Early Stormy Thoughts

I would like to talk about turbulence. I think my life is not turbulent, though it has turbulence in it. The plane ride is smooth and (relatively) comfortable, and then suddenly the plane begins to bounce about, and my hands tighten on the armrests and my toes curl under trying to grasp on to the soles of my shoes that I have planted to the floor of the airplane. What happened? The pilot from the cockpit announces that we have come upon “a bit of turbulence” and we should fasten our seat belts and refrain from walking about the cabin, even if I have to use the bathroom! What happened? When asked what he would ask God, Heisenberg is said to have responded, “When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe He will have an answer for the first.” What happened up there that bounced the plane as if it were a mere  toy in the hands of some giant. That seems to me Heisenberg’s unanswered question.
     Turbulence is the chaotic motion of air and water. Turbulence characterizes hurricanes and tornadoes and ocean waves breaking onto shore; turbulence is the smoke that rises from a cigarette or the movement of air during airplane flight that causes the plane to jounce and me become alarmed. Turbulence is a “wild erratic dance of fluids.” Drip by drip the water drops from my faucet and each drop lands exactly in the same location., but the more I turn the handle the more turbulent the flow becomes. Suddenly drops appear somewhat randomly on the sides of the sink: a drop here and a drop there. Why? How? How there? Why now? I think we have the capacity to predict the movement of water in a lazily flowing river, but the challenge of the movement of the rapids assumes uncertainty. Somehow, in a situation, depending on speed, pressure, velocity, viscosity, etc., the particles interact in ways that are ultimately unpredictable. Where is this storm heading: we remain essentially unsure. There would be great benefit to human life (and safety) if we were able to to predict the movement of such flow for such phenomena as hurricanes, etc. But, in fact, we cannot do so with any high degree of certainty. In fact, in my experience the weather people are fairly consistently inaccurate: they predict a heavy snowfall and no snow falls; they warn that a hurricane should strike land at a certain hour and alas, with good fortune the storm heads out to sea. The ten-day forecast is usually good for at least several hours! We imagine that everything about our natural world will follow predictable patterns and that formulas can be written to enable accurate prediction. But as yet the problem of turbulence has not yet been solved.
     The Navier-Stokes equation, developed independently by Claude-Louis Navier and George Gabriel Stokes in the early 1800s,  measure the motion of fluid—and these formulas, used in a wide variety of instances including weather forecasting, might be used to predict turbulent flow. In the novel The Mathematician’s Shiva, by Stuart Rojstaczer, (2014) the narrator, a PhD topologist and the son of a world famous mathematician who has spend her life attempting to solve the Navier-Stokes formulas, protests, “Understanding a physical phenomenon like turbulence ultimately means predicting its behavior, or at the very least understanding just what can and what cannot be predicted over time. Prediction means quantification of the basic physical processes that drive turbulence. But this is something we cannot currently do with any reasonable degree of sophistication” Navier-Stokes occupies a central place in mathematical culture: a solution to the Navier Stokes would earn its solver the Millennium Prize—a Nobel-like prize in mathematics worth one million dollars. A solution to the Navier-Stokes would show that the Navier Stokes formula works in all cases. So far, however, Navier-Stokes remains unsolved. Turbulence, when a particle becomes chaotic and unstable behaving, cannot be accurately predicted. Richard Feynman has said that turbulence is the last unknown in physics: “ . .  