Time-Reversed Mills Mess (It's easier than you think)

Introduction

Well, I finally figured out Time-Reversed Mills Mess. It was during the Lodi Festival this year,(1998) while talking to Rick Rubenstein and Ben Schoenberg about it. Ben said he had worked on it before and showed us a strange pattern that looked really funky and confusing, and wasn't quite right. Maybe that was the reverse meatchop thingy? Needless to say, while Rick and Ben argued the finer points of theory, I stepped aside with renewed determination and worked it out myself. It was one of those patterns that had been stuck on the tip of my fingers, so to speak, for about seven years. I always just thought, "one of these days I'll watch a video backwards", but never got around to it.

Anyway, I finally got it in Lodi, but not very smooth. Since then, I was reading Dancey's Encyclopedia and noticed that he claims that TRMM (Time-Reversed Mills Mess) is the same as MM (Mills Mess). (He also incorrectly uses an apostrophe and the article "the", which gets annoying) Anyway, I studied his appendix on Mike Day's MMSTD,(Mills Mess State Transition Diagram) which is supposed to be the notation which conquers MM. Well, it's missing a couple of throw vectors. Or at least, it describes throws in a more limiting way. I would define a reverse throw as one which is thrown on the outside of the pattern, and is caught in the middle. A non-reverse throw (cascade or fountain) is thrown from the middle and caught on the outside. These descriptions are independent of which hand we are talking about or how it is moving prior to the throw, which seems to be the criteria MMSTD uses to define its throws. This explains why some people think TRMM is the same as MM. Why? Because if you don't differentiate between reverse and regular throws, the MMSTD displays both patterns as the same.

How can that be? Both patterns follow the same sequence of "states". (or hand position + hand about to throw - there are six of these) The only difference is that MM uses only reverse throws, and TRMM uses only regular throws. Reversing the sequence of states gives a pattern in which the balls do the same thing, but the hands don't. This was the pattern I described in my last post which C.D. Wright called the funky mess. A similar seeming-paradox holds true for siteswaps - the time reverse of a siteswap is often the same siteswap. In fact, reversing the order of a siteswap often results in an invalid siteswap. (such as 534 - 435 is invalid) Some time-reversals of siteswaps do result in different number sequences, but they still won't look correct unless you also reverse the throws.

(Interesting side note: All juggling patterns have a time-reversal which is juggleable. The only patterns in which the time-reverse is identical to the regular pattern are those in which the balls travel in both directions along the same path. This includes columns, the box, and some arching patterns, such as 1up 2up with the 1 over the top.)

The Simple Instructions for TRMM:

If you already know Mills Mess, you are two-thirds of the way there. First let me define my terms: When I juggle MM, I call the ball which "tennises" back and forth over the top "Ball 1". This is also the lead ball of the snake, if you think of the pattern that way. "Ball 2" is the ball which follows a reverse cascade pattern. "Ball 3" is often called the "U Ball", or the tail of the snake. The numbers designate the throwing order, so obviously "Ball 2" is thrown after 1 and before 3.

Now the steps: Juggle MM normal for a bit, counting those numbers as you juggle. Now throw ball 1 as in MM, and throw ball 2 also as in MM, only more or less straight up. 3 is the tricky one. Instead of reaching all the way under and throwing it outside ball 2, only reach halfway and throw it up between 2 and 1, in what amounts to a normal cascade throw. Repeat on the other side.

That's it. Really. If you want to analyze it, read on. Ball 1 stays the same, because the reverse of an arc is still an arc. Balls 2 and 3 switch roles. Ball 2 becomes the "U" ball, and the reverse of a "U" is still a "U". Ball 3 becomes the reverse cascade ball, which reversed is a cascade.

To smooth out the pattern and make it look better, I find it helpful to realize that now ball 2 is the head of the snake, and ball 1 is the tail. So the emphasis becomes "231" instead of "123". I really like this pattern because every other MM variation seems to add or subtract something from the pattern, which detracts from the purity and flowing nature of it. TRMM does not do this, because it _is_ the same pattern. And yet, it _does_ look different.

Good Luck! I know it's difficult to learn these things from written descriptions. I’d be happy to show you what I mean in person. You can find me almost every Friday at the Orange Juggler’s meeting. I’m the extremely tall guy who always has a prop in his hands and appears to be consumed by it’s power - but don’t worry, I’m just making up for a week of pushing paper, phones, and keyboards.

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