#computation

P≠NP: wow! that is shocking that there are some problems that can be checked in a reasonable anoint of time, but cannot be solved in a reasonable amount of time! just like the halting problem, this goes to show how there is a major limit in computational problems, and i wonder how future computer scientists will build off of these ideas!

There’s a peculiar asymmetry emerging.

We can now map fragments of the human brain in petabytes — trace synapses, reconstruct pathways, simulate structure — and still not explain the presence that moves through it.

At the same time, we’re deploying artificial agents into the world. Systems that act, decide, persuade, optimise. Systems that behave like minds, while built atop architectures we only partially understand, pursuing goals defined by incentives we barely examine.

The black box has stopped being a passive instrument. It has become a participant.

This isn’t a technical problem. It’s an ontological one.

Science can describe behaviour. It can map structure. It can measure correlation. But the relationship between structure and experience — between computation and presence — remains unresolved.

The deeper we look, the sharper the boundary becomes.

The ontology gap isn’t shrinking. It’s becoming measurable.

Filed under ongoing Process documentation — signal emerging from noise.

In 2015, the Defense Advanced Research Projects Agency, or DARPA, which is often referred to as the Department of Defense’s “mad science division,” adapted a flight simulator so a woman named Jan Scheuermann, who is paralyzed due to a neurodegenerative condition, could fly an F-35 fighter jet using only her mind—and the probes they implanted in her motor cortex. Scheuermann is a self-described “cutting-edge brain-computer interface lab rat” for DARPA’s Revolutionizing Prosthetics program, which in 2006 began “to expand prosthetic arm options for today’s wounded warriors.”

The Revolutionizing Prosthetics program consisted of two separate projects: the LUKE arm system, which, at $250,000, carries the distinction of being “the world’s most expensive prosthetic arm,” and the Modular Prosthetic Limb, which was “designed primarily as a research tool.” For a prosthetic with an unknown life span, it is not surprising LUKE hasn’t gained much adoption even from the self-pay amputee elite. Such experimental equipment is decades away from acceptance in a draconian insurance system that has demonstrated intractable commitment to gatekeeping technological advancements from most disabled people until they are no longer effective, relevant, or desirable.

But once researchers realized they could detach the LUKE arm from its human operator, they began working on a new plan to integrate “militarized ver­­sions of these terminal devices onto mobile-robotics platforms, making them efficient enough that human operators won’t have to go into the hazardous zones themselves.” Years on, that is where this technology has found its use: in “small robotic systems used by the military to manipulate unexploded ordnance.” [...]

The story of how we got here is a tangled one, one that tracks back over a century of history. But we may as well begin with Microsoft, which, despite its well-documented toxic culture, has long believed itself to be uniquely equipped to “provide Corporate America with a blueprint” for disability inclusion best practices. “In 2015, Microsoft published an inclusive design tool kit that has since become a bible for inclusive design. The tool kit has been downloaded more than 2 million times’’ and has been used to shape such products as its HoloLens augmented reality/virtual reality headset, which was announced that same year.

Not long after the Microsoft HoloLens Development Edition was made available, the Israel Defense Forces tweeted it was “using the … Hololens to bring augmented reality to the battlefield.” Microsoft’s subsequent $22 billion contract with the Department of Defense to supply the U.S. Army with more than 120,000 headsets extended the disabled use case to “the killer use case.” [...]

The 2019 deal was a follow-up to the initial phase of the project, during which Microsoft supplied DARPA’s Next-Generation Nonsurgical Neurotechnology, or N3, program with the HoloLens so the agency could create “brain interfaces for able-bodied warfighters.” Up until this point, DARPA had claimed it was “focused on technologies for warfighters who have returned home with disabilities of the body or brain.” But suddenly, DARPA’s focus had shifted away from disabled vets, and N3 was now using “cooking as a proxy for unfamiliar, more complex tasks, such as battlefield medical procedures, military equipment sustainment, and co-piloting aircraft,” to develop the HoloLens for war.

In 2023, Microsoft addended its Inclusive Design Toolkit with an Inclusive Design for Cognition Guidebook that somehow also managed to propose cooking as a method to identify “what cognitive demands are being asked of the user.” This means it’s not just N3 as the program, Inclusive Design as the methodology, and HoloLens as the technology. The way developers used cooking—a common household task—as their use-case exemplar fairly explicitly put disability, writ large, at the heart of their work: an unimpeachably “feel-good” north star to follow.

