Montag, 2. Juli 2018

Variations on a theme

The bottom line is that invention is much more like falling off a log than like sawing one in two. Despite Thomas Alva Edison's memorable remark, "Genius is 2 percent inspiration and 98 percent perspiration", we're not all going to become geniuses simply by sweating more or resolving to try harder. A mind follows its path of least resistance, and it's when it feels easiest that it is most likely being its most creative. Or, as Mozart used to say, things should "flow like oil"-and Mozart ought to know! Trying harder is not the name of the game; the trick is getting the right concept to begin with, so that making variations on it is like taking candy from a baby. 

Uh-oh-now I've given the cat away! So let me boldly state the thesis that I shall now elaborate: Making variations on a theme is really the crux of creativity.


It's not that we say to ourselves, "I think I shall now slip from one concept into a variation of it"; indeed, that kind of deliberate, conscious slippage is most often quite uninspired and infertile. "How to Think" and "How to Be Creative" books-even very thoughtful ones such as George Polya's How to Solve It- are, for that reason, of little use to the would-be genius.

Strange though it may sound, nondeliberate yet nonaccidental slippage permeates our mental processes, and is the very crux of fluid thought. That is my firmly held conviction. This subconscious manufacture of "subjunctive variations on a theme" is something that goes on day and night in each of us, usually without our slightest awareness of it. It is one of those things that, like air or gravity or three-dimensionality, tend to elude our perception because they define the very fabric of our lives.

To make this concrete, let me contrast an example of "deliberate" slippage with an example of "nondeliberate but nonaccidental" slippage. Imagine that one summer evening you and Eve Rybody have just walked into a surprisingly crowded coffeehouse. Now go ahead and manufacture a few variants on that scene, in whatever ways you want. What kinds of things do you come up with when you deliberately "slip" this scene into hypothetical variants of itself?

If you're like most people, you'll come up with some pretty obvious slippages, made by moving along what seem to be the most obvious "axes of slippability". Typical examples are: 

I could have come with Ann Yone instead of Eve Rybody. 
We could have gone to a pancake house instead of a coffeehouse. 
The coffeehouse could have been nearly empty instead of full. 
It could have been a winter's evening instead of a summer's evening. 

Now contrast your variations with one that I overheard one evening this past summer in a very crowded coffeehouse, when a man walked in with a woman. He said to her, "I'm sure glad I'm not a waitress here tonight!" This is a perfect example of a subjunctive variation on the given theme-but unlike yours, this one was made without external prompting, and it was made for the purposes of communication to someone. The list above looks positively mundane next to this casually tossed-off remark. And the remark was not considered to be particularly clever or ingenious by his companion. She merely agreed with the thought by saying "Yeah." It caught my attention not so much because I thought it was clever, but mostly because I am always on the lookout for interesting examples of slippability.

I found this example not just mildly interesting, but highly provocative. If you try to analyze it, it would appear at first glance to force you as listener to imagine a sex-change operation performed in world record time. But when you simply understand the remark, you see that in actuality, there was no intention in the speaker's mind of bringing up such a bizarre image. His remark was much more figurative, much more abstract. It was based on an instantaneous perception of the situation, a sort of "There-but-for-thegrace-of-God-go-I" feeling, which induces a quick flash to the effect of "Simply because I am human, I can place myself in the shoes of that harried waitress-therefore I could have been that waitress." Logical or not, this is the way our thoughts go.

So when you look carefully, you see that this particular thought has practically nothing to do with the speaker, or even with the waitresses he sees. It's just his flip way of saying, "Hmm, it sure is busy here tonight." And that's of course why nobody really is thrown for a loop by such a remark Yet it was stated in such a way that it invites you to perform a "light" mapping of him onto a waitress, just barely noticing (if at all) that there is a sex difference. What an amazingly subtle thought process is involved here!

And what is even more amazing (and frustrating) to me is how hard it is to point out to people how amazing it is! People find it very hard indeed to see what's amazing about the ordinary behavior of people. They cannot quite imagine how it might have been otherwise. It is very hard to slip mentally into a world in which people would not think by slipping mentally into other worlds-very hard to make a counterfactual world in which counterfactuals were not a key ingredient of thought.

Another quick example: I was having a conversation with someone who told me he came from Whiting, Indiana. Since I didn't know where that was, he explained, "Whiting is very near Chicago-in fact, it would be in Illinois if it weren't for the state line." Like the earlier one, this remark was dropped casually; it was certainly not an effort to be witty. He didn't chuckle, nor did I. I simply flashed a quick smile, signaling my understanding of his meaning, and then we went on. But try to analyze what this remark means! On a logical level, it is somewhat like a tautology. Of course Whiting would be in Illinois if the Illinois state line made it be so-but if that's all he meant, it is an empty remark, because it holds just as well for cities thousands of miles from Chicago. But clearly, the notion he had in mind was that there is an accidental quality to where boundary lines fall, a notion that there are counterfactual worlds "close" to ours, worlds in which the Illinois-Indiana line had gotten placed a couple of miles further east, and so on. And his remark tacitly assumed that he and I shared such intuitions about the impermanence and arbitrariness of geographical boundary lines, intuitions about how state lines could "slip".

