An Analysis of Eongatubabo and Burbot

I originally intended to go through the endings in the same order I listed them in my "Presenting a Transverse Exchange" article, which is why I started with the "Apache Door Ending" a few days ago. However, I've been doing some thinking and experimenting with Eongatubabo, and some ideas are starting to gel. I figured I'd do this one next.

Eongatubabo. It's a Nauruan name for a technique known in various places throughout Micronesia. Honor Maude also documented it as the "Banaban Movement". Done as originally shown to Maude, the movement has a smooth elegance to it, although it is tricky to describe because it is such a fluid maneuver. Beginning with a three-loop configuration (loops on 1, 2, and 5):

1. 1 hooks down 2n and holds it to the palm.
2. 2 enters the 5 loop from above, hooks 5n and 2f back over 1n, and then picks up 1n, rotating up and back to position.
3. 1, still hooking down 1f and 2n, moves under 5f and returns with it, releasing 1f and 2n in the process.
4. Release 5.
5. 5 removes upper 2 loop from above.
6. Release 2.
   

If you started with Opening A, at this point you'll have a figure the Nauruans call the "shuttle"--basically a mostly-uninteresting hourglass figure.


You'll get something more interesting if you give the index fingers a full twist away from you; that's the figure called "Two Noddies".


Note that Eongatubabo is usually finished with a Caroline ending, for a stronger presentation:

1. 2 removes 1 from above.
2. 1 moves under 2 loops and picks up 5n.
3. 1 removes upper 2 loop.
4. Caroline extension.

Murphy's Power Lift or the two-diamonds extension also work well.

Done right, this all flows quickly, and the strings seem to dance on the fingers. However, it can be difficult to analyze, because the entire sequence is executed as essentially a single maneuver.

Now, it might surprise you to learn this, but the Inuit "Burbot" figure (from Jenness) is actually very closely related to the Eongatubabo maneuver, though you'd probably never know it to see the two techniques side-by-side. Here's the Burbot:

1. Opening A.
2. Transfer 2 to 1, then 5 to 1 (so you have three loops stacked on the thumbs). Keep the loops separated, and in order.
3. 5 enters 1 from below, then moves to the far side of the upper loop from below and hooks it down, holding it to the palm (this will be the transverse string that was originally 5f).
4. 2 enters 1 from above, then moves to the near side of the lower loop and hooks it up, returning to position (this will be the transverse string that was originally 1n).
5. Release 1.

At this point you'll have two double-walled diamonds, known as the "Burbot" (a kind of fish).


Now, aside from looking similar to "Two Noddies", how exactly is this related to Eongatubabo?

Try this excercise. Do Eongatubabo, starting with Opening A, and with the index loops rotated a half turn away from you.

What do you get? The Burbot!

Now, try this. Do the Burbot, but with the index loops turned a half turn toward you. The result? Two Noddies!

Mathematically, you could represent this relationship like:

2ba + burbot = eongatubabo
2ab + eongatubabo = burbot

(Where 2ba is mizz code for a half rotation of the index toward you, and 2ab is a half rotation away from you.) Setting those equal to zero:

2ba + burbot - eongatubabo = 0
2ab - burbot + eongatubabo = 0

And then reducing:

2ba + 2ab = 0

Which, since 2ba and 2ab are additive inverses (a half rotation away from you cancels out a half rotation toward you), this is what you'd expect. Burbot and Eongatubabo are the same! Mostly. The difference is only in how the fingers move the strings.

Scott (a member of the ISFA mailing list, and I realize I don't even know his last name. Throw me a bone, here, Scott!) shared a thought with me in a recent email. He pointed out that although the Burbot, as it is generally executed, doesn't exchange transverse strings (the original 5f and 1n end up on 5f and 2n), it could be done that way. Instead of starting with Opening A on 1, 2, and 5, try doing Opening A on 2, 3, and 4.

1. Place loops on 2 and 4.
2. R3 picks left palmar string.
3. L3 picks up right palmar string through R3 loop.
   

Then:

1. 1 moves under 2n, over 2f, under 3n, over 3f, under 4n, and returns with 4f.
2. 5 then does the same from the other direction: 5 moves over 4f, under 4n, over 3f, under 3n, over 2f, and returns with 2n.
3. Release 2, 3, and 4.

The result? The Burbot! And the transverse strings exchanged sides. Essentially, this is what you're doing when you stack the strings on the thumb. By moving the fingers through the stacked loops, you're basically threading your finger over and under the near and far strings, and returning with the transverse strings. Try the original Burbot instructions and pay attention to where your fingers go, relative to the strings, and you'll see what I mean.

Now, if you do Eongatubabo about a million times, in slow motion, and give yourself a splitting headache by trying to watch the strings, you'll see a similar thing happens. However, it's easier to see if you break Eongatubabo into two discrete steps. Following James Murphy's naming pattern in his "North American Net System" article, I call these two steps "First Micronesian Weave" and "Second Micronesian Weave".

Begin with Opening A, with the index loop rotated a half turn. Then do the First Micronesian Weave:

1. 1 moves through 2 from above, and returns with both 5n and 2f.
2. 3 picks up 1f.
3. Release 1.

