A latent monadology: An extended revisitation of the mind-body problem

Image by Genis Carreras

In an earlier post, I’d spoken about a certain class of mind-body interfacing problems (the way I’d identified it): evolution being a continuous process, can psychological changes effected in a certain class of people identified solely by cultural practices “spill over” as modifications of evolutionary goals? There were some interesting comments on the post, too. You may read them here.

However, the doubt was only the latest in a series of others like it. My interest in the subject was born with a paper I’d read quite a while ago that discussed two methods either of which humankind could possibly use to recreate the human brain as a machine. The first method, rather complexly laid down, was nothing but the ubiquitous recourse called reverse-engineering. Study the brain, understand what it’s made of, reverse all known cause-effect relationships associated with the organ, then attempt to recreate the cause using the effect in a laboratory with suitable materials to replace the original constituents.

The second method was much more interesting (this bias could explain the choice of words in the previous paragraph). Essentially, it described the construction of a machine that could perform all the known functions of the brain. Then, this machine would have to be subjected to a learning process, through which it would acquire new skills while it retained and used the skills it’s already been endowed with. After some time, if the learnt skills, so chosen to reflect real human skills, are deployed by the machine to recreate human endeavor, then the machine is the brain.

Why I like this method better than the reverse-engineered brain is because it takes into account the ability to learn as a function of the brain, resulting in a more dynamic product. The notion of the brain as a static body is definitively meaningless as, axiomatically, conceiving of it as a really powerful processor stops short of such Leibnizian monads as awareness and imagination. While these two “entities” evade comprehension, subtracting the ability to, yes, somehow recreate them doesn’t yield a convincing brain as it is. And this is where I believe the mind-body problem finds solution. For the sake of argument, let’s discuss the issue differentially.

Spherical waves coming from a point source. The solution of the initial-value problem for the wave equation in three space dimensions can be obtained from the solution for a spherical wave through the use of partial differential equations. (Image by Oleg Alexandrov on Wikimedia, including MATLAB source code.)

Hold as constant: Awareness
Hold as variable: Imagination

The brain is aware, has been aware, must be aware in the future. It is aware of the body, of the universe, of itself. In order to be able to imagine, therefore, it must concurrently trigger, receive, and manipulate different memorial stimuli to construct different situations, analyze them, and arrive at a conclusion about different operational possibilities in each situation. Note: this process is predicated on the inability of the brain to birth entirely original ideas, an extension of the fact that a sleeping person cannot be dreaming of something he has not interacted with in some way.

Hold as constant: Imagination
Hold as variable: Awareness

At this point, I need only prove that the brain can arrive at an awareness of itself, the body, and the universe, through a series of imaginative constructs, in order to hold my axiom as such. So, I’m going to assume that awareness came before imagination did. This leaves open the possibility that with some awareness, the human mind is able to come up with new ways to parse future stimuli, thereby facilitating understanding and increasing the sort of awareness of everything that better suits one’s needs and environment.

Now, let’s talk about the process of learning and how it sits with awareness, imagination, and consciousness, too. This is where I’d like to introduce the metaphor called Leibniz’s gap. In 1714, Gottfried Leibniz’s ‘Principes de la Nature et de la Grace fondés en raison‘ was published in the Netherlands. In the work, which would form the basis of modern analytic philosophy, the philosopher-mathematician argues that there can be no physical processes that can be recorded or tracked in any way that would point to corresponding changes in psychological processes.

… supposing that there were a mechanism so constructed as to think, feel and have perception, we might enter it as into a mill. And this granted, we should only find on visiting it, pieces which push one against another, but never anything by which to explain a perception. This must be sought, therefore, in the simple substance, and not in the composite or in the machine.

If any technique was found that could span the distance between these two concepts – the physical and the psychological – then Leibniz says the technique will effectively bridge Leibniz’s gap: the symbolic distance between the mind and the body.

Now it must be remembered that the German was one of the three greatest, and most fundamentalist, rationalists of the 17th century: the other two were Rene Descartes and Baruch Spinoza (L-D-S). More specifically: All three believed that reality was composed fully of phenomena that could be explained by applying principles of logic to a priori, or fundamental, knowledge, subsequently discarding empirical evidence. If you think about it, this approach is flawless: if the basis of a hypothesis is logical, and if all the processes of development and experimentation on it are founded in logic, then the conclusion must also be logical.

