Monday, July 9, 2018

Shalizi On Jaynes’ Arrow Of Time

Though early, grossly Orientalist, commentators* described Jnana Yogi Swami Cosma Rohilla Shalizi in terms similar to Descartes, it is clear from the historical record that Sw. Shalizi wrote his works in robes of saffron and kermes. As a small contribution to restoring historical reality, this paper is demonstrates how the recent publication by Carnegie-Mellon of Sw. Shalizi’s deutero-canonical writings throws new light on one of the canonical Shalizi texts in the Cornell Canon.

Some historical background is necessary. It is well known that Sw. Shalizi was a controversialist in the school of Guru Josiah Gibbs, opposing the faction led by Adhyapakah Edwin Jaynes. Gershom Scholem’s wonderful essay on the politics of saints “Religious Authority & Mysticism” gives a wonderful examination of how Sw. Shalizi likely felt about his work.

Adhyapakah Jaynes proclaimed, in seeming harmony with the tradition from Laplace to Schopenhauer, that the so-called “thermodynamic functions” - heat, pressure, etc. - had a mere conventional existence. Reality - the microstate - is something much stranger.

Against this preaching, Sw. Shalizi proposes that the true tradition would affirm the existence of heat even when there was no observer present. There seems to be an error in transcription in the Carnegie-Mellon text, as sometimes the text seems to be implying that without thermodynamic functions there would be no history prior to consciousness. But evolution of the objective microstate is not a function of the subjective macrostate. Fortunately, examination of the Cornell Canon is sufficient to demonstrate that Sw. Shalizi was aware of this.

Sw. Shalizi’s objection was much more subtle. Adhyapakah Jaynes essentially denied Mahapandita Ludwig Boltzmann’s claim that large numbers of particles play a role in thermalization, arguing that subjective ignorance is sufficient. Of course, Sw. Shalizi could not stand such a rejection of tradition.

We now move to the main text, Sw. Shalizi’s controversial article “False Jnanachakra”. In it, Sw. Shalizi imagines a contest between a mighty asura Andhaka and  Bhagvan Shiva. The Mahayogi bets that if Andhaka can turn the Jnanachakra then Andhaka may have a night with Parvati. Of course, Andhaka cannot resist such a carnal opportunity. The price he pays is this: if Andhaka cannot but Shiva can, then Andhaka must die and live the rest of his lives in non-violence and celibacy.

The Jnanachakra is a weightless Jade wheel with a single needle along it’s rim which may be lowered or raised. It has no effect on the pendulum. The Jnanachakra, as its name suggests, is merely a metaphor for the player’s knowledge. Beneath the Jnanachakra is an n-ary pendulum whose fobs beyond the first are invisible. Based only on macroscopic observation, the player attempting to turn the wheel must raise or lower the needle which will be pushed by the pendulum in the correct direction.

The observable state space of a single visible fob is a cylinder with one axis, up-down, as the velocity of the fob and the the other axis, around, as the velocity of the fob. The same for the Jnanachakra. Holding the current velocity of the Jnanachakra constant gives us a circle around the phase space. We want the needle down only when the fob is above the current circle in phase space. 

Andhaka’s strategy is to lower the needle in front of the fob when the fob is swinging right faster than the Jnanachakra. He believes this will allow him to rotate the Jnanachakra counterclockwise. For a short time, this works. But the hidden fobs cause the visible fob to bounce randomly on a long timescale - a timescale which can be calculated from coupling of the fobs (cite pg 44 Chaos & Coarse Graining In Stat Mech). Eventually, Andhaka’s predictions of will be no better than chance. Therefore Andhaka’s strategy will fail in the long run.

Now the Mahabuddhi goes to the wheel. He follows a similar strategy. At first the Jnanachakra seems to thermalize - bounce randomly. But soon the wheel begins turning counterclockwise. Why? Shiva can *learn* the motion of hidden fobs by observing the system at large. Since the state space of the system is fixed, in the long run Shiva learns the whole system perfectly. Following the teachings of Guru Shannon, Sw. Shalizi calculates the rate at which one may learn and finds it is either 0 (for Andhaka) or exponentially rapid (for Shiva).

Now Sw. Shalizi makes his attack. Nrityapriya’s dance requires only learning a finite state space and converges rapidly. Why cannot Andhaka do the same? Sw. Shalizi challenges the anti-Boltzmannian to explain without reference to the enormous size of the state space. If he cannot, then the anti-Boltzmannian has admitted that an objective property of reality - the dimension of the state space - plays the role Adhyapakah Jaynes has denied.

The case for Bhagavan Shiva and against the asura Andhaka can be made explicit. Start by recalling that the rate of learning is either zero or exponential. 
Andhaka’s capacity to learn is constant. As dimension of the state space - the number of fobs - grows large large, one soon finds that the asura cannot converge on the true state because he doesn’t have enough memory to hold the state in his mind. Therefore his learning rate is zero.
But Akshayaguna is different. His capacity to learn grows large holding the dimension of the state space constant. Therefore his learning rate is exponential.

There is no denying that Sw. Shalizi’s logic is absolutely sound. But before the publication of Three Toed Sloth, the full extent of his argument couldn’t be appreciated. Sw. Shalizi's implicit claim is that subjective arrows of time must have a consistent direction only if the state space of possibilities is much larger than the capacity any relevant learner. But Sw. Shalizi’s Cornell Canon piece doesn’t explicitly argue that why the learning capacity of a mere asura is insufficient.

Only now are we learning that Sw. Shalizi intended this work as part of a campaign of Arhat Ashby against the Jaynesians. Sw. Shalizi intends to use Ashby’s Law Of Requisite Variety, showing that a model of a system must be as complex as the system itself. This demonstrates that nobody but one who is unified with Brahman may have a backwards arrow of subjective time.

In sum, Carnegie-Mellon’s publication of Shalizi’s deutero-canonical work has opened new fields for scholarship. Already his brief note has been revealed to be more than a mere grumbling of a lover of controversy. His is a philosophical distinction between the monotonic subjective arrow of time of an ordinary being and the free arrow of time of an extraordinary one. All philologists of this canon  must take note.
*In case it isn't clear: this is written as a parody of Western commentary on Eastern religion - thus all the Sanskrit jargon despite none of the figures speaking the language. Why? Well, it seemed funny at the time. Of course, this blogpost shouldn't be considered scientific, much less serious theology.

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