FOUR FORMS OF FAMILIARITY

A big-picture look at how to attain mastery in almost anything.

EDITED 8/30/15


INTRODUCTION

I routinely tell my cello students that mastering a particular musical concept or technical passage isn't about whether the item in question is easy or hard, it’s about whether or not it can be made familiar.

I then remind them that cello playing is roughly as complex as simultaneously rubbing your stomach and patting your head, while also jumping up and down, tap-dancing, and saying the alphabet backwards!

Nevertheless, the complex act of cello playing is also very much like walking, or driving, or running up a flight of stairs, or any of a thousand other familiar human actions, in that any of them can be familiarized over time, if you so desire.

If a compound skill is too complex to grasp at a glance (if it outstrips your real-time cognitive capacity), then common sense suggests that it should be reduced to a series of smaller, more easily solvable puzzles. Once these smaller steps have been solved, then they can be layered together into more and more complex combinations until mastery is achieved. The catch is that there are four distinct forms of familiarity, and if at any point your developing understanding should become fixed in the wrong form, then your overall performance will suffer.

In this post, I introduce the four forms of familiarity and demonstrate their relationship to one another.

ROAD MAP

Draw yourself a 2x2 table, and label the rows "negative" and "positive" and the columns "static" and "dynamic."

static

dynamic

negative	I. II.
positive	III. IV.

This gives us the four forms, one per quadrant: negative/static, negative/dynamic, positive/static, and positive/dynamic.

Let's explore each form in turn, using the alphabet game "Can you guess what letter I am thinking of?" as a recurring example.

Technical note: In our example, the domain containing the answer (hint: it's in the alphabet) is known from the start, but you must still start the game without any information from within that domain. We are using a small, bounded, discrete domain for clarity, but the same informational principles also apply across unbounded, unspecified, continuous, or uncountably large domains.

QUADRANT I: NEGATIVE/STATIC

The simplest way to begin collecting information is to try guessing a letter.

"Is it A?" "No."

Congratulations! You have obtained your first piece of negative/static information!

static

dynamic

negative	I. "NOT this." II.
positive	III. IV.

Information from the negative/static quadrant is cheap, easily collected, offers a low-resolution view of the true solution, and comes in the form "it isn't this" or "don't do that." For some situations ("Don't raise your bow shoulder"; "Thou Shalt Not..."), including those uniquely strange parental instructions given to small children ("Hey! Stop eating the cat!"), this is sufficient.

But negative/static information doesn't really tell us very much about what TO do...

Some additional information can be extracted from the negative/static quadrant by making multiple guesses ("is it B? ...Q? ...X?"), but this strategy has its limits. The cheapness of each separate piece of information comes at a collective attentional cost, and that cost grows exponentially higher as problems grow more complex. Remembering which guesses have been tried becomes harder and harder as the number of uncoordinated guesses mounts. We quickly approach our cognitive limits, winding up right back where we started!

The problem has again become too complex to grasp at a glance.

Fortunately, that complexity is easily reduced by a shift into the second quadrant:

QUADRANT II: NEGATIVE/DYNAMIC

Ordered groups of negative/static information ("Is it A? ...B? ...C? ...D? ...E?" etc.) can be efficiently collapsed into dynamic ranges ("Is it before F?" "After M?"), substantially reducing the cognitive load of the assembled information. Therein lies the value of the second quadrant! Where the negative/static quadrant can take up to 25 pieces of information to guess the letter in question and requires all 25 to specify it, the negative/dynamic quadrant can specify the letter in two and guess it in no more than seven.

static

dynamic

negative	I. "NOT this." II. "NOT those."
positive	III. IV.

Information found in the negative/dynamic quadrant ("It isn't those," or "Don't bother with that region") is also relatively cheap, provided you trust the information source. Its compact smoothness is useful in real-time situations, where conditions are often continuous rather than discrete. "Don't play that passage in the lower half of the bow" is far easier to remember than "Don't play that passage in this part of the bow, or in this part, or in this part...".

The mental shift from the first quadrant to the second is so easy as to be practically automatic, and in situations where exact answers are unnecessary the results it produces are often “good enough.” Most daily habits live in the second quadrant.

But negative/dynamic information still isn't all that precise, nor is it streamlined enough for every situation. While it is effective in simple one-axis problems such as our letter puzzle, it is far too unwieldy to handle complex problems with lots of parameters, such as residential construction, professional-level auto racing, or orchestral string playing.

Sometimes life calls for a more powerful class of solutions.

QUADRANT III: POSITIVE/STATIC

The third quadrant is where the Eureka! moment is found.

When enough negatives have been nailed down, a powerful phase change occurs. Suddenly, the collected negative information crystallizes, collapsing all at once into a single, positively defined solution:

"The letter is W!"

As this phase change occurs, clouds of no-longer-needed negative definitions dissipate like smoke. An essential clarity is revealed, and the mind frees itself from unneeded clutter. The harder the problem—the more parameters that are in play—the more satisfying the mind-clearing "Aha!" moment is when it finally arrives.

static

dynamic

negative	I. "NOT this." II. "NOT those."
positive	III. "THIS." IV.

