Three Times — General Comments
Layering. This film was originally to have three directors, each making one of the three segments. However, due to budget cuts Hou took over the entire project. This is also probably the reason the same actors and actresses play roles in each segment. In other words, while this is layering, I don't think there is an artistic or philosophical reason for it, or that is has any real effect on how we interpret the film beyond this one thing: context is everything, it determines the quality and outcome of love affairs as much or more than the personalities themselves.
Identity. The director was part of the Taiwan New Wave movement; indeed, he was central to it. Part of that movement embraced "self-criticism" about the status of Taiwan itself (especially the gap between countryside and urban cultures) and his early films were about Taiwan history and Taiwan identity. (Hou was born in mainland China in 1947 but came to Taiwan in 1948.) This film certainly presents Taiwan as on a wrong path, a Taiwan that needs to become self-aware of its erroneous ways. In Story 3 (2005), modern Taiwan has sold itself to Japan (notice the yen sign branded on the throat of Jing in Story Three, and the consumer-oriented images of watches and such on the wall in the bar). Gender identities or at least sexual orientations are somewhat blurred in this story as well. To me Hou seems to be suggesting, probably accidentally, that gender confusion is mainly just a symptom of the confusion of modern life. In Story 2 (1911) the occupation of Taiwan by Japan is ultimately the "third apex" of the love triangle: Ah-Mei 1 / Mr. Chang / Mr. Chang's political life, and succeeds in breaking the bond between them. Overall, it seems that Hou is suggesting that a Taiwan without Japan is a better Taiwan, more or less. A Taiwan who doesn't know what she wants to be does not provide a context where love can bloom (as in Story 1).
Love in the three stories. My reading: Story 1 — Love is not a grand event. Love is a charmingly simple thing that happens between simple people in simple contexts. Story 2 — Love can only be secondary to larger issues of employment duties, contractual promises, and politics. Story 3 — Modern love is hobbled love because of unclear identity which allows for the selfish pursuit of pleasure, misunderstood to be love.
The status of women. I really like Hou as a director. I like his sensitivity, his earnest approach, his respect for human feelings, his gentle ways of going deep into a topic. But, I do think this is what he thinks of women: a) a woman's pain is a beautiful thing to behold, and b) they deserve whatever solution the man determines is enough for them. In Story 1, "Smoke Gets in My Eyes" does a good job of establishing that Chen's love is true. But "Rain and Tears" on the other hand suggests that May must endure the unpredictability of men. That song tells of the necessity of hiding your pain—"in the sun you've got to play the game". Mr. Chen's offer is not much; he is a nice guy but won't ever be all that successful in life. May seems to be completely happy with this, as long as he likes her. That's means her happiness is solely derivative of her man's status and actions. In Story 2, Mr. Chang stands by his "principle" that concubines are inappropriate, thus leaving Ah-Mei 1 to live a very lonely life. The double-standard he holds actually further supports this: by buying out Ah Mei 2 so she can be a concubine he enables the system of second-class status for women. Better than brothel work but not as good as being a wife. This isn't presented as a depressingly partial solution for Ah Mei 2 as far as I can tell. In Story 2, the personal pain of women who have lost their love, or need love or are feeling lonely is the entertainment for the men who dine. The new 10-year-old girl is being properly trained in this art as the segment ends. So, this isn't very far from the world of "Rain and Tears" in Story 1. The woman must perform her pain, without actually crying about it. In Story 3, the best thing Jing has going for her at the moment is hanging on tight as her man zips through the city. Where this love will end up is not clear but seems like it will be as bumpy and risky as the motorcycle ride. By the way, this relationship (you are the man, I will hold on tight and go wherever you wish to go) seems pretty much like the 3-Iron relationship we will see later, except it is modified, turning the man into a kept ghost. Not sure what sort of romantic status that turns out to be ...