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(The Attributes of Deliberate Practice: A Framework of Domain-Specific Knowledge)How many numbers in a row can you memorize?
Maybe it’s a weird question, but have you ever tried to memorize a really long string of digits?
Try it. We’ll start with something reasonably short. How about this?
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
Stare at that sequence of numbers for a moment, memorize them, then turn away from your screen and try to recall them in order….
(Go ahead. I’ll wait.)
So, how’d you do?
Probably not very well, I’m guessing. That string of numbers above — which just happens to be the first fifteen digits of 𝛑 (Pi) — is beyond the capacity of most people to instantly recall. In fact, it turns out that researchers have consistently found a limit to short-term number-string recall.
Memory Recall — Phoning It In
It seems cutely antiquated now, but there was a time when:
- Human beings called each other on the telephone,
- Those telephone numbers were not automatically stored in a pocket computer, and
- People mostly called friends, family, and neighbors within the same area code.
So when it came time for the early telephone companies to start doling out numbers for everyone, they had a basic question to answer: how should these telephone numbers be constructed?
On the one hand, they wanted to make sure they didn’t issue conflicting or redundant numbers within a given area. Each telephone number needed to be unique.
On the other hand, the early pioneers of phone technology (Alexander Graham Bell et al.) were rightfully concerned about achieving widespread adoption of their newfangled device; if it was too complicated, no one was ever going to use it! (Textbook example from history: the Vasa, a Swedish warship so complicated it literally sank less than a mile into its maiden voyage.)
So they achieved a compromise based on the cutting-edge research of the day: on average, the upper limit of numbers in sequence that we can store in short term memory is seven. For some it’s six. Others maybe eight or nine. But on average, human short-term memory is limited to seven consecutive random things. Luckily, seven digits affords 10 million unique numbers in an area code, more than sufficient to cover future-envisioned megalopolises like the NYC-metro area. And that’s why our phone numbers look like:
But it turns out there are workarounds to this 7-item brain limitation. In fact, using the right workarounds, humans have pushed far beyond that basic limitation — almost unimaginably far. And these workarounds constitute a common theme of elite performance, existing as a shared attribute of deliberate practice among musicians, chess grandmasters, spelling bee champions, and number-memorizing competitors (yes, that’s a thing). The workaround leverages the more powerful region of our memory: our short-term memory is fundamentally constrained, but our long term memory is almost infinitely powerful. So the workaround takes short-term information and attaches it to long-term knowledge, embedding it in something bigger…something unique…something that’s part of a larger story. Thus, rather than attempting to memorize a scattered pile of unrelated bits of information, you take each bit and hang it somewhere on your preexisting long-term memory tree, thus enabling you to remember one detailed story instead of a thousand unrelated plot points.
This “memory tree” is an essential concept of deliberate practice. It can take many forms, and it has been called many things. “Science of Expertise” researchers call it a “Framework of Domain-Specific Knowledge” (FDSK). The Greeks and Romans called them mnemonic devices. Cumberbatch’s Sherlock calls it his “Mind Palace”:
…but whatever name we give it, this sophisticated mental framework interrelates the information specific to our skills, and harnessing its power is key to achieving expert-level performance in any field.
FDSK by the Numbers
Like many scientific discoveries, the origin of Anders Ericsson’s work in frameworks of domain-specific knowledge (FDSK) — and thereby the germination of much of his subsequent research on deliberate practice — was almost accidental:
“The idea for the [number memorizing] study came from an obscure paper…published in a 1929 issue of the American Journal of Psychology…. [The authors] reported that two undergraduate subjects had been able, with four months of practice, to increase the number of digits they could remember when given the digits at a rate of about one per second. One of the students had improved from an average of nine digits to thirteen, while the other had gone from eleven to fifteen.”
In Peak, Ericsson chronicles the evolution of his landmark study on number memorization — a study which would reveal many of the critical principles of deliberate practice:
“The subject we had recruited was Steve Faloon, who was about as typical a Carnegie Mellon undergraduate as we could have hoped to find…. His scores on achievement tests were similar to those of other Carnegie Mellon students…and he was a serious runner — a fact that did not seem meaningful to us at the time but that would turn out to be crucial to our study.
“On the first day that Steve showed up for the memory work, his performance was dead-on average. He could usually remember seven digits and sometimes eight but no more…. Then on [the fifth day] something happened that would change everything. Steve found a way to break through…. [He] had succeeded by developing a collection of mental structures — various mnemonics, many of them based on running times, plus a system for keeping track of the order of the mnemonics — that allowed him to use his long-term memory to sidestep the usual limitations of short-term memory….”
