Why didn't the DNA scanner find Fry to be the Professor's great^n grandfather?

Question

In Futurama, Fry did the nasty in the pasty, so he's his own grandfather. This means he's also the grandfather to his brother, Yancy Jr. In the pilot episode, Space Pilot 3000, the DNA scanner that Leela uses to check for living relatives to Fry indicates the Professor is a great^n nephew. Shouldn't the device have found the Professor to be a great^n grandchild?

Answer 1

From a computer science perspective, this is an easy answer: it is using an optimized search algorithm that searches 'down' the tree, not 'up' it.

It detected that Fry had no children below his generation, so it looked at his direct parent's generation, and found his brother as a sibling.

It ran a search down his brother's family tree, found the Professor, and returned him as a living relative, and listed his relationship to Fry (based on Fry's position at the start of the search). Had Fry not had a brother, it would have checked from his parent's siblings, then his grandparents. At that point it would have likely found (but not cared) that Fry was his own grandfather. It would not have cared since it was told to find a living relative and that sort of anomaly isn't one it was designed to detect or care about.

Answer 2

The answer may depend somewhat on how the DNA scanner does what it does. I see two possibilities:

1. The DNA scanner only compares DNA samples (i.e. Fry's compared to all samples on record) and, using some complex algorithm, determines the familial relationship between any two samples based on similarities in the DNA patterns.

2. The DNA sample is used initially to find possible relatives in a DNA database, then a historical record database is searched to determine the exact familial relationship with each potential relative.

However, regardless of which possible mode of operation for the DNA scanner is the correct one, the device would still likely report the nephew relationship over the grandchild relationship for the following reasons:

1. If only using DNA, the algorithm for determining DNA similarity and familial relationship would probably report the closest possible relationship (i.e. the fewest number of "greats") since this will likely represent either a global minimum in a potential search space or at least the first local minima the algorithm would hit upon. Based on the graph below, a greatⁿ grandnephew of Fry's would also be a greatⁿ⁺² grandchild, which is two more greats further away in relation:

   Fry (grandfather to himself)
      v
   Yancy Sr. (father and son to Fry)
      v
   Yancy Jr. (brother and grandson to Fry)
      v
   Philip (nephew and great grandson to Fry)
      v
   Unknown (grandnephew/niece and great great grandchild to Fry)
      v
   Unknown (great grandnephew/niece and great great great grandchild to Fry)
      v
     ...
      v
   Hubert Farnsworth (great^n grandnephew and great^(n+2) grandson to Fry)
   

2. If using a family history database, then there's no chance the grandchild relationship would show up since Enos was always assumed to have been Fry's true grandfather. Public records about his family history would have therefore turned up Enos, with only his grandmother, the Planet Express crew, and the Nibblonians knowing the real truth about his lineage.

Answer 3

There is an entirely different explanation, which depends on the time-travelling rules of Futurama.

It's possible, that Fry actually was Enos' grandson at the point where we see the scene with the DNA scanner. Later events in his personal timeline led to an event where he went back in time and messed with Enos' life. That would imply, he's technically not his own grandfather but the grandfather of an individual in the newly forked reality.

This would mean that the Fry we meet in the first episode has a non-anomalous family tree. The Fry we later meet, defeating the Brains, is a descendant of that first Fry (or maybe even an iterator further down, provided the altered Fry goes back to Roswell and kills the previous Fry). Maybe Fry being another Fry's grandfather oscillates through their personal histories, implying that every iteration produces universes where the Earth is destroyed by the flying Brains and not destroyed, always alternating.

This would imply that the Professor's evaluation that Fry is his own grandfather at the end of "Roswell that Ends Well" is a bit misleading.

This is the only reasonable explanation I see for Fry not vanishing (Marty-McFly-style) after (accidentally) killing Enos.

_{P.S.: Maybe I watched tringle one time too often.}