Remarks like this betray the hidden "fault lines of the mind"; they show which things are solid and which things can slip. And yet, they also reveal that nothing is reliably unslippable. Context contributes an unexpected quality to the knobs that are perceived on a given concept. The knobs are not displayed in a nice, neat little control panel, forevermore unchangeable. Instead, changing the context is like taking a tour around the concept, and as you get to see it from various angles, more and more of its knobs are revealed. Some people get to be good at perceiving fresh new knobs on concepts where others thought there were none, just as some people get to be good at perceiving mushrooms in a forest where others see none, even when they stare mightily.

It may still be tempting to think that for each well-defined concept, there must be an "ultimate" or "definitive" set of knobs such that the abstract space traced out by all possible combinations of the knobs yields all possible instantiations of the concept. A case in point is the concept of the letter V A'. The typographically naive might think that there are four or five knobs to twiddle here, and that's all. However, the more you delve into letter forms, the more elusive any attempt to parametrize them mathematically becomes. One of the most valiant efforts at "knobbifying the alphabet" has been the letterform-defining system called "Metafont", developed at Stanford by the well-known computer scientist Donald Knuth.

Knuth's purpose is not to give the ultimate parametrization of the letters of the alphabet (indeed, I suspect that he would be the first to laugh at the very notion), but to allow a user to make "knobbed letters "-we could call them letter schemas. This means that you can choose for yourself what the variable aspects of a letter are, and then, with Metafont's aid, you can easily construct knobs that allow those aspects to vary. This includes just about anything you can think of: stroke lengths, widenings or taperings of strokes, curvatures, the presence or absence of serifs, and so on. The full power of the computer is then at your disposal; you can twiddle away to your heart's desire, and the computer will generate all the products your knob-settings define.

Going further than letters in isolation, Knuth then allowed letters to share parameters-that is, a single "master knob" can control a feature common to a group of related letters. This way, although there may be hundreds of knobs when you count the knobs on all the control panels of all the letters of the alphabet, there will be a far smaller number of master knobs, and they will have a deeper and more pervasive influence on the whole alphabet. What happens, in effect, is that by twiddling the master knobs alone, you have a way of drifting smoothly through a space of typefaces.


One of Knuth's main theses is that with computers, we now are'in the position of being able to describe not just a thing in itself, but how that thing would vary.


One way to imagine how slippability might be realized in the mind is to suppose that each new concept begins life as a compound of previous concepts, and that from the slippability of those concepts, it inherits a certain amount of slippability. That is, since any of its constituents can slip in various ways, this induces modes of slippage in the whole. Generally, letting a constituent concept slip in its simplest ways is enough, since when more than one of these is done at a time, that can already create many unexpected effects. Gradually, as the space of possibilities of the new concept- the implicosphere-is traced out, the most common and useful of those slippages become more closely and directly associated with the new concept itself, rather than having to be derived over and over from its constituents. This way, the new concept's implicosphere becomes more and more explicitly explored, and eventually the new concept becomes old and reaches the point where it too can be used as a constituent of fresh new young concepts.


This is an important idea: the test of whether a concept has really come into its own, the test of its genuine mental existence, is its retrievability by that process of unconscious recall. That's what lets you know that it has been firmly planted in the soil of your mind. It is not whether that concept appears to be "atomic", in the sense that you have a single word to express it by. That is far too superficial.


The point is that the concept itself has been reed-this much is proven by the fact that it acts as a point of immediate reference; that my memory mechanisms are capable of using it as an "address" (a key for retrieval) under the proper circumstances. The vast majority of our concepts are wordless in this way, although we can certainly make stabs at verbalizing them when we need to.


Careful analysis leads one to see that what we choose to call a new theme is itself always some sort of variation, on a deep level, of previous themes. The trick is to be able to see the deeply hidden knobs!


My own mental image of the creative process involves viewing the organization of a mind as consisting of thousands, perhaps millions, of overlapping and intermingling implicospheres, at the center of each of which is a conceptual skeleton. The implicosphere is a flickering, ephemeral thing, a bit like a swarm of gnats around a gas-station light on a hot summer's night, perhaps more like an electron cloud, with its quantummechanical elusiveness, about a nucleus, blurring out and dying off the further removed from the core it is (Figure 12-5). If you have studied quantum chemistry, you know that the fluid nature of chemical bonds can best be understood as a direct consequence of the curious quantummechanical overlap of electronic wave functions in space, wave functions belonging to electrons orbiting neighboring nuclei. In a metaphorically similar way, it seems to me, the crazy and unexpected associations that allow creative insights to pop seemingly out of nowhere may well be consequences of a similar chemistry of concepts with its own special types of "bonds" that emerge out of an underlying "neuron mechanics".

