Erdős-Bacon Quaternion

You’ve heard of the Erdos number.

You’ve heard of the Bacon number.

Now, you’ve even heard of the Imaginary Erdos number.

I am proposing the Erdos-Bacon Quaternion, a quaternion representation of one’s real & complex separation from co-authorship with Erdos and co-actingship with kevin Bacon:

$a + bi + cj + dk$

For example, if you’ve written a paper with Erdos, written a paper with a dream coauthor of Erdos, and have acted in a film with an actor 2 steps removed from Bacon, you have number 1 + 2i + 3k.

Patents pending.