given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time. Now the point is that this length of time is not very large . . . It turns out that in only a very, very tiny time we lose all our information . . . We can no longer predict what is going to happen . . .” Rojstaczer’s narrator, the topologist, says that “Tornados start from small disturbances that don’t mean a thing and almost always dissipate. But somehow one particular random bad event attracts others and all of them grow and attract some nasty stuff.” Tornadoes, hurricanes, and air turbulence cause great tragedy. If we understand turbulence, then we can predict its behavior; thus far all attempts have failed to solve the Navier-Stokes formulas.
     Turbulence is the movement of the particles that comprise air and water. Navier-Stokes attempts to predict the movement of these substances that are, of course, comprised of ‘particles.’ Sasha says in the novel, “The movement of such particles depends on so many factors: density, velocity, speed, viscosity, pressure . . . From the standpoint of a mathematician . . . the problem of turbulence is fundamentally one of being certain, to prove, that there exists in the universe a set of descriptors, in this case partial differential equations, that can encompass the behavior of fluids as they move at velocities that cause chaos. . .”. But in fact, the Navier-Stokes formula, which seems to be based on Newton’s second law of motion, has not been solved: we don’t know that it works to describe the motion of fluids “when they flow as lazily as rivers as when they “dance around an airplane wing” (208).  Feynman says, “If water falls over a dam, it splashes. If we stand nearby, every now and then a drop will land on our nose. This appears to be completely random . . . The tiniest irregularities are magnified in falling, so that we get complete randomness.” At such moments, I think of the classroom.
     In the classroom exists the conditions for the appearance of turbulence. There are particles in movement and interaction both within and between individuals. There is pressure, speed, viscosity, time, etc. How to predict the movement of particles within the classroom may be approximated but never absolutely defined. Every day a teacher walks into her classroom with a diagram (a lesson plan) that (like the Navier-Stokes formula) should predict the direction and movement of the mass of particles, but in fact, like the Navier-Stokes have not as yet been solved. If I apply the formulas (my lesson plans) then every student should move (learn) in a pattern predictable: I should be able to measure that movement with great accuracy. Classes in class room management (themselves not always well managed) teach students how to direct the flow of learning in the classroom. But the existence of turbulence suggests that any small disturbance (any particle or tiny combination of particle events at all) will grow and potentially produce a situation of chaos. Charles Fefferman says concerning Navier-Stokes, “Since we don’t know whether these solutions exist, our understanding is at a very primitive level. Standard methods from PDE appear inadequate to settle the problem. Instead, we probably need some deep, new ideas.” We try to control our lives with rationality, with predictive formulas, “but in fact, the Navier-Stokes formulas have no solutions . . . {and] this difference between our wish for an orderly universe and the reality of the calamity of the natural world makes us deny reality” We imagine a world that doesn’t exist.
     I stand in the classroom and the weather is calm. I think. But there are particles in motion and I do not know—I cannot know—which particles will attract others and lead to some rather nasty stuff. My lesson plans deny reality because they offer some false picture of the appearance of order. It is false. Is it possible to make a theoretical model to describe the behavior of a turbulent flow¾in particular, its internal structures? At this time the answer is, no. In the meantime, I stand in the classroom and look out on the horizon for the threat of tornado with only my lesson plan as protection.