(L to R) Gottfried Leibniz, Baruch Spinoza, and Rene Descartes

However, where this model does fall short is in describing an anomalous phenomenon that is demonstrably logical but otherwise inexplicable in terms of the dominant logical framework. This is akin to Thomas Kuhn’s philosophy of science: a revolution is necessitated when enough anomalies accumulate that defy the reign of an existing paradigm, but until then, the paradigm will deny the inclusion of any new relationships between existing bits of data that don’t conform to its principles.

When studying the brain (and when trying to recreate it in a lab), Leibniz’s gap, as understood by L-D-S, cannot be applied for various reasons. First: the rationalist approach doesn’t work because, while we’re seeking logical conclusions that evolve from logical starts, we’re in a good position to easily disregard the phenomenon called emergence that is prevalent in all simple systems that have high multiplicity. In fact, ironically, the L-D-S approach might be more suited for grounding empirical observations in logical formulae because it is only then that we run no risk of avoiding emergent paradigms.

“Some dynamical systems are chaotic everywhere, but in many cases chaotic behavior is found only in a subset of phase space. The cases of most interest arise when the chaotic behavior takes place on an attractor, since then a large set of initial conditions will lead to orbits that converge to this chaotic region.” – Wikipedia

Second: It is important to not disregard that humans do not know much about the brain. As elucidated in the less favored of the two-methods I’ve described above, were we to reverse-engineer the brain, we can still only make the new-brain do what we already know that it already does. The L-D-S approach takes complete knowledge of the brain for granted, and works post hoc ergo propter hoc (“correlation equals causation”) to explain it.

[youtube http://www.youtube.com/watch?v=MygelNl8fy4?rel=0]

Therefore, in order to understand the brain outside the ambit of rationalism (but still definitely within the ambit of empiricism), introspection need not be the only way. We don’t always have to scrutinize our thoughts to understand how we assimilated them in the first place, and then move on from there, when we can think of the brain itself as the organ bridging Leibniz’s gap. At this juncture, I’d like to reintroduce the importance of learning as a function of the brain.

To think of the brain as residing at a nexus, the most helpful logical frameworks are the computational theory of the mind (CTM) and the Copenhagen interpretation of quantum mechanics (QM).

xkcd #45 (depicting the Copenhagen interpretation)

In the CTM-framework, the brain is a processor, and the mind is the program that it’s running. Accordingly, the organ works on a set of logical inputs, each of which is necessarily deterministic and non-semantic; the output, by extension, is the consequence of an algorithm, and each step of the algorithm is a mental state. These mental states are thought to be more occurrent than dispositional, i.e., more tractable and measurable than the psychological emergence that they effect. This is the break from Leibniz’s gap that I was looking for.

Because the inputs are non-semantic, i.e., interpreted with no regard for what they mean, it doesn’t mean the brain is incapable of processing meaning or conceiving of it in any other way in the CTM-framework. The solution is a technical notion called formalization, which the Stanford Encyclopedia of Philosophy describes thus:

… formalization shows us how semantic properties of symbols can (sometimes) be encoded in syntactically-based derivation rules, allowing for the possibility of inferences that respect semantic value to be carried out in a fashion that is sensitive only to the syntax, and bypassing the need for the reasoner to have employ semantic intuitions. In short, formalization shows us how to tie semantics to syntax.

A corresponding theory of networks that goes with such a philosophy of the brain is connectionism. It was developed by Walter Pitts and Warren McCulloch in 1943, and subsequently popularized by Frank Rosenblatt (in his 1957 conceptualization of the Perceptron, a simplest feedforward neural network), and James McClelland and David Rumelhart (‘Learning the past tenses of English verbs: Implicit rules or par­allel distributed processing’, In B. MacWhinney (Ed.), Mechanisms of Language Acquisition (pp. 194-248). Mah­wah, NJ: Erlbaum) in 1987.

