Topical Guide 79
Moon: Daytime Illusion of Transparency
I had drawn several pictures, each of which was a landscape that featured a pond (because I had just learned to draw ponds with pretty convincing perspective and particularly enjoyed complicating their shorelines with points and lagoons), clouds (because I had also just learned to draw nice, plump, billowy cumulus clouds), shadows (because I got a kick out of using the side of the pencil point to shade things), a disproportionately large duck (because Guppa had a nice little cast-metal Merganser paperweight that I wanted very much to learn to draw), and the transparent moon that sometimes graces the daytime sky (because I had begun to develop a fondness for it that still persists).
Little Follies, “The Static of the Spheres”
Sometimes in the afternoon sky a white moon would creep up like a little white cloud, furtive, without display, suggesting an actress who does not have to “come on” for a while, and so goes “in front” in her ordinary clothes to watch the rest of the company for a moment, but keeps in the background, not wishing to attract attention to herself. I was glad to find her image reproduced in books and paintings, though these works of art were very different—at least in my earlier years, before Bloch had attuned my eyes and mind to more subtle harmonies—from those in which the moon seems fair to me today, but in which I should not have recognized her then. It might be, for instance, some novel by Saintine, some landscape by Gleyre, in which she is cut out sharply against the sky, in the form of a silver sickle, some work as unsophisticated and as incomplete as were, at that date, my own impressions, and which it enraged my grandmother’s sisters to see me admire. They held that one ought to set before children, and that children showed their own innate good taste in admiring, only such books and pictures as they would continue to admire when their minds were developed and mature. No doubt they regarded aesthetic values as material objects which an unclouded vision could not fail to discern, without needing to have their equivalent in experience of life stored up and slowly ripening in one’s heart.
Marcel Proust, In Search of Lost Time, Swann’s Way, “Combray”
January sunlight fell in shafts through the windows, and in the shafts of sunlight, dust was dancing.
Why, I wondered, does the dust dance that way?
After some experimentation, I thought that I had found the answer. The dust was alive. …
I sat down and thought. The idea came to me that everything, everything I saw and touched, even the air I moved through, was moving, was in a sense alive.
“Peter, are you down there?” It was Gumma, calling me from the top of the cellar stairs.
“Yes, Gumma,” I called. “I was just—”
I hesitated. Was I going to say that I was just looking at dust?
Little Follies, “The Static of the Spheres”
“Dust” . . . seems to be a technical term meaning a bounded set of uncountably many disconnected points. Further examples are given by the two-dimensional analogues of the triadic Cantor set, known in the triangular case as the Sierpinski gasket and in the square one as the Sierpinski carpet. (I think it’s especially fitting for a carpet to be composed of dust. I’ve had a few like that.)
Alan Wachtel, personal communication with Kraft
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.
Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. . . .
The Cantor ternary set is created by iteratively deleting the open middle third from a set of line segments. . . .
The first six steps of this process are illustrated below.
Cantor dust is a multi-dimensional version of the Cantor set. It can be formed by taking a finite Cartesian product of the Cantor set with itself, making it a Cantor space. Like the Cantor set, Cantor dust has zero measure.
Cantor cubes recursion progression towards Cantor dust:
A different 2D analogue of the Cantor set is the Sierpinski carpet, where a square is divided up into nine smaller squares, and the middle one removed. The remaining squares are then further divided into nine each and the middle removed, and so on ad infinitum.
The construction of the Sierpiński carpet begins with a square. The square is cut into 9 congruent subsquares in a 3-by-3 grid, and the central subsquare is removed. The same procedure is then applied recursively to the remaining 8 subsquares, ad infinitum.
Six steps of a Sierpinski carpet:
Wikipedia, “Cantor Set” and “Sierpinski Carpet”
Dust is what connects the dreams of yesteryear with the touch of nowadays. It is the aftermath of the collapse of illusions, a powdery cloud that rises abruptly and then begins falling on things, gently covering their bright, polished surfaces. Dust is like a soft carpet of snow that gradually coats the city, quieting its noise until we feel like we are inside a snow globe, the urban exterior transmuted into a magical interior where all time is suspended and space contained. Dust makes the outside inside by calling attention to the surface of things, a surface formerly deemed untouchable or simply ignored as a conduit to what was considered real: that essence which supposedly lies inside people and things, waiting to be discovered. Dust turns things inside out by exposing their bodies as more than mere shells or carriers, for only after dust settles on an object do we begin to long for its lost splendor, realizing how much of this forgotten object's beauty lay in the more external, concrete aspect of its existence, rather than in its hidden, attributed meaning.
Dust brings a little of the world into the enclosed quarters of objects. Belonging to the outside, the exterior, the street, dust constantly creeps into the sacred arena of private spaces as a reminder that there are no impermeable boundaries between life and death. It is a transparent veil that seduces with the promise of what lies behind it, which is never as good as the titillating offer. Dust makes palpable the elusive passing of time, the infinite pulverized particles that constitute its volatile matter catching their prey in a surprise embrace whose clingy hands, like an invisible net, leave no other mark than a delicate sheen of faint glitter. As it sticks to our fingertips, dust propels a vague state of retrospection, carrying us on its supple wings. A messenger of death, dust is the signature of lost time.
Note to self: Include “Dust” in The Topical Autobiography of Mark Dorset (many amusing anecdotes).
[more to come on Wednesday, September 1, 2021]
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