Gradient Ascent by James Bridle

“For a mountain to play the role of Mount Analogue, its summit must be inaccessible but its base accessible to human beings as nature has made them. It must be unique and it must exist geographically. The door to the invisible must be visible.”
—René Daumal, Mount Analogue: A Novel of Symbolically Authentic Non-Euclidean Adventures in Mountain Climbing

In Greek mythology, Mount Parnassus was sacred to Apollo and Dionysus, and was home to the Muses, the inspirational goddesses of literature, science, and the arts. To ascend Parnassus is thus to be elevated to the peak of knowledge. In the seventeenth century, Parnassus was explicitly associated with the quarrel of the Ancients and the Moderns, and its classical adherents gave form to Parnassism, which named Montparnasse.

In Jonathan Swift’s Battle of the Books, published as part of the prolegomena to his A Tale of a Tub in 1704, two camps occupy the twin peaks, one higher than the other, of Mount Parnassus. The greatest of the two is, since time immemorial, the possession of the Ancients; the other is held by the Moderns, who grow restless. They send ambassadors to their neighbours, complaining that their view is spoiled, and in order to avert a war suggest either that the two camps exchange positions, or that the Moderns, using various tools of their invention, level the Ancients’ hill to a more convenient height. This ultimatum is rejected by the Ancients, who suggest the shade they afford is more than recompense for the restricted prospect, and furthermore, if the Moderns are so affronted then they should seek, by their own efforts, to raise their position. The result, needless to say, was not a harmonious accommodation, but a long and obstinate war, which continues, in one form or another, to the present day.

Such has always been the condition of mountains: as much metaphor as mound of rock. In the twentieth century, René Daumal, a student of George Gurdjieff, described Mount Analogue, a symbolic peak located somewhere on the surface of the Earth, but impenetrable to the ordinary traveller. Mount Analogue must be thought before it can be seen: its base rests on the Earth, but its summit forever escapes our gaze. In Daumal’s novel, a party of mountaineers led by a Father Sogol set out on an expedition to conquer Mount Analogue, which they have calculated must appear somewhere in the latitudes of the South Pacific. By careful sailing, they approach the mountain at sunset from the west: as Sogol has explained, this vector is symbolically predictable: “Civilizations in their natural movement of degeneration move from east to west. To return to the sources, one should go in the opposite direction.”

Upon their sudden arrival on the rocky coast of Mount Analogue, which falls directly to the sea, the travellers are introduced to the unit of local currency, the peradam; an object that is revealed only to those who seek it.

“One finds here, very rarely in the low lying areas, more frequently as one goes farther up, a clear and extremely hard stone that is spherical and varies in size — a kind of crystal, but a curved crystal, something extraordinary and unknown on the rest of the planet. The clarity of this stone is so great and its index of refraction so close to that of air that, despite the crystal’s great density, the unaccustomed eye hardly perceives it. But to anyone who seeks it with sincere desire and true need, it reveals itself by its sudden sparkle, like that of dewdrops.”

Daumal died before completing his account of the ascent of Mount Analogue — his narrative ends mid-sentence, the last words of which are “shifting earth”. Today the peak of Mount Analogue is still shrouded in Cloud, the metaphor which has come to replace the high mountain peak as the place of knowledge.

On the graph of progress, and of technological determinism, everything goes up and to the right. But this shape is a visual illusion caused by the direction of the light, just as Mount Analogue is hidden by certain perturbations in the atmosphere. We may observe a similar effect in relation to what are termed ‘Gravity Hills’, places on the Earth’s surface where the usual direction of gravity is apparently reversed. A car, placed in neutral gear and with the handbrake released, will seem to roll uphill. The illusion is supposed to be produced by a combination of factors: the local topography, including hills and trees when sited in unusual configurations, and the mind’s tendency to assume perspective; that is, to attempt to order the world by a preceding set of expectations. Through the machine, we disprove the world.

The map is not two-dimensional either; rather, what we face is a multidimensional terrain, composed of many local maxima and minima, a scattered massif of diverse facets, different temperatures, and variable inclines. In order to evaluate the terrain, we train certain functions, which perform a graduated ascent of the topography — what is called an optimization algorithm. By careful step on step, the algorithm evaluates its situation, and takes the increase in any variable as evidence of its improved position. On reaching a point from which no further step is possible, a problem arises: How do we know that we have reached the highest peak, when we might only be trapped in some local maximum, a spur or lesser summit, ignorant of yet higher ground?

One solution, in terms of computer science, is the random walk: a stochastic resampling of the terrain which incorporates random changes in position, flights of fancy, and leaps of the imagination. While true randomness is impossible, it may be approximated by the movement of gas molecules, or the erosion of mountain ranges. In this way, we create an abstract symbol of a mathematical topology: an abstract thing which symbolizes a concrete thing, contrary to custom.

Technology is a form of active storytelling, or reified myth. By encoding our ideas and intentions into machines, we make them literal constructors of the world. The stories we choose to tell with our technologies shape our environment, and its future. We do not have to heedlessly accept the myths we are offered, because they can be retold and revivified in every generation. We can construct test cases, compose oppositional and adversarial examples, and catch exceptions. The myths are alive in our time.

Daumal again: “Keep your eyes fixed on the way to the top, but don’t forget to look at your feet. The last step depends on the first. Don’t think you have arrived just because you see the peak. Watch your feet, be certain of your next step, but don’t let this distract you from the highest goal. The first step depends on the last.” Or, as Aldous Huxley had it, means determine ends.

There are many routes to the summit of Mount Parnassus, and many mountaineers. Deye mon, gen mon, as the Haitians say. Beyond the mountains, there are mountains.

Gradient Ascent by James Bridle