Petar Maymounkov

Chomsky, Valiant and the algorithmic mirror

Fri, Oct 11, 2013

I recently had the pleasure of listening to some of Chomsky's lectures on linguistics, philosophy, and the mind (on YouTube), reading some of Chomsky's work within Linguistics (although certainly not enough) and reading Leslie Valiant's Probably Approximately Correct: Nature's Algorithms for Learning and Prospering in a Complex World. I was prompted to read the latter by a recent blog post on Michael Mitzenmacher's blog and also due to my close familiarity with Valiant's academic work and his less-known, eye-opening book Circuits of the Mind, which I will turn to another time.

Valiant and Chomsky have very different but, in my judgment, entirely complementary—not mutually exclusive—theories about the nature of intelligence, consciousness and the like. It is no coincidence, of course, that their theories are compatible with each other, as one easily imagines an intimate familiarity of Chomsky's work on Valiant's part, considering chronology and their academic pedigrees.

What I find is that their approaches—considered together in a broader modern context—inspire a new point of attack on attaining an explicative theory of the mind's mechanism. Here I intend to make a fascinating dive into ideas of how to act on and "materialize" hopefully much of Chomsky and Valiant's ideas.

Chomsky is known to have opened a new science that studies the mind by close association with the presumed-universal underlying structure of linguistic expressions that we produce and observe. Henceforth much attention has gone into studying natural languages both qualitatively (in Linguistics) and statistically (in Computer Science). While undoubtedly much has been learned, these directions appear to fall far from bridging the gap between observed natural language and a rigorous but concise explicative theory of the mind's mechanism (if one should exist). Certainly, in part this difficulty is due to the complexity and degrees of freedom that acceptable natural grammars could have, according to the data.

Perhaps this difficulty is not coincidental.

Chomsky stipulates that externalized language as well as conscious thinking are only the tip of the Iceberg that is the mind's universal ecorithm—ecorithm, being Valiant's broad term for an algorithm occurring in Nature. If this is indeed the case, why should we expect to be able to recover the Iceberg's internal workings just through looking at the tip?

There is something puzzling about the tip. The tip—metaphorically, the externalized and observable informational output of the mind—is not limited to the linguistic mode of expression alone. Humans have many modalities of output. The kinematics of the human body, just as one example, are an informational output of the mind as well. Some kinematic motions have been accepted into the subject of linguistics, namely sign language and other such explicit kinematic means of expression, because they obviously piggy-back deeper thoughts, while others seemingly "duller" ones like the kinematics of walking have not. This is probably a reasonable choice: There doesn't seem to be much "intellectual" content (and therefore insight into the mind) into the kinematics of walking, being a reflexive process, and therefore a focused study of it likely won't enlighten a theory of the Iceberg's deliberate intelligence. The Iceberg appears to be outputting its "deeper" thoughts through the linguistic faculty. But what about other channels of thought output—henceforth faculties—that might invite even deeper thoughts for transmission to the outside? I think they abound.

Linguistic expression is not the only "intellectual" product of the mind.

Consider intellectual theories which are communicated through the language faculty but themselves have a very different structure from it. To them the language faculty is merely a modaility of transmission. These theories are another higher-order faculty of the mind that is not structurally synonymous with the reflexive linguistic faculties, which are natural languages. It is natural to conclude that to get exposure to the deeper—or simply other—circuits of the Iceberg, one must study the output of the higher faculties of the mind.

Just as the language faculty is modulated over—i.e. is encoded within—the kinematic faculty, higher-order faculties are modulated over the linguistic faculty. These higher-order faculties seem to reflect the mind's deeper, more deliberate, and more iterated thoughts.

Which faculty is higher than natural linguistic expression? I believe, it is called "mathematical maturity" in universities across the country. It is the ability to think and gradually build provably-verifiable statements within formal linguistic systems. Those formal languages are the higher faculty. Traces of them are found within the knowledge output by the hard sciences.

This observation might not be a surprise to some.

While it might sound like an obvious idea to turn the linguist's attention to the product of scientists—i.e. their formal theories—there are also obvious reasons why this course is potentially misleading and certainly hard to follow, which would explain why it has not been undertaken.

This course is misleading, because we do not know whether the shape of formal scientific theories is influenced more by the external Nature that they study or more by the way our minds prefer to structure thoughts. I firmly believe this is a quantitative phenomenon. It is not one or the other. Formal theories allow for too much flexibility (contrary to popular belief) in what they can express; Nature's description, perhaps influenced by our tastes, requires a much smaller set of expressive flexibilities.

Therefore materialized, observable hard science is an odd mixture of tastes and necessities.

This course is hard to follow, because the real-juicy accomplishments of science (reflecting on the deepest of thought, coming from the deepest circuits of the Iceberg) are theories so advanced, that we do not know how to put fully in formal writing, instead we nurture them through a lineage of scientists that dedicate decades of their lives to attain universally—i.e. mutually among those scientists—verifiable mastery. Due to this inability to fully formalize the highest accomplishments of science, we have been unable to study the output of science with our most powerful tool: digital computation.

There is a beautiful middle ground between creative natural languages and philosophical thought. And that is: Engineering.