For No One

How do we learn to be kind and caring and how do we learn to be cruel? The front page of today’s (or any day’s) New York Times offers a remarkable sample of the latter and even some evidence of the former.
     “Concern,” says Winnicott, “refers to the fact that the individual cares, or minds, and both feels and accepts responsibility” towards an other, or an Other. How this capacity for concern develops is the thrust of Winnicott’s essay, “The Development of the Capacity for Concern.” Winnicott says that a sense of destructiveness (hate and aggression) appears before an experience of constructiveness (a foundation of responsibility) even as in an earlier essay, “Hate in the Countertransference,” he claims that the mother hates (destructiveness) the baby before she loves (constructiveness) the baby. In the latter essay he offers a surprisingly long list rationalizing the precedence of hate before love. (I intend to use that essay for class this semester: I think that teachers hate their students before they love them!) In the essay, Winnicott says that in the fulfillment of instinctual needs/drives, the infant “attacks” the object-mother and intends to consume her seeking satisfaction of those needs. This aggressiveneness is perceived by the child as destructiveness, and as as result of this awareness of destructiveness, the child experiences anxiety, a sense of guilt felt by the child that she will actually ‘consumes’ the object-mother: the child senses that if she “attacks” the mother, then the mother will disappear. Of course, it is important that the mother be known as a subject who can survive the destructiveness of the child: hence the importance of the good-enough mother.
     Along with the object mother, she who can be attacked and consumed, the child learns that there exists as well what Winnicott calls “the environmental mother,’ a caregiver “who wards off the unpredictable and who actively provides care in handling and in general management.” The child comes to understand that s/he can use the environmental mother with “affection and sensuous co-existence,” and can ‘contribute’ to the environmental mother. In his relations with this mother the child experiences constructiveness and can offer to this caregiver reparation for the destructiveness and attack s/he has practiced and yet practices upon this caregiver. Without that environmental care-giver, and without the opportunity for reparation for the destructiveness the child exhibits to the the object-caregiver, the child experiences merely guilt. Guilt is the negative side of concern, and is characterized by anxiety linked with the concept of ambivalence, the latter term, says Winnicott, expressing the existence of eroticism and aggressiveness combined, the experience of a desire for, and a hatred of the object-imago. But I suppose the child will also come to experience from the reliability of the environment mother (or caregiver) the opportunity for reparation, since s/he will manage the child’s freer expressions of even the child’s id-drives and instinctual life. Winnicott says that in health the child’s guilt lies dormant or as mere potential—and will appear as depression or sadness when the opportunity for reparation does not exist.  For Winnicott this ambivalence assumes a degree of ego integration (an earlier development) that allows the child to understand that the same object (mother) is both object and subject. The child must know that just as the child has an outside and an inside, so must the mother possess an outside and an inside.
     Over time, this cycle of instinctual drives and the desire for reparation (of destructiveness and constructiveness) becomes modified and turns to what we can now call concern. Concern, the positive side of guilt, develops when the child accepts responsibility for her instinctual drives. And to take responsibility seems to mean to be able (and willing) to offer reparation. What starts as guilt in this regard transforms into concern.

For Amy

Oldest daughter has passed her licensing exam as a social worker. I am thrilled. All of the anxieties and insecurities that studying for the test called up are now put to rest temporarily¾alas, there are an infinite variety of licensing exams we must continue to take throughout our lives¾ but for now the immediate is now the past. And oldest daughter steps further into responsible adulthood (?) and maturity. Kurt Vonnetgut once said that maturity is a disease for which laughter is the only cure, if laughter can be said to cure anything. I hope neither of my children will ever achieve that maturity that contains not the possibility of laughter and not a little insanity. As Winnicott said, “We are poor indeed if we are only sane.” I would wish complete sanity on no one—and have perhaps never known it myself.
     And so this movement of the daughter throws me into some depression. Winnicott (again and still) asserts that depression occurs when the individual knows that he “has an inside,” and has the capacity to endure (to suffer through) and to contain the strains and stresses that arise in the personal inner psychic reality” as a product of living in this world. I think what Winnicott refers to here is the occurrence in depression in the shift in the forces that give structure to the ego-¾to the self¾and which then  threaten the stability of the individual. But depression, Winnicott argues, may be understood as a sign of health because depression indicates that the ego is not ‘disrupted,’ and may soon again be a sum. “Depression coming on, continuing and lifting, indicates that the ego structure has held over a phase of crisis. This is a triumph of integration.” I have hope.
     Depression arises, says Winnicott, with a new experience of destructiveness and of destructive ideas that accompany loving, and along with loving the feelings of hate. These new experiences require a reassessment by the individual of the interplay of forces and objects that constitute the inner reality of the individual at any one time.” The threat that the individual experiences, of course, is of disintegration: the coming apart of the ego, of the Self. Depression that lifts signals the survival of the Self in its new dynamics.
     With the children’s movement into adulthood (whatever that might be, in truth, I really don’t know with any certainty) I am required to reassess the interplay of forces and objects that constitute my inner reality because in their growths the children have established, indeed demand, different relationships with me and require of me different attitudes, needs, and responses. I love them yet, but the love contains necessary elements of hate.  I am no longer what I once was but am not yet sure who I am still to be. I am depressed.
     Winnicott says the best thing the analyst could do for the depressed person is to tolerate the depression until it spontaneously lifts, which is to say, I think, to assure the depressed person (in this case, c’est moi!) it will spontaneously lift and only that experience will feel right.