Sy: The world. The world is wrong. It looks like my world... but everything's different.
The Law of Vacant Places
The Principle of Restricted Choice
The Law of Non-Contradiction
The sad journey of Tad Mobley through Hollywood; a naive young science-fiction writer, he gets taken by Howard Zimmerman, who cheats him out of all of his money with the promise of a big-screen adaptation that ends up bogged down in Development Hell until his money runs out, at which point he loses his temper and nearly kills Howard, forcing him to change his name and relocate to the midwest. Parallel to this is the story of Minsky, a robot who becomes lost on a strange planet, wandering helplessly and trying to carry out his sole objective of helping people, only to get brutalized by the locals. Eventually, he is scooped up by aliens, who praise him for his perseverance and then reward him by ordering him to shut himself down. For added tears, he is informed that he was on that planet for tens of millions of years.
The Narrow Escape Problem
The House of Special Purpose
The Lord of No Mercy
In "The Lord of No Mercy," the Stussy feud comes to a sad end as Ray is accidentally killed in a fight with Emmit. He's stabbed in the neck with a shard of glass when Emmit accidentally shoves the framed stamp at him. What makes it worse is that Emmit came to Ray to bury the hatchet and repatriate the stamp, but Ray refuses his brother's overture of peace, leading to the accident itself. As he falls to the floor bleeding, he asks for his brother's help one more time before he Dies Wide Open.
The Law of Inevitability
Sy weeping in his wife's arms about how his world has changed. See the page quote above.
Who Rules the Land of Denial?
Mr. Wrench has been adrift since the death of his partner Mr. Numbers and their employers in Fargo, to the extent of getting caught and heading to prison. Meeting Nikki - another analytical figure, like Numbers - gives him new purpose and direction, and their shared escape solidifies a bond as partners.
This is all but confirmed by Paul, who claims that 'they' wanted to have Wrench 'stay' (i.e., in purgatory), but argued that he was on a better path.
Aporia
The very powerful scene in which Emmit confesses to killing Ray and shares with Gloria the sad story of their life. Their dad died when they were just teens, and when Emmit inherited the Corvette instead of the stamps, he convinced Ray to switch their inheritance by telling his chubby brother that the chicks would be all over him with the car. When he uses the stamps as collateral to start his business, Ray can only bitterly watch, and in the present Emmit finally understands how cruel it was.
Emmit: Thirty years I’ve been killing him. That was just when he fell.
Not to mention that Emmit heavily implies that he murdered their father with a tennis ball and then blamed it on Ray, an avid tennis player.
Later, there's both his and Gloria's reaction to realising that they've been hopelessly checkmated by Varga. Emmit's attempt to atone accomplished nothing beyond getting two people killed simply because they were unlucky enough to share his surname, and Gloria watches helplessly as the justice system to which she's dedicated her life takes the lazy route and accepts Varga's coverup.
Winnie lamenting about how she and her husband still haven't been able to conceive and the passion is draining out of their relationship as their sex life gets more mechanized.
Three months after meeting Wrench, Nikki has bonded with him not just as a co-conspirator against Varga but as a partner - to the extent of learning sign language to communicate with him.
Somebody to Love
In the finale, Varga leaves Meemo to die in an ambush to save his own skin. The last time we see Meemo alive, he's looking at Varga with an expression of hurt and betrayal on his face.
Nikki misled Mr. Wrench to believe that they were going fifty-fifty on the job by asking Varga for two million dollars, only to take a handful of the money and leave Wrench with the rest. She only wants revenge - and she doesn't want him to risk his life for her grudge.
After three months of careful scheming, Nikki finally comes close to getting revenge on Emmit, the "Parking Lot King of Minessota" only to die in a random accident over wrongful parking.
Emmit, the last person who deserves a second chance, gets away with financial misconduct and seems set for a happy ending with his extended family five years after his brother's death. Only for Mr. Wrench to give him the death he deserved, a quick shot in the head. Nikki's last words to Wrench were "All I want is the brother". If he'd been going along with her plan only for the money he could have gone on his merry way and never thought of the Stussys again. But he chose to keep tabs on Emmit for five years, just to keep a debt to someone he'd known three months. A debt he was under no obligation to honour.
Not to mention this represents a moment of closure for Wrench as well - he never got to take revenge on Lorne Malvo for killing Mr. Numbers, since it would have been too dangerous. Now, finally, he is able to complete the loop and exact justice for one of his murdered partners.
Moments before his death we see Emmit's fridge is hung with photographs of himself and all of his loved ones - and Ray is noticeably absent.
After all the emotional (and later physical) torment Varga has put him through, it's bittersweet to see Sy back and sitting with Emmit (and Emmits family) but with implied brain damage. It's even more depressing that in a few minutes, Emmit the friend he's reunited with, will be shot by Mr. Wrench.
