Point Eight Five: The Surfer's Coin

One number decides how the most influential ranking method ever built balances the web's own link structure against pure chance, and that number was never derived. PageRank imagines a random surfer who, at each page, follows a link with probability α and teleports to a random page with probability 1 − α. In 1998 Brin and Page suggested α = 0.85. Twenty-eight years later the suggestion is still the shipped default: the documentation of the standard graph libraries sets the damping parameter to 0.85 unless the user changes it, and the literature that examined the choice says plainly, in words quoted in this paper, that the choice is eminently empirical and that an analytical justification of the value is still missing. This paper prices the choice in both directions: at α = 0.85 the standard computation takes about 142 power-iteration steps to shrink its error by a factor of ten billion and carries a perturbation-sensitivity scale of 6.7; at α = 0.5 the same work takes 34 steps at a sensitivity of 2; at α = 0.99 it takes 2,292 steps at a sensitivity of 100. The interval (0, 1) is a theorem; the point inside it is a choice. Grade: THE INTERVAL IS MATHEMATICS — THE POINT IS A CHOICE, PRICED IN BOTH DIRECTIONS. This paper is part of the breadth program of the author's corpus; it touches no claim of the physics core.