The Still Point

The short version

Take any value of time — a wavelength, say — and carry it once round all the dimensions it can be read in: a free fall, an energy, a radial mass, a mass, and back to a wavelength. It comes back changed. Do it again and it changes again, but by less. Every value is moved towards one value, and that one value never moves: 589.1017256368 (5¹³/(2⁵·3⁸·π²)) — the free fall of the G2 register, 9.818362093947, written as a wavelength. Times forty, it is the Earth's own turn against the stars, 23 hours 56 minutes 4.069 seconds.

The ladder below it has four rungs, and every reading of time has a face on each: G0, the sodium register, two G-bond steps down; G1, the Earth's surface register, one step down; the dual, half a step down; and G2, the still point itself. The G-bond step is the smallest step between neighbouring registers, 1.000090150603356 (5¹⁰/(2⁴·3⁹·π³)).

One turn round the dimensions

A turn is seven fixed steps. Divide a wavelength by 60 and it is a free fall; divide by 24 and it is an energy; take the square root and it is a radial mass; multiply by 9375 and it is a mass; divide by π²/8 and it is a wavelength again; divide by 7776/(5π) and it is a free fall; multiply by 60 and it is back where it started — a wavelength, one register higher. Six of the steps multiply; one takes a root. So the whole turn collapses to one rule:

Here is the turn worked in full, starting from the yellow light of sodium, the D2 line at 588.9955242462. Halfway round it passes through 4,860 exactly — hydrogen's blue line, 486 — and it lands on the G1 rung.

What the picture shows. The eight boxes are the eight readings of one value as it goes round a turn; the purple label on each link is the step that turns one reading into the next. The gold box is the halfway point, 4,860, hydrogen's blue line. Sodium's yellow line goes in on the left; the G1 rung comes out on the right.

The still point

Put 589.1017256368 into the turn and it comes back unchanged — at forty digits. Every other value moves: the turn multiplies it by √(still point ÷ value), which is more than one below the still point and less than one above it, and exactly one at the still point. Nothing can step over it from either side.

The ladder, and the half-life

Count the distance below the still point in G-bond steps. Sodium's D2 line is two steps down, on G0. One turn up halves that: G1, one step down. Another turn: the dual, half a step down. Then a quarter, an eighth, a sixteenth — each turn halves the gap, like a radioactive half-life, so the climb goes on for ever and comes to rest, in the limit, on the still point.

What the picture shows. The four rungs on one line, placed by their distance below the still point in G-bond steps: G0 two steps down, G1 one, the dual half a step, G2 at rest on the right. The labels between the dots are the gaps. Each turn up the dimensions moves a value one rung to the right and halves its gap.

The same ladder in the speed of light

The speed of light is not one number. It has a face on every rung of the same ladder, the same distances apart, and it climbs by the same rule: the next face is √( c × c_G2 ). It comes to rest on c_G2, the speed of light's still point.

What the picture shows. The four faces of the speed of light, on the same scale of G-bond steps as the wavelength ladder above: c_G0, the sodium face, two steps below c_G2; c_G1, the Earth-surface face, one step below; the dual half a step below; and c_G2 at rest. One turn takes c_G0 to c_G1, and the next takes c_G1 to the dual. The G1 face is the one the free fall builds: 9.817477042468² × 864 × 3600 = 299,789,233.683089.

Down the dimensions, every turn doubles

Run the same seven steps backwards and the square root becomes a square: one turn down is the old value squared, divided by the still point, and every gap doubles. From G1 the values fall 2, 4, 8, 16, 32, 64 steps below the still point — 588.9955242462, 588.8893420012, 588.6770349345, 588.2526503969, 587.4047989333, 585.7127602823. Going up, the still point draws values in; going down, it pushes them away. Time gathers on the way up and disperses on the way down.

What the picture shows. Each bar is the distance below the still point after one more turn, in G-bond steps. The green bars, turning up, halve at every turn: 2, 1, ½, ¼, ⅛, 1/16. The brown bars, turning down, double: 1, 2, 4, 8, 16, 32. The same rule, read in the two directions.

Questions This Paper Answers

What is the still point of time?

589.1017256368 (5¹³/(2⁵·3⁸·π²)) — the G2 free fall, 9.818362093947, multiplied by 60. One turn round the dimensions of time returns it unchanged; every other value is moved towards it.

Does the cascade of time close or run away for ever?

It closes. Each turn up the dimensions halves the distance to the still point, so the climb never ends and never overshoots; it comes to rest, in the limit, on the still point.

What are the four faces of the speed of light?

c_G0 (sodium) 299,762,209.938999 (c_G1 ÷ the G-bond step); c_G1 299,789,233.683089 (2³·3⁵·5⁶·π²); the dual 299,802,746.468698 (2·√3·5¹¹·√π); c_G2 299,816,259.863385 (5¹⁶/(2·3⁴·π)). They sit two steps, one step and half a step below c_G2, which is the speed of light's still point.

Where does sodium's D2 line sit?

Two G-bond steps below the still point, on the G0 rung: 588.9955242462 (2³·3¹⁰·π⁴/5⁷), which is the G1 rung squared and divided by the still point.

What happens when time moves down the dimensions?

The square root becomes a square: one turn down is the old value squared, divided by the still point. Every turn doubles the distance — 2, 4, 8, 16, 32, 64 steps.

What does the still point have to do with the Earth?

The still point × 40 is the Earth's sidereal day, 23,564.0690254726 (5¹⁴/(2²·3⁸·π²)) — 23 hours 56 minutes 4.069 seconds.