Oh, to be a fly on the wall of the San Francisco room where Apple (Nasdaq: AAPL) CEO Tim Cook and Samsung Electronics head Choi Gee-sung will meet for a mediation session. This meeting idea is not something that the men came up with of their own accord. Cook and Choi were instructed to undergo mediation by a federal judge in the hopes of putting an end to their all-consuming patent battles.

The confidential sessions will start Monday and cover two days. They will be overseen by a U.S. Magistrate Judge. The CEOs will be accompanied by their general counsels.

Whether a face-to-face meeting would be able to end the bitter courtroom battles these companies have been waging in 20 court cases around the world remains doubtful to some dedicated patent-war correspondents.

Longtime patent blogger Florian Mueller told Reuters that we shouldn't expect too much when Cook and Choi leave the room Tuesday evening: "[They] should spend a couple of fun days in Yosemite Park or Napa Valley, rather than meet in court only to pretend they're being constructive."

"Slavishly" copying the iPhone and iPad is how Apple has described Samsung's design efforts for the South Korean company's Android devices. Samsung has replied with suits of its own, claiming Apple has infringed on its patents.

One Samsung claim --- which some might describe as a bit bizarre -- is that Apple, in fact, copied the iPad design from the handheld computing device used by the astronauts in Stanley Kubrick's classic 1968 film, 2001: A Space Odyssey.

Anyway, what I would really like is to witness the conversation Cook and Choi might have regarding a particular claim Samsung brought against Apple in a German court last December. I imagine it may go something like this:

Cook: Look, Mr. Gee-sung, maybe we can agree on that whole Space Odyssey thing, but suing us over smiley faces! Well, that's just something we'll never agree upon.

Choi: Oh, come on, Tim. I can't believe you took that seriously!

OK, probably not. With Samsung's 30.6% share of the global smartphone market and Apple's 24.1% share, these guys won't be joking around.