Novelist Arthur Koestler has long been a champion of a mystical view of human creativity, advocating occult views of the mind while at the same time eloquently and objectively describing its workings. In his book The Act of Creation, he presents a theory of creativity whose key concept he calls "bisociation"-the simultaneous activation and interaction of two previously unconnected concepts. This view emphasizes the comingtogether of two concepts, while bypassing discussion of the internal structure of a single concept. In Koestler's view, something new can happen when two concepts "collide" and fuse- something not present in the concepts themselves. This is in keeping with Koestler's philosophy that wholes are somehow greater than the sum of their parts.

By contrast, I have been emphasizing the idea of the internal structure of one concept. In my view, the way that concepts can bond together and form conceptual molecules on all levels of complexity is a consequence of their internal structure. What results from a bond may surprise us, but it will nonetheless always have been completely determined by the concepts involved in the fusion, if only we could understand how they are structured. Thus the crux of the matter is the internal structure of a single concept and how it "reaches out" toward things it is not. The crux is not some magical, mysterious process that occurs when two indivisible concepts collide; it is a consequence of the divisibility of concepts into subconceptual elements. As must be clear from this, I am not one to believe that wholes elude description in terms of their parts. I believe that if we come to understand the "physics of concepts", then perhaps we can derive from it a "chemistry of creativity", just as we can derive the principles of the chemistry of atoms and molecules from those of the physics of quanta and particles. But as I said earlier, it is not just around the corner. Mental bonds will probably turn out to be no less subtle than chemical bonds. Alan Turing's words of cautious enthusiasm about artificial intelligence remain as apt now as they were in 1950, when he wrote them in concluding his famous article "Computing Machinery and Intelligence": "We can only see a short distance ahead, but we can see plenty there that needs to be done."


Some readers objected to the slogan of this column-that making variations on a theme is the crux of creativity. They felt-and quite rightly -that making variations (i.e., twisting knobs) is as easy as falling off a log. So how can genius be that easy? Part of the answer is: For a genius, it is easy to be a genius. Not being a genius would be excruciatingly hard for a genius. However, this isn't a completely satisfactory answer for people who pose this objection. They feel that I am unwittingly implying that it is easy for anybody to be a genius: after all, a crank can crank a knob as deftly as a genius can. The crux of their objection, then, is that the crux of creativity is not in twiddling knobs, but in spotting them!

Well, that is exactly what I meant by my slogan. Making variations is not just twiddling a knob before you; part of the act is to manufacture the knob yourself. Where does a knob come from? The question amounts to asking: How do you see a variable where there is actually a constant ? More specifically: What might vary, and how might it vary? It's not enough to just have the desire to see something different from what is there before you. Often the dullest knobs are a result of someone's straining to be original, and coming up with something weak and ineffective. So where do good knobs come from? I would say they come from seeing one thing as something else. Once an abstract connection is set up via some sort of analogy or reminding-incident, then the gate opens wide for ideas to slosh back and forth between the two concepts.

A simple example: A friend and I noticed a fuel-delivery truck pulling into a driveway, and on it was very conspicuously printed "NSF", standing for "North Shore Fuel". However, to us those letters meant "National Science Foundation" as surely as "TNT" means "trinitrotoluene" to Eve Rybody. Now, we could have just let the coincidence go, but instead we played with it. We envisioned a National Science Foundation truck pulling up to a research institute. The driver gets out of the cab, drags a thick flexible hose over to a hole in the wall of a building and inserts it, then starts up a loud motor, and pumps a truckload of money-presumably in large bills-into the cellar of the building. (Wouldn't it be nice if grants were delivered that way?) This vision then led us to pondering the way that money actually does flow between large institutions: usually as abstract, intangible numbers shot down wires as binary digits, rather than as greenbacks hauled about in large trucks.

This very small incident serves well to illustrate how a simple reminding- incident triggered a series of thoughts that wound up in a region of idea-space that would have been totally unanticipable moments before. All that was needed was for an inappropriate meaning of "NSF" to come to mind, and then to be explored a bit. Such opportunities for being reminded of something remote- such double-entendre situations-occur all the time, but often they go unobserved. Sometimes the ambiguity is observed but shrugged off with disinterest. Sometimes it is exploited to the hilt. In this example, the result was not earthshaking, but it did cast things in a new light for both of us, and the image amused us quite a bit. And this way of exploiting serendipity-that is, exploiting coincidences and unexpected perceived similarities-is typical of what I consider the crux of the creative process.

