Six Degrees and the Erdös Number
Recently there has been a lot of talk about small networks and how people are connected to one another. One of the more popular manifestations of this in the world of movies is the Kevin Bacon number. An actor's Kevin Bacon number is 1 if he or she was in a movie with Kevin Bacon. The number is 2 if the actor was in a film with someone who has a KB number of 1, and 3 if in a film with a KB number 2 and so on. There are a number of web sites devoted to the Kevin Bacon Game, click here to see one of them. For a popular discussion of Small World Networks you can take a look at Duncan J. Watt's book, "Six Degrees."
The equivalent of the KB game for scientists, or at least mathematicians, is the Erdös number. Paul Erdös, who recently died, was a prolific mathematician with many collaborators, and any association with him is a statement of ones connectedness with the top echelons of the community. The interesting discovery about small world networks, as discussed in Watt's book, is that groups contain both specialists and generalists. While the specialists may be considered the most important members of the group, it is the generalists that connect the group to the wider world. Without such people the group's activities remain isolated. With them some surprising connections can follow. Therefore even non-mathematicians may have a relatively low Erdös number. So I wasn't too surprised when a friend of mine, Joe Marasco, sent me an email reference to his web site where he discusses how he found his Erdös number to be 5. Joe, the recent author of a book on software development (referenced on this site) was also an experimental high energy physicist. His work is far removed from the type of "pure" math that Erdös was involved in, so he seemed quite pleased to find he had such a low Erdös number. Being a native New Yorker, (Joe is also one) I couldn't help taking up the challenge. So after using the Google Scholar web site and the Erdös number project data page I found the following set of references:
The acoustic cavity containing small scatterers as a singular perturbation problem
LESSER, M B; LEWIS, J A
Journal of Sound and Vibration. Vol. 33, pp. 13-27. 8 Mar. 1974
Charge Singularity at the Corner of a Flat Plate, J. A. Morrison and J. A. Lewis, SIAM J. Appl. Math., 31:2 (September 1976), pp. 233-250.
Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions, P. Diaconis, R. L. Graham and J. A. Morrison, Random Structures and Algorithms, 1:1 (1990), pp. 51-72.
On a Linear Diophantine Problem of Frobenius, R.L. Graham (with P. Erdös), Acta Arithmetica, 21, (1972), pp. 399–408.
To my delight my Erdös number of 4 is lower than Joe's 5. The key to this was that R.L.Graham, with Erdös number 1, also worked at Bell Labs (I worked there from 1966 to 1971). This of course was the connection from the world of pure to the world of applied math.
If you want to compute your own Erdös number you should take a look at the Erdös number project web site (linked to above). I would be interested to hear from any friends as to what their Erdös number might be. At least one person in my academic department has an Erdös number of 3 so all of his collaborators are also at least E4s.
Cheers,
Marty
The equivalent of the KB game for scientists, or at least mathematicians, is the Erdös number. Paul Erdös, who recently died, was a prolific mathematician with many collaborators, and any association with him is a statement of ones connectedness with the top echelons of the community. The interesting discovery about small world networks, as discussed in Watt's book, is that groups contain both specialists and generalists. While the specialists may be considered the most important members of the group, it is the generalists that connect the group to the wider world. Without such people the group's activities remain isolated. With them some surprising connections can follow. Therefore even non-mathematicians may have a relatively low Erdös number. So I wasn't too surprised when a friend of mine, Joe Marasco, sent me an email reference to his web site where he discusses how he found his Erdös number to be 5. Joe, the recent author of a book on software development (referenced on this site) was also an experimental high energy physicist. His work is far removed from the type of "pure" math that Erdös was involved in, so he seemed quite pleased to find he had such a low Erdös number. Being a native New Yorker, (Joe is also one) I couldn't help taking up the challenge. So after using the Google Scholar web site and the Erdös number project data page I found the following set of references:
The acoustic cavity containing small scatterers as a singular perturbation problem
LESSER, M B; LEWIS, J A
Journal of Sound and Vibration. Vol. 33, pp. 13-27. 8 Mar. 1974
Charge Singularity at the Corner of a Flat Plate, J. A. Morrison and J. A. Lewis, SIAM J. Appl. Math., 31:2 (September 1976), pp. 233-250.
Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions, P. Diaconis, R. L. Graham and J. A. Morrison, Random Structures and Algorithms, 1:1 (1990), pp. 51-72.
On a Linear Diophantine Problem of Frobenius, R.L. Graham (with P. Erdös), Acta Arithmetica, 21, (1972), pp. 399–408.
To my delight my Erdös number of 4 is lower than Joe's 5. The key to this was that R.L.Graham, with Erdös number 1, also worked at Bell Labs (I worked there from 1966 to 1971). This of course was the connection from the world of pure to the world of applied math.
If you want to compute your own Erdös number you should take a look at the Erdös number project web site (linked to above). I would be interested to hear from any friends as to what their Erdös number might be. At least one person in my academic department has an Erdös number of 3 so all of his collaborators are also at least E4s.
Cheers,
Marty
posted by Marty Lesser at 10:01
5 Comments:
Hi!
As of today, I can officially claim an Erdös number of 3, via the just-published paper
Hereditarily Optimal Realizations of Consistent Metrics
Andreas Dress, Katharina T. Huber, Alice Lesser, Vincent Moulton
Annals of Combinatorics 10 1 (2006)
Andreas Dress has Erdös number 2 via Laslo Lovasz.
/alice
Hi! Love you blog articles.
A passionate fan for years so I started my own blog :-)
science-fiction@theblogverse.com
I've taken a hiatus from my writing endeavors. You have an interesting blog and more importantly, seem to have been a part of many rich, indeliable experiences. Currently, I work as a freelance journalist and have taken an interest on writing my first novel. I'm not sure how this will be successful but rest assured I expect perfection.
I couldn't connect to the link you recommended on your most recent entry for a "How To" on writing a book. Any constructive criticisms and suggestions from proven achievers will definitely be beneficial. I want to fulfill my unyielding lifelong passion and love for writing. I'm sure you're someone who feels the same.
Hello, great site, I found a lot of useful information here, thanks a lot for Your work!
With the best regards!
David
Hello, thanks a lot, You'v done a great job.I can only realize how much time and resources does it take to create such a resource!Great work, I am impressed!
Post a Comment
<< Home