Information from the positive/static quadrant is densely packed and can be cognitively expensive to acquire, but it is incredibly easy to use. Its compressed precision ("do it this way") makes it invaluable in real-time situations where decisive competence is needed. (“This goes here, and that goes there.”)

Many people stop once they reach this level of familiarity (“It is the way it is, we’ve figured it out, discussion over”), but this form is not the end of the story either.

Why?

Because despite human hopes to the contrary, the world never stands still under our feet. Change is ubiquitous, even when it is very slow, and the world has a way of shifting out from under our pre-assembled expectations when we least expect it. Perfect circles conceived in the abstract tend to become fuzzy approximations when drawn in real life. People act very differently in different situational contexts. Language, culture, and political parties evolve over time.

Even at the shorter time scales of daily life, many of our most engaging human activities are dynamic in nature. Conversing with other people requires that we keep up with a flow of shifting topics. Your cello bow may be perfectly placed on the string, and your posture may be completely free of tension, but you are not making any music unless your bow is moving. Driving a winding road through the mountains at high speed requires anticipating just where in your lane you need to be, in combination with just when and how hard to gun the engine into the turns. Static solutions are not always enough.

The fourth quadrant comes into play when aspects of the dynamics themselves turn out to be predictable.

QUADRANT IV: POSITIVE/DYNAMIC

If the third quadrant is the quadrant of competence, the fourth is the quadrant of mastery. The fourth quadrant is entered when a whole series of positive/static data points can be collapsed into a single elegant equation, or heuristic: the simpler, the better. Once again, any unneeded information dissipates like smoke.

If the letter game were a repeated affair (“W...” “H...” “E...” “...”) with the eventual goal of guessing an entire quotation (“W H E N I N T H E C O U R S E O F H U M A N E V E N T S...“) then the equation would call up the entire quotation as a familiar whole, thereby eliminating the need to serially discover its individual letters.

[Note: Fourth quadrant equations are continuous. That is, they apply not just at the sampled points, but at all possible points within the domain they specify, and perhaps beyond. This is hugely important.

For example, while the third quadrant can tell me that my bow is perfectly (but differently) balanced here, and here, and here, and here, the fourth quadrant collects those points into a single unifying curve, comprehensively integrating the changes in bow balance, speed, pressure, positioning, and overall posture over time and space. This newfound freedom from technical micromanagement allows me to direct my limited attention to the higher-level task of making beautiful music, which is the whole point.]

static

dynamic

negative	I. "NOT this." II. "NOT those."
positive	III. "THIS." IV. "THOSE, across THESE contexts."

Whether the fourth quadrant equation describes a rigorously formal relationship, a nonverbal sense of events, or a purely physical action is irrelevant. Its establishment confers an intuitive fluency in any domain, an easy, flexible mastery of the material that leaves the mind clear and the body relaxed. The positive/dynamic quadrant is what enables great musicians to engage in on-the-spot virtuosic improvisation, and chess masters to see many moves ahead, and you not to trip over your own feet as you run up a flight of stairs, and politicians to manipulate the emotions of their constituents. Psychologist Mihaly Csikszentmihalyi (link goes to TED talk) refers to being engaged in this performance experience as “flow.”

Making the transition from the third quadrant to the fourth is not so much a matter of raw computing power—you gain back much more than you spend—as it is an act of imagination. You simply have to learn to look past the static logic of a local solution to imagine how it might vary (or not!) across wider domains, and then test for fit.

This is an important real-life skill to cultivate, because all too often things that work well here turn out not to work at all well over there.

Music students routinely rediscover this fact of life every week, when pieces that [they say] they can play perfectly well at home crash and burn in their lessons, or in competitions, or in recitals. Giving a speech to thousands of people feels different from practicing in front of the mirror the night before. Inexperienced travelers quickly learn that different cultures can have wildly varying standards of appropriate behavior. But, once you have latched onto an essential continuity, a stable equation that works across a whole range of possibilities, you can easily adapt to whatever circumstances are on the ground, intuitively flowing around obstacles that would stop a less fluent understanding in its tracks.

Once acquired, mastery can be deepened through layering. Our fourth quadrant equation can borrow from the second quadrant the idea of ranges, so that the curve it describes gains a margin of error. Another fourth-quadrant equation can be layered in that draws an increasing fraction of your conscious attention to the situation whenever you approach the edges of your error margin. Further higher-level dynamic equations can even be written that integrate two or more existing but previously unrelated equations, like, say, “tap-dancing” and “saying the alphabet backwards,” or the relative motions of your bow shoulder, first finger, and the small of your back. The possibilities are endless.

Not all such fourth quadrant connections will be useful. Not all of them will be meaningful. Not all of them will be true. And almost none of them will truly apply equally well across all domains in the real world (failing to recognize this sometimes leads to nasty surprises). But any time you find anyone demonstrating intuitive mastery of even a moderately complex activity, the fourth quadrant is in play.

