Formula Versus Proportionality
The act of calculating with a formula is like triggering a cine‑camera shutter: the motion freezes into a single, sharply defined frame. Proportionality calculation, by contrast, is a strip‑film camera – it reveals the emergence, growth and transformation of a phenomenon frame by frame. A formula delivers the final result, but proportionality tells the entire story.
 A film, by contrast, must be experienced from beginning to end. The rhythm of viewing is set by the length of the reel, and the meaning unfolds only through time.A calculation formula captures a phenomenon as a single point on a curve, leaving all other points undefined. Proportionality, describing the same phenomenon, extends the value of that point both forwards and backwards, bringing the entire curve into view.
Proportionality is the analogue of a strip‑film camera: a long sequence of exposed frames that can be examined one by one. This corresponds to the lifting lugs along the curve – each frame is its own data point, and together they reveal the complete shape of the phenomenon.
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