Tuesday, November 05, 2013

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.

  1. Erdos Numbers- Put an edge between a and b if they have a paper together.
  2. Bacon Numbers- Put an edge between a and b if they appear in the same movie.
  3. Handshake Numbers (I am not sure its every been called that)- Put an edge between a and b if they have shaken hands.
  4. knows-number (likely not defined). Put a DIRECTED edge from a to b if a will return b's phone calls and/or email.
  5. 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

Diameter of the web and

Tools to study the web graph

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


  1. 'Benedict, Pope emeritus' is the preferred designation. I don't think you can casually call him Pope the way an emeritus professor is still Prof.

  2. I don't think Odifreddi is "in politics" in any way. He's just a mathematician who's written popularization and opinion articles about sundry topics. He's become well known to the public mostly because he's an outspoken atheist who often criticizes the Catholic church (as well as other religions). Hence the chance of getting a reply from the pope.

  3. Anon 1- YES, that is a better way to refer to him, and I have made the change.

    Anon 2- YES, `in politics' is not correct' and I have changed it.

    I responded to your comments- does that make your Pope Number 3? :-)

  4. How does one define "connection" for this? Co-authors is fairly well-defined. Co-stars (Bacon Game) is less well-defined since a "co-star" might not even share a scene with the other "co-star" and still count. Calling "connected" vague would be an understatement. If I rode on a bus with someone, are we "connected" in terms of the degrees of separation? I was at the inauguration with a million or so people, are we connected?

    1. Agreed that the term is ill-defined.
      For my Pope Number I am using `will return an email from' as the metric.
      Odilfreddi would return and email from me, and the Pope Emeritus would return an email from him.

  5. Link to wiki should be http://en.wikipedia.org/wiki/Six_degrees_of_separation

  6. Thanks, Fixed.
    (I had the pointer to the page talking about the page, rather than the page itself.)

  7. My Pope number is 2. Is there a measure that qualifies 2 depending on the number of different approaches one can define. I can count the Pope number 2 through six different paths. My 2 may be a stronger 2 than yours in that event.