(L to R) Walter Pitts (L-top), Warren McCulloch (L-bottom), David Rumelhart, and James McClelland

As described, the L-D-S rationalist contention was that fundamental entities, or monads or entelechies, couldn’t be looked for in terms of physiological changes in brain tissue but in terms of psychological manifestations. The CTM, while it didn’t set out to contest this, does provide a tensor in which the inputs and outputs are correlated consistently through an algorithm with a neural network for an architecture and a Turing/Church machine for an algorithmic process. Moreover, this framework’s insistence on occurrent processes is not the defier of Leibniz: the occurrence is presented as antithetical to the dispositional.

Jerry Fodor

The defier of Leibniz is the CTM itself: if all of the brain’s workings can be elucidated in terms of an algorithm, inputs, a formalization module, and outputs, then there is no necessity to suppress any thoughts to the purely-introspectionist level (The domain of CTM, interestingly, ranges all the way from the infraconscious to the set of all modular mental processes; global mental processes, as described by Jerry Fodor in 2000, are excluded, however).

Where does quantum mechanics (QM) come in, then? Good question. The brain is a processor. The mind is a program. The architecture is a neural network. The process is that of a Turing machine. But how is the information between received and transmitted? Since we were speaking of QM, more specifically the Copenhagen interpretation of it, I suppose it’s obvious that I’m talking about electrons and electronic and electrochemical signals being transmitted through sensory, motor, and interneurons. While we’re assuming that the brain is definable by a specific processual framework, we still don’t know if the interaction between the algorithm and the information is classical or quantum.

While the classical outlook is more favorable because almost all other parts of the body are fully understand in terms of classical biology, there could be quantum mechanical forces at work in the brain because – as I’ve said before – we’re in no way to confirm or deny if it’s purely classical or purely non-classical operationally. However, assuming that QM is at work, then associated aspects of the mind, such as awareness, consciousness, and imagination, can be described by quantum mechanical notions such as the wavefunction-collapse and Heisenberg’s uncertainty principle – more specifically, by strong and weak observations on quantum systems.

The wavefunction can be understood as an avatar of the state-function in the context of QM. However, while the state-function can be constantly observable in the classical sense, the wavefunction, when subjected to an observation, collapses. When this happens, what was earlier a superposition of multiple eigenstates, metaphorical to physical realities, becomes resolved, in a manner of speaking, into one. This counter-intuitive principle was best summarized by Erwin Schrodinger in 1935 as a thought experiment titled…

[youtube http://www.youtube.com/watch?v=IOYyCHGWJq4?rel=0]

This aspect of observation, as is succinctly explained in the video, is what forces nature’s hand. Now, we pull in Werner Heisenberg and his notoriously annoying principle of uncertainty: if either of two conjugate parameters of a particle is measured, the value of the other parameter is altered. However, when Heisenberg formulated the principle heuristically in 1927, he also thankfully formulated a limit of uncertainty. If a measurement could be performed within the minuscule leeway offered by the constant limit, then the values of the conjugate parameters could be measured simultaneously without any instantaneous alterations. Such a measurement is called a “weak” measurement.

Now, in the brain, if our ability to imagine could be ascribed – figuratively, at least – to our ability to “weakly” measure the properties of a quantum system via its wavefunction, then our brain would be able to comprehend different information-states and eventually arrive at one to act upon. By extension, I may not be implying that our brain could be capable of force-collapsing a wavefunction into a particular state… but what if I am? After all, the CTM does require inputs to be deterministic.

How hard is it to freely commit to a causal chain?

By moving upward from the infraconscious domain of applicability of the CTM to the more complex cognitive functions, we are constantly teaching ourselves how to perform different kinds of tasks. By inculcating a vast and intricately interconnected network of simple memories and meanings, we are engendering the emergence of complexity and complex systems. In this teaching process, we also inculcate the notion of free-will, which is simply a heady combination of traditionalism and rationalism.

While we could be, with the utmost conviction, dreaming up nonsensical images in our heads, those images could just as easily be the result of parsing different memories and meanings (that we already know), simulating them, “weakly” observing them, forcing successive collapses into reality according to our traditional preferences and current environmental stimuli, and then storing them as more memories accompanied by more semantic connotations.