Smoke Ring of Now

Each small circle, the cross-section of the tube, is one person’s moment. The moment starts at origination on the outer equator. It runs down the outside through sense (quadrant 1), under the bottom through perception (quadrant 2), and reaches the threshold on the inner equator. Then it rises up the inside through thought (quadrant 3) and comes back over the top through expression (quadrant 4) to origination.

The horizon is the plane through the middle of the ring. Everything below it is pre-conscious and everything above it is post-conscious. All twelve people turn together by default, so the dots move as one circle rolling round the tube.

This is how a real smoke ring circulates as it travels: fluid streams forward through the hole and back round the outside. A ring circulating this way moves upward, so up is forward in time.

The earlier page, Psychosocial Torus, ran the moment around the hole. This page runs it around the tube, through the hole, and spreads people around the hole. Those are the torus’s two circles with their roles swapped.

The spindle is the small circle cut at origination and straightened onto the axis. The bottom is the beginning. Quadrants 1 and 2 run up to the horizon, and quadrants 3 and 4 run above it to the top. The ticks are the twelve people; when they are in step they form one collar sliding up the spindle.

The attention sliders set how long the moment dwells in each quadrant. A thicker segment means more of each cycle is spent there, so the dots slow down as they pass through it.

On the sphere the spindle runs from 0 at the bottom to ∞ at the top. As the shape moves toward the horn, 0 and ∞ slide along the spindle and meet at the horizon.

The time cone enters from below, narrows into the hole and opens out above. Its stripes flow upward. On the ring, time passes through the open hole. At the horn the two cones meet at a single point, like the past and future light cones of relativity meeting at here and now. On the apple and the sphere the cones end at 0 and ∞, and time runs inside the shape from one pole to the other.

Wake shows the ring’s past positions falling away below it as it rises.

The bright point is an object of attention. You can move it anywhere above the horizon but not below it. It throws a cone of light down at 45°, and anyone whose small circle stands inside the lit footprint is attending to it. Their circles turn gold, and while they are in thought or expression a line runs from them to the object.

Height matters. Held low, in the thought zone just above the horizon, the object lights only the few people directly beneath it. Raised into the expression zone, it lights more, and above the centre at a height greater than the ring’s radius it lights everyone.

This part is my addition. With Own pace, each person has a slightly different natural speed, so the twelve drift apart. People inside the light of a shared object pull toward each other’s phase, as coupled oscillators do in Kuramoto’s model (1975). Gather the group under the object and they fall into step; move it away and they drift. The In step readout is the model’s order parameter: 100% when everyone is at the same phase.

It treats shared attention as the coupling that keeps people in phase. That is a modelling choice to try against your experience, not a finding.

On the sphere each small circle is a great circle through the poles. Its four turning points are the numbers +1 at origination, 0 at the bottom, −1 at the threshold and ∞ at the top. Your four quadrants are the four arcs of the real line between them: sense is (0, 1), perception (−1, 0), thought (−∞, −1) and expression (1, ∞). The pre-conscious half is |z| < 1, the post-conscious half is |z| > 1, and the horizon is the unit circle.

Moving toward the horn, the threshold slides from −1 through the inside of the apple to the node, and on the ring it is the inner equator, where 0 and ∞ are joined. Along the moment, 0 and ∞ also move: from the ends of sense and thought toward the threshold, where they meet at the horn. The spindle shows the same meeting from the outside.

On the sphere the circle is shared: your perception and thought run back along the sense and expression of the person opposite. On the ring every person has a circle of their own.

• Speed round the circle. The moment turns at an even rate except where attention dwells. A real smoke ring turns faster on the inside, near the hole.
• The spindle’s scale. It maps the whole cycle onto the axis from −1 to 1, with the horizon at the threshold, rather than unrolling the circle at its true length.
• Which way the cone of attention points. Here it spreads down from the object like light. It could instead gather up from the people to the object.
• In step by nature, or by coupling. In step follows your description; Own pace asks what keeps people in phase.
• The fourth quadrant’s name. Expression here; representation on the earlier pages.