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From talking to my father-in-law, and probably from reading your haiku posts as well, I have a fuzzy understanding (or misunderstanding) that haiku (traditionally?) try to describe an image, often of nature, in the first two lines, and then in the third try to do something a little different that maybe surprises the reader, or inverts the ideas hinted at in the first two lines, or maybe just deepens the meaning and feel of the haiku by taking a left turn, so to speak.

Now that I’m trying express what I think I know, I’m realizing that I can’t do it. Hmmm …

Anyway, with this half-developed idea in mind, I tried writing haiku yesterday, but found the surprise in line three to be very difficult to write due to the limited amount of words I was letting myself use.

If I hadn’t limited the number of words, though, I have a feeling that I still wouldn’t have been able to capturing what I was trying to, and in the end I would have ended up with an unfinished haiku. Does that ever happen to you?

That's basically right. That change in focus is usually set off by the kiriji, the cutting word. But it doesn't have to take place before the last line, it could be near the beginning. It's not necessarily a surprise or an inversion, it is just usually a change in focus. I gave some examples in my post explaining haiku here.

I also covered in that post a little of what you are talking about. Haiku as it original was was highly influenced by Zen. It inherited the idea that we can often describe reality better by saying less. The more you try to explain, the less you do, the more words you use, the more complicated you make it, and so on. The challenge of haiku then is deleting everything except what is essential.

See the issa snail haiku on that post I wrote. I think that illustrates the difference quite well. Look at how sparse the Japanese really is but yet how it can suggest so much. That is one of Issa's most famous haiku and one of the most famous in Japan and for good reason.

I remember reading that post when you published it. I’ll take a look at again sometime today.