Indexing the archive…
Your Universe of Digital Possibilities
Can a published forecast ever stay true? Yes, if the world responds smoothly to it: then there is always a forecast that predicts its own effect. Publish the poll, find the one that comes true, and see the nine worlds of this edition each with its own curve — and the bar where the curve breaks.
A continuous map of a closed ball into itself fixes some point. On the interval [0, 1] it is the intermediate value theorem: a continuous curve from the bottom edge to the top must cross the diagonal. A jump can step over it.
R is what happens when the forecast f is published. A forecast that accounts for its own effect is a fixed point of R; Brouwer says one exists when R is continuous. Iterating publication — publishing what happened last time — reaches it only where R is a contraction.
The Prophecy’s model electorate: voter i leans zᵢ, and a published poll f moves every voter toward the leader it shows by the gain b (against it when b < 0). Simon’s argument needs only that R be continuous; this logistic form is the instrument’s choice, smooth and with R′ in closed form.
The tenth prophecy is the theorem behind the other nine. Morgenstern said a public forecast cannot be right, because it is read; Simon and Grunberg & Modigliani answered that it can, if the world answers it smoothly — then a forecast that predicts its own effect exists, and a pollster who knows the response can find it. Popper called the prediction’s pull on the predicted the Oedipus effect. Every instrument of this edition is one response map: The Cobweb’s farmers and The Score’s retraining iterate theirs; The Bubble finds two extra crossings past its gain of one; The Run and The Herd jump. The edition opened on The Bar, where no shared forecast can be right — and that is exactly where Brouwer fails, at a jump. Let each patron go with a probability and the forecast that stays true appears, at sixty.