02 · The Scale
From number to growth
A slider gives a number between 0 and 1. The number is not the point. The point is what the number projects to, once you let it run for a year, ten years, a lifetime.
Abstract → 0th order
The slider is dimensionless. 0.7 means nothing in particular. It's a ratio, an abstract quality. The reading on the dial.
First order — linear × half-exponent
Multiply the abstract number by itself, the way interest compounds. Each year adds a small exponent to the previous. This is linear growth in the exponent: the kind of curve a savings account draws. Calm, predictable, with the second-order surprise hidden inside.
life₁(t) = t · x½·t
Second order — quadratic, with a hidden bend
Now square the abstract number and let it compound on a different rhythm. The curve bends. The bend is the gold. The first-order path is the road; the second-order path is the destination the road could not have predicted from inside the road.
life₂(t) = t² · xt²
Why the difference matters
A life lived at first order is well-fed and steady. A life lived at second order bends early, slowly, in ways that look like nothing from inside the year. From outside the lifetime, the bend is the whole story. The alchemist's task is to live in the bend — not to optimise the slope, but to choose the order.