Your comment made me wonder if someone has diaried here about "Ta-DAH" moments... or was it "Aha!" moments?

If I read you right, you are talking about new cognitive structures/patterns forming dynamically, and this reminded me of a blog entry/paper I perused recently (but am far from comprehending in detail, much less evaluate) by Cosma Shalizi:

Discovering Functional Communities in Dynamical Networks

Abstract: Many networks are important because they are substrates for dynamical systems, and their pattern of functional connectivity can itself be dynamic — they can functionally reorganize, even if their underlying anatomical structure remains fixed. However, the recent rapid progress in discovering the community structure of networks has overwhelmingly focused on that constant anatomical connectivity. In this paper, we lay out the problem of discovering functional communities, and describe an approach to doing so. This method combines recent work on measuring information sharing across stochastic networks with an existing and successful community-discovery algorithm for weighted networks. We illustrate it with an application to a large biophysical model of the transition from beta to gamma rhythms in the hippocampus.

In college, I read a book called A Man With No Words by Susan Schaller, who teaches sign language to Ildefonso, a 27-year old deaf man who has grown up without language (oral or sign), but first must lead him to see the world through "symbolic meaning" (for want of a better term), which turns out to be a colossal task which makes the subsequent teaching of signs small in comparison.  Schaller compares Ildefonso's intense epiphany, an instantaneous event in which he grasps the concep in a flash, to Helen Keller's "water" moment at the well.  I had watched The Miracle Worker as a kid, but had not yet read Story of My Life.  When I did, I was convinced that Schaller was right, and the experiences that Ildefonso and Helen Keller shared were of the same nature, no less than a cognitive quantum leap, a satori of sorts, that literally transformed their reality and moved them from one world into a whole new vast one in an instant.

Unfortunately, I could not find the passage in Schaller's book describing Ildefonso's experience online, but here is Helen Keller's describing her own "awakening" into the world of words:

We walked down the path to the well-house, attracted by the fragrance of the honeysuckle with which it was covered. Some one was drawing water and my teacher placed my hand under the spout. As the cool stream gushed over one hand she spelled into the other the word water, first slowly, then rapidly. I stood still, my whole attention fixed upon the motions of her fingers. Suddenly I felt a misty consciousness as of something forgotten--a thrill of returning thought; and somehow the mystery of language was revealed to me. I knew then that "w-a-t-e-r" meant the wonderful cool something that was flowing over my hand. That living word awakened my soul, gave it light, hope, joy, set it free! There were barriers still, it is true, but barriers that could in time be swept away.

I left the well-house eager to learn. Everything had a name, and each name gave birth to a new thought. As we returned to the house every object which I touched seemed to quiver with life. That was because I saw everything with the strange, new sight that had come to me. On entering the door I remembered the doll I had broken. I felt my way to the hearth and picked up the pieces. I tried vainly to put them together. Then my eyes filled with tears; for I realized what I had done, and for the first time I felt repentance and sorrow.

I learned a great many new words that day. I do not remember what they all were; but I do know that mother, father, sister, teacher were among them--words that were to make the world blossom for me, "like Aaron's rod, with flowers." It would have been difficult to find a happier child than I was as I lay in my crib at the close of that eventful day and lived over the joys it had brought me, and for the first time longed for a new day to come.

Isn't it somehow amazing that this single cognitive switch had such an explosive impact on Helen Keller's reality, extending even into her moral and emotional universe: for the first time I felt repentance and sorrow.

It is interesting to compare Keller's words with a passage by D.T. Suzuki's description of the Zen Buddhist concept of satori, or enlightenment, i.e. the experience that Siddhartha Gautama himself had that transformed him into the so-called Buddha:

Without the attainment of satori no one can enter into the truth of Zen. Satori is the sudden flashing into consciousness of a new truth hitherto undreamed of. It is a sort of mental catastrophe taking place all at once, after much piling up of matters intellectual and demonstrative. The piling has reached a limit of stability and the whole edifice has come tumbling to the ground, when, behold, a new heaven is open to full survey. When the freezing point is reached, water suddenly turns into ice; the liquid has suddenly turned into a solid body and no more flows freely. Satori comes upon a man unawares, when he feels that he has exhausted his whole being. Religiously, it is a new birth; intellectually, it is the acquiring of a new viewpoint. The world now appears as if dressed in a new garment, which seems to cover up all the unsightliness of dualism, which is called delusion in Buddhist phraseology.

An Introduction to Zen Buddhism

I am no sutra or koan thumper, but I do not find the religious terminology used by Keller or Suzuki off-putting, strange, or incompatible.  In fact, I would feel comfortable calling the experiences of Helen Keller shooting into the firmament of language and those described as "awakening" in the Buddhist context by Suzuki religious in the most basic, purest sense.  Ironically, the two categories of experience are in another way diametrically opposed, as the former is a transition from a world of non-language (or pre-language) to a world of language, while the latter is a transition from the world of language to a world of non-language (or meta-language).  Having said this, the non-language world of Suzuki is certainly not of the same nature as the non-language world of Helen Keller before her experience with Anne Sullivan at the well.  This movement could indeed be schematized as thesis (Helen Keller before the well experience) moving to anti-thesis (Helen Keller after the well experience/Siddhartha Gautama before his enlightenment) and then onto synthesis (Siddhartha Gautama after his enlightenment.)

These super "Aha!" moments described by Schaller, Keller and Suzuki, I suspect, are in fact "Ta-DAH!" moments happening among the neurons and axons and synapses in our brains, along with the juices and fluids and cells running through our endocrine system and glands and muscles and nerves, all of which are dynamical systems organized hierarchically and in cooperation with one another in our bodies.  Cosma Shalizi's paper might describe how in the flux and flow and ebb of these processes new patterns and structures might emerge, and I wonder if even the "Aha!/Ta-DAH!" experiences of Ildefonso and Helen Keller and Siddhartha might be cases of "biophysical functional community discovery" in their brains and bodies on the order of supernovas.

Here is Stuart Kauffman on page 24 of his book At Home in the Universe: The Search for the Laws of Self-Organization and Complexity:

Borrowing a metaphor from physics, life may exist near a kind of phase transition. Water exists in three phases: solid ice, liquid water, and gaseous steam. It now begins to appear that similar ideas might apply to complex adapting systems. For example, we will see that the genomic networks that control development from zygote to adult can exist in three major regimes: a frozen ordered regime, a gaseous chaotic regime, and a kind of liquid regime located in the region between order and chaos.

And Suzuki again from the above extract:

When the freezing point is reached, water suddenly turns into ice; the liquid has suddenly turned into a solid body and no more flows freely.

Superficial and accidental coincidence, but maybe not altogether meaningless.

Fortunately, she soon snapped back into reality where flossing only had import in dental hygiene not a metaphysical certainty.

A fine example of entropy at work!

The sun has risen in Manhattan (where I am spending the holidays): time for me to snap back into reality myself.