Dual-Gravity / Multi-dimensional juggling

RustyJuggling - 2026-07-21 15:40:07 UTC #

Dual-Gravity / Multi-dimensional juggling

So I've been exploring the idea that a juggling pattern's state is basically a piece of the pattern that doesn't move through time, meaning it lacks one dimension that the full pattern has; The state drops from four (3 space 1 time) to three (no time dimension). This made me wonder if the concept could be extended any further. There are two ways that I can think of to represent a 5-dimensional juggling pattern, and I thought I would explain my thought process for both.

First of all, how can such a thing be conceptualized? I decided it would be best to look at how adding a dimension alters a state, to see how it might alter a full juggling pattern. Before adding time, a state is a static form. Afterwards, gravity appears and the height of the objects decays over time. So one way we might conceptualize adding a dimension to juggling is by adding another source of gravity.
If you add a source of gravity that pulls objects towards yourself, your throws now have to account not only for the height of a throw, but also its depth. A basic cascade, tilted away from the juggler, might be written as {33}. And because you now have an extra layer to play with, you can actually juggle two patterns completely simultaneously; one pattern is thrown when objects are at height 0, and the other is thrown when they are at depth 0. So {35}{33}{31} viewed from the front would look like a cascade, but viewed from above would look more like 531. Obviously, executing this kind of pattern would require very precise hands.

But if that's not a good enough representation, you might do a little bit better by using hyperspheres instead of normal spheres. In the same way that a sphere passed through a 2-dimensional plane would appear as a circle that grows and shrinks, a 4-dimensional sphere passed through our 3-dimensional plane would likely look like a sphere that grows and shrinks. Therefore, you could imagine a system where your objects change size as they are thrown. The effects of this are much the same as adding another source of gravity, but the pattern remains confined to the wall-plane we like to work with. One pattern thrown at height 0, the other at an arbitrary size 0.
As a trade-off, though, this form of juggling is much harder to simulate in our world. I would love to see a program that can animate these kinds of patterns, but of course I don't have the skills to create one.

Beyond that, I feel like there should be other ways of thinking about higher-dimensional forms of juggling that make more sense progressively. For example, when state is extended it begins to changes over time, but with the systems I've constructed the base pattern can remain exactly the same, just with another aspect added on top. Is that the natural result of adding a dimension or is there a better way to think of it? I'd love to hear ideas.