The first of the undecoded messages read: "Popeye sits in thunder, Unthought of. From that shoebox of an apartment, From livid curtain's hue, a tangram emerges: a country." (1-3)
The speaker tells us that the undecoded message in quotation marks is "the first" of several. But we never are told what any of the other messages are. Where's the second, or the third? The poem all but announces that it's a puzzle that can't be solved. A tangram is a Chinese puzzle with seven pieces, and a sestina is a poem with seven stanzas – see what we're getting at? You might want to consider whether Popeye is sending the messages.
And was going to ask Wimpy if he had bought any spinach. "M'love," he intercepted, "the plains are decked out in thunder Today, and it shall be as you wish." (7-9)
How does Wimpy know the Sea Hag's thoughts before she even opens her shriveled mouth to speak? Maybe he has telepathy or is just really good at ready body language. Also, did you expect him to sound like a character from a British period drama? Ashbery is known for mixing different kinds of social speech.
But Swee'pea looked morose. A note was pinned to his bib. "Thunder And tears are unavailing," it read. "Henceforth shall Popeye's apartment Be but remembered space, toxic or salubrious, whole or scratched." (16-18)
This poem opens up all kinds of questions at the most basic level that can't be answered. For example, who wrote this note? Was it poor baby Swee'pea? We have a sneaking suspicion that Popeye might be responsible. We learn that Popeye has been exiled and is responsible for the thunder, so it would make sense for him to say that "thunder and tears" are of no use and the apartment exists only in his memory. Also, is this note another "undecoded message"?
"I have news!" she gasped. "Popeye, forced as you know to flee the country One musty gusty evening, by the schemes of his wizened, duplicate father, jealous of the apartment And all that it contains, myself and spinach In particular, heaves bolts of loving thunder At his own astonished becoming (20-24)
Olive's language combines several different kinds of speech, from the childish enjoyment of words ("musty gusty") to difficult philosophical reflections ("his own astonished becoming"). From quotes like this, you can see why Ashbery is often considered a postmodern or experimental writer.
She grabbed Swee'pea. "I'm taking the brat to the country." (28)
Right after delivering her "news," which is full of complicated phrases and lots of adjectives, Olive makes this matter-of-fact statement. How can this quote be the same person speaking?
Popeye chuckled and scratched His balls: it sure was pleasant to spend a day in the country. (38-39)
Popeye is the only character who does not speak in the poem – unless you think that the undecoded messages were written by his hand. But the final line paraphrases his thoughts of contentment. He's not ecstatic about the country, but he finds it "pleasant." Also, the crudeness of Popeye scratching his balls is almost like a response to the slightly pretentious, upper middle-class tone of the rest of the poem.