Is it possible to deduce the shape of a drum from the sounds it makes? This is the kind of question that Iosif Polterovich, a professor in the Department of Mathematics and Statistics at Université de Montréal, likes to ask. Polterovich uses spectral geometry, a branch of mathematics, to understand physical phenomena involving wave propagation. Last summer, Polterovich and his international collaborators—Nikolay Filonov, Michael Levitin and David Sher—proved a special case of a famous conjecture in spectral geometry formulated in 1954 by the eminent Hungarian-American mathematician George Pólya. The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk.

You can blame it all on Turing. When Alan Turing invented his mathematical theory of computation, what he really tried to do was to construct a mechanical model for the processes actual mathematicians employ when they prove a mathematical theorem. He was greatly influenced by Kurt Gödel and his incompleteness theorems. Gödel developed a method to decode logical mathematical statements as numbers and in that way was able to manipulate these statements algebraically. After Turing managed to construct a model capable of performing any arbitrary computation process (which we now call "A Universal Turing Machine") he became convinced that he discovered the way the human mind works. This conviction quickly infected the scientific community and became so ubiquitous that for many years it was rare to find someone who argued differently, except on religious grounds.

There was a good reason for adopting the hypothesis that the mind is a computation machine. This premise was following the extremely successful paradigm stating that biology is physics (or, to be precise, biology is both physics and chemistry, and chemistry is physics), which reigned supreme over scientific research since the eighteenth century. It was already responsible for the immense progress that completely transformed modern biology, biochemistry, and medicine. Turing seemed to supply a solution, within this theoretical framework, for the last large piece in the puzzle. There was now a purely mechanistic model for the way brain operation yields all the complex repertoire of human (and animal) behavior.

Obviously, not every computation machine is capable of intelligent conscious thought. So, where do we draw the line? For instance, at what point can we say that a program running on a computer understands English? Turing provided a purely behavioristic test: a computation understands a language if by conversing with it we cannot distinguish it from a human.

This is quite a silly test, really. It doesn't provide any clue as to what actually happens within the artificial "mind"; it assumes that the external behavior of an entity completely encapsulates its internal state; it requires "man in the loop" to provide the final ruling; it does not state for how long and on what level should this conversation be held. Such a test may serve as a pragmatic common-sense method to filter out obvious failures, but it brings us not an ounce closer to understanding conscious thinking.

Still, the Turing Test stuck. If anyone tried to question the computational model of the mind, he was then confronted with the unavoidable question: what else can it be? After all, biology is physics, and therefore the brain is just a physical machine. Physics is governed by equations, which are all, in theory, computable (at least approximately, with errors being as small as one wishes). So, short of conjuring supernatural soul that magically produces a conscious mind out of biological matter, there can be no other solution.

Nevertheless, not everyone conformed to the new dogma. There were two tiers of reservations to computational Artificial Intelligence. The first, maintained, for example, by the Philosopher John Searl, didn't object to idea that a computation device may, in principle, emulate any human intellectual capability. However, claimed Searl, a simulation of a conscious mind is not conscious in itself.

To demonstrate this point Searl envisioned a person who doesn't know a single word in Chinese, sitting in a secluded room. He receives Chinese texts from the outside through a small window and is expected to return responses in Chinese. To do that he uses written manuals that contain the AI algorithm which incorporates a comprehensive understanding of the Chinese language. Therefore, a person fluent in Chinese that converses with the "room" shall deduce, based on Turing Test, that it understands the language. However, in fact there's no one there but a man using a printed recipe to convert an input message he doesn't understands to an output message he doesn't understands. So, who in the room understands Chinese?

The next tier of opposition to computationalism was maintained by the renowned physicist and mathematician Roger Penrose, claiming that the mind has capabilities which no computational process can reproduce. Penrose considered a computational process that imitates a human mathematician. It analyses mathematical conjecture of a certain type and tries to deduce the answer to that problem. To arrive at a correct answer the process must employ valid logical inferences. The quality of such computerized mathematician is measured by the scope of problems it can solve.

