 3 different positions instead of the normal 2?
> A bit like the right-middle-left pattern or 3 ball columns, maybe some
> jiggery pokery with 4 ball columns/pistons.
>
> It needs more pondering however,
>
> juggle on,
>
> Kelhoon
>
> --
> ----== posted viawww.jugglingdb.com==----
-boppo
Kelhoon
On a symmetrical figure 8 track, an even number of balls spaced evenly
will collide at the crossover point, an odd number of balls spaced evenly
creates a "hole" for the balls to go through.
Sure, for juggling, a mid point collision could be avoided by juggling in
2 different planes. It would however be a synchronous pattern and
therefore no longer meet the alternating convention.
Thornhill
Alternatively, you could also throw the crossing balls in slightly
different planes (one in front of
another)..
--
Jay Linn
been along the lines of "What is a real cascade anyway?" I'd like to offer
an answer.
A true, pure, simple, unadulterated cascade contains, but is not limited
to, the following constraints :-
* It is two-handed.
* The hands always alternate LRLRLRLR etc. in an asynchronous rhythm.
* Balls are always thrown to the opposite hand (not just the opposite
side of the pattern).
* The tempo is even, not galloped.
* Throw heights are uniform (within the bounds of normal throwing error).
* Throw release heights are uniform (within the bounds of normal throwing
error).
* Dwell ratio is uniform (within the bounds of normal error).
* Dwell ratio is middling, i.e. not too jerky, nor with excessive holds.
* Hand movement is repetitive and consistent, and the hands maintain the
same catching and throwing positions throughout.
* The hands are essentially uncrossed and move around notional points
that are roughly shoulder width apart.
I've picked all these things because to my mind they represent the very
essence of a classic cascade, but they are just my own choice and not some
hard and fast definition that the rest of you have not been told about, so
feel free to argue with them but please remember that I'm not trying to
impose a definition of a cascade on anybody, just trying to nail what I
feel characterises the quintessential cascade. I chose them because I feel
a cascade that conforms to all these conditions could be shown to a
muggle, and they'd say "Yeah, that's *proper* juggling that is", just as
the same muggle would say "Four ball juggling? You're cheating because
they don't cross over!"
Notice that the one thing I haven't stipulated is whether there should be
an odd or even number of objects, because that turns out to be an innate
property of all the other things I've suggested. Observe all the
stipulations and you'll discover that true cascades fundamentally require
odd-numbers of objects. The easiest way to break this, to my mind, is to
alter the first rule "It is two-handed".
Interestingly, most of those stipulations are broadly consistent with
what Colin Wright suggested when I first saw his site swap lecture back in
the late 80s, when he was busy trying to develop a theory of SS at roughly
the same time as other people. I'm not sure he even called it site swap
back then, but the rules seem to be robust regardless of the name.
Hope this helps.
Will Helm
emphasized before leaving this topic is that it is a formal
description of a 3-ball Cascade. If you release that one stipulation,
as suggested early on by 'HanS', then we are led to these other
creative explorations and learning opportunities.
The siteswap code '3' describes only limitations. The hundreds of
other wonderful and popular patterns and tricks that share that
minimal notion and notation are possible only outside and beyond the
stupid restrictions of siteswap. It isn't until one deals with the
form, not the formal, that all the other forms can exist. In other
words, what makes a pattern Cascade is everything about it *other
than* its ss code.
If we had followed the "end of story" dictum, what a story would have
been missed!
wH
Boppo
>
> The siteswap code '3' describes only limitations. The hundreds of
> other wonderful and popular patterns and tricks that share that
> minimal notion and notation are possible only outside and beyond the
> stupid restrictions of siteswap.
Siteswaps pose no restrictions, let alone stupid ones. Calling a
pattern "siteswap 3" does not prevent it from being backcrosses or
Mills Mess or anything else. It just means that there are three
objects and each object thrown is dealt with again three throws
later. Vanilla siteswaps make some simplifications, but primarily
for the benefit of understanding what siteswaps are about - note that
when they were first described, very few people understood them,
unlike the case today.
But if, for example, you decide you are only interested in
asynchronous patterns, that is a decision that you make and not one
that siteswaps artificially impose on you, although the notation
changes if you later want to do synch patterns as well, or morph
between synch and asynch. Siteswaps don't force you to do anything,
although some things are less convenient to notate than other things.
They were not intended to notate Mills Mess, but that doesn't mean
they prohibit Mills Mess.
