My Pope Number is 2: The Smaller World Hypothesis

I proofread Piergiogrio Odilfreddi's book (which is on Lance's List of Favorite Complexity Books) for which I got a generous acknowledgment. I have also

visited him in Italy, though not for a while. 



Benedict.Pope Emeritus (I think that's what he is still called) broke his silence with a letter to Odilfreddi, see here.



Hence I am two handshakes away from Pope Benedict.  It used to be said that there were Six degrees of separation.-- for all people a,b there is a path of length at most 6 that links them. The graph varies with you you ask, but it tries to pin down that a and b know each other.



Is six now too big? One measure is how many Google hits

`X degrees of separation' gets


Six degrees gets 1,760,000 hits
Five degrees gets 97,300 hits
Four degrees gets 159,000 hits
Three degrees gets 605,000 hits
Two degrees gets 843,000 hits

The last one may not be quite fair- there was an episode of Pokemon

with the title `Two degrees of Separation' and also a company with that name.





How well two people know each other has to be defined carefully.




Erdos Numbers- Put an edge between a and b if they have a paper together.
Bacon Numbers- Put an edge between a and b if they appear in the same movie.
Handshake Numbers (I am not sure its every been called that)- Put an edge between a and b if they have shaken hands.
knows-number (likely not defined). Put a DIRECTED edge from a to b if a will return b's phone calls and/or email.
Twitter Numbers (Not sure if its ever been defined). But a directed edge between a and b if a follows b on twitter.

Odilfreddi may be an articulation point in the handshake graph or the knows-graph since he is in math AND known to the public (at least in Italy) as an outspoken atheist, so he connects two worlds. Another articulation point might be David Seetapun who has a PhD in computability theory (he worked on Recursive Ramsey Theory which is how I know of him), Finance (Goldman Sacks), Gambling in Las Vegas, and swordfish fishing (he won the Golden Fly Tarpon Tournament). He may be the key to connecting mathematicians to fisherman.



The following is probably known but I couldn't find it- what is the longest distance between two websites (number-of-links to go from one to the other)?

The average? Are these numbers getting larger or smaller?



ADDED LATER: Christian Sommer emailed me the following two

RELEVENT links:



Diameter of the web and



Tools to study the web graph



The first link claims the avg diameter of the web is 19.