Look familiar? It should. I talked about a family of similar maneuvers in my article titled "Variations on the Transverse Exchange". Murphy has also written extensively about three weaves in this family in his "North American Net System" article, where he calls them the First Inuit Weave, First Klamath Weave, and First Navaho Weave.

Now, do the Second Micronesian Weave:

1. 1 moves through the 2 loop from above, into 5 loop from below, and then continues into the 3 loop from below.
2. 1 hooks down 3f through the 5 loop.
3. 1 picks up 5f and returns, releasing 3f in the process.
4. Release 5.

Lastly, finish Eongatubabo:

1. 5 removes 3 from above.
2. Release 2.
3. Display (via Caroline ending, or other).

By breaking Eongatubabo into those two separate weave steps, I found it much easier to consider what the loops are doing. Let's take a close look:

First, 1 pulls 5n and 2f toward you. This creates a "window" in the 5 and 2 loops, and the 1 loop is essentially pulled through that. This is similar to what happens with the Burbot, when you pull the near transverse string through the stacked loops. Note, though, that because 1 opens the window by grabbing 2f, the 2 loop is "flipped"; the 1 loop is then pulled through the 2 loop from above, instead of below. This is why you need to give the 2 loop a half turn in order to get the same Burbot figure, while Burbot needs no rotation.

The second weave does the same, in the opposite direction: it pulls the 5 loop through the old 1 loop (which is now the 3 loop), and the 2 loop. This isjust what you do when, in Burbot, your index finger enters the stacked thumb loops from above and pulls out the lower near transverse string.

The only bit that had me bothered by this analysis was the necessity of giving the index finger a half rotation when doing Eongatubabo, in order to get Burbot. What I wanted was a transverse exchange that was equivalent to Burbot. And, having broken Eongatubabo into pieces, I was able to see my way clear to it.

The solution was in analyzing the first step of the first weave. As I mentioned before, by grabbing 2f, you introduce a half rotation toward you into the 2 loop. What if you pick up 2n instead? Go ahead and try it, starting at Opening A (with no loop rotations). Move the thumb under 2n, over 2f, and return with 5n and 2n.

If you complete that first weave and then do the Second Micronesian Weave, you'll see that this is not quite the solution. It's almost there, but not quite. The problem is that you wind up with a knot of strings intersecting the far transverse string.

What's the difference between the modified version and the original? Only a half rotation of the index loop. Because the original weave introduced a half rotation of the 2 loop (due to how it was picked up), we need to reconsider the first move of the second weave. If the 2 loop is no longer flipped, and we enter it from the same side as we did when it was flipped, then we're essentially introducing a half-rotation again, later in the system. So, instead of entering the 2 loop from above, let's try entering the 2 loop from below.

In other words, try these modified weaves:

Modified First Micronesian Weave:

1. 1 moves under 2n, over 2f, and returns with 5n and 2n.
2. 3 picks up 1f.
3. Release 1.

Modified Second Micronesian Weave:

1. 1 moves through the 2 loop from below, into 5 loop from below, and then continues into the 3 loop from below.
2. 1 hooks down 3f through the 5 loop.
3. 1 picks up 5f and returns, releasing 3f in the process.
4. Release 5.

And it works! Starting with Opening A, we can use this modified Eongatubabo to exactly mimic the Burbot (with the exception that Eongatubabo will turn the figure upside down, because it exchanges the transverse strings).

All that's left is to put the pieces back together into a maneuver that flows as fluidly as the original Eongatubabo. Here's my attempt:

Modified Eongatubabo:

1. 1 moves under 2n and hooks down 2f, holding it to the palm.
2. 3 moves into 5 loop from above, hooks back 5n and 2n, and hooks up 1n.
3. 1, still holding down 1f and 2f, moves under and returns with 5f.
4. Release 5.
5. 5 removes 3 from above.

This modified Eongatubabo retains the same fluidity as the original, but does not introduce a half rotation into the index loop. It is the same as the Burbot maneuver (excepting only the near/far swap of transverse strings).

So, hopefully you stayed with me through all of that! To get this back on the topic of presenting a transverse exchange, let's use Burbot, Eongatubabo, and our modified version to present the Inuit Net Opening (see the Apache Door Ending article for a description of that).

If you start with the Inuit Net Opening on your hands, and then you do Eongatubabo, you'll get the following figure.


Now, try our modified Eongatubabo:


Significantly different! However, it should be the same as what we'd get if we did the Burbot, only upside down. And, sure enough, if you take the Inuit Net Opening, stack the loops on the thumbs, and then finish the Burbot figure, you get:


Success! (Depending on how you extend the figures, your results may look dramatically different. In the above I'm using the Power Lift and Caroline Extension.) I encourage you to experiment, applying these to other three-loop configurations. Let me know if you find something interesting!

Postscript:

In case anyone is interested in mizz code, here is my attempt at describing the various maneuvers described in this article, in mizz code.