So, go and find it!

The Illusion of Imperfection

People are flawed, right?

Maybe not.

Flaws and imperfections are measures of things that aren't there. Realizing this is an important step in problem solving.

Human brains are pretty slow. Enough so, that in most of the complex things we do in life we must rely upon anticipation.

EXAMPLE: I can run down this flight of stairs, but only because my memory continuously sifts previous similar experiences to build a moving predictive "window" of what balance adjustments I might need to make, and when I might need to make them, with enough lead time for me to do something about it.

A COUNTEREXAMPLE: Imagine the consequences of trying to consciously micro-manage each and every muscle movement, in real time, in perfect sequence, while staying purely in the moment...

Memory-driven expectations are a fact of life.

They do, however, come with a significant TRADE-OFF:

Our human talent for anticipation makes for a fantastic end run around our built-in attentional limits, which are far more stringent then most of us realize. Unfortunately, that talent also leads to certain specific pitfalls in thinking.

SOME OF THESE are obvious...

Embarrassing, stupid mistakes are common while operating on fuzzy autopilot (I left the coffee on top of the car again!), or when a change in routine hasn't finished settling in, or when the rules for a new social situation aren't quite (!) what we expect them to be.

...WHILE OTHERS are much less obvious—at least, that is, until you look right at them:

As seen in this remarkable demonstration, having a set of pre-formed expectations can actually prevent us from seeing what is right in front of our faces. And, as the video also shows, most of us will never even know that we have missed seeing something important, and will even vigorously deny that such a thing could have happened.

Think on that for a moment.

The effect is more pronounced when strong emotion is involved. You can see for yourself by carrying out the following experiment:

Find a short article written by someone whose political positions you find upsetting, and read it through as closely as you can tolerate. Then, from memory, make a rough list of the arguments the author used in the piece. If you like, write a rebuttal. After you have finished, go back through the article and check explicitly to see whether the author argued exactly what you think he or she argued.

As in the attentional blindness video, most of us will find our initial comprehension has been sharply skewed by our existing expectations.

PLEASE NOTE! I am not saying the arguments in the upsetting piece cannot be rebutted; I am only saying that their true substance is easily missed in the heat of the moment. ALSO NOTE that the emotional blindness effect is in force whether you are for or against the sentiments displayed in the piece! As a general rule, the stronger and more emotionally charged your preconceptions are, the more likely you are to have misread what the author has actually written.

This, of course, is why politicians, performers, and advertisers work so hard to establish brand loyalty.

* * * * * * * * * *

So, if we are all condemned to navigate the world through a haze of memory-driven expectations, and if many of those expectations are limited, biased, or even flat-out wrong, then how can I possibly argue that human beings are not seriously flawed?

The answer turns out to be unexpectedly simple, and it lies in the direction of the comparison.

From a cognitive standpoint, we have a tendency to evaluate the real world's imperfect performance against our expectations, rather than the other way around. This is a critical distinction.

An action, an outcome, an object, or anything else in the real world is only said to be "flawed" or "imperfect" when it fails to live up to our expectations or desires.

We measure the degree of imperfection—"nearly perfect" versus "deeply flawed"—as a function of the size of the gap between reality and expectation, not as a measure of any intrinsic qualities possessed by the item in question.

Flaws and imperfections describe things that aren't there.

Why does it matter? Because reality doesn't care, and reality always wins out. Maintaining the comfort of our expectations may be easier than measuring what is really there, but in the long run that tends to lead to trouble. We create for ourselves a dangerous cultural blind spot, and an inability to find workable solutions, when we dismiss human nature as flawed or imperfect.

On the flip side, learning to look directly at ourselves may reveal hopeful solutions that have been sitting right under our noses all along, if we could but learn to see them.

People aren't as stupid as they (we) often look. We aren't imperfect, or even unintelligent, we are just emotionally driven, incredibly myopic creatures of habit. And on that count, we're certainly all stuck in the same boat.

I find this to be an oddly encouraging thought.

Blog News: What Have I Been Reading?

The official Bibliography Page is now up, over on the reference layer of the blog. Stop by and check it out!

PRESENTATION AND ACCESSIBILITY: NOTES ON NESTED STRUCTURE

Recursive blogging as an informational strategy. Where do we go from here?


In "Rationality Is Dead, Long Live Rationality," I argued on informational grounds that humans are not and cannot be intrinsically rational beings.

In "Oh, Humanity! Three Recalibrations of "Rational Self-Interest"," I declared a second, emotional basis for intrinsic irrationality, connected it to the informational grounds given above, and used the resulting combination to sketch a disturbingly accurate picture of the circular pattern of political discourse. In closing, I suggested that both flavors of irrationality arise unavoidably from a deeper logic, a Universal Logic of Human Nature if you will, that in turn is driven by the interaction of just four basic factors.

I have stated that illuminating that deeper logic is the purpose of this series.

However, many of my readers will have noted a number of important things that I have not done. I have not yet defined my terms, or laid out an overarching road map. Nor have I explained the significance of my unique perspective, placed its origins within a proper academic context, or supported any of my assertions with hard evidence.


