On knots and naught; by way of a Sufi wormhole.
On night one thousand and two, Mullah Nasruddin was walking a dark and desolate byway when, in feeble light, he could make out shadowy figures approaching in the far distance. As the shadows loomed closer, he knew they were horsemen. A cold chill shot up his spine and he began to run. The horsemen, seeing the shadowy figure, spurred their mounts, following him. Now the mullah was petrified. He saw a wall, jumped over it, and found himself in a cemetery. In the far corner, and just in time, he discovered an open casket and climbed in, closing the lid behind him. The horsemen, however, had seen him jump the wall, and rode into the graveyard. After searching for a while, they found the unburied casket and opened the lid with the mullah lying inside like a frightened vampire.
“Is there anything wrong?”
“Well, it’s a long story, replied the mullah.”
“Can we help you? Why are you here?”
“I am here because of you.”
“And we are here because of you.”
Douglas Hofstadter has dubbed such a situation in which a cause cannot be located as a tangled hierarchy, in other words, a hierarchy with neither an upper level nor an inferior level.
Another example of a tangled hierarchy is the sentence I am a liar. If we chase the truth value in the sentence, we are caught up in an infinite loop. If the sentence is telling the truth, it is lying; if it is lying, it is telling the truth, and so–ad infinitum.
Tangled hierarchies form Godelian knots, and the harder you pull on the knot, the tighter it tenses.
Artistic attempts to represent the tangled hierarches of Godelian knots are found in the works of Escher and Cubists.
The Mobius strip is a mathematical topology that represents the infinite loop within the tangled hierarchy, with films such as La Jetee/Twelve Monkeys based on Mobius-like narrative curvatures.
Escher’s Print Gallery expands the Mobius strip to the architectural level. Please take note of the white circle in the middle of the drawing, which erases the problematic discontinuity between inside/outside the gallery. This can be called the inviolable point, the point that transcends the infinite regress within the knotted, tangled hierarchy.
Deep within the gargantuan black hole in Interstellar resides a sort of neo-Cubist singularity, a tangled hierarchy, a knot wherein gravity becomes gravitas and is so compressed that past and present, far and near, matter and the emotion of love not only co-exist, but interact. Is it the past influencing the future or the future influencing the past? Like the mullah and the dark riders in the graveyard, they are there for each other. The play of causalities forms an infinite loop, and knot. Can we pinpoint who causes books to drop off Murph’s bookshelf and dust to fly, or are these caught up in a tangled hierarchy between past and future? Forget that in physics a singularity would destroy human life. This singularity serves the narrative purpose of allowing Coop to send Murph (through her watch) the data she needs to solve Professor Brand’s gravity equation, which allows those NASA dudes to levitate those enormous space stations into the akasha. The wormhole helps daughter Brand reunite with her hot astronaut on planet Edmunds.
Yet, there is another dimension to this and to any knot: pull on the both ends of the rope, but you cannot pull the knot apart. Slacken the rope and you can slide the knot up and down the length of it. The knot is neither the nylon nor the silk nor the cotton. The knot is naught: simply a pattern the rope makes visible.
The inviolable naught transcendental to the infinitely recursive knots of tangled hierarchies is consciousness itself, which has written its own volume of Mobius-shaped narratives within certain collections of hoary Hindu tales.