Eongatubabo:

1. 1.6,2a
2. 2adh,(2b&5a)1a
3. 1,(2ah&2blj&5aj)5b (auto-off 1.6)
4. 5
5. 5T2h
6. 2
   

Burbot:

1. 1,2
2. 1,5
3. 5.6,(1bl)1bh (1bl=two strings,1bh=transverse string)
4. 2.3,(1ah)1al (1ah=transverse string,1al=two strings)
5. 1

First Micronesian Weave:

1. 1,(2b)5a
2. 1,2b
3. 3,1b
4. 1

Second Micronesian Weave:

1. 1,(2b&3a&5a 3b*)5b
2. 5

Finish Eongatubabo:

1. 5T3
2. 2
3. SPR & arrange (caroline ending, etc.)

Modified First Micronesian Weave:

1. 1,2a
2. 1,5a
3. 3,1b
4. 1

Modified Second Micronesian Weave:

1. 1,(2a&3a&5a 3b*)5b
2. 5

Modified Eongatubabo:

1. 1.6,(2a)2b
2. 3adh,(2a&5a)1a
3. 1,(3bj&2b&5aj)5b (auto-off 1.6)
4. 5
5. 5T3

Apache Door Ending

Alright, I'm going to start going through as many endings as I can, applying them to a "three loop" configuration: loops should exist on thumb, index, and little finger, and the near thumb string and far little finger string should be transverse. I'll begin with the Apache Door ending.

Because "Apache Door" is an attractive figure in its own right, I think it's easy to forget that it's simply a unique ending technique applied to "Opening A". But what happens when you apply it to a different three-loop configuration?

I'm going to be using as the basic figure what James Murphy calls "First Inuit Weave", "Second Inuit Weave", and "Continuation Move". (See his North American Net System article, here.) For the sake of brevity, I'll just call it "Inuit Net Opening":

1. Opening A.
2. 1 moves through 2 from above and returns with 5n.
3. 3 picks up 1f.
4. Release 1.
5. 1 moves through 2 from above, under 3, under 5n, and returns with 5f.
6. Release 5.
7. 5 removes 3 from above.

If you're interested in learning "Mizz Code", the same opening is described like this:

1. base
2. 1,(2b)5a
3. 3,1b
4. 1
5. 1,(2b 3 5a)5b
6. 5
7. 5T3

(Lovely how concise that is, no?)

Alright, so you've got the "Inuit Net Opening" on your hands. It should look something like this:


Now, just do "Apache Door":

1. Transfer 2 loop to the wrist (inserting hand into 2 loop).
2. 1 gets 5n.
3. 5 gets 1f.
4. L1 moves under all strings (so all strings should rest between 1 and 2).
5. R1 and R2 grasp both L1 loops (NOT the left wrist loop) and remove them from L1.
6. L1 returns to position, moving under all loops.
7. R1 and R2 replace the grasped loop on L1.
8. Repeat 4-7 on the right hand.
9. Release the wrist loop over each hand, and extend.

Or, in mizz code:

1. 0,2
2. 1,5a
3. 5,1b
4. 1,(s)1
5. 0
6. SPR & arrange

The result should look something like a double-walled diamond with wings. (It kind of reminds me of Pippi Longstocking!)


Now, that figure alone is attractive, but it's hiding a little secret. If you poke your fingers into the little knots on either side of the diamond, they'll open up, and you'll get this beautiful mesh figure:


Try this with other three-loop configurations! I described several possibilities (and hinted at many more) in my "Variations on the Transverse Exchange" article; see what patterns emerge when you apply the Apache Door ending to them.

Mizz Code quick reference

Along with James Murphy's articles that I mentioned in my last post, I've also been studying "mizz code" (http://home.p07.itscom.net/nenemei/v2/index.html), a novel approach to describing string figures that focuses on where the strings move, rather than how they move. It's a challenging notation to learn!

As I was going through his code guide I took notes, and tonight I finished formatting those notes. The resulting "Mizz Code quick reference" is now available here:

http://stringfigures.info/mizz-quickref.html

I'll be updating it and clarifying it (and fixing it!) as I receive feedback, but hopefully this will help others get started with Mizz code!

Investigating String "Systems"

I've been silent here for a couple weeks, but not because I've been neglecting string figures. On the contrary, I've been studying the writings of James Murphy (a.k.a. Inoli), a luminary in the string figure world. His ISFA articles were written as a means of demonstrating how string figures can be used to help students build a solid foundation for studying mathematics, but they are fascinating simply as a study in how to really investigate string figure systems.

His articles are all available as PDF's, here:

http://www.torusflex.com/torusflex%20project1/isfa%20articles.html

I can't recommend these enough. If you have any interest (at all!) in learning how to really explore permutations on a string figure, these articles are full of incredible insight. He presents techniques such as his amazing "power lift" extension, as well as tricks like "rolling", inverse weaves, vertical nets, and more. Along the way you'll learn how to make such beautiful figures as his "Inuit Bowl", "Cherokee Seven Stars", "Lightning Across the Middle", and many others, as well as how to discover your own variations.

Extremely inspirational reading. Well worth the time spent!