At his peak, Steve Faloon could memorize a sequence of 82 digits. This is absolutely amazing to me. It was to Ericsson too. Laboring under the existing paradigm of “innate talent,” it would have been easy to assume that Steve was magically gifted with innate memory talent. But Ericsson had a different theory, and wanted to prove that Steve’s result was not a fluke. So he and his team recruited another student, Dario Donatelli. Using their nascent tools of deliberate practice and leveraging Dario’s FDSK, they were able to get him to a sequence of 113 digits.
Not only was this not a fluke: Ericsson and his research subjects had inadvertently revolutionized a new field of competition — one which would learn from their research, build upon it, and extend it. Throughout the next 15 years, number-memorizing competitors would blow Steve’s and Dario’s records out of the water.
An excellent and related historical example of this concept exists in running. In 1954, Roger Bannister became the first person ever recorded to run a 4 minute mile. It was an extraordinary accomplishment, a testament to the physical gifts bestowed upon certain lucky individuals…
…except, not at all. Because as it turns out, once Bannister proved it could be done, countless others have not only matched his record — they’ve exceeded it. So in spite of the fact that breaking the “4-minute-mile barrier” was once deemed impossible, a man named Hicham El Guerrouj holds the current world record with an astonishing time of 3:43.13. And it’s only a matter of time before he’s bested too.
How can this be? Starting in 1954, did human evolution turn on a dime to start cranking out genetically enhanced homo sapiens with superior quadriceps, hamstrings, and lung capacity? Or is possibly something else going on?
In a way, the post-Bannister results shouldn’t be surprising. I previously wrote …
“Look at any field to which deliberate practice applies: the current level of expert-level performance surpasses that of previous generations. As it should, by design…. One of the ways this is accomplished over time is that teachers get better at teaching, and students get better at learning. Training methods are improved, and learning tools proliferate.”
In retrospect, it’s obvious. “Duh.” Yes — this is why world records trend in only one direction: upward! The Olympics don’t backslide. Modern symphony orchestras have a technical standard far exceeding those recordings we hear from the 1930s. Number-memorizers are reciting ever-longer strings.
So, reader, as you’re mulling your inability to recall those ten digits of 𝛑, consider that the current world-record for number-memorizing is held by Lance Tschirhart: 456.
That’s not a typo. Four-hundred and fifty-six freaking numbers. 456! The numbers were read out loud one second apart, and Lance repeated them back once the string was concluded. It took nearly 8 minutes just to read through all the numbers. This is truly incredible to me; there are days where I can hardly remember anything that was happening 8 minutes ago; to be able to perfectly recall a string of random digits read aloud continuously for that length of time seems super-human, like some sort of mutant superpower.
Except, we know that’s not so. We have been consistently establishing that these bewildering feats are accomplished through application of deliberate practice, in this case leveraging the power of a framework of domain-specific knowledge.
But what does this have to do with music? Isn’t music all about feeling and emotion?? Can’t we just ditch class and all that boring “book learning” and just feel the music at people real hard???
To answer these questions in order:
And definitely not.
As I previously wrote, “successful musicians don’t just sit there and ‘feel the music at you real hard.’ Most musicians are more analytical and ‘scientific’ than they realize. Artistry is supported by craft, and craft is supported by analysis.” And knowledge. It takes knowledge to refine your craft, and as Brahms said, “without craftsmanship, inspiration is a mere reed shaken in the wind.” (i.e., You might believe you’re phrasing beautifully, but it really doesn’t matter if I can’t decipher those subtleties amidst the jumble of your lack of dynamic control!)
I call attention to this attitude because it’s one I consistently encounter in younger players: “book-learning and knowledge is for nerds, whereas music-making is all about emotion!” At a conceptual level, this superficial idea of elite musicianship couldn’t be more wrong. But also at a practical level of craft refinement, this “aversion to knowledge” is deeply counterproductive. As Colvin writes in Talent is Overrated, “great performers know more than average ones.” In a study comparing average vs. world-class chess players, it was found that “the world-class players didn't consider more possible moves than the less-accomplished players, nor did they search any deeper (more moves into the future), nor were their rules of thumb for choosing moves any different. In sum, their intellectual engines didn't seem to be turning any faster. So what made them better? Part of the answer, which seems to apply in every domain, is that they had more knowledge about their field.”