The fact Baskin Robbins sells vanilla ice cream does not prevent you
from getting any other flavor. (Except, there are only 30 other
flavors of ice cream at BR, but there is an infinite number of
siteswaps - most of which, I dare say, would never have been
discovered/invented without the scheme.)
> It isn't until one deals with the
> form, not the formal, that all the other forms can exist.
You are mistaken. (Most of) the other forms existed prior to
siteswaps first being described, and siteswaps took absolutely nothing
away from them. Their existence is not in the least diminished by
siteswaps. I suggest you rethink what the scheme of siteswaps does and
doesn't do. It is a generalization of the concept of {throw heights,
throw times, launching order vs. landing orders}.
Furthermore, there are formal ways of dealing with body throws and
choreography too. Dancers can write down their routines as well in
various notations. Siteswaps aren't they, and they aren't siteswaps.
None of the schemes takes anything away from any other of them. They
describe different aspects, and the aspects are additive in a
dimensional sense; they are orthogonal. The more you add, the more
dimensions you can describe. Where the feet are, where the body is,
where the hands are, where the balls go, what the expression on the
performer's face is ... and so forth. There's even musical notation
that stipulates every nuance of what each instrument in an entire
orchestra is supposed to be doing at any given time.
The only difference that I know of, is that with siteswaps there is a
deterministic way to generate everything that is possible within that
scheme. To my knowledge, the other schemes don't produce that as a
natural consequence. (I know about music, I don't know about
choreography notations except that they exist.)
> In other
> words, what makes a pattern Cascade is everything about it *other
> than* its ss code.
I don't think that anyone is arguing that what makes a cascade a
cascade is its siteswap code. The five ball cascade was known as "the
five ball cascade" prior to siteswaps ever being described. This is
true regardless of the fact that the definition given above about what
constitutes a cascade includes a lot of aspects that are defined
explicitly in the vanilla siteswap scheme: throws alternate in even
rhythm, all "3" throws go to same height, etc.
> If we had followed the "end of story" dictum, what a story would have
> been missed!
Who made that dictum? It wasn't me. Maybe it was you. Whoever it
was, the dictum is wrong.
-boppo
Michał
>
> Hello,
> Since I started juggling about three years ago, I have done both four and
> five balls and their respective patterns; fountain and cascade, although
> there are site-swap patterns that will make it look like you are juggling
> four balls in a cascade pattern.
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
> Sure, you can put up juggling diagrams of left and right hand and and note
> that with four beats, the ball is going to land in the same hand.
>
> But it just doesn't seem to cut it. I want an intuitive explanation. I
> will try to juggle four balls in a cascade pattern, but even then, it is
> not entirely clear why it won't work.
>
> By the way, if you threw the balls at different heights, I think one
> should be able to get it work. I suppose there is a site-swap for that too.
>
> So if anyone has paid attention to the same question, I would be happy to
> hear from you.
>
Seems to be long thread.
My idea to do 4b cascade is to throw 55550 -> 180 -> 55550 -> half spin
etc.:)
Al Teal
>
> On Dec 27, 9:35 pm, Will Helm <hillw...@gmail.com> wrote:
> > Dave Altman wrote:
> > > cascade. A cascade can only be done with an odd number of objects, end
of story.
> >
> > DAVE: "end of story" is so contrary to what juggling has always been,
> > that it sounds like a satyrical troll.
> >
> > Whether BruceT or Norbi or somebody else gets it out on video first,
> > we'll want to see it. Whether the tactic is called variable dwell or
> > polyrhythmic is not going to be as interesting to me as there being a
> > waiting list of jugglers going for this stunt: a next "challenge",
> > yay! I like the consternation over the definition of what must be
> > done to do it: why isn't an async 53 a four-ball cascade? Why isn't a
> > synchopated (4x,4x) just as good? If you can do it, and an audience
> > likes it, or you like it, what difference does someone else's
> > "definition" make?
> >
> > Who's going to troll, and who's going to throw?
> >
> > WillH
>
> Throw!!
>
> Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
>
> Please note the category I put the video in.
>
> As an added bonus, I also do the 5 wimpy pattern as well as the
> mythical 4 cascade and the 5 fountains. I am perhaps the first person
> in the world to attempt the 5 wimpy pattern, and with any luck, also
> the last.
>
> -boppo
>
>
I like the way you have the fire extinguisher handy in case one of the
"dangerous patterns" catch on fire. I think I saw smoke coming from the
wimpy 5.