Escaping a strategic bottleneck...

For a variety of reasons, I am operating outside of the standard academic template. Therefore, it is best to think of these two essays not as the launch of a dissertation, but as the opening pawn moves in a metaphorical game of chess. These moves engage the general reader’s attention, hint at the broad outlines of a complex attack, and lay the groundwork for the development of more consequential arguments that are waiting, as yet unspecified, on the back rank. The essays aim to capture the high-level flow of the game.

Implicit in my chess analogy, however, is that a lot of off-stage grunt work has necessarily already been done. Someone has already set up the board, manufactured a diverse array of pieces, invented a game around their movements, explained the rules, and developed entire schools of strategy. Attempting to front-load all of this information at an academically rigorous depth would crush one of this blog’s major goals, which is to render the high-level flow of the game [of human nature] as easily accessible to as wide a range of readers as possible. A better solution is needed.


...with an unorthodox solution.

I have decided to solve the staging problem by writing subroutines.

• Higher-level essays will continue to be featured, hopefully about twice a month (or as time and inspiration permit). But, for those who wish to dig deeper, I will also be continuously adding layers of supporting material: conceptual set-pieces, elaborations by request, terminological clarifications, back-and-forth discussions, scholarly citations, cross-linked references, and the like.

• For clarity, these will appear on a small circle of satellite blogs, new spaces dedicated to providing depth without inducing narrative whiplash. Sidebar links will be added as the structure solidifies.

• In order to facilitate browsing, all new off-stage content will be announced here, at center stage. These announcements will wind up sandwiched in between the high-level essays.

• Appropriate navigational tools will eventually appear in the sidebars of each blog.

• Lastly, internal cross-links will be added to existing posts as the constellation of subroutines continues to grow in size and power.


Variations on a recursive theme:

Careful readers will have noticed certain structural resemblances between my declared architectural strategy and my initial hints at the architecture of intelligence.

This is no coincidence.

On the one hand, the bottom-up creation of subroutines gives me the flexibility I need to develop the many pieces of my arguments in whatever order I want to write them, and the flexibility to answer questions as they are asked, without bogging everybody down in a sea of unwanted details. On the other, having a ready-made constellation to draw on will allow me to sustain the high-level flow of a complex narrative much more easily, by reaching down and tapping the appropriate subroutines as they are needed.


That’s the theory, anyway. We'll see if it works.

OH, HUMANITY! THREE RECALIBRATIONS OF “RATIONAL SELF-INTEREST”

How to account for the effects of emotion upon rationality.


(EXPANDED on 11/19/13)
(EDITED on 4/18/14)

So if you want to build a functioning society, and you need to use rational inquiry to figure out a proper design, but that design has to take into account the fact that none of the actors in the society will be intrinsically rational, what do you do?

You look past the rationality that isn’t there, to the wider mental universe that is.

______________________________


The notion of "rational self-interest" is central to Western economic and political thought, and for good reason, but it needs three major recalibrations if we are to restore functionality to either system.


I. The self is not only not singular, it is metaphorically diverse. Human analogical intelligence causes the cognitive sense of self to expand, variously encompassing areas such as family members, prized possessions, beliefs, and political worldviews—my sister, my guitar, my religion, my party affiliation, and so forth. Through a process described elsewhere, these identity-extensions have become structurally entangled with the instinctive machinery of the physiological self, resulting in the vast and subtle world of emotions.

EXAMPLE: That is to say, if you threaten my job or my political worldview, my body must react emotionally, in proportion to the intensity of the threat. Cognition steers, but instinct drives.


II. The self is irrational, per the logic of intelligence. Human intelligence automatically integrates concepts from the bottom up as well as from the top down. This means that locally functional bits of understanding are often habituated without any regard for their global consistency. The flexibility we gain from this procedural logic is wonderful—cultural immersion and focused study are each valid forms of learning, and exploration of contradictory new ideas is not difficult—but it comes with a tradeoff: we cannot help but accumulate identity facets that are not fully rationally consistent.

EXAMPLE: When interpreting events, your perspective as a friend will sometimes conflict with your perspective as a co-worker, or as a parent. Where you stand depends on where you sit.


III. The spotlight of attention is far narrower than the reach of the metaphorical self. All identity-related facets are defended by emotion, but your conscious awareness can only attend to a few of them at any given time. These two factors combine to make a fully rational accounting of the self doubly impossible, while also giving a false sense of rational consistency. The actual dynamics, which encompass classical rationality without being bound by it, are much more interesting.



SYNTHESIS: the three recalibrations in action!

On informational grounds alone, conceptual discrepancies are easy enough to miss. Rational introspection requires conscious attention in order to work; the narrowness of human attentional focus permits only small subsets of beliefs to be cross-checked at once; tenuous analogies are just as easily internalized as rigorous arguments; and deeply internalized bits of understanding are so easily taken for granted that they are often overlooked during testing.

But emotional effects add a whole new type of obscuration.

