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Initial Question

 

Over the course of time, phenomena enter our collective consciousness as mysteries—things in our environment that excite our curiosity but elude our understanding. The mystery of what we now know as gravity confounded our ancestors: when they looked around them, they saw that most objects—apples, famously—seemed to fall to the ground quickly; but others, such as leaves, seemed to take forever to reach the ground. And then there were birds, which didn’t seem to fall at all. In the visual arts, one of the most enduring mysteries was how to represent what we see in front of us in three dimensions on a two-dimensional surface. In both cases, people struggled for centuries to come to an understanding of the phenomena. Even the most baffling mysteries, though, eventually crumble under the force of human intelligence. With sufficient thought, a first-level understanding emerges from the question at hand. We develop heuristics—rules of thumb—that guide us toward a solution by way of organized exploration of the possibilities.

Being precise about concepts is important, because they are the critical building blocks of any human enterprise, intellectual and otherwise. One way to analyze concepts is to describe the ways in which they are used in particular situations—that is, to highlight their “use cases.”

The route out of a mystery begins with a hunch. Hunches are prelinguistic intuitions. You are in a dense fog high up in the Rocky Mountains. Darkness is on its way. You can see no more than five feet ahead. As you worry about your next step—and the rest of the way—your peripheral vision “sees” a slanted spruce at 11:00, and you experience a “sense” that you should turn right. If someone were to ask you at the time, “Why do you want to go right?” you could not, of course, answer the question in a way that would seem objective to that person. “Just a hunch,” you might say. “Something beyond words.” You turn and you get safely to the lodge. You never become aware of the fact that you have seen this tree before, on the way to the woods. The hunch remains a hunch. It remains beyond words but not, obviously, beyond either reason or sense.

Heuristics are open-ended prompts to think or act in a particular way. For instance, “Look in the rearview mirror before passing,” “Go with the first instinct when trying to decide if someone is lying to you in a face-to-face interaction” (this is a heuristic that recognizes the value of a hunch), or “Buyer beware!” Heuristics offer no guarantee that using them produces a certain result. Rather, they contain the vague promise that, all things being equal, using the heuristic in the context it is meant for may, or on average, will be better for you than not using it. Heuristics are different from hunches in that they are explicit: they bring intuitions to language.

Algorithms are certified production processes. They guarantee that, in the absence of intervention or complete anomaly, following the sequence of steps they embody will produce a particular result. For instance, an algorithm (PRIME_SEARCH) designed to figure out if a given number is a prime number—by brute force—will systematically try to divide that number by every number smaller than itself and return the answer “PRIME” if no divisor is found and “Divisor = …” if a divisor is found. Algorithms differ from heuristics in that they offer a performance guarantee that comes along with using them: you cannot use the algorithm PRIME_SEARCH on the number 209870987403987 and not get an answer, except if some catastrophe intervenes and stops you from executing the steps prescribed by the algorithm.

Consider the falling objects. After a long period of observation and contemplation, human beings in various cultures more or less simultaneously developed the notion of a universal force that tends to pull physical objects earthward. Understanding advanced from a mystery—why do things fall to earth?—to a heuristic or a rule of thumb for explaining why things fall: a force we call gravity causes things to fall to earth.

In art, after literally centuries of questioning and experimentation, the heuristic of perspective emerged as a solution to the mystery of three-dimensional representation. First, in about the fifth century BC, came a tool called skenographia, which historians conjecture was developed by Greek dramatists to make their sets appear to have depth. A heuristic had begun to emerge.

Heuristics represent an incomplete yet distinctly advanced understanding of what was previously a mystery. But that understanding is unequally distributed. Some people remain stuck in the world of mystery, while others master its heuristics. The beauty of heuristics is that they guide us toward a solution by way of organized exploration of the possibilities. With a heuristic to guide his further thought and consideration, the great scientist Sir Isaac Newton derived precise rules for determining how fast an object will fall under any circumstance. Newton’s rule—that an object dropped from any height will accelerate at a constant rate of 32 feet per second squared—advanced the understanding of gravity to the third stage, the algorithm. An algorithm is an explicit, step-by-step procedure for solving a problem. Algorithms take the loose, unregimented heuristics—which take considerable thought and nuance to employ—and simplify, structuralize, and codify them to the degree that anyone with access to the algorithm can deploy it with more or less equal efficiency.

As with gravity, the algorithm for perspective took centuries to develop. By the eleventh century AD, early physicists had arrived at the understanding that the conical shape of the eye influences how we see three-dimensional objects. A few centuries later, the Florentine painter and architect Filippo Brunelleschi studied the heuristic until he innovated a repeatable method—an algorithm—that allowed him and other artists to reliably create the illusion of three-dimensional space.

