# 230: Hamiltonian

Hamiltonian |

Title text: The problem with perspective is that it's bidirectional. |

## [edit] Explanation

Cueball, presumably in class, decides that the subject of optimizing routing algorithms is not important in the larger context of life and love. However, he later realizes while in bed with Megan that there is a flaw in the proof presented, and suddenly wants to focus on the mathematics again, in a humorous reversal of his position about what is meaningful.

In graph theory, a Hamiltonian path is a path that connects all the vertices (nodes) and passes through each one exactly once. (Think connect the dots with rules!) A Hamiltonian cycle is a Hamiltonian path such that the final vertex is adjacent to the initial one (intuitively, it "begins and ends with the same vertex," but recall that paths are required to only pass through each vertex once). The presenter is using graph theory to optimize a routing algorithm by solving a Hamiltonian path problem. Cueball's realization is that the proof he had followed in part actually requires a Hamiltonian cycle, not just a path, so the presenter's proof of the existence of a Hamiltonian path is insufficient to solve the problem.

The title text plays on a dual interpretation of bidirectional: just as any graph cycle can be traversed in two directions, a change in perspective can be traversed in two directions (from mathematics to love, and then from love to mathematics).

## [edit] Transcript

- Lecturer: And therefore, based on the existence of a Hamiltonian path, we can prove that the routing algorithm gives the optimal result in all cases.
- Cueball: Oh my God.

- [Close-up of Cueball.]
- Offscreen: What? What is it?
- Cueball: A sudden rush of perspective. What am I doing here? Life is so much bigger than this!

- [Cueball running out of room.]
- Cueball: I have to go.

- [Cueball enters darkened room, where Megan waits by window.]
- [Cueball and Megan embrace...]

- [...and get into bed.]

- [A heart appears over the supine bodies.]
- Megan: Ohh...
*grip*

- Cueball (out of frame): Wait a moment.
- Megan (out of frame): What is it?

- [Silence.]

- Cueball (out of frame): His proof only holds if there's a Hamiltonian
__cycle__as well as a path! - Megan (out of frame): ...excuse me?
- Cueball (out of frame): Paper, I need some paper. Hey, do you mind if I jot down some notes on your chest?

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# Discussion

I don't agree with the title's explanation. IMO the title refers to the fact the "sudden rush of perspective" happens to Cueball also when he is making love, but starts to think about the algorithms. 37.128.6.132 (talk) *(please sign your comments with ~~~~)*