And we're in the present day again, except it's kind of hard to tell, because everyone in the room – Valentine, Chloë, and Gus – is wearing clothes in the style of the early nineteenth century. Valentine's laptop might give it away, though.
New on the table this time: a pyramid and a cone, as well as a pot of dwarf dahlias.
Chloë is going through the newspapers, reading accounts of Bernard's supposed Byron discovery.
Chloë asks Valentine if she is the first person to have thought of this, and Valentine immediately says no.
Unfazed, Chloë goes on with her idea: there's already a theory that, if you had a computer big enough, you could predict the future from the physical laws of motion.
Valentine interrupts to say that someone came up with that in the 1820s, but it wouldn't work. Valentine says the reason you can't do this is because the math works differently from how people used to think it does.
Chloë thinks it's impossible to predict the future using physics because of sex.
She explains: the universe is deterministic – once you set it going, it'll just keep going according to the rules – but what prevents things from working out they way they're supposed to is people getting horny for other people they wouldn't otherwise run into.
Valentine replies that yes, Chloë is probably the first person to think of that.
Hannah comes in with another newspaper (with a particularly sensational headline: "Bonking Byron Shot Poet").
Chloë leaves with Gus to get him shoes to match his costume.
Hannah is still skeptical about Bernard's Byron theories; Valentine says it could be true, and Hannah replies that, at this point, Bernard's theory can only not be false yet.
Valentine says that's just like science.
Valentine and Hannah sit at opposite ends of the table, working on their research.
Hannah asks Valentine if he's working on the grouse again.
Valentine asks Hannah if she agrees with Bernard that his work is trivial, and Hannah replies that it's all trivial, but the desire to know anyway is what makes this meaninglessness all worthwhile.
Turns out Valentine isn't working on the grouse: he's plugged Thomasina's equations into the computer and followed them out a few million times further than Thomasina was able to do by hand.
Hannah thinks the resulting images are beautiful.
Hannah asks what it all means, and Valentine says if Thomasina had really been on to something, she would have become famous.
Hannah replies that she didn't have time to be famous: she died in a fire the night before her seventeenth birthday.
Hannah says that Septimus, as Thomasina's tutor, could have worked with her to produce something, but Valentine waves her off and they return to their research.
And here something strange happens: 1812 comes running through the present day, in the persons of Thomasina and her younger brother Augustus (who bears a strong resemblance to present-day Gus – they're played by the same actor). They're fighting.
Septimus follows closely behind them, and demands order.
Septimus asks Augustus if he is joining Thomasina in her drawing lesson (she's sketching the pyramid and cone on the table), but he says that at Eton (a swanky private boys' school; schools for girls didn't really exist at this time in England, which is why Thomasina has Septimus while her brother is off at school) he only draws naked women, scandalizing Thomasina.
Septimus returns Thomasina's math homework, and she's surprised to receive zero points for her "rabbit" equation.
Septimus says it doesn't look like a rabbit to him, and Thomasina replies that the rabbitness is in the fact that it eats its own babies: in math terms, the output becomes the input.
Septimus looks through Thomasina's math notebook again, as Hannah looks through the same notebook a few centuries later.
Hannah asks if this new understanding of how the world works means that we're not doomed to disorder after all. Valentine says no, but it might help to explain how the next world will start after ours dissolves into chaos.
Valentine explains to Hannah that her tea is getting cold. While that may seem normal, it's actually really weird: tea goes to room temperature, and so does everything else – the whole universe will eventually end up at room temperature, but no one knew this in 1812.
Hannah thinks it's possible that either Septimus or Thomasina could have been genius enough to figure it out, but Valentine argues that's impossible: "you can't open a door till there's a house."
Hannah replies that she thought genius was just that, and Valentine counters that that's only true for madmen and poets.
Hannah answers with a few lines of poetry about the dying earth, sunless and starless, and tells Septimus that they're by Byron.
Valentine and Hannah return to their research, and 1812 returns to the forefront.
Thomasina asks Septimus if he thinks she will marry Lord Byron, whom she's got a crush on.
Septimus doesn't think Byron even knows Thomasina exists.
Thomasina and Augustus go back to sniping at each other, and Septimus tries to shut them up; finally Augustus leaves, with the mysterious announcement that he has something of value to tell.
After his departure, Thomasina explains: she told him that Septimus kissed her, but she does not think he will tell anyone else.
Septimus has already forgotten the kiss, which was to seal a promise that he would teach Thomasina the newest dance craze: the waltz.
Septimus and Lady Croom have recently returned from waltz-mad London, and Lady Croom has brought back a souvenir, a pianist named Count Zelinsky.
Thomasina asks Septimus what he is reading, and he says it's about a possible contradiction to Newton's laws of physics.
Thomasina borrows the book to read, pausing to note that her mother is in love with the count, who Septimus insists is nothing more than a piano tuner.
Lady Croom enters from one door, shortly followed by Chloë (looking for Gus).
Lady Croom comments on the noise coming from Mr. Noakes's engine.
Chloë and Valentine go off in search of Gus, leaving Hannah the only representative of the present day.