Renovate Your Musical Mind Palace
As musicians, we tend to glorify the “intuitive geniuses” of our art form — the individuals for whom music-making seems to flow effortlessly and without intense intellectual deliberation. Generally speaking, that glorification is misplaced. With respect to a titan like Mozart, I previously wrote that “Mozart was a human being, not a god…. In spite of beginning musical studies at the age of 4 with his father Leopold, one of the leading musical pedagogues in Europe, Mozart would put in 24 years of deliberate practice before he produced anything that history would truly consider ‘great’…. For me, [this only] enhances [my appreciation]…because Mozart’s genius wasn’t gifted, it was earned.”
This is just as true for performers as it is for composers…or as it is for early twentieth century physicists. Einstein’s world-changing Theory of Relativity was necessarily preceded by the laborious accumulation of domain-specific knowledge. Contrary to popular myth, relativity didn’t just “spring into his mind” — it was preceded by massive, immersive, deep study.
As it turns out, nearly every field imaginable requires experts to accrue a lot of knowledge. And this is not just any knowledge — it is knowledge which is highly specific and relevant to that field, i.e., “domain-specific.”
Students can absorb this knowledge in many different ways, but regardless of how this knowledge is soaked up, the most effective performers are moving toward the same destination: it’s not just a list of facts, nor a static bowl of trivia, nor a pile of unrelated sundries. No — the point of this knowledge acquisition is to construct an interrelated, multidimensional framework. It’s your Musical Mind Palace.
The bricks and mortar of your mind palace are pieces of domain-specific knowledge, and these are exactly what the name implies: all of the relevant knowledge that supports our work in a given field. In music, this multidimensional framework certainly includes factual basics like rhythm reading, pitch recognition, scales, harmony, music theory, music history, and orchestration. It also includes the manifold particulars for individual instruments, such as the attributes of different makes and models, performing traditions, period-specific performance practice, fundamental techniques, and extended techniques. Domain-specific knowledge can also include information that is more abstract, such as an understanding of “Mozartean style,” or “romantic phrasing,” or “Baroque improvisation.”
Pertinent to auditioning, domain-specific knowledge then begins to encompass the relevant audition excerpts, an understanding of the audition process (and its variations), and elite-level peak performance psychology.
In short, this framework comprises things you can know. But interrelating them is key. Because this is long-term memory terrain, and the framework is what makes the individual bits accessible and relatable. The framework helps you recall the relevant bits years later.
Colvin writes “researchers find that excellent performers in most fields exhibit superior memory of information in their fields.” Chess provides another illustrative example that goes beyond the seemingly simpler concept of memorizing digits; researchers show novices and experts a chess board full of pieces for a few seconds, take it away, and then ask them to recall it. On its surface, this would seem like the digits competition — a straightforward test of short-term memory, with a likely limit of seven things. And sure enough, “the chess researchers found that the masters possessed only average short-term memories when it came to recalling randomly arranged pieces.” But when the pieces were rearranged into formations that would occur in real games, the novices still floundered whereas the masters recalled the configurations nearly perfectly. How does this work? “Researchers proposed what has become known as the chunk theory. Everyone in the experiment remembered more or less the same number of chunks of information. For the novices, a particular piece on a particular square was a chunk. But for the masters, who had studied real positions for years, a chunk was much larger, consisting of a whole group of pieces in a specific arrangement.” (Incidentally, this is how chess grandmasters are able to play twenty simultaneous games blindfolded.)
Colvin continues that “the difference is much like the difference between letters and words,” and “when top-level chess players look at a board, they see words, not letters.” It’s part of a larger story. The pieces fit into a preexisting interrelated framework, encompassing the history of famous chess matches, and all of their various configurations. Moreover, “the best players understand the strategic importance of each group, its role in attacking, defending, and distracting the opponent, and so on. In the letters-versus-words analogy, it isn't just that novices see letters while experts see words; the experts also know the meanings of the words.”
And this finding applies across nearly all fields: “Top performers understand their field at a higher level than average performers do, and thus have a superior structure for remembering information about it. The best medical diagnosticians remember more about individual patients because they use the data to make higher-level inferences for diagnoses than average performers do. The best computer programmers are much better than novices at remembering the overall structure of programs because they understand better what they're intended to do and how. Beginners at electronic engineering look at a circuit diagram and see components, while experts see major functional groups and remember them better.”
