Elementary - Recap: Nothing Quite So Toxic As Guilt

The case this week involves the murder of a mathematician named Felix, who is shot and killed over his work on the nigh-unsolvable math problem, P versus NP, which is a problem that asks whether every problem capable of being quickly verified by a computer can also be quickly solved by a computer. In essence, the solution to this problem could render all forms of encryption obsolete, providing any hacker with a "skeleton key" to bypass securities and access/manipulate information at will. Centering the case this week on math seems a risky proposition, since it's a subject that isn't exactly accessible to all audiences, yet the episode succeeds by not making it any more complicated than it needs to be, as the story isn't really about the math, it's about what the math has compelled people to do. In that respect, we get an investigation that inevitably leads to the discovery of two other victims: the partner with whom Felix was working to solve the problem, and a mugger who was incidentally shot by the killer on the night of the murder. While the partner is dead, the mugger is actually still alive, though he's in a coma. Thus, Sherlock (Jonny Lee Miller) and Joan (Lucy Liu) team up with Bell (Jon Michael Hill) to piece this one together themselves, along with the help of eccentric mathematician Harlan Emple (Mad Men's Rich Sommer in a role I'd love to see again in a future episode).

The resulting investigation leads the team to Tanya Barrett (Lynn Collins), a colleague of Felix's who feigns ignorance about how close the dead man was to solving the problem. Yet even though all the evidence points to Tanya (from the presence of the dog hair that was found on Felix's body, which matches the Boston Terrier she owns, to the crime having been committed with a gun registered to her), restaurant security cameras prove that she couldn't have committed the crime. Complicating matters is the presence of a jilted ex-boyfriend who had apparently purchased ammunition for Tanya's supposedly-stolen gun mere days before the murder, leading Sherlock and Joan to suspect that Tanya may have been framed. But this is where the entire case begins to unravel, as Sherlock and Joan come to realize that the timestamp on the security cam footage has been altered, and that the angry emails from Tanya's boyfriend, along with the receipt for the purchase of ammunition, had all been faked. How? By using the solution to the P versus NP problem to forge the emails and receipts, bypass security at the restaurant, and alter the timestamp by making it appear that Tanya was at the restaurant during the time in which the killings were committed.

Thus, the motive is not that Tanya killed Felix and his partner to prevent them from solving it first, but to prevent them from solving it and then taking credit, since Tanya had already solved the problem and was waiting for the proper moment to leverage that information for greatest personal gain. When the mugger awakes from his coma, the case is all but solved, as he identifies Tanya as the shooter. She's taken into federal custody, along with all her data on the problem, in order to prevent the solution to P versus NP from getting out and compromising national (if not global) security. It's a very tight, neat solution to the case, and it's all the more compelling for how efficiently it's all handled, as the story features enough twists and turns to cast doubt on what we already know, yet it doesn't linger on those plot points long enough for it to become obvious where the story is headed. It's a refreshing approach that carries over into the more character-oriented storyline of the week.

While Joan is visiting the grave of the patient whose death prompted her to quit her career as a surgeon, she encounters the man's now-adult son, Joey (Jeremy Jordan). The two greet each other as old friends, having spent the last several years in intermittent contact with one another. They go out for a cup of coffee to catch up, and Joey reveals that he's dropped out of college and is looking to buy a bar, and offers Joan the opportunity of investing, since he wants to be able to pay her back for all she's provided him over the years. Joan asks Sherlock for the advance, and he's immediately skeptical of Joey's motives, as he suspects that the boy is trying to prey upon Joan's continued guilt over having accidentally caused his father's death during what should have been a routine surgery. Joan insists this isn't the case, and swears that Joey is a good kid. She recalls that after causing the man's death, Joey's mother rightly sued her, yet the boy himself never seemed to hold his father's death against her. Joan discusses receiving a letter from the then-seventeen-year-old Joey in which he stated that he didn't blame her for what happened, granting her his forgiveness. The weight of Joan's guilt is primarily what prompts her to entertain Joey's offer for so long, as she presses Sherlock for a $5,000 advance on her salary, despite Sherlock's constant declarations that she needs to kick Joey out of her life. Things grow even more complicated when we learn that this isn't even the first time Joey has asked Joan for money, as he needed a car to ferry himself to and from college.

Ultimately, Sherlock provides Joan with a substantial cash advance: $20,000, a one-time buyout intended to force Joey to leave her alone for good. But Joan doesn't want to cut off contact, even if she can admit that her guilt is at least partially what's motivating her desire to keep helping him. So she comes up with a compromise: instead of buying into his bar, Joan offers to pay for Joey to go back to college and to finish his engineering degree. She states that his father was always so proud of his accomplishments, particularly when Joey received his initial scholarship to study engineering, and she wants to help him realize his full potential. "I'm not investing in the bar," she tells Joey, "I'm investing in you." However, Joey resents Joan's offer as he feels that she's withholding the money unless he does what she thinks is right, a proposition he doesn't see as fair. In his anger, he lashes out at Joan for causing his father's death, saying that she's the only reason he isn't here to have a say.

Yet, in a remarkable little moment, Joey goes back on the statement almost as soon as he says it, apologizing to Joan for lashing out, adding that she doesn't deserve being spoken to that way. It's a wonderfully adult bit, as common story logic for a plot like this would end up revealing that Joey was entirely false in his affection for Joan. I could have easily predicted Joey would inevitably lash out at Joan, that his facade would crumble away the minute Joan didn't give him his way. Hell, that's what I was predicting as the episode rolled on. But I loved how it was shown that Joey's "facade" wasn't really a facade, per se. He's not a bad guy, and he wasn't pretending to care about Joan. Maybe deep down, in some dark corner of his heart, he blames her for his father's death, but he's a guy that knows that, as Sherlock admits he's loathe to say, "mistakes happen." He says he'll take Joan's offer under consideration, though she tells Sherlock she doesn't expect to hear from him again, and I like that the storyline remains open. Not because I'm hoping it will be addressed again down the line, but because in many ways it serves as a parallel to life, as not every problem can be tied up in a bow as neatly as this week's murder case.

Joan knows this, as does Sherlock, who outright states that while mistakes happen, there's "nothing quite so toxic as guilt." That shared knowledge informs their relationship in more ways than even they themselves might know, as Sherlock's season one storyline was, in many ways, driven by his guilt over the death of Irene Adler (although that ended up becoming a situation that got completely turned on its head by season's end. But the scars are still there). He recognizes the same capacity for excessive guilt in Joan as he sees in himself, but Sherlock also sees Joan's capacity for generosity and care. He recognizes the transformative effect Joan's late patient had on her, and he expresses a desire to accompany her the next time she visits his gravesite. It's the episode's most poignant moment, as Sherlock recognizes how Joan's vulnerability has led to a new strength, and wants to share in it with his friend. Though Elementary is a procedural, at its heart it remains a story about two people, each of whom are the only one really qualified to understand the other.

"Solve For X" is about solving more than a crime, but about piecing together emotional puzzles. How much guilt is too much guilt? What's the limit on how long a person should beat themselves up for their mistakes? And how does one piece their life, and their emotional well-being, back together in the wake of insuperable guilt? It's hard to ever really know the answer, but as with any problem, it's worth exploring.