Engineering is a mixture of playful thinking and formal constraints. Engineering is a constant tug-of-war between our playful desire to build a fancier device and the cognitive costs of fanciness imposed by formal constraints. It then follows that those engineering quests—a.k.a. technologies—that survive the test of time are sheer acts of Nature, reflecting on the immaculate balance between our creatively wanting minds and the cognitive costs of formal systems.

It is thus in the makings Engineering where we should search for the perfect fossils of the mind's work.

The yield of Engineering has been enormous and of growing might over time. Since the playful energy and cognitive limitations of the engineers have stayed the same (as believed by Chomsky and many others), one has to deduce that either the formal cognitive constraints imposed on engineers have relaxed over time, or that the design power of the formal systems that engineers created within–i.e. the technologies available to them from peers or prior generations of engineers—was greater.

Assuming an unbound drive for creativity—we would always strive to utilize our brains to their maximum capacity—it is safe to say that the latter is the case: The formal cognitive constraints of engineering practice stayed at the same level due to our competitive or otherwise drive to create at our limit, while the technologies (which are formal systems to us) that we built for ourselves increased in might by utilizing prior technologies in a manner that did not cause increase in cognitive demands on the engineers. This point has an enlightening consequence:

A common technology, from any generation, considered solely in the context of its supporting technologies is as good a reflection of the mind at work—at maximum capacity and perfect balance between creativity desire and cognitive ability—as any other such.

If a representative technology from any generation will tell us just as good a story, then why not pick the most convenient for studies? This liberates us to pick from technologies most amenable to digital inspection, our investigative weapon of choice (and necessity). Well, there is no better choice than the weapon itself: Algorithms.

Systems and their algorithms truly seem to capture the limitations of human thinking. They are the best we've got. Aren't they?

While maybe not perfect, our algorithms are wildly deep and magical, reflecting on the mysterious intelligence of the mind's Iceberg. They control airplanes, save lives, materialize imaginary three-dimensional movies, and do much more. Our algorithmic systems are vastly complex, yet we manage to sustain them relatively uneventfully while placing our lives to various extents in their hands. We have developed routines and conventions, suitable to us, perfected with time, that help us stay on top of this blooming buzzing confusion of a world that we have largely created for ourselves. Perhaps our own algorithms, routines and conventions reflect us best.

The algorithmic mirror is a shorthand for the notion that the algorithmic output of humans should be studied seriously in its own right of a faculty, differing from linguistic expression, that sheds light onto the mind's Iceberg from a different angle and often in a deeper way, as it encodes casual as well as carefully deliberated thoughts, in some cases spanning decades.

We seem to find ourselves in an exceptionally serendipitous moment. The formal descriptions of algorithmic technologies created by human engineers are readily available to us in a format convenient for inspection by means of our current best tool: these same algorithmic technologies. Perhaps the imminence of this moment—whereby the current deepest formally-encodable human thought coincides with the current best man-made technology for investigative enquiries, the Algorithm—will not be surprising in retrospect. But it is surely serendipitous that we are around to witness it and take part. (Well, that depends on what you mean by "we", one might say. That's another story.)

Computer Science alone, a young science, has proliferated an immense amount of well-encoded ideas like operating systems, file systems, the World Wide Web, interoperability technologies, and countless others. These technologies and the mysterious reasons why we seem to converge to them, in a stable and systematic manner, over and over again should be the focus of anyone who studies the human mind with rigor. The algorithms that we create are the most formal encoding of human intention, perhaps human afterthought, perhaps even human deep thought. They are easily accessible to everyone and they come unburdened by the computation complexity of deciphering Context Free Grammars, imposed in the study of natural (informal) languages.

The algorithmic mirror offers exciting investigative opportunities, some of which unseen in natural languages:

Applying the algorithmic mirror to legacy algorithmics is akin to observing the shadows of intelligent strangers as they go about their mysterious business for millions of human years.

This is already useful.

Changing our future algorithm design and implementation in accordance with inquiries by the algorithmic mirror is akin to being able to shout back at the strangers, albeit in a foreign language, in a playful effort to affect their confusing pattern and maybe even get a faintly recognizable response.

Considering that Chomsky has chosen a generative process, the universal grammar, as his model of choice for the workings of the Iceberg, it is encouraging to note that software engineering is a generative process be definition.

This is tremendous: It is the prospect of being able to talk back at the intelligence of mind.

The take-away is clear: Carefully study of the cognitive aspects of the designs of time-tested algorithmic systems and programming languages is way overdue. A concrete example of this kind of inquiry is helpful in putting some flash around it. Consider software technologies as human-facing interfaces. Notice, for example, how those interfaces of operating systems and programming languages differ in the cognitive vs. design power sense. Operating systems aim to enable a more immediate and interactive command at a coarser level. Whereas programming languages offer a slower, more demanding but more expressive facility which better suits the deliberate thinker. Why is the gap between these two interfaces so wide? Is there a sharp qualitative difference between them or can there be shades of grey in between? Or, perhaps, are there entirely different types of interfaces for encoding human intention, presently not conceived of? Why have they not been conceived yet? A cognitive obstruction is in the way perhaps? Just a few questions to ponder.

The role of Valiant's Mind's Eye in the algorithmic mirror will find its place in a following article.

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