Crossover phenomenon in the performance of an Internet search engine

TL;DR

This paper investigates how the Google search engine's ability to find random N-letter strings exhibits a sharp transition at N=6, indicating a phase transition-like phenomenon in search performance.

Contribution

It reveals a transition-like behavior in search success probability for random strings and introduces a susceptibility measure suggesting criticality in search space geometry.

Findings

Probability drops sharply at N=6

Presence of a transition-like phenomenon

Maximum susceptibility near the transition

Abstract

In this work we explore the ability of the Google search engine to find results for random N-letter strings. These random strings, dense over the set of possible N-letter words, address the existence of typos, acronyms, and other words without semantic meaning. Interestingly, we find that the probability of finding such strings sharply drops from one to zero at Nc = 6. The behavior of such order parameter suggests the presence of a transition-like phenomenon in the geometry of the search space. Furthermore, we define a susceptibility-like parameter which reaches a maximum in the neighborhood, suggesting the presence of criticality. We finally speculate on the possible connections to Ramsey theory.