Hannah reads one of Lady Croom's garden books as the woman herself speaks of Mr. Chater's death from a monkey bite, Mrs. Chater's marriage to Captain Brice, and Lady Croom's own receipt of the first dahlias in England.
Hannah stands up during Lady Croom's speech and leaves the room as she finishes. It's all nineteenth-century in here now.
Thomasina finishes Septimus's book and says that it jibes with her own thoughts: Newton's system doesn't entirely work to describe "the action of bodies in heat."
Lady Croom mutters to herself that Mrs. Chater could destroy Newtonian physics by herself.
Septimus speaks in praise of geometry, and Thomasina says that she's working on figuring out another, better geometry, one that can actually describe the forms we see in nature.
Lady Croom asks her daughter how old she is today, and Thomasina replies that she is sixteen years, eleven months, and three weeks.
Lady Croom says she will need to get married soon, and Thomasina replies that she already has her husband picked out: Lord Byron.
Lady Croom says that Byron himself didn't mention it, despite her running into him with an underdressed (Lady Croom thinks undressed) companion at the Royal Academy art gallery.
Mr. Noakes enters, and Lady Croom chews him out for his noisy steam engine, his massive production of mud, and the lack of a real live hermit for her hermitage.
Thomasina has her own complaint: she shows Noakes a diagram proving that his steam engine can never produce as much energy as it uses up, based on the book she just borrowed from Septimus.
Mr. Noakes and Lady Croom leave.
Septimus asks Thomasina about her diagram, and she explains that Newton's equations go both ways, but the heat equation only goes one way.
For homework, Septimus tells her to explain her diagram
While he's been talking, Thomasina has been busy making a drawing of Septimus and Plautus the tortoise, which she gives to Septimus.
Thomasina leaves, and Augustus returns to apologize.
Augustus asks if Septimus has an older brother, and he does: the editor of the Piccadilly.
Augustus reveals that his real reason for wanting to talk to Septimus, which is that no one's given him the birds-and-bees talk yet, and he thinks Thomasina's notions on the subject are crazy talk.
Septimus promises to put him right, and the two leave.
As they do, we hear the present day approaching: it's Bernard, and he is not happy.
Valentine and Hannah come in after him, and Hannah shares her latest discovery in Lady Croom's garden books.
It's bad news for Bernard's Byron theory: Lady Croom's entry about her shiny new dahlia makes it clear that Ezra Chater died of a monkey bite in Martinique, not in a duel with Byron.
Bernard bemoans the swift pulling of the plug on his newfound fame for his Byron theories, and wonders how long it will be until someone else figures it out.
Hannah's on it: she's planning a letter to the Times forcing Bernard to eat crow.
Chloë comes in and starts dressing Bernard up in period clothes for the costume ball photograph.
Bernard finds a nice big hat to hide his face.
Valentine, Chloë, Bernard, and Hannah all leave.
The light changes to evening, and Septimus enters with Thomasina's papers to grade.
Thomasina enters in her nightgown, and gives Septimus a kiss.
He thinks she's hitting on him, but she's just reminding him of his promise to teach her to waltz before her seventeenth birthday, which is tomorrow.
The Count plays the piano in the next room. Septimus tells Thomasina that it is too slow for waltzing, but Thomasina says she will wait until the music is right.
Septimus has the math textbook with her note in the margin echoing Fermat, and says it will indeed drive him crazy.
Hannah and Valentine enter. Valentine's a bit tipsy.
Valentine digs out Thomasina's diagram from the pile of things on the table, and tells Hannah he's finally figured out what it is: heat exchange .
The conversations of Septimus and Thomasina and Valentine and Hannah weave together: both pairs are discussing Thomasina's diagram, which shows how energy is always being dispersed and can never be brought back together, and we will be left, as Septimus says, "on an empty shore."
Thomasina replies, "Then we shall dance," and again asks Septimus to teach her: this time, he agrees, and the two slowly begin to waltz.
Bernard comes in to grab his clothes.
Septimus kisses Thomasina; she looks at him, he kisses her again, and she puts her arms around him.
Chloë runs in, furious; apparently her mother caught her making out with Bernard in the hermitage.
Bernard says he's going back to London and he doesn't want Chloë coming with him. She runs out, followed by Valentine.
Bernard tells Hannah he's looking forward to her book on the hermit of Sidley Park.
Hannah says that she thinks she knows the identity of the hermit, but she can't prove it; Bernard replies, "Publish!"
Thomasina and Septimus finish their waltz.
Gus (who, you'll remember, looks exactly like Augustus, especially now that he's dressed in period costume) appears at the door.
Septimus gives Thomasina her essay back, which he has given an A because it's beyond his understanding.
Septimus lights Thomasina's candle and warns her to be careful with the flame.
Thomasina says she will wait for Septimus in her room, but he tells her he cannot, may not, will not come.
Thomasina insists on one last waltz, for her birthday.
Gus comes into the room, startling Hannah.
He gives her something: a folder containing Thomasina's drawing of Septimus and Plautus.
Gus silently invites Hannah to dance, and after a pause, she agrees.
The two couples, two centuries apart, waltz across the stage.