Instinct as emotion: The instinctive defenses are very old, and they were not designed to handle jumbled self-images, analogical or otherwise. Consequently, their physiological defenses of the jumbled identity constellation are applied to the human body simultaneously, across-the-board, and quite impartially, without regard to consistency of self-image.

This makes the overlapping emotional defense of many conflicting ideals a universal hallmark of the human condition.

How does it play out? Well, whenever aspects of your personal identity come into conflict, your instinctive machinery simply responds to the circular threat by rendering the areas of contention emotionally uncomfortable to think about. This is experienced as cognitive dissonance.

This applied instinctive pressure solves the problem of identity protection by deflecting the spotlight of your attention away from the identity conflict (see below), sending it in search of more comfortable waters. The force of this deflection is roughly proportional to three things: the personal significance of each identity facet in question (how important?), the urgency of the issue (how immediate?), and the proximity of the attentional spotlight (how relevant?) to the area of conflict.

EXAMPLE: "He was a good kid, he never would have tried to rob anybody. That isn't him in the surveillance video."

The multifaceted analogical structure of human identity ensures that many, many such aversion gradients are active at any given time. They operate for the most part under the attentional radar, although most of us do tend to notice the stronger surges.


The logic of deflection is straightforward... In the short run, it is simply less painful to maintain conflicting identity investments in the dark—they were adopted for good reason, and they work well enough when considered separately—than it is to risk losing any of them to the light of rational inquiry. Pretzel logic is preferable to ritual sacrifice.

...and its consequences are significant. Unfortunately, it also means that you don’t know what’s really down there, because the very areas that are most in need of rational introspection are among the hardest to reach. Sharp attentional limits, a mobile attentional spotlight, and ingrained identity-driven deflections combine to make us think we are more rational than we actually are, often with disastrous results. They also prevent many of us from noticing that our attention is being internally deflected, or even suspecting the existence of the emotional investments that are driving the deflection.


(Advertisers know this.)


Again, cognition steers, but instinct drives. Even if you have managed to notice that there are places your thoughts won’t go, there is no guarantee that applying cognitive counter-steering will take you there. Counter-steering takes mental energy; the emotional currents are too numerous, too quick, too dynamic, and too complex to be mapped; and the very reason the currents exist is to mask the conflicts that such a map would reveal. Moreover, in areas of extreme personal importance, the maelstrom of emotional deflection can become forceful enough to sweep the spotlight of attention entirely out of operating range, making certain lines of questioning literally unthinkable.


Achieving this protected status is the holy grail of political advertising.




AN APPLIED EXAMPLE: the three recalibrations in politics.

Consider how differently the old and new versions of “rational self-interest” handle the time-worn cliché of circular political discourse:

If you were to logically refute a cherished political position of mine, then the classical reaction of my “rational self-interested” self should be to reconsider. If I have been wrong, would I not improve my chances by accepting the better understanding that comes with the more accurate information?

In my "recalibrated" self, however, that option frequently loses out to faster, gut-level, emotional inclinations. Instinct dictates that I rescue my beleaguered identity-position, by:
1) saying “Oh yeah, but what about this?” while
2) slipping the anchor on my besieged attentional spotlight,
3) riding its automated deflection across the identity constellation;
4) settling into whatever emotionally fortified position it is drawn to (there is great strength in anger) and quickly returning fire; in hopes of
5) deflecting you from your initially effective attack, in exactly the same way that a mother bird whose nest is endangered feigns an injured wing to draw away predators.

6) Rinse, and repeat.

I never have to change my mind if I don't stay in one place long enough to witness any of my positions being destroyed around me. Is this not the classic pattern of political conversation?


Defense in Depth

These emotional tactics are deeply unsuited to figuring out what is going on the real world, but that is not their purpose. They are simply an unreasoned manifestation of instinct, an unthinking method of protecting already invested identity-beliefs, no matter how contradictory. This is often all that matters in the heat of battle.

And they are remarkably effective. So long as I am arguing with another person and not with an unfeeling real-world event like a car accident, my beliefs and I can evade existential conflict more or less indefinitely. If you follow me to my new position and refute that one too, then I simply repeat my escape maneuver, and around and around in circles we go.

What’s more, the defenses have defenses. If I have strongly self-identified as an intrinsically rational person (a belief only made possible, ironically enough, by the same sharp attentional limits that preclude intrinsic rationality), then any of your insinuations that my cherished beliefs might not actually be rationally consistent will be loftily dismissed, and my defense will be to find fault with you for being uncredentialed, unreasonable, or just plain mean.

Finally, if you do somehow manage to corner me rhetorically in spite of my tactics, then as a last resort I can simply disengage! I can change the subject, change the channel, leave the room, tune you out, put down the book, deny everything, or turn off the computer. Or, on a darker note, I can call in allies and attempt to bully you into submission.

Instinctive self-preservation is powerful stuff.


To be continued...

Fortunately, robust strategies exist for turning the vicious cycle against itself, but I will save them for another post. For now, I will merely hint that both the informational and the emotional aspects of human irrationality arise inexorably from the very same logic that enables us to construct rational arguments.

