Compose movement from a physical relation or a scientific image

Use this application when a physical idea has produced an interesting gesture but not yet a phrase or composition. It develops a technique used in Western concert, contemporary and postmodern choreography: make movement material under a constraint, investigate transformations, then compose the resulting material through transitions, development and viewer placement. It does not prescribe how every dance tradition creates material.

Coates and Demers’ Physics and Dance (Yale University Press, 2019, ISBN 9780300195835), particularly its choreographic studies on printed pages 177–180, supplies this construction. The cases below are new, fully specified teaching examples. Their conditions and choices are stipulated; they report no dancers, learning experiment or safe-performance qualification. They can first be inspected as scores or animated traces. Any embodied realization uses familiar, individually suitable movement and appropriate instruction; no jump, fall, lift or maximal movement is prescribed.

Make the source useful to a composition

First decide what the source contributes. A mechanical relation can exclude a movement under named conditions. A scientific image can suggest a movement without explaining its physical mechanism. Keep that decision visible when making the phrase.

Choose a short, recoverable movement seed. Specify its beginning, changes and ending, including what happens between positions. Select a relation worth retaining: an arrival, order of changes, continuing path, response between performers or contrast visible to a viewer. Then change one feature that matters to the intended composition. The same seed can acquire another spatial path, duration distribution or quality. Compare the whole variants, including how each leaves the next action possible.

Use MDPE.9 to make a retain, revise, branch or reject decision for these variants. It supplies the comparison; the phrase construction here supplies the domain generation method. Use MDPE.11 to state what is fixed beforehand and what may be interpreted or generated while performing. Compose a beginning that establishes the relation, a development that changes something consequential and an ending that resolves or deliberately suspends it. Return to movement technique or learning only for a contribution the selected composition actually needs.

Case A — Keep an apex in the music without demanding a longer flight

Situation and physical decision. A maker has a four-second motif: rise and return during its first second, wait during its second, extend sideways during its third and return during its fourth. The intended effect is a brief visible summit at 0.5 seconds followed by a longer low interval. The initial idea assigns the entire first second to a dancer’s airborne center of mass. Its idealization neglects air resistance and uses equal takeoff and landing COM heights.

For flight duration T, v_y = gT/2 and the rise is h = gT²/8. At T = 1 s, these are 4.9 m/s and 1.225 m. The supplied capability basis for this fictional brief permits only the already familiar 0.2-second flight variant, not one second. Its idealized rise is 0.049 m. The timing change therefore increases the modeled height twenty-fivefold; slowing the music does not merely slow the same jump. Neither number is a training prescription.

Compare three candidates:

The selected variant is a changed choreography, not proof that supported hand motion is physically equivalent to an airborne body. If the brief requires actual flight, this selection is unavailable; return to timing, means or the brief.

Selected phrase. Use a comfortable supported position with no partner contact and no required weight transfer. For the score, let H be an individually chosen familiar hand-height change and W a familiar sideways reach. Coordinates are relative to the hand’s low home position, not prescribed anatomical dimensions. The other hand remains at home.

Join each moving interval with a smooth start and finish; for a drawing or animation, q(u) = 3u² − 2u³, 0 ≤ u ≤ 1, specifies the interpolation between its two endpoints. It is a controlled trajectory with zero endpoint speed, not a ballistic path. The hold is an intentional interruption between the vertical and horizontal gestures. At four seconds the phrase is ready to recur. Repeat the motif with the left hand and the opposite sideways direction to obtain an eight-second phrase A.

Now make phrase B by changing the vertical path into a diagonal: during each rise travel from (0,0) to (W/2,H), then return along that diagonal. Retain every duration, the summit at 0.5 s of each motif and the later horizontal out-and-back. B develops spatial reach without requiring a higher summit or faster sequence. Reject an alternative that moves the summit to one second: it removes the brief’s midpoint arrival.

Composition and continuation. The selected twenty-four-second score is A, then B, then A with half the hand-path dimensions. The last eight seconds retain timing while contracting visible scale. Each four-second motif ends at home with zero prescribed hand velocity, so the next hand can begin without an unspecified reset. The last return at 24 s is the ending; do not add an unscored retreat. The viewer sits in front with both hands visible. The form establishes a vertical gesture, opens it diagonally and recalls it at reduced scale. Those are chosen compositional relations; whether viewers find the effect compelling remains a receiving-use question.

Specific practice need. Suppose a later realization can produce the rise and the horizontal reach separately but rushes the 1–2 s hold. RHY.12 can keep one complete four-second motif, including that hold and the following reach, while making its durations recoverable through a timed demonstration. HCD.9 supplies feedback on the premature reach and a retry; additional strength work does not answer that timing error. If the hand contour instead causes unwanted whole-body bracing, SOM.2–.4 supplies a small perceptible contrast and reintegration under a qualified teacher, while the chosen support stays unchanged. Keep the needed support in the final arrangement. A correct animation settles the score’s times and joins, not the performer’s ability.

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.

Adapt the construction without losing its distinction

When reusing either case, change the seed, retained relation or receiving conditions deliberately. Recompute a physical constraint when mass, contact, height or timing changes. Reconstruct transitions when a transformation changes the state from which the next phrase begins. If the wanted artistic relation survives a different realization, compare that realization rather than treating the original body action as mandatory.

The joint use of PHY, SOM, RHY and HCD is conditional on the difficulty: physical modeling, bodily regulation, rhythmic coordination and human learning supply different results. Use an adequate direct dance or teaching method when it already supplies the needed result. The examples need no new universal hierarchy of those methods, and no single success judgement can substitute for physical correctness, usable movement and the intended artistic effect.