As understanding moves from mystery to heuristic to algorithm, extraneous information is pared away; the complexities of the world are mastered through simplification. That is why my graphic model of the advance of knowledge is a funnel that tapers as knowledge moves through its stages of refinement. The gain in understanding comes from picking salient features of the environment and out of them constructing a causal explanation of the mystery. From the inchoate phenomenon of falling objects came the concept of a universal force that pulls things earthward, which in turn was painstakingly developed, through trial and error, into a simple formula that described the unchanging properties of this once-mysterious force.

There’s significant value to pushing knowledge to the algorithm stage. It is quite handy to have at one’s disposal a logical, arithmetic, or computational procedure that, if correctly applied, guarantees success. When Brunelleschi created the precise “vanishing point” algorithm for perspective during the first two decades of the fifteenth century, he provided a significant advantage to the Florentine artistic community until the algorithm became more widely disseminated and understood.

The ultimate destination of algorithms as of the late twentieth century is computer code. Once knowledge has been pushed to a logical, arithmetic, or computational procedure, it can be reduced to software. Armed with the algorithm for gravity, clever engineers at Honeywell were able to create autopilot systems for giant commercial aircraft so that they could be made to fall out of the sky in a passenger-friendly fashion without human intervention. And what about Brunelleschi’s algorithm for perspective? Computers now use the three-dimensional data transferred from a camera to spit out a two-dimensional representation of it based on the formulas handed down by Brunelleschi and codified in matrix-multiplication software.

Of course, not every mystery can become an algorithm; not all logic can be pushed through to the end of the funnel. Consider the mystery of the oldest art, music. How can certain arrangements of notes, timbres, and rhythms have such a profound effect on our emotions, and how can we harness that power to soothe or rouse our listeners? Norman Greenbaum stumbled on the answer to that mystery once and once only, coming up with the 1969 smash “Spirit in the Sky.” Wildly catchy and instantly recognizable, the song continues to spin off royalties that provide Greenbaum with a comfortable living. But the mystery of the hit song remains just that for Greenbaum. He has never produced a follow-up to the fuzzed-up hippie spirituality of “Spirit in the Sky.”

Contrast Greenbaum’s career with that of U2, the band that developed a heuristic—a way of understanding the world and conveying that understanding through harmony, melody, and rhythm—that enables it to write songs that resonate with millions of people worldwide, not once but over and over. From the release of the earnest, anthemic album Boy in 1980 to the eclectic pleasures of Achtung Baby in 1991, U2’s mastery of heuristics produced a string of industry awards and top-forty hits. But when the band consciously stepped away from the heuristic that had served it so well—experimenting with techno, dance, and electronica on Zooropa and Pop—fans promptly voted with their feet. When, in 2000, the band reunited with producers Brian Eno and Daniel Lanois to record All That You Can’t Leave Behind, it also returned to its pre-Zooropa heuristic, leading to Bono’s famous remark at that year’s Grammy Awards: “The whole year has been quite humbling,” he said. “Going back to scratch, reapplying for the job. What job? The best-band-in-the-world job.” 2 The heuristic still worked; Rolling Stone called All That You Can’t Leave Behind U2’s third masterpiece (after The Joshua Tree and Achtung Baby). 3

Yet even U2’s greatest albums contain some forgettable songs; its mastery of the heuristics of the pop song falls short of a surefire algorithmic formula. The occasional failures of a serial hit maker like U2 tell us something important about heuristics: they don’t guarantee success. Heuristics can do no more than increase the probability of getting to a successful outcome or at least getting there more quickly.

Thus far at least, pop music has proven resistant to advance from heuristic to algorithm. But there have been movements in that direction: in the late 1970s, musical innovators like producer Brian Eno experimented with the sound of the human heart and determined that songs with a synthesized heartbeat as their rhythm track are instinctively enjoyed by listeners, no matter what musical setting sits atop the heartbeat. As a producer, he was able to help bands turn out hits in a variety of genres, from the jittery dance-pop of Talking Heads’ “Once in a Lifetime” to the orchestral strings of Coldplay’s “Viva la Vida” to those massively successful U2 albums. Other producers in search of a success algorithm created a succession of disposable boy bands, pop princesses, or lip-synching electro-pop acts like Milli Vanilli. And even now we have the mass populism of Simon Fuller’s American Idol, which has produced bona fide stars in Kelly Clarkson and Carrie Underwood, and a few forgettable flashes in the pan. The algorithm remains elusive. There is still nothing close to a formula for producing consistent success in the music business. Yet.

 

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