This human logic is universal—we really are all in this together!—and it unfolds as a direct consequence of putting analogical thinking, habitual pattern recognition, and a limited attention span into a body defended by instincts.



In other words, Pandora's box isn't a box at all, it's some sort of Klein bottle.

RATIONALITY IS DEAD, LONG LIVE RATIONALITY

Human beings are not and cannot be intrinsically rational. Here's why.


Every human being walks around with a personalized understanding of the world, cognitively constructed and then internalized over time, that is vast, analogically extensive, conceptually hazy, incomplete, and not strictly bound by the limits of classical rationality (which, it turns out, is only a special case of the larger and more general cognitive logic: think of rational and irrational numbers sharing space on the mathematician’s number line, only in more dimensions, and you’ll have the general idea). I’ll flesh out the specifics in another piece.

This is strike one against the baseline assumption of rationality. The mental architecture just doesn’t fit.

Everybody also walks around with a profoundly limited attention span, from a cognitive processing standpoint, that prevents us from being fully conscious of more than a tiny fraction of this understanding at once.

This is strike two against the assumption of rationality. Omniscience is unavailable.

So, without even having gotten into the complex effects of emotion—strike three, and the eventual heart of this series—we can already stick a fork in classical rationality as a default mode of operation for human beings, because rationality requires unambiguous domain limits to function properly (all the relevant data, and only the relevant data) and all human decisions are influenced by active volumes of analogically cross-threaded experiences that, like icebergs, cannot help but remain almost entirely below the waterline of consciousness.

Note that I am not claiming that people cannot make rational arguments, just that they are universally incapable of making rational decisions.

The distinction is important. Science, philosophy, and other systemic interrogations of the world advance our understanding by relying upon rational arguments. Arguments are powerful because they are constructed from information that is both bounded and verifiable, meaning that their internal logic can be tested philosophically, a priori, in accordance with the rules of rationality. Consistency carries no guarantee of success—science routinely eviscerates huge numbers of logically valid arguments, proving them experimentally false and incrementally advancing human understanding—but consistency is a necessary precondition if meaningful scientific testing (whether of the professional or back yard tinkering sort) is to take place. Internal structure matters.

By contrast, human decisions are made “inside the head” using information that is bounded but not verifiable, even in principle, given the logical interplay of conceptual architecture, analogical cross-threading, and attentional limits. This is especially true of the personal decision to accept/adopt any given rational argument, without which its rationality will find no purchase. The decision to do so is often mistaken for evidence of intrinsic rationality itself, when in fact it is evidence of just the opposite: without the rigorous mental training needed to achieve a degree of logical fluency, and without a cultivated interest in doing so, that “rational” reaction is easily swamped by other informational and emotional considerations that are supplied by the wider cognitive logic. Once again, internal structure matters.

To sum up, several points:

1) The world yields up its secrets to sustained rational inquiry, but humans are not and cannot be intrinsically rational beings;

2) While humans are capable of exercising rationality in limited domains through the power of rational argument, and while we can decide to act in accordance with those rational guidelines, the decision to do so is not and cannot ever be rational (although it is likely to be pragmatic);

3) Criticizing your opponents for being irrational is therefore exactly as meaningless as criticizing them for breathing (a point that provides a nicely barbed defense against airs of superiority);

4) Criticizing their arguments is always fair game.

A corollary:

The widespread existence of a deeper layer of decision-making logic is triply confirmed by the conspicuous absence of rational argument from political and other effective mass market advertising, by the structural conformity of the current appeals that are being used, and by the enormous amounts of money poured into constructing them.

An aphorism or two:

“Humans can make rational arguments, but never rational decisions.”

“There are no rational people, there are only rational arguments.”

A handful of policy recommendations:

1) It is terribly important to teach rationality in schools, precisely because it is not an innate function, and because it is our only reliable means of interrogating the world;

2) It is equally important to teach that rationality is not innate (especially your own!), but is rather a special case within a much wider and wilder suite of cognitive operations whose influence cannot be turned off;

3) Emphasizing pure human rationality over the wider cognitive logic, rather than placing it in its proper context, is not only guaranteed not to solve persistent human problems, it will in fact make them worse.

And finally, a short restatement of purpose:

ILLUMINATING THAT WIDER CONTEXT IS THE PURPOSE OF THIS DEVELOPING SERIES.


Update (11/13/13): A second post, Oh, Humanity! Three Recalibrations of “Rational Self-Interest” is now available. It introduces the second type of irrationality (emotional) and touches on how both kinds interact to shape our politics.

Bach, Universality, and the Power of Historical Fiction

The following argument is an I assignment I wrote for a music history class last fall, but it says some interesting things about universality in music that might be worth sharing. So here it is!

