I don't understand this.
Let us define a position by a set of coordinates for every single "part"
of a dancer. Let's say you have n (something like 20) different such
markers.
If you set up, for each position, a set of possible future positions (from
which you choose chaotically or randomly or whatever), you will get a
very large structure, an exponentially growing tree, which will explode
with a power something like n. Not nice.
But you don't need this. You only need to specify contraints on each
marker's movement, possibly subject to a couple of other markers, but (and
this is the major point), not all. For example, you clearly can't have a
shoulder springing left and the connected elbow springing right, since
this would stretch the arm. Ouch. In this case the two markers become 1
INDEPENDENT piece of information. However, that's not all, because, for
example, the shoulder is indeed connected to another marker, with suitable
contraints, so the contraints are TRANSMITTED from one piece to another
(this is why Lagrangean mechanics works so well; you exploit the
INDEPENDENT degrees of freedoms through nice contraints). It's like
asking you brother for your mother's phone number instead of remembering
it yourself.
Otherwise your brain wouldn't have a chance calculating all possible
positions as you walk; you'd spend all your time thinking about
impossible bodily configurations instead of spending your mental-power
sending signals to the muscles that move THE VERY FEW JOINTS that you
require to walk. (Remember, muscles don't move, they move joints and
limbs. There are fewer joints and limbs than muscles.
Setting up a highly contrained dynamic system, such as the body, with
something like 500 possible degrees of freedom (I'm guessing here) does
not require a large data structure. You can then course through the
possible motions of this structure (exploring the unstored infinities)
storing occasional snapshots of the configuration (all of the possible
ones, the sort dancers or yogi might manage).
If you try to store redundant information you'll get in trouble. Are you
storing all phone numbers of all friends of all friends' friends for each
of those friends, or just the friends of each friend ?
Darren
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