Paradigm · Motion

The Voyage: Z · X · Y

From zero to unit to infinity. Z counts the linear lane, X the exponential, Y the ordered double-struck infinity — and the four digits ride along. Because your speed to infinity equals where you reach, the whole journey collapses into an angle.

zero
∞
I
O
A
E
Locality · 0th octave · 1-to-1 · linear 1D

Z — Linear Lane

Grow the value by 2 and every point to infinity is bigger by 2. It does not know in infinity — O-notation lives here.

octave Z · 1/3
Z

Linear Lane

0th octave · 1-to-1 · linear 1D

Grow the value by 2 and every point to infinity is bigger by 2. It does not know in infinity — O-notation lives here.

X

Exponential Lane

1st octave · 1-to-2 · exponential 2D

Grow acceleration by 2 and every point to infinity is bigger 2 times. One point change is change into every point that follows.

Y

Ordered Infinity

2nd octave · 2D of 2D digits · double-struck 𝕆

Grow the quadratic base-2 exponent by 2 and boundary reach stays constant. Speed to infinity equals where you reach — it collapses into angle.

Linear vs Exponential collapse

Grow the linear value by 2 and every point is bigger by 2. Grow the acceleration by 2 and every point is bigger 2 times. Slide the growth factor to watch the exponential lane collapse into its precision angle.

linear · Zexponential · X
Growth factor×2.00

The exponential lane's speed to infinity equals where it reaches — so it collapses to a precision flag, an angle of 63.4°. Fill digit precision fast; the angle directs toward the infinities.

The number scale

Twelve digits, exponent 0% to 100%. Base-4 IE / OA sampling shows, by digit value alone, where the exponential and where the linear ratio grows.

0%
A
9%
A
18%
O
27%
A
36%
A
45%
O
55%
O
64%
O
73%
E
82%
E
91%
I
100%
I

Twelve digits map exponent 0% → 100% across the lane. IE / OA sampling shows, by digit value alone, where the exponential and where the linear ratio grows. Whole-word decimal: 10917361.