What Penrose proved is that such a process can never verify in any logically valid way that its own processing procedures represent valid logical deductions. In fact, if it assumes, as part of its knowledge base, that its own operations are necessarily logically valid, then this assumption makes them invalid. In other words, a computational machine cannot be simultaneously logically rigorous and aware of being logically rigorous.

A human mathematician, on the other hand, is aware of his mental processes and can verify for himself that he is making correct deductions. This is actually an essential part of his profession. It follows that, at least with respect to mathematicians, cognitive functions cannot be replicated computationally.

Neither Searl's position nor Penrose's was accepted by the mainstream, mainly because, if not computation, "what else can it be?". Penrose's suggestion that mental processes involve quantum effects was rejected offhandedly, as "trying to explicate one mystery by swapping it with another mystery". And the macroscopic hot, noisy brain seemed a very implausible place to look for quantum phenomena, which typically occur in microscopic, cold and isolated systems.

Fast forward several decades. Finaly, it seemed as though the vision of true Artificial Intelligence technology started bearing fruits. A class of algorithms termed Deep Neural Networks (DNN) achieved, at last, some human-like capabilities. It managed to identify specific objects in pictures and videos, generate photorealistic images, translate voice to text, and support a wide variety of other pattern recognition and generation tasks. Most impressively, it seemed to have mastered natural language and could partake in an advanced discourse. The triumph of computational AI appeared more feasible than ever. Or was it?   

During my years as undergraduate and graduate student I sometimes met fellow students who, at first impression, appeared to be far more conversant in the academic courses subject matter than me. They were highly confident and knew a great deal about things that were only briefly discussed in lectures. Therefore, I was vastly surprised when it turned out they were not particularly good students, and that they usually scored worse than me in the exams. It took me some time to realize that these people hadn't really possessed a better understanding of the curricula. They just adopted the correct jargon, employed the right words, so that, to the layperson ears, they had sounded as if they knew what they were talking about.

I was reminded of these charlatans when I encountered natural language AIs such as Chat GPT. At first glance, their conversational abilities seem impressive – fluent, elegant and decisive. Their style is perfect. However, as you delve deeper, you encounter all kinds of weird assertions and even completely bogus statements, uttered with absolute confidence. Whenever their knowledge base is incomplete, they just fill the gap with fictional "facts". And they can't distinguish between different levels of source credibility. They're like Idiot Savants – superficially bright, inherently stupid.

What confuses so many people with regard to AIs is that they seem to pass the (purely behavioristic) Turing Test. But behaviorism is a fundamentally non-scientific viewpoint. At the core, computational AIs are nothing but algorithms that generates a large number of statistical heuristics from enormous data sets.

There is an old anecdote about a classification AI that was supposed to distinguish between friendly and enemy tanks. Although the AI performed well with respect to the database, it failed miserably in field tests. Finely, the developers figured out the source of the problem. Most of the friendly tanks' images in the database were taken during good weather and with fine lighting conditions. The enemy tanks were mostly photographed in cloudy, darker weather. The AI simply learned to identify the environmental condition.

Though this specific anecdote is probably an urban legend, it illustrates the fact that AIs don't really know what they're doing. Therefore, attributing intelligence to Arificial Intelligence algorithms is a misconception. Intelligence is not the application of a complicated recipe to data. Rather, it is a self-critical analysis that generates meaning from input. Moreover, because intelligence requires not only understanding of the data and its internal structure, but also inner-understanding of the thought processes that generate this understanding, as well as an inner-understanding of this inner-understanding (and so forth), it can never be implemented using a finite set of rules. There is something of the infinite in true intelligence and in any type of conscious thought.

But, if not computation, "what else can it be?". The substantial progress made in quantum theory and quantum computation revived the old hypothesis by Penrose that the working of the mind is tightly coupled to the quantum nature of the brain. What had been previously regarded as esoteric and outlandish suddenly became, in light of recent advancements, a relevant option.

During the last thirty years, quantum computation has been transformed from a rather abstract idea made by the physicist Richard Feynman into an operational technology. Several quantum algorithms were shown to have a fundamental advantage over any corresponding classical algorithm. Some tasks that are extremely hard to fulfil through standard computation (for example, factorization of integers to primes) are easy to achieve quantum mechanically. Note that this difference between hard and easy is qualitative rather than quantitative. It's independent of which hardware and how much resources we dedicate to such tasks.