Serendipitous observation and quick exploration of potential are vital elements in the making of a knob. What goes hand in hand with the willingness to playfully explore a serendipitous connection is the willingness to censor or curtail an exploration that seems to be leading nowhere. It is the flip side of the risk-taking aspect of serendipity. It's fine to be reminded of something, to see an analogy or a vague connection, and it's fine to try to map one situation or concept onto another in the hopes of making something novel emerge-but you've also got to be willing and able to sense when you've lost the gamble, and to cut your losses. One of the problems with the ever-popular self-help books on how to be creative is that they all encourage "off-the-wall" thinking (under such slogans as "lateral thinking", "conceptual blockbusting", "getting whacked on the head", etc.) while glossing over the fact that most off-the-wall connections are of very little worth and that one could waste lifetimes just toying with ideas in that way. One needs something much more reliable than a mere suggestion to "think zany, out-of-the-system thoughts".

Frantic striving to be original will usually get you nowhere. Far better to relax and let your perceptual system and your category system work together unconsciously, occasionally coming up with unbidden connections. At' that point, you-the lucky owner of the mind in question-can seize the opportunity and follow out the proffered hint. This view of creativity has the conscious mind being quite passive, content to sit back and wait for the unconscious to do its remarkable broodings and brewings.

The most reliable kinds of genuine insight come not from vague reminding experiences (as with the letters "NSF"), but from strong analogies in which one experience can be mapped onto another in a highly pleasing way. The tighter the fit, the deeper the insight, generally speaking. When two things can both be seen as instances of one abstract phenomenon, it is a very exciting discovery. Then ideas about either one can be borrowed in thinking about the other, and that sloshing-about of activity may greatly illumine both at once. For instance, such a connection (i.e., mapping) -between sexism and racism-resulted in my "Person Paper" (Chapter 8). Another example is Scott Kim's brilliant article "Noneuclidean Harmony", in which mathematics and music are twisted together in the most amazing ways. It can be found in The Mathematical Gardner, an anthology dedicated to Martin Gardner, edited by David Klarner.

A mapping-recipe that often yields interesting results is projection of oneself into a situation: "How would it be for me?" This can mean a host of things, depending on how you choose to inject yourself into the scene, which is in turn determined by what grabs your attention. The man who focused in on the bustling activity in the coffeehouse and said, "I'm sure glad I'm not a waitress here tonight!" might instead have been offended by the sounds reaching his ears and said, "If I were the owner here, I'd play less Muzak" -or he might have zeroed in on someone purchasing a brownie and said, "I wish I were that thin." People are remarkably fluid at seeing themselves in roles that they self-evidently could never fill, and yet the richness of the insights thus elicited is beyond doubt.

When I first heard the French saying Plus ga change, plus c'est la meme chose, it struck me as annoyingly nonsensical: "The more it changes, the samer it gets" (in my own colloquial translation). I was not amused but nonetheless it stuck in my mind for years, and finally it dawned on me that it was full of meanings. My favorite way of interpreting it is this. The more different manifestations you observe of one phenomenon, the more deeply you understand that phenomenon, and therefore the more clearly you can see the vein of sameness running through all those different things. Or put another way, experience with a wide variety of things refines your category system and allows you to make incisive, abstract connections based on deep shared qualities. A more cynical way of putting it, and probably more in line with the intended meaning, would be that superficially different things are often boringly the same. But the saying need not be taken cynically.

Seeing clear to the essence of something unfamiliar is often best achieved by finding one or more known things that you can see it as, then being able to balance these views.


The cycle shown above spells out what I intend by the phrase "making variations on a theme", and it is this loop that I am suggesting is the crux of creativity. The beauty of it is that you let your memory and perceptual mechanisms do all the hard work for you (pulling concepts from dormancy); all you do is twiddle knobs. And I'll let you decide what this odd distinction is between something called "you" and the hard-working mechanisms of "your memory".


So in that sense I am gravely doubtful about courses or books that promise to improve your thinking style or capabilities. Sure, you can add new ideas-but that's a far cry from adding pizzazz. The mind's -'perceptual and category systems are too much at the "subcognitive" level to be reached via cognitive- level training techniques. If you are old enough to be reading this book, then your deep mental hardware has been in place for many years, and it is what makes your thinking-style idiosyncratic and recognizably "you".

When a new idea is implanted in a mind, an implicosphere grows around it. Since this means, in essence, the linking-up of this new idea with older ideas, I call it "diffusion in idea-space".


Slippage of thought is a remarkably invisible phenomenon, given its ubiquity. People simply don't recognize how curiously selective they are in their "choice" of what is and what is not a hinge point in how they think of an event. It all seems so natural as to require no explanation.

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