tag:blogger.com,1999:blog-4367190233877799632.post8198366151138977500..comments2024-02-27T09:51:03.152-08:00Comments on On Memetics: Graph evolutionTim Tylerhttp://www.blogger.com/profile/06623536372084468307noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4367190233877799632.post-15310043988143501482016-03-15T20:07:34.971-07:002016-03-15T20:07:34.971-07:00Hi. If you want an undirected graph, put nodes whe...Hi. If you want an undirected graph, put nodes where three branches meet - and where the branches go off the sides of the diagrams.<br /><br />Regarding gradualism, I was thinking that having a link appear between two separate nodes is a dubious operation in many physical systems - and that link formation can be modeled in a more gradual fashion using node splitting and joining operations.<br />Tim Tylerhttps://www.blogger.com/profile/06623536372084468307noreply@blogger.comtag:blogger.com,1999:blog-4367190233877799632.post-25291214111255345732016-03-14T04:16:45.797-07:002016-03-14T04:16:45.797-07:00I'm a member of the Community of Interest on t...I'm a member of the Community of Interest on this one (I spend most of my time coding graph-theory software for representing memetic evolution). Obviously you are enumerating a taxonomy of atomic operations - the basic splitting and joining that evolution does. I wouldn't want to get too mathematical (being a computer scientist), but how might these look in G=(V, E) format. <br />I gather the second diagram of splitting might be something like {a1} -> {a1, a2}; which is just a set of nodes.<br /><br />Where as the fourth, at first glance, might be ({a1}, {}) -> ({a1, a2}, {(a1, a2)}) [but that would produce a "lambda" shape (often seen in cladograms) and not a "Y".] where the links are denoted by the set of edges.<br /><br />But this doesnt offer a gradualistic scheme (keeping cladists happy) If we took asexual evolution<br />({i}, {})->({i, j, k}, {(i, j) (i, k)})->({j, k, l, m}, {(j, l), (k, m)})->({k, m}, {}) which produces generational syblings of {j, k} and cousins {k, m} then are you suggesting some kind of distance measure within those sets? eg. distance(k, m)<br />salimanderhttps://www.blogger.com/profile/10512109696789865793noreply@blogger.com