My son has taken an interest in Rubik's Cube. It was a big fad from 1980-1982. At the time, as a pre-teen, I learned to solve it and even competed in a speed cubing competition at our town's rec center. I didn't win, but I was a credible competitor.
A quarter of a century later, I remember what it felt like to solve it, and even the general outlines of how the solution and the concepts behind the notation used to describe that solution. But even on a good day, I can't solve more than the top two layers of one any longer, and many days are not good days. I suspect that if I try to relearn how to solve it, that I will pick it up more quickly than I did the first time, but that isn't certain.
Indeed, in addition to charting the limits of human memory, the Rubik's Cube is also a good illustration of the nature of expertise. Despite its simple rules (so simple that they are all inherent in the device itself without any need for formal description), and despite the fact that almost anyone with time and interest can make a certain amount of progress towards a solution, not one person in a hundred thousand can solve one without being taught the solution. Probably not one person in a hundred who knew the solution a quarter of a century ago can solve one today.
This isn't because it is terribly hard to solve a Rubik's Cube. It took me no more than a week or two of part time effort to learn to solve it when I had an instructional guide. The guide itself is quite short, although, much like mathematics, it can be tough going until you have mastered it once. It doesn't take exceptional intelligence to master it, although I imagine that many people with weak structural visualization ability might never be able to manage it, with or without instruction. But the Rubik's Cube is really an excellent example of a nearly impossible task that becomes elementary to much of the population with a modicum of instruction. Also, while I mastered it myself from a book, far more people would be capable of mastering it with in person tutoring.
Few people will bother to manage a task, even if their inability to do so is terribly frustrating, if it takes even a modest amount of disciplined study to master it. Juggling or riding a unicycle are similar tasks. Both are nearly impossible to do without some focused and guided instruction. I know from people who have mastered each that it doesn't take a terribly amount of time or effort to manage either. But I have not made that effort despite numerous half hearted efforts to master them, nor have most people.
We make it a cultural norm to systemically teach certain skills like this to large numbers of people as part of their upbringing. A large percentage of children are taught to ski or to play instruments or to ice skate or type, for example. Some such skills, like free hand drawing or taking shorthand, appear to have once been much more common than they are today when technologies like the camera and tape recorder make them less important to most people. Some skills once widely known, like knitting, appear to have lapsed for a generation but have seen a resurgence in the current generation.
Arguably, literacy is such a skill. At a certain age, literacy in the narrow sense of being able to convert an oral language already mastered into writing, comes quite easily. Even very dull Japanese youngsters manage to learn not only multiple Japanese alphabets, but also thousands of ideograms, to the point at which they can read a newspaper. Attaining this same mastery when trying for the first time as an adult is much more difficult. Attaining this kind of narrowly defined literacy without formal instruction is an extremely rare feat, however, even though ever child almost automatically learns spoken language through osmosis with little apparent effort and no formal instruction.
One of the more problematic pedagogical constructs, in my view, is the confounding of literacy narrowly defined, and broader concepts like "functional literacy" which place emphasis on vocabulary, familiarity with basic technical knowledge about fields like medicine, and comfort in handling complex grammatical structures, rather than a mere ability to translate the spoken word into writing and to similarly translate the written word into oral concepts. A lack of functional literacy generally refers to a language/knowledge deficit shared both orally and in writing, not to an inability to master the relatively straightforward and technical business of committing a fundamentally oral means of communication into images on a page and back. Thinking of functional illiteracy as a mere literacy skill problem understates the magnitude of what is absent and what must be done to remedy that lack.
Also, many genuinely illiterate people, blind poets, folk taught clergy, Native American elders in early American history, and aristocratic women of much of the last half-millennium, for example, were not "functionally illiterate" in any sense meaningful for the time and place in which they lived, despite their inability to write or read.
Indeed, there is no mention of Confucius, Jesus Christ, Socrates, or the prophet Mohammad, ever writing anything of importance personally. The teachings of each of the legendary religious/philosophical figures comes to us, according to tradition, from the dictation of their disciples at moments in history when literacy, narrowly defined, was not widespread. Certainly someone wrote down the classic works we read today that retain their intellectual importance today. But how much of those texts were really dictation from a great master, and how much of those texts were really original to the immediate authors of those works will never be known with certainty.
Alas, not all skills are like the Rubik's Cube. Many skills crucial to prospering in our society, like facility with the spoken language, are rather indifferent to formal instruction. Truly dire conditions can impair one's ability, and truly perfect conditions can enhance it, but in the ordinary mill run of environments, education seems to have a dismally slight impact one way or the other. Genes and socio-economic environment seem to overwhelm the impacts of formal instruction. Mastery of skills like these cannot be imparted quickly through formal instruction (the literacy charm of productions like My Fair Lady, itself derived from George Bernard Shaw's play, Pygmalion, notwithstanding), and as a result, education does not have the leveling and improving effects that one might wish that it did. Many skills that manifest in a social setting, like the ability to influence groups of people, likewise seem impervious to serious formal instruction for better or for worse.
Americans tend not to like to acknowledge that this is the case. As a result, we place an excessive premium on formal credentials, perhaps unrivaled outside of Africa, while insufficiently policing what people actually know and are able to do as a result of their training. Certainly, there are some fields, like accounting, where the relationship between instruction and mastery is strong. But in many others fields, like management and teacher's education, the link between instruction and ability is woefully weak.