Al
Boppo
I also have a handy arch I can duck under in case of earthquake.
Safety first!!
-boppo
Brer Licky
AKA, wimpy.
TraxxasJedi
>
>
> A true, pure, simple, unadulterated cascade contains, but is not limited
> to, the following constraints :-
>
> * It is two-handed.
> * The hands always alternate LRLRLRLR etc. in an asynchronous rhythm.
> * Balls are always thrown to the opposite hand (not just the opposite
> side of the pattern).
> * The tempo is even, not galloped.
> * Throw heights are uniform (within the bounds of normal throwing error).
> * Throw release heights are uniform (within the bounds of normal throwing
> error).
> * Dwell ratio is uniform (within the bounds of normal error).
> * Dwell ratio is middling, i.e. not too jerky, nor with excessive holds.
> * Hand movement is repetitive and consistent, and the hands maintain the
> same catching and throwing positions throughout.
> * The hands are essentially uncrossed and move around notional points
> that are roughly shoulder width apart.
>
>
That's definitely a great start towards a definitive definition, by most
of our standards anyway. The only thing I could think to add would be some
stipulation that requires all throws to be thrown underneath the previous
one. Based on the list you provided a reverse cascade would be considered
a cascade (I will maintain that cascade and reverse cascade are very
different, if only for aesthetic reasons).
Thornhill
roughly even height crossing
throws. I've always achieved this by throwing one of the throws lower
than the other, rather than
one in front of the other...
Lewis Kennedy
>
> Hello,
> Since I started juggling about three years ago, I have done both four and
> five balls and their respective patterns; fountain and cascade, although
> there are site-swap patterns that will make it look like you are juggling
> four balls in a cascade pattern.
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
> Sure, you can put up juggling diagrams of left and right hand and and note
> that with four beats, the ball is going to land in the same hand.
>
> But it just doesn't seem to cut it. I want an intuitive explanation. I
> will try to juggle four balls in a cascade pattern, but even then, it is
> not entirely clear why it won't work.
>
> By the way, if you threw the balls at different heights, I think one
> should be able to get it work. I suppose there is a site-swap for that too.
>
> So if anyone has paid attention to the same question, I would be happy to
> hear from you.
>
i have seen josh turner do it.
he like hits 1 ball with one have instead of catching it.
if that makes sence
lewis
Brer Licky
Well, that's the way I always did wimpy until I finally gave up on doing
it "without cheating", but I suppose you could argue I had it backwards.
Dave Altman
I like Jay's list and your addition, I agree that a regular cascade and a
reverse cascade are different, but obviously related, hence the
similarities and differences in their names, but I find it hard to believe
a cascade definition isn't already written down somewhere! Hasn't the most
basic pattern in juggling been clearly defined before now? People should
review some old books about juggling. I bet there is a clear definition of
a cascade even before the 1900's.
Not being a siteswap person, I appreciate patterns with names, instead of
numbers. Descriptive names are helpful in explaining and/or teaching the
trick. Tricks named after people honor the "inventors" and even when they
are named after the wrong people and just the people that made them
popular, it still invites a story and a discussion, but a list of numbers
just leaves me cold. For those into siteswaps, I understand their use and
even importance, but I don't want to join your cult. I might learn some
so-called siteswap patterns, but I might give them a name.
Dave Altman
Boppo
wrote:
Not nearly enough beautiful young nubile women have offered themselves
to me, the would-be cult leader, for it to make the grade as a cult.
Alas.
Some tricks do have names for example "a complete waste of a five ball
juggler" (450) or "the 9-level six-ball shower-chicken-
out" (7899918171). But really, siteswaps are just a language and
when you become facile with it, when you hear "441" you think of the
trick itself and not about a bunch of numbers.
-boppo
Dave Altman
> > ...but a list of numbers
> > just leaves me cold. For those into siteswaps, I understand their use and
> > even importance, but I don't want to join your cult. I might learn some
> > so-called siteswap patterns, but I might give them a name.
> >
> > Dave Altman
> Not nearly enough beautiful young nubile women have offered themselves
> to me, the would-be cult leader, for it to make the grade as a cult.
>
> Alas.
That doesn't mean it's not a cult, it just means it's a lousy cult to be
the cult leader. You said "Not nearly enough...women...offered
themselves..."so, that means some have because you developed siteswaps? If
so, that is a little surprising, but, good for you!
Boppo
wrote:
Let me check my records .... nope, actually, zero have. Lousy cult
indeed!
