In voiceover, Jake says that the shortest path between two points is a straight line. But what if that path gets blocked? We see a cabbie driving in New York. An Italian woman named Ipolita accidentally breaking her compact mirror. A Frenchman slipping a goodbye note under a door. Jake plays cat's cradle with red yarn and continues: When two points are destined to touch, but a direct connection is impossible, the universe will always find another way.
On the bus, Martin sees a vacuum tube fall out of the ham radio another passenger's carrying. He retrieves it for the grateful man.
As Martin prepares Jake for the facility's museum outing, Clea mentions the custody fight with his sister-in-law, Abigail. Jake's got to show progress. When Jake makes a pattern of triangles with his cat's cradle, Clea notices it resembles the logo of Abigail's company, Aster Corps.
At the museum, Sheri deflects Clea's questions about the last patient in Room 6, and later about Aster Corps' connection to the facility. Jake runs into a woman, knocking her phone from her bag. He secretly slips it into Martin's pocket. When the woman calls the phone, Martin says he'll meet her at the exhibition that has a live video link to the courtyard pyramid at the Louvre in Paris (another triangle). Jake fixates on Veronique, a young Frenchwoman. When Veronique spots the phone's owner arriving, she's stunned. Clea speaks French, and the women borrow phones from two bystanders. Veronique tells Clea to ask the cell owner if her name is Simrin.
Simrin gets emotional and runs out. Veronique thinks she's her birth mother, who supposedly died 21 years ago. Martin goes after Simrin as Veronique tearfully tells Clea her husband left today. He wants a family, but she's afraid, because her mother died of complications during childbirth. Finding her alive would change everything.
The cabbie from before listens to the dispatcher, Sal - the man Martin helped on the bus - tell his drivers that a stranger just did him a solid. Sal suggests they all try making a little human contact. But, as usual, he gets no response.
Ipolita video-chats with her husband, Gio, who is an International Space Station astronaut. He and his colleague, Allegra, will be testing Ipolita's new comm gear during his spacewalk today. Ipolita's nervous about the broken mirror. Gio thinks it's cute that his wife, the radio communications expert, is superstitious.
Martin rushes over as Jake steps briefly off the curb, spooking that same cabbie. An older man gets into the taxi. At the Hotel Trio, Jake leads Martin to a maid who looks just like Veronique. Nundu says she's an only child, who came here from India as an infant. Turns out she and Veronique were born in the same town on May 1, 1991. Soon, Nundu's staring at Veronique on the museum screen: She has a sister.
During Gio's spacewalk, Allegra loses contact with him, probably because the ISS structure is blocking his signal.
The cabbie's fare, Dr. Knox, separately meets with a woman who hands him an envelope and a nervous man who gives him some documents. Sal chats up his drivers again. No response - again.
At the facility, Clea says Martin can't leave again while Sheri's watching. Everyone views a webcast by Allegra, who explains that Gio's temporary comm blackout is normal. In fact, once every orbit the ISS loses all contact with Earth while passing through the "zone of exclusion."
Allegra's talk about triangulation brings up the number 5,191 - May 1, 1991, the twins' birthday. The number represents two sides of an isosceles triangle, and Jake calculates the third: 1,604. That's what he wants Martin to know. Sheri's watching, but Martin leaves anyway.
Allegra cuts the chat short when instruments show elevated carbon dioxide in Gio's blood. They have to purge his suit immediately, but they haven't regained comm.
Nundu tells Martin that 1604 is the medallion number of her father, a cabbie. Meanwhile, her dad confronts Knox, the black market baby-dealer who took his child. Knox bails. Later, Nundu's dad tells Martin that he and Simrin were just 18 when Nundu was born, and they panicked when her twin arrived unexpectedly an hour later. Knox paid them for the baby, and they moved far away, devastated by their secret. Now he's doing it again! Martin asks for details.
Allegra remembers that Ipolita's comm gear includes ham radio. It's low-tech but worth trying. They're two minutes from the zone of exclusion, and then won't have comms for 10 minutes. Suddenly, she loses Houston too.
Sheri and Clea have a meeting, during which Clea confronts her about Room 6.
Sal hears Allegra's mayday over his ham radio. The signal's fuzzy, until he replaces the vacuum tube. Wow, he's talking to space! He contacts Gio, and after a tense moment, Gio replies. He heads to the airlock. Woohoo!
Martin confronts Knox, informing him that the nervous man will testify to altering adoption documents for payment. Knox is arrested.
Sal tells his drivers that today he used the so-called junk in his dispatch box to save an Italian astronaut's life. Replies flood in: "Seriously?" "Now this I gotta hear!" Sal happily starts talking.
Veronique reunites with Nundu and her parents. Her husband's with her.
Jake holds out the cat's cradle. Martin takes the next turn. Jake looks at the threads in Martin's hands. Clea arrives, announcing she's off Jake's case. Not because of Jake. She just asked too many questions. Aster Corps, the girl in Room 6 - Jake's led them to both. They're connected, but how?