And obviously, this framework of domain-specific knowledge doesn’t just happen. No one is born with a preformed FDSK. “It can be achieved only through years of intensive study…acquired through many years of deliberate practice.” And for me, enriching that framework is an integral part of the joy of music-making. It enhances my appreciation, and provides me with more to contribute. Knowing that Debussy premiered Pelléas et Mélisande in 1902 makes the impressionistic atmospheres and exotic harmonies of Puccini’s 1910 La Fanciulla del West all the more comprehensible and relatable. Knowing that Wagner premiered Parsifal in 1882 reassures me that I’m not crazy when I hear the heartbreaking similarity in the Act 4 english horn solo in Verdi’s 1887 Otello.
Or more broadly, it’s fascinating to consider how major trends in world history impacted the mind palaces of the time, and the emotions coursing through the composers attempting to channel that zeitgeist. Many books have been written about how Beethoven exists as a perfect bridge between the rational enlightenment and the emotionally-charged romantic era…and how this manifested in the idealism of the French Revolution being dashed upon the imperial rocks of Napoleonic Europe…and subsequently how this so greatly enraged Ludwig that he violently scratched out Bonaparte’s name from the dedication of the “Eroica” Symphony.
In The Rest Is Noise, Alex Ross documents connections like these throughout music history, fascinatingly focusing on some of the great “frenemy” couples. One can chart Beethoven’s influence upon Brahms and Wagner, follow it through to Strauss and Mahler, and eventually arrive at Britten and Shostakovich over 100 years later. Sometimes they were more friends than enemies. Other times they would view the works of their “competition” with jealous respect and grudging admiration, learning from those different styles, and incorporating them in their own ways. The mind palaces of these greats were interrelated and significantly influenced by each other. You don’t get the 1905 Salome chord without the 1865 Tristan chord. And you don’t get the tragic hammer blows of Mahler’s 6th Symphony (1906) without the enabling “satanism” — as contemporary critics described it — of his frenemy’s Salome.
And here’s a fun thing: understanding these relationships becomes part of my mind palace, and helps me form a deeper relationship with those composers’ music. Because at the end of the day, cultivating an FDSK is about efficacy and impact: the framework of knowledge enables greater craft refinement through better practicing, and better practicing makes you a better performer. A framework of domain-specific knowledge is a critical part of delivering an impactful performance.
Now, the specific aspect of “domain-specific” is important — this framework of interrelated information needs to have explicit bearing on the relevant skills. (For musicians, that would be persuasive performing.) So, while I would argue that it’s important for a timpanist to possess reasonable knowledge of Beethoven’s biography, periods of work (early, middle, late), and stylistic evolution, holding a Ph.D. in musicology is not a prerequisite for performing the “Eroica” Symphony. Similarly, an audience member isn’t required to read the program notes; any experience of the music is legitimate. But over time, I’ve found that my own evolving FDSK can definitely enrich my experience of the concerts I attend.
All that being said, the nature of domain-specificity can be unorthodox: I don’t know of a conservatory anywhere in the world that requires physics classes for its percussion majors, but I have personally found physics knowledge to be extremely relevant to my own playing. It has explicit bearing on my job on a daily basis, and my understanding of acoustics, mechanics, signal processing, and thermodynamics has informed my timpani career immeasurably. I believe that physics knowledge provided me with shortcuts for evolving my technique and sound concepts, without which I would have been fumbling for years according to random trial and error.
Building to the Ultimate Goal: Mental Representations
Persuasive music-making is a skill, and knowledge is the pathway to any skill. Along that pathway, knowledge is power…but a framework is better. That framework of domain-specific knowledge is like the I-beams, braces, trusses, and girders of a young skyscraper, the skeleton upon which everything else will be built. This structure ultimately supports the final building — the thing that Anders Ericsson considers to be the true goal of all deliberate practice: refining mental representations.
If some cataclysm were about to wipe out all human knowledge and I could only pick two attributes of deliberate practice to describe on a golden record aboard an outbound Voyager I probe, it would be these:
1. Continuous feedback loops, and
2. Sophisticated mental representations.
We’ll explore mental representations thoroughly in the next post. Sorry to leave you with a cliffhanger, but schedule-permitting I’ll get to that soon…as we start resolving other cliffhangers like (a) how the Avengers will un-dust half the universe and (b) how the hell Daenerys & Co. expect to defeat the Night King and his freaking zombie dragon.
Mental representation winter is coming.