Ballroom Dancers generally evolve from Individual Dancers (dancers dancing in front of each other) to Pattern Dancers (each dancer dances their own part of the pattern) to Partnership Dancers (employing a lead and follow interaction) and finally the Singularity Dancer, (the infamous two-headed four-legged entity). This evolution requires a continuous adjustment to the physics and geometry of the dance entity. The Individual Dancer and the Singularity have very different implementations of Ballroom Dance physics and geometry.
In a basic Waltz "Forward Progressive" pattern (forward, side-right, together) the ladies backward momentum must be controlled to effectively accomplish the side step of the pattern. The power generated by the leader's forward step initiates a backwards momentum for the lady that results in a slightly backward side step for the lady. If the leader takes a 90 degree side step, the lady will open up away from the leader. In each successive "Progressive", the lady will get further and further away from the leader. The leader must take a slightly forward side step in order to accommodate the ladies momentum and maintain the partnership.
In a Rumba "Crossover Break" with an "Inside Turn" pattern, the leader must control the ladies rotational momentum or she will over rotate the turn. The "Inside Turn" is powered by the leader. If the leader powers the whole turn, the ladies momentum will spin her slightly out of control. The leader's hand moving above the ladies head initiates the power for the turn. The leader's hand moving down stops the turn. The leader powers the first half of the turn and allows the ladies momentum to finish the second half of the turn. The leader's hand must come down (stop the turn) when the ladies back is facing him. This allows the lady time to control the momentum and stop the turn facing the leader. It is very common for the leader to "Over Lead" and the lady has to deal with the consequences.
In Silver and above Waltz and Foxtrot, there is a sequence where a "Back Lock Step" is followed by an immediate stop. The "Back Lock" is danced in Outside Partner dance position but the sudden stop causes the dance position to change to a Promenade dance position. Dancing several "Back Locks' to generate a lot of momentum and then jamming on the brakes to go into Promenade creates a great feeling. If the leader maintains a vertical position during the stop, the momentum will take the partnership out of control. The leader must maintain a quite severe lean against the direction of the momentum to control this sequence and counteract the momentum created.
As the dancer's evolve from Individual dancers to the Singularity, the center-of-gravity must evolve as well to successfully accomplish the transformation. Up until the transition to the Singularity, each dancer has had their own center-of-gravity (two centers-of-gravity for the partnership). The Singularity has only one center-of-gravity. The Singularity deals with the single center-of-gravity of the four-legged entity, not the two individual dancer's centers-of-gravity.
The Singularity is a single unit composed of two dancers. The two dancers act and move as one entity. A single center of gravity exists within the two dancers. The dancers must re-train themselves to be larger than what they used to be. If you were on a long hike and carrying a heavy backpack, your body would instinctively adjust your center-of gravity to include the weight of your backpack. This is basically what you want to achieve in a Ballroom Singularity.
When carrying a backpack, the center-of-gravity is a natural (almost unknowing) adjustment. When that backpack is another dancer, it becomes a little more difficult. The backpack is completely supported by the hiker. In Ballroom dancing, the other dancer has its own support, power, and movement. The backpack is only a physical relationship to the hiker while the dancer is a physical as well as a logical relationship. The Singularity must have a unified feeling, physicality and power.
The Singularity dancers must become more than what they were as partnership dancers (physically and logically). To achieve this, the two dancers must actually become a new physical and logical entity (a Singularity). The mind set must change to include your other half as actually you. The Singularity can only exist if both dancers are of the same mindset. The momentum problem described above is now almost non-existent. There is only one momentum to deal with and that is the momentum of the Singularity. The Singularity regains the natural feeling of a single entity, just as the individual dancer originally had.