-boppo
Peter Bone
>
> Hello,
> Since I started juggling about three years ago, I have done both four and
> five balls and their respective patterns; fountain and cascade, although
> there are site-swap patterns that will make it look like you are juggling
> four balls in a cascade pattern.
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
> Sure, you can put up juggling diagrams of left and right hand and and note
> that with four beats, the ball is going to land in the same hand.
>
> But it just doesn't seem to cut it. I want an intuitive explanation. I
> will try to juggle four balls in a cascade pattern, but even then, it is
> not entirely clear why it won't work.
>
> By the way, if you threw the balls at different heights, I think one
> should be able to get it work. I suppose there is a site-swap for that too.
>
> So if anyone has paid attention to the same question, I would be happy to
> hear from you.
>
I'm going to try to explain in a different way using an analogy I just
thought of which can be possibly more easily visualised.
Imagine a standard juggling ball with a given number of panels and looking
at the point where the panels meet so it looks like a pie with slices. The
number of panels is equivalent to the number of balls. The panels have one
of 2 colours which represents the hand (left of right). The colours must
alternate since the hands alternate throws in standard juggling. The
ability of being able to alternate all the way round the ball depends on
whether you have an even or odd number of panels because it wraps back on
itself. If you have an even number of panels then you can alternate the
colours, but this means that each panel (ball) will always have the same
colour (hand) - balls cannot change hand. If you have an odd number of
panels then you can't alternate colours around the ball and continuing the
alternating pattern will switch the colours of the panels at each rotation
- the balls must swap hands.
Pete
Matthew Tiffany
read above..... my post, and i knicked it off ben i think of possibly
luke, it was at a manchester convention.
me
x
Sondre �verby
>
> Hello,
> Since I started juggling about three years ago, I have done both four and
> five balls and their respective patterns; fountain and cascade, although
> there are site-swap patterns that will make it look like you are juggling
> four balls in a cascade pattern.
>
> Moreover, I have read a fair bit on the mathematics of juggling, and the
> site-swap notation makes things a lot more interesting, doubly so as I am
> a physics undergrad.
>
> Now, just recently I started thinking about why exactly it is that you
> cannot juggle four balls in a cascade pattern. And it just seems a lot
> trickier to explain, than I had though.
>
> Sure, you can put up juggling diagrams of left and right hand and and note
> that with four beats, the ball is going to land in the same hand.
>
> But it just doesn't seem to cut it. I want an intuitive explanation. I
> will try to juggle four balls in a cascade pattern, but even then, it is
> not entirely clear why it won't work.
>
> By the way, if you threw the balls at different heights, I think one
> should be able to get it work. I suppose there is a site-swap for that too.
>
> So if anyone has paid attention to the same question, I would be happy to
> hear from you.
>
I've got a more interesting question.
Who are you?
Sondre
sean_
Ben I believe, I was stood next to you when he done it and it hurt my poor
diaboloist head.
Tiff, could you bazz a quick video clip of it out? I seem to recall it
looking different to the one Boppo posted.
Happy new year and all that. I hope to get around to seeing more of the
Leeds lot this year.
Dave Cheetham
>
> A true, pure, simple, unadulterated cascade contains, but is not
> limited
> to, the following constraints :-
>
> * It is two-handed.
> * The hands always alternate LRLRLRLR etc. in an asynchronous rhythm.
> * Balls are always thrown to the opposite hand (not just the opposite side of the pattern).
> * The tempo is even, not galloped.
> * Throw heights are uniform (within the bounds of normal throwing error).
> * Throw release heights are uniform (within the bounds of normal throwing error).
> * Dwell ratio is uniform (within the bounds of normal error).
> * Dwell ratio is middling, i.e. not too jerky, nor with excessive holds.
> * Hand movement is repetitive and consistent, and the hands maintain the same catching and throwing positions throughout.
> * The hands are essentially uncrossed and move around notional points that are roughly shoulder width apart.
>
>
> stipulations and you'll discover that true cascades fundamentally require
> odd-numbers of objects. The easiest way to break this, to my mind, is to
> alter the first rule "It is two-handed".
I like your definition, Jay, and I think that rather than just defining
"Cascade" you're almost closer to defining both the cascade and the
fountain for standard two handed toss juggling. This thought stemmed
from you talking about using an even number of balls by using an odd
number of hands; whereas, you can allow all the other points to hold
true for any number of balls if you remove the restriction that all all
balls must cross.