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BACH, UNIVERSALITY, AND THE POWER OF HISTORICAL FICTION

In chapter four of his 1989 book The Music of Johann Sebastian Bach: the Sources, the Style, and the Significance, Robert L. Marshall argues that even though the appeal of his works is relatively limited, the musical talent of J. S. Bach is truly universal in scope and is therefore much less confined to the cumulative but backward-looking mastery of Baroque tradition than is commonly thought. A sympathetic point of view can be implicitly discerned within the twelfth chapter of James R. Gaines’s 2005 book Evening in the Palace of Reason: Bach Meets Frederick the Great in the Age of Enlightenment, and the contrapuntal resonances between the two works are further sustained and subtly amplified by the additional context provided by Morris’s 2005 review of Gaines.

Interestingly, while the conclusion ultimately reached by Marshall has a profound and insightful validity, the strength of his supporting argument suffers somewhat from a misplaced focus and an overall lack of clear direction. Marshall’s attempts to define the universality of Bach wander so unpredictably and for so long in a tangle of competing considerations—is it the music’s popular appeal, its brilliant stylistic construction, or the transcendent power of the mind behind its conceptual approach?—that the resultant loss of clarity obscures much of the impact of an otherwise excellent conclusion, as does its apologetic and scattered presentation.

Marshall begins his exploration of the topic by declaring that he wishes to de-emphasize the aspect of appeal (p. 66), but then he immediately veers into a tangential discussion of the popular accessibility of Bach’s music, both then and now. The appeal of various subsets of Bach’s output—cantatas, masses, and concerti, among others—is evaluated as a combined function of dramatic impact, intended audience (“public” or otherwise?), and effective media popularization. Ultimately, Marshall winds up arguing that while many of these works “provide ample testimony of his genius” (69), and while the Mass in B Minor in particular “occupies a unique place in Bach’s oeuvre…that gives it special significance in any consideration of the composer’s universality” (69), taken collectively these works do not provide sufficient grounds to justify the claim of Bach’s universality on their appeal alone.

Having reached this somewhat confusing conclusion, Marshall now switches musical subsets, suggesting that “the actual source of Bach’s supreme stature at the pinnacle of Western culture…is to be found in…the awesome collections of instrumental music” (69). But rather than actually locating the universality of Bach in this music, as he seems about to do, he uses the idea of performance-oriented study of these works to segue into a loosely intermingled discussion of the philosophy behind the music, which I take to be his real target. While the imprecision of this transition may create the unfortunate impression that Marshall is moving his definitional goalposts, the longer-term goal of illuminating the extraordinary seamless stylistic meld of philosophy, intelligence, talent, and execution that universally informed the production of Bach’s music remains unchanged, if not strongly articulated.

Indeed, the point Marshall is dancing around, but which he never quite trusts his supporting argument enough to make decisively, is that the true magic of Bach’s music is found in the remarkable scope, consistency, economy, and artistry of its internal and external coherence, and that it is precisely this coherence which appeals so greatly to anyone who has dipped far enough beneath the surface, whether through listening, study or performance of Bach, to appreciate the musical uniqueness of its extent. It is as if Bach took the many established musical facets which had been carefully and individually polished by other masters, mentally assembled them according to an entirely unexpected but remarkably elegant new three-dimensional pattern, and then filled in what remained by deriving the simple laws which governed the formation of the entire musical crystal. This effectively allowed him to write at whatever stylistic intersections he wished (including several which had not yet been attempted!) with great economy and unsurpassed artistic clarity.

The significance of this stunning achievement resonates universally for two interrelated reasons. Firstly, as partially indicated by the related writings of Douglas Hofstadter (which are also mentioned in Morris’s review of Gaines below), the deep symmetries and patterns Bach reveals in his music are closely aligned with some of the fundamental workings of human intelligence, and this renders his music both deeply familiar and beautiful to those who are open to Bach’s complex layers of audible and logical symmetry. At the same time, by revealing profoundly simple linkages between apparently diverse musical styles, Bach’s unique musical perspective reinforces the Enlightenment belief in Reason’s ability to discern the fundamental order of the universe; thus, the very scope of his achievement can provide philosophical inspiration to those who seek deeply simple solutions to persistent and intractably complex problems, but also to those who merely search for graspable meaning in daily events.

None of this is ever stated so explicitly and unambiguously by Marshall; whether his seeming inability to do so reflects trouble finding the right words, a personal ambivalence towards the idea of external and verifiable truths, or (more likely, given the bald fact of the chapter’s title) a calculated judgment about the prevailing winds of academic philosophy at the time of publication, it certainly diminishes the effect of the chapter in a way that Bach himself probably would not have countenanced, as will be seen in Gaines’s quasi-historical treatment below. But perhaps more tellingly, scattered throughout the remainder of Marshall’s chapter are several clues that can be assembled in support of both my assessment of his implied position and his ambivalence in presenting it.

