Free How We Learn by Benedict Carey

math, states that adding the square of the two short sides of a right triangle equals the square of the longest side. It existed in my head as a 2 + b 2 = c 2 , and I have no idea where I was when I learned that.
    On that night, however, I learned a simple way to derive it—a beautiful thing it is, too—and I still can see what the guy was wearing (blue slacks, up to his chest), hear his voice (barely, he mumbled), and recall precisely where on the board he drew the figure (lower left corner):

    The proof is done by calculating the area of the large square (c squared) and making it equal to the sum of the figures inside: four triangles (area: ½ b x c times 4) plus the area of the little box ((a—b) squared). Try it. Simplify the right side of that equation and watch what you get. I remember it any time I sit alone in some classroom or conference room under dimmed fluorescent lights, like if I’ve arrived first for a meeting. Those cues bring back the memory of that night and the proof itself (although it takes some futzing to get the triangles in place).
    Those are contextual cues, when they’re conscious and visible. The reason I can recall them is that they’re also part of a scene, an autobiographical memory. The science tells us that, at least when it comes to retention of new facts, the subconscious ones are valuable, too. Not always—when we’re submerged in analytical work, they’re negligible—and not necessarily all of them. Only sometimes. So what, though? When it comes to learning, we’ll take any edge we can get.
    I recall something else about that night, too. Normally, when visited by the Ghost of Physics Past, I was not entirely patient. I had work to do. I could do without the lecture about the properties of quartz. That night, though, I’d finished most of my studying and was in an open, expansive mood. I was happy to sit and listen and even hear about how “physics students today, they don’t learn any of this …”
    That mood was part of my “environment,” too, wasn’t it? It had to be—I remember it. I wouldn’t have sat still for the lesson otherwise. If psychologists’ theory about reinstating sights and sounds was correct, then they’d have to show that it applied to internal mental states as well—to jealousy, anxiety, grumpiness, confidence—the entire mix-tape of emotions running through our heads.
    The question was, how?
    • • •
    No one who’s gone through a bad breakup while trying to be a student will doubt the impact of mood on learning. Moods color everything we do, and when they’re extreme they can determine what we remember. The clearest demonstration comes from psychiatry, and the study of bipolar disorder. People with this condition are the extreme athletes of the emotional realm. Their moods cycle between weeks or months of buoyant, manic activity and periods of dark, paralyzing depression, and they know too well that those cycles determine what they remember and what they don’t. “There is a particular kind of pain, elation, loneliness, and terror involved in this kind of madness,” wrote the psychologist Kay Redfield Jamison, who has a diagnosis of bipolar. “When you’re high it’s tremendous. The ideas and feelings are fast and frequent like shooting stars, and you follow them until you find better and brighter ones.… But, somewhere, this changes. The fast ideas are far too fast, and there are far too many; overwhelming confusion replaces clarity.Memory goes.”
    Indeed, researchers showed in a 1974 study that people with bipolar disorder have state-dependent memory: They remember best what happened during manic phases whenthey’re again manic. And vice versa: When depressed, they recall events and concepts they’d learned when they were down. As the study’s authors put it, “associations or episodic events … can be regenerated more completely in a similar mood state than they can in a different mood state.”
    Yet bipolar is an