This set of rules now defines any base pattern with any number of balls.
My thoughts, anyway.
Dave
Dave Altman
>
> This is turning into quite a thread. Some of the recurring comments have
> been along the lines of "What is a real cascade anyway?" I'd like to offer
> an answer.
>
> A true, pure, simple, unadulterated cascade contains, but is not limited
> to, the following constraints :-
>
> * It is two-handed.
Can't three balls be done in a cascade pattern in one hand?
Dave Altman
Boppo
wrote:
It can be - among other ways by using a lot of scoop. Which is
incidentally the same way to give the appearance of cascading four
balls in two hands.
Coincidence?
Or just a cruel joke?
-boppo
Dave Altman
Oh, okay, I'll take two scoops and a cherry on top.
Haavard
> I've got a more interesting question.
>
> Who are you?
>
>
> Sondre
This is kind of encryptet. But I just thought I would let you know that I
wrote you an email, to your jugglingdb e-mail address.
Haavard
Aymeric
>
> Ameron Rosvall wrote:
> >
> > Boppo wrote:
> > >
> > > Here's my video: http://www.youtube.com/watch?v=rvODxVJ0Oao
> > >
> > > Please note the category I put the video in.
> > >
> > > As an added bonus, I also do the 5 wimpy pattern as well as the
> > > mythical 4 cascade and the 5 fountains. I am perhaps the first person
> > > in the world to attempt the 5 wimpy pattern, and with any luck, also
> > > the last.
> > >
> > > -boppo
> > >
> > >
> >
> >
> > ball cascade". I'm uploading a video response at writing moment, and I'd
> > like to get a bit more insight in what happens in the pattern I'm doing.
> >
> > It's really simple to juggle, and it really feels a bit like a real 4 ball
> > cascade (not that I really know how a real 4 ball cascade would feel...),
> > but it is still very confusing to look at for me.
> >
> > -Ameron
> >
>
> And here it is...
>
> http://www.youtube.com/watch?v=NgQdtf5pvic
>
Hey Ameron!
I was disappointed to find out that your video was taken down!
What's happened to it?
I'd love it if I could watch it again!
Aymeric.
Julius
>
> Imagine you try to juggle a 4 ball cascade.
> You throw right-left-right-left. Now the next throw would be right, but
> the first throw was a right throw(this ball is in the left hand now) , so
> the next throw comes from the left hand. There is no more detailed
> explanation than this.
>
This is exactly the explanation; I wonder if most people just missed your
post or if they're just arguing for fun.
Boppo
wrote:
"Why you can't juggle a 4 ball cascade "
Because you don't have three hands.
(Or, in general, you don't have a number of hands >1 so a "cascade" is
meaningful, <4 (the number to be juggled, so that it's really
juggling, b>h) and relatively prime to 4 so you don't just do some in
each hand in a fountain or other non-cascade pattern.)
-boppo
Mats1
to work...
Boppo
??
I just tried to watch it and it worked for me. I don't know what the
problem could be.
Anyone?
I'm guessing that if YouTube takes it down, I wouldn't be able to
watch it either. Right?
Link is: http://www.youtube.com/watch?v=rvODxVJ0Oao
-boppo
Aymeric
>
> Boppo, your Youtube video with the 4 cascade/5 fountain in no longer seems
> to work...
>
I watched it on jtv yesterday...
Aymeric.
thegoheads
http://www.youtube.com/watch?v=r6NabbqzlDw
Really interesting! I've never seen anyone do this before. And it
definitely does look like a normal cascade if you ignore the criss-cross
arm movements.
-Steve
Mats1
It always stops just at the point where you finish talking initially. I
tried to download it, but it came up with an error.
Ameron Rosvall
Hey!
Yeah I took it down a while ago, the novelty value wore off or something.
Doesn't really feel necessary to re-upload now either, as the tutorial
thegoheads linked to is on the same pattern.
( http://www.youtube.com/watch?v=r6NabbqzlDw )
Ameron
David Cherepov
>
> I just came across this recent video
> http://www.youtube.com/watch?v=r6NabbqzlDw
>
> Really interesting! I've never seen anyone do this before. And it
> definitely does look like a normal cascade if you ignore the criss-cross
> arm movements.
>
> -Steve
>
Yeah, I saw that, it is really cool.
Aymeric
Well, to be honest, I preferred your vesion :)
Would you mind puting it up on jugglingtv? That would be great!
Aymeric.