By definition an Erdős number, honouring the late Hungarian mathematician Paul Erdős [1], is a way of describing the “collaborative distance” between a person and Erdős, as measured by authorship of mathematical papers. [2]

Lately The web Comic XKCD made a comic named Apocalypse [3], as doom day approaches dead people rises from their graves. And some mathematitions write a paper and signs for co-authership with honourable living dead Paul Erdős. Waiting at his grave to make him sign the paper.

Later on Danah Boyd [4] a researcher at Microsoft Research at New England wrote a blog named XKCD meets real [5]. Mentioning about an email she got from her friend named Henry Cohn[6] about a paper  named “Higher algebraic K-theory of schemes and of derived categories” co-authored by R. W. Thomason and Thomas Trobaugh. The thing is at this paper being written, Thomas Trobaugh was deceased and R. W. Thomason says Mr. Trobaugh gave a start on the paper.

As written at the blog:

By the way, there’s no need to wait until the end times to write papers with dead mathematicians. One example of this is the paper “Higher algebraic K-theory of schemes and of derived categories” by R. W. Thomason and Thomas Trobaugh, which Thomason wrote with his deceased friend Trobaugh after Trobaugh appeared to him in a dream:

“The first author must state that his coauthor and close friend, Tom Trobaugh, quite intelligent, singularly original, and inordinately generous, killed himself consequent to endogenous depression. Ninety-four days later, in my dream, Tom’s simulacrum remarked, ‘The direct limit characterization of perfect complexes shows that they extend, just as one extends a coherent sheaf.’ Awaking with a start, I knew this idea had to be wrong, since some perfect complexes have a non-vanishing K_0 obstruction to extension. I had worked on this problem for 3 years, and saw this approach to be hopeless. But Tom’s simulacrum had been so insistent, I knew he wouldn’t let me sleep undisturbed until I had worked out the argument and could point to the gap. This work quickly led to the key results of this paper. To Tom, I could have explained why he must be listed as a coauthor.”

So I’ve came with an idea of “Imaginary Erdős Number or Trobaugh Number”. By my definition an Imaginary Erdős Number is a way of describing the “collaborative imaginary distance” between a person and Erdős’s simulacrum as he appears in one’s dream, as measured by authorship of mathematical papers. [2]

To be assigned an Imaginary Erdős number, an author must co-write a mathematical paper with an author with a finite imaginary Erdős number. Paul Erdős having 0+i0 imaginary Erdős number, and author having written a paper with Paul Erdős’s dream image has 0+1i Imaginary Erdős number. A person co-authoring a paper with dream image of a person having an Imaginary Erdős number 0+ni, has an Imaginary Erdős number 0 + (n+1)i. The co-author with the Imaginary Erdős number can be alive or deceased. People being out of the chain has an Imaginary Erdős number of 0+∞i
[1]http://en.wikipedia.org/wiki/Paul_Erd%C5%91s
[2]http://en.wikipedia.org/wiki/Erdos_number
[3]http://xkcd.com/599/
[4]http://www.danah.org/
[5]http://www.zephoria.org/thoughts/archives/2009/06/21/xkcd_meets_real.html
[6]http://research.microsoft.com/en-us/um/people/cohn/