Thursday, May 29, 2008

Technical Corner: May08

Last June, I posted about juggling trick "chains". I was talking with Tim about them tonite, and I likened them to musicians running scales, and we kinda liked that name better. I'll likely use them interchangeably for a while. :)

Back to the point, Tim found them really valuable tools to practice for other tricks with, and the more advanced usages of starting from tricks one knows, and taking small steps to get to tricks one wants to know... So, to that end, I'm adding this blog, and will later add links to various siteswap related tools in the sidebar on the right.

Let's start with the basics... 3 object scales. Ok, this will be rather short (read: potentially boring), but it lays the foundation for adding objects to the base patterns, but I'm getting ahead of myself.

Take the first simple one of the two digit sequences: 33, 42, 51, 60
{in geeky math terms: f(n)=( x+n , x-n ) ... where 'x' is the number of objects, and 0<=n<=x }

To get from the first to the second, one can do it after the '3'. To get from the second to the third, you simply throw the '5' after the '4'. Finally, you can get from the third to the fourth by throwing the '6' after the '5'. Putting that all together, one can have the useful sequences: ...333 333...333 42 333...333 4 51 2 333...333 4 5 60 1 2 333...

Basically, each subsequent pair is a 'trick' out of the previous pair. This illustrates how we can step thru other patterns to end up in an excited state pattern [ie: you can't just start throwing '51' directly from a '33' pattern, so that makes '51' an excited state from the '33' base pattern].

Now, taking that to a logical level, one can run the full sequence of transitions back to back: 34512 or 3456012. One would reorder those and come up with the sequences 12345 and 0123456. Personally, I find the first one more interesting, but both are worth trying. These will really hone your throw heights relative to each other. Any given day, your hand speed will vary a little faster or slower, and your throw heights will change accordingly. Running either of these will baseline your throw heights for that day, because if your heights are off, the pattern won't flow well, but once it smoothes out, you have established muscle memory for that day's practice.

The above example might be tricky for those just beginning, and it should be more a goal than an expectation.
Now, lets further explore the 42 root for other sequences.

The obvious way of extending this out: 42, 441, 4440
{geeky math terms: f(n)=( (x+1)^n , x-n ) }

Take 42 and extend it out: 42, 522, 6222, 72222, ... [kinda boring, but useful for 360s and other flourishes]
{ f(n)=( (x+n)^1 , (x-1)^n ) }

Taking 441 to the next level: 441, 5511, 66111, 771111, ...
{ f(n)=( (x+n)^2 , (x-2)^n ) }

Taking 4440 the same way: 4440, 55500, 666000, 7770000, ...
{ f(n)=( (x+n)^3 , (x-3)^n ) ... see the trend yet?}

I know, these seem boring, but there is potential in them...

Taking 51 compared to 33 { f(n)=( (x+2n) , (x-2)^2n ) } gets the sequence: 51, 711, 9111, ...
And the utterly useless 60 extension: 60, 900, c000, ...
Another style of sequence is: 3, 42, 531, 6330
This becomes a bit more obvious in style when written out sorta diagonally like Pascal's Triangle and for higher numbers of objects like: 5, 64, 753, 8552, 95551, a55550 or 7, 86, 975, a774, b7773, c77772, d777771, e7777770

OK, so "all that is just a bunch of numbers and simple patterns - now what?" right? :) Well, starting with the basics, let's "do something similar, but with one more object".

The simplest way to add an object is to add '1' to every digit in the sequence. The trivial example is '3' plus '1' gets the pattern '4', thus '5', '6', and so on. Pretty obvious, eh? :) Take '42', and one to each, and your get '53', and so on..

The other simple way to add an object is to add the number of digits in the sequence to one of the digits in the sequence. That seems a little strange, so here are a few examples:
'3' add '1' to one of the digits and you get '4'
'33' add '2' to one of the digits and you get '53' or '35'
'42' add '2' to one of the digits and you get '62' or '44'
'333' add '3' to one of the digits, and you get '633', '363', or '336'
'441' add '3' to one of the digits, and you get '741', '471', or '444'
'531' add '3' to one of the digits, and you get '831', '561', or '534'
'6330' add '4' to one of the digits, and you get 'a330', '6730', '6370', or '6334'
'12345' add '5' to one of the digits, and you get '62345', '17345', '12845', '12395', or '1234a'

Of course, both of these techniques works in reverse as well, thus giving one more options of related tricks that one might already be able to do or might pick up easily enough. One example of thought logic might be:

"I can do 441, I can add an object making it 741, then I can remove one ball and get 630, adding one back, I get 633, and removing one again I get 522, which I can add one back and get 552, and removing one I can get 441 again"

So, if one can do any of those listed, with a few minutes practice, one should be able to so any of the other related ones [even if one just sticks to the 3 object ones at first].

Therefore, you homework for this week is:
- extend out a few 'juggling scales' for your number-of-objects of choice and try them
- take your favorite sequence for however many objects, and try adding a ball to it using the above techniques

Oh, and let us know how it went for ya! Obviously I'd be glad to help you thru direct emails or face to face at juggling club sometime!

Cheers! --Crizzly



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