The Doubling Map

Set:2 couple radial.
Music:The Gypsy Hornpipe.
Trivia:"The Doubling Map" is a fancy name for multiplying by two (more specifically, it's what dynamicists call the map on the unit interval x -> 2x (mod 1)). It's a large part of the PhD for the person who wrote it; the dance is all about multiplication by two.

Start in place.
4 3  1 2
Figure 1:Right arm turns
1-8In pairs, right arm turn once around (quite slow).
On 8, as you drop, middles back turn and take waist hold with their partner.
9-16 Repeat but in pairs (middles take right arms, ends punch on the appropriate beats).
All drop on 16 and face your partner.
1-4Sidestep right and left, moving backwards to switch places and face each other, finishing standing.
5AClap own hands.
5BClap right hands with each other.
6Clap own hands under lifted left leg.
7-8Repeat, clapping left hands and clapping under lifted right leg.
9-12Sidestep right and left, middles moving forwards to switch places and face their partner again, finishing standing.
13-16Clapping as before with partner.
Figure 2:Gypsy
1-8Gypsy with your partner.
On 8, middles Back turn three quarters while ends turn right a quarter, to face 45 degrees out to the left in the same direction as each other.
9-16"Double gypsy": same movement as before, but a bit larger and going around the other couple in pairs, alternating between a line and square.
  4 3
  1 2

1 2 4 3

  1 2
  4 3

4 3 1 2
On 16, all turn to face your partner.
Figure 3:Back-to-back
1-8Back to back right shoulders with your partner.
Middles back turn on 8 to face each other.
9-16"Double back-to-back": same as before, but couples acting as a unit and performing a back-to-back with the other couple.
Because of the distance, it will probably take two steps to go forward (beats 9-10) and three to go back (beats 13-15).
On 16, middles back turn to face their partner again.
Figure 4:Polka Changes
1-6Three-quarter polka turn on the spot.
7-14Polka round to place with the other couple.
15-16Quarter polka turn on the spot back to place.
Figure 5:Zig-zags
1Pass partner left shoulders, not going too wide.
2Back turn into their place.
3-4Repeat back to your own place.
5-8Repeat 1-4 to go round again.
9-16Zig-zag hey for 4, finishing home.
15AClap own hands as before.
15BClap partner's left hand as before.
16ATurn one quarter to the right with the right foot with a stamp.
Dance off
1Step forward.
2Quarter turn right.
3-Lead off

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