Erdős Number vs. Six Degrees of Bacon

Attribute	Erdős Number	Six Degrees of Bacon
Origin	Mathematics	Film
Named after	Paul Erdős	Kevin Bacon
Connection	Collaboration in mathematical papers	Acting in films together
Number of steps	Integer	Integer
Popularized by	Mathematicians	Hollywood

Introduction

Erdős Number and Six Degrees of Bacon are two popular concepts that measure the "closeness" of individuals within a network. While Erdős Number is used in the academic world to determine how closely connected a person is to the prolific mathematician Paul Erdős, Six Degrees of Bacon is a fun game that connects actors to Kevin Bacon through their film roles. Both concepts have gained popularity and are used to showcase the interconnectedness of individuals in various fields.

Definition

Erdős Number is a measure of how closely connected a person is to Paul Erdős through co-authorship of mathematical papers. If a person has collaborated directly with Erdős, their Erdős Number is 1. If they have collaborated with someone who has an Erdős Number of 1, their Erdős Number is 2, and so on. The goal is to minimize one's Erdős Number by collaborating with as many people as possible. On the other hand, Six Degrees of Bacon is a game that connects actors to Kevin Bacon through the films they have appeared in together. If an actor has appeared in a film with Kevin Bacon, their Bacon Number is 1. If they have appeared in a film with someone who has a Bacon Number of 1, their Bacon Number is 2, and so on.

Popularity

While Erdős Number is primarily used in academic circles to showcase collaboration networks in mathematics, Six Degrees of Bacon has gained widespread popularity as a fun game among movie enthusiasts. The concept of Six Degrees of Bacon was popularized by the "Six Degrees of Kevin Bacon" game, which was created in the mid-1990s. The game gained so much traction that it led to the creation of the website "The Oracle of Bacon," which calculates the Bacon Number of any actor in Hollywood. On the other hand, Erdős Number is less known outside of academic circles and is mainly used by mathematicians and researchers to study collaboration networks in mathematics.

Calculation

Calculating an Erdős Number involves tracing the collaboration path between a person and Paul Erdős through their co-authored papers. This process can be time-consuming and requires access to academic databases and research publications. On the other hand, calculating a Bacon Number is relatively straightforward, as it involves tracing the film roles of actors and identifying common films with Kevin Bacon. The simplicity of calculating a Bacon Number has contributed to the widespread popularity of the Six Degrees of Bacon game, as it is easy for anyone to participate and determine their connection to Kevin Bacon.

Network Size

The network size for Erdős Number is limited to the academic world, specifically within the field of mathematics. As a result, the pool of individuals with finite Erdős Numbers is relatively small compared to the general population. On the other hand, the network size for Six Degrees of Bacon is much larger, as it encompasses actors from all genres and eras of film. This larger network size allows for a wider range of individuals to participate in the Six Degrees of Bacon game, making it more accessible and inclusive compared to Erdős Number.

Impact

While Erdős Number is primarily used as a measure of academic collaboration and prestige within the mathematics community, Six Degrees of Bacon is more of a social phenomenon that brings people together through a shared love of movies and entertainment. The Six Degrees of Bacon game has inspired various spin-offs and adaptations, such as the "Six Degrees of Separation" theory, which posits that everyone is connected to each other through a chain of six acquaintances. On the other hand, Erdős Number remains a niche concept within the academic world and is not as widely recognized or celebrated outside of mathematical circles.