Case B — Use relativity to generate a spatial duet, not to explain the dancers’ bodies

Situation and source choice. A maker wants a duet whose spatial organization becomes unfamiliar while its phrasing remains recognizable. The source is the distinction between proper length and a moving frame’s simultaneous length measurement. In the ideal relativistic calculation L = L_0 sqrt(1 − v²/c²); a half-length corresponds to v/c = sqrt(3)/2, approximately 0.866. This is a mathematical source relation. No dancer approaches that speed, and a viewer walking to another seat does not perform that Lorentz measurement.

Take only an artistic operation from it: halve one chosen spatial dimension while preserving the other dimension and the times of arrival. The choice is explicit, so the scientific source can be explained accurately even if the finished dance no longer resembles a textbook diagram.

Generate the phrase. Work first with a hand trace in a plane in front of a comfortably supported performer. Choose familiar half-width W and height H. All coordinates below are scaled to that person’s chosen range. Make an eight-second closed phrase S through five positions:

Use the same smooth interpolation q(u) = 3u² − 2u³ on each two-second segment. The selected phrase therefore draws a rectangle with brief zero-speed arrivals, then is ready to repeat. This is one deliberately chosen organization, not a claim that all phrases consist of poses.

Produce C by replacing every x coordinate with x/2. Keep the y coordinates and all five arrival times. Its width becomes W instead of 2W; horizontal path speed and acceleration scale by one half for the same interpolation, while the vertical segments remain unchanged. This construction retains ordering, closure and the two-second arrivals. It is not uniform shrinking.

Compare C with U, which halves both x and y, and F, which traverses S in four seconds. Select C for the brief: it changes only the chosen spatial dimension while retaining the phrase’s timing and height. U loses the retained height; F loses the eight-second duration and increases movement-rate demands. They remain possible material for other briefs, not errors in all choreography.

Compose the duet. Place two performers in separate non-overlapping hand-reach areas, visible side by side from the front. They share eight-second beginnings but do not touch or exchange weight. Use this thirty-two-second fixed score:

Define the transition phrase rather than asking performers to jump from one left-low starting point to another. It starts at (−W,0), arrives at (+W/2,0) after two seconds, then (+W/2,H), (−W/2,H), and ends at (−W/2,0), each after another two seconds. This first horizontal segment changes the width and starting offset together; it is not a pure scaled copy of S. Its explicit purpose is to join S’s ending to C’s starting position. Every segment again has zero prescribed endpoint speed. At the boundary between 16 and 24 s, B’s compressed ending already equals C’s beginning; A’s final transition ends at the same normalized position at 32 s. No hidden repositioning remains.

The maker has chosen establishment, divergence, sustained comparison and convergence, with an exact ending. MDPE.11 keeps this fixed score separate from interpretation: performers may select familiar small ranges before beginning, but they do not improvise new arrival times or path order during this version. Changing ranges independently does not promise equal absolute widths; the retained comparison is within each performer’s earlier and later phrase. If equal absolute geometry matters to the brief, select compatible ranges and a common spatial reference before rehearsal.

Specific practice and observation need. A useful first reading is an animation or plotted trace of both parts, checking the boundary positions and timing. It can expose an incorrect transition without asking a person to perform it. In bodily practice, suppose a performer makes C by rushing its shorter horizontal segments and waiting early at the corners. The path endpoints are right, but its two-second moving intervals are lost. RHY.3 helps preserve the continuing path; RHY.10 supplies shared landmarks without requiring continuous mutual imitation. HCD.6 constructs one eight-second attempt in which both the segment durations and width change are visible, and HCD.9 gives feedback on the early arrival. If the issue is not timing but inability to vary reach without bracing, use SOM’s bodily contrast and return to the same phrase. Removing music or a teacher’s count is a separate support change, relevant only if the intended performance omits it.

A front-view trace can confirm the designed geometry; a performer report can inform ease and attention; an audience response can inform the intended perceptual effect. None of those alone establishes the others. The first completed result here is the two selected phrases, the necessary transition, the full score and the next discriminating practice question. Claims about actual performance, learning or artistic success await their corresponding observations.