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First, the scene: two people sit at a messy table in a country house. The place: rural England. The time: April 1809. The people: Thomasina, a thirteen-year-old schoolgirl, and Septimus, her twenty-two-year-old tutor.
Oh, and the topic: sex. Sort of. Thomasina wants to know what "carnal embrace" is, but Septimus hides behind the Latin root of "carnal" (think "carnivore") and tells her that it means to hug a piece of meat.
But this class period isn't really sex ed: Thomasina is supposed to be working on Fermat's Last Theorem, a famously unsolved math problem, while Septimus reads a ridiculous love poem written by Mr. Chater, a guest at Sidley Park, the house that belongs to Thomasina's parents.
The topic of carnal embrace is, however, more interesting than either of these occupations, so Thomasina goes on to explain the reason for her curiosity: she overheard Jellaby, the butler, telling the cook that the groom told Jellaby that Mr. Noakes, the gardener saw Mrs. Chater in the gazebo in carnal embrace, and told Mr. Chater so. (And you think your gossip network is complicated.)
Thomasina is suspicious of Septimus's definition, and nags him to explain exactly what this "carnal embrace" is.
Septimus explains sex to Thomasina in more detail than she was expecting.
Thomasina's response: ew, gross, and please tell me more.
But they are interrupted by Jellaby the butler, who arrives with a note for Septimus from Mr. Chater, inviting the tutor to join him in the gun room.
Septimus tells Jellaby that he will join Mr. Chater after he finishes Thomasina's lesson, and the butler leaves.
While this has been going on, Thomasina has realized something strange: when you stir jam into rice pudding, it gets more and more mixed, but you can't stir in the opposite direction and make it unmix.
Septimus says that time always goes forward, and that this is called free will or self-determination.
Thomasina has a new idea and asks Septimus if she's the first person to have thought of it, but Septimus is pretty sure she hasn't, before he even hears what it is.
This is because Septimus assumes that Thomasina's idea is that, if all matter follows Newton's laws of motion, then there's no such thing as free will, which is a cliché even in 1809.
Turns out he misjudged his pupil, however: her idea is that if you could know just for an instant what all the atoms in the universe were doing, then you could write a mathematical formula that would predict the future.
Septimus is now a bit more impressed, and replies that yes, Thomasina is probably the first person to think of that.
Septimus tells Thomasina that, in the margin of the book where his Last Theorem was published, Fermat wrote that he knew the proof, but he didn't have enough space to show his work.
Thomasina replies with an "aha!" and says that the answer is obvious, but before she can explain, Chater enters.
Septimus sends Thomasina out of the room, telling her to write out her mathematical proof, but on her way out she replies that her "aha" was about Fermat, not his Theorem: his note was a joke intended to drive later mathematicians crazy.
Chater accuses Septimus of insulting his wife in the gazebo, and Septimus counters that he made love to Mrs. Chater in the gazebo after she asked him to meet her there. (Hint: they're both actually talking about the same thing.)
Chater is ready to fight a duel with Septimus over his wife's honor, but Septimus replies that that's pointless, since Mrs. Chater has had affairs with plenty of men.
Septimus distracts Chater by praising his poetry, and Chater appears all too willing to be distracted.
Septimus mentions that he's at work on a review of Chater's latest poetic accomplishment, but he needs time and a relaxed mind truly to do it justice.
Chater fills in the gaps (falsely), and decides that his wife had sex with Septimus in order to ensure Septimus writes a really good review of the poem.
Noakes the gardener comes in just as Chater is writing a dedication to Septimus on the front page of Septimus's copy of his poem. The mistress of the house, Lady Croom, her brother, Captain Brice, and Thomasina soon follow Noakes into the room.
As she enters, Lady Croom is saying "Oh, no! Not the gazebo!," leading to confusion: Septimus thinks she's talking about carnal embrace again, but really she's upset that Noakes's landscaping plans involve knocking down her gazebo and replacing it with a hermitage. (See "The Garden" in "Symbolism, Imagery, Allegory" for more.)
Thomasina manages to clear everything up, and the conversation turns to something far more exciting than carnal embrace: landscaping.
Both Lady Croom and Mr. Noakes have strong opinions on gardening style: Lady Croom goes for classical elegance, while Mr. Noakes likes his landscape a little more goth.
Lady Croom bases her criticism on a book Noakes has made with "before" and "after" pictures of his plans for the garden. Before? Open fields and orderly gardens. After? If Slytherin had a backyard at Hogwarts, this would be it.
Gunshots sound outside, but it's not the rival gangs of Sidley Park having a face-off: it's just the men of the house killing off some birds for fun.
Lady Croom & Co. go out to join the menfolk in their joyous slaughter, leaving Septimus and Thomasina behind.
Thomasina draws in a hermit on Noakes's picture of his proposed hermitage.
Thomasina asks Septimus if he's in love with her mother, and he calls her clever but sidesteps actually answering the question.
Thomasina passes Septimus a note that Mrs. Chater had given her to deliver to him, then leaves.
Septimus reads the note to himself, then sticks it in the book he's been reading: Chater's The Couch of Eros.