# 230: Hamiltonian

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

## Explanation

Cueball, presumably in class, decides that the subject of Hamiltonian circuits in graphs is not important in the larger context of life and love. Later, however, he realizes there is a flaw in the proof presented, while in bed with Megan, and suddenly wants to focus on the mathematics, in a humorous reversal of his position about what is meaningful.

In graph theory, a Hamiltonian is a traceable path that connects all the vertices (nodes) by passing through each one exactly once (Think connect the dots with rules!). If this is not possible, then it can be said that no Hamiltonian exists for the given set of vertices. A Hamiltonian cycle is a Hamiltonian where the path begins and ends at the same node. The professor is using the graph theory to optimize some algorithm by solving a Hamiltonian path problem. He meant to say "Hamiltonian Cycle", but instead said only "Hamiltonian Path".

The title text explains that the Hamiltonian Cycle can be solved in two different directions around the cycle.

## 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?

# 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 ~~~~)

Fixed. Tenrek (talk) 08:56, 1 January 2014 (UTC)

When in math class, he walks out, likely offending his peers, because his mind is occupied with thoughts of love. When making love, he offends his partner because his mind is occupied with math. Some perspective! Mountain Hikes (talk) 01:28, 25 September 2015 (UTC)

I always thought that the talk about the algorithm providing an "optimal result in all cases" was the reason Cueball left - he decided to apply the algo to his life somehow in a way that he would always find a positive outcome, such as love. That also made the end panel funnier for me because as he found a flaw in the algorithm, he self-fulfilled it by interrupting his romance, thus ruining the "optimal path in all cases". Could be wrong here... 108.162.237.254 03:54, 2 April 2016 (UTC)

There's an anecdote about the mathematician Carl Friedrich Gauß, who is said to have jumped out of the bed in the middle of his wedding night, to write down some proof he just found... 162.158.203.144 19:39, 29 April 2016 (UTC)