Passing mentions of the Age of Reason and the Enlightenment age are found on page 73, but appear too late to provide any important philosophical context to the introduction of the aesthetic principle of “Unity of Affect” (p. 70) and the attendant importance of “logic and consistency in the development of musical ideas.” After a short detour toward aesthetic transcendentalism, “universal validity” briefly re-emerges (71) to be tentatively declared the source of Bach’s universality, but the halting and almost apologetic manner of the declaration robs it of any real weight. The concept does return with more force on the next page: “[These phrases] all document Bach’s conviction that music…is constructed according to God-given, that is, eternally and universally valid, principles, call them “laws”…[and that Bach’s purpose] was to demonstrate these universal musical laws in operation” (72), and is almost definitively established on page 73, but its effectiveness is sapped once again by a rather timid framing:

…I think it may be fair to say that Bach’s unification of linear counterpoint and tonal harmony represents an accomplishment in the art of music hardly less impressive than that which would be achieved if a physicist someday would realize Albert Einstein’s hope of formulating a theory—a unified field theory—in which the nature of the relationships obtaining among the various forces at work in the cosmos—gravitation, magnetism, electricity, and so on—were precisely defined and established once and for all. But I suspect I may be rushing in where angels properly fear to tread.

The effect of this back-and-forth pattern greatly weakens what should be a much stronger thrust toward a decisive conclusion.

A final piece of evidence for Marshall’s indirectly stated support for coherence comes from his choice to include a neat bit of analysis (76-9), in which he shows how the opening chorus from one of Bach’s cantatas (BWV 78) is an effortless structural synthesis of several stylistic traditions—several of which, moreover, appear at first glance to be mutually exclusive—although again he softens the impact by closing the chapter abruptly with an almost offhand description of how the new, lighter musical lingua franca being developed by the next generation of composers will end up leaving Bach’s magisterial contrapuntal mastery far behind. Nonetheless, it is clear from the above hints that Marshall believes historical circumstances combined in some way with the religion, philosophy, talent, intellect, and industriousness of Bach to produce a unified understanding of music that was qualitatively different from that of his contemporaries, and quite justifiably beyond the vast majority of his successors as well.

But Marshall is not entirely out of line in his equivocation; broad philosophical extrapolations are not really the province of the most rigorous scholarly writings about music, as they are often impossible to nail down with definitive sourcing. Fortunately, alternative venues are available. A judicious loosening of the academic ties that bind logical inferences firmly to hard evidence is not without its disadvantages, but as the excerpted chapter from James R. Gaines’s Evening in the Palace of Reason illustrates, the many advantages conferred by a successful such attempt make various gradations of this form well worth exploring.

While the narrative constraints imposed by a marketable appeal to a less educated audience can at times overwhelm authorial respect for historical and/or scientific accuracy (for an extreme case, see Alexander Dumas’s The Three Musketeers, or virtually any science fiction movie), in careful hands they can also result in enough of an accurate taste that the end product actually creates a renewed desire to experience more of the real thing. The power of this lever is potentially enormous; recall that Marshall touched on Bach’s popular appeal before taking his argument anywhere else. A successful presentation can result in a ground swell of interest which actually has the potential to alter the course of future scholarly work, for it can generate more widespread performance opportunities or even inspire the donation of targeted research funding. In either case, the vitality and relevance of the scholarly community in question are expanded, and so the risks inherent in this type of approach (which include being branded a “popular writer” by your academic peers) are generally trumped by the larger rewards.

Gaines is surely not the first careful author to write for a wider audience about Bach, and he is not even the first to explore the significance of the Musical Offering in this format; as both he and his reviewer Morris point out, Douglas Hofstadter did so brilliantly in 1979 with Gödel, Escher, Bach: An Eternal Golden Braid, a justifiably renowned exploration of the links between music, logic, mathematics, and intelligence. Gaines frames his more conventionally centered discussion of the Musical Offering as the dramatic centerpiece of a double biographical format.

The narrative balance required by his chosen approach does not come without some risk of academic distortion—as Morris (who notes the trade-off) tells us, the volume of biographical documentation for J. S. Bach is far surpassed by that concerning Frederick the Great, leading to interesting problems of selection—but it also provides compensating payoffs. The dramatic positioning of the Musical Offering at the confluence of the two biographical accounts makes Gaines’s account quite memorable, and it also allows him to bring to bear the previously presented philosophical, social, and religious backgrounds of the two men as he interprets the significant subtext of the entire exchange.

The nature of Gaines’s interpretation provides a nicely supportive counterpoint to Marshall’s not-quite-stated defense of “universality through coherence” above, as does Morris’s perfectly in-line description of the Musical Offering itself as “a contrapuntal achievement that uniquely allies cerebral and auditory beauty” (review, p. 1). Gaines paints a picture of Bach as an unshakably pious but “hardheaded, hot-tempered man” (241) whose industrious and superbly reasoned approach to the craft of counterpoint is backed by an existential religious faith, a combination that provided him with both the capability and the intransigence to rebuke a sitting monarch (using his own theme!) with an extraordinary gift of compositional genius. This devotional foundation may have prevented Bach from fully embracing the questioning spirit of the Enlightenment, and thus may have aided in cutting him off from the newly evolving musical styles of Berlin, but it also lent his musical reasoning an unmatched depth of certainty as he strove to illuminate the bottomless coherence of his God.