Indexing the archive…
Your Universe of Digital Possibilities
Two clouds of dots flash up side by side — which has more? You will know without counting, and how well you know depends on the ratio. The instrument fits your Weber fraction for number with the confounds controlled, finds the elbow where seeing a number turns into counting it, and measures how straight your inner number line has become.
Each numerosity n is represented as a noisy magnitude whose spread grows with n (scalar variability, Weber fraction w). The chance of picking the larger of two depends only on their ratio; w is fitted to the visitor’s answers by maximum likelihood.
The smallest change ΔI that can be told apart grows in proportion to the intensity I: a fixed fraction k, the Weber fraction. For number, the same law means two quantities are discriminated by their ratio.
Count just-noticeable differences up from the threshold I0: if each is a constant fraction of I (Weber), the count — the sensation S — grows with the logarithm of the stimulus. The logarithmic number line is the same idea laid out in space.
The eighth percept is a sense for quantity. A forager choosing the fuller tree, a bird the larger flock, needs the ratio fast, not the exact count — and the approximate number system delivers it with Weber’s law built in. How few items one glance can hold is The Glance; what exact number makes of the same integers is The Prime; how a part relates to a whole is The Fraction.