By
Sudeep Adhikari
Thought is an inexact certitude of present. “Expression of Thoughts”, either oral or written, happens in the plane of reference, a Euclidian kind of space of representational exactness.
Thought lacks the clearly defined contours and tends to be a pregnant fuzz; it does not conform to the rules of language, logic and mathematics. We certainly don’t think in language! As a process, it has an uncanny penchant to chaos and nonequilibrium, and an ever tendency to proliferate endlessly into the inconceivable realms. Thought; the mighty mother Gaia, always restless and pregnant, IdeaConceptPhilosophies; the lonely Mars, cursed with equilibrium and inertia!
Mathematical Thinking as the subset of “Thought”: Mathematics operates on the plane of reference with clearly defined rules, axioms and theorems. But this is not the case with “mathematicalthinking”, if we consider the works of medieval mathematicians, ancient Greek mathematical thinkers and preNewtonian mathematicians. For instance, if we consider the works of Pythagoreans, Plato, Kepler or Newton, we can notice that they have a certain sense of mystery about them. For the Pythagoreans, numbers are more than the mathematical objects subject to rules of mathematics; they were thought to be of divine origin with much larger spiritual significance. The same is the case with Plato and Kepler. This can be attributed to the animisticalchemical worldview that was prevalent before the Newtonian revolution. Newtonian paradigm paved the way to scientific renaissance, thus leading to the formation of more formalisticscientific worldview. Under this light, evolution of Mathematical thinking can be divided into following two groups:

AnimisticAlchemical Mathematical Thinking: Before scientific revolution, Mathematics enjoyed a different kind of sovereignty. Rather than being a formal language that science speaks of, prerenaissance mathematics was an independent method to understand nature, a kind of science in itself. Without enough understanding of matter and its mechanics, the ancient and medieval thinkers developed a patternbased study of our material universe, for instance, ancient astronomy. Numbers and geometrical objects were thought to be the archetypal images of God’s thought and the most singular key to understand the trinity of God, Man and Nature.

FormalisticScientific Mathematical Thinking: With the advent of Newtonian Mechanics, the role of mathematics underwent a qualitative shift. Euclidian Geometry, as the science of pattern, was found to be inadequate to express the complex interaction of matter with other fields in quantitative terms. Mathematics then had a new role to play; that is, providing a formal language to the rapidly developing science of Mechanics. For instance, the discovery of Differential Calculus, independently by Newton and Leibnitz, was an attempt to find a proper formal language that could encapsulate the newly discovered laws of motion and theory of gravity. And with the advent of relativistic and quantum mechanics at the start of 20th century, mathematics was creatively bound to evolve with much broader and abstract proliferations, such as Riemannian geometry and topology. Under the new scientific paradigm, mathematics is not a science, but a formal language which science speaks of.
One of the implications of the new paradigm is, mathematics was robbed of its prerenaissance “presumed transcendentality” and was reconsidered as the most rational, exact and formal system. Now here comes the important part:
Considering Mathematics as a purely formal method, does it also imply that “mathematical thinking” which forms a small subset of the whole process of thought, also acts in the similar fashion?
It is to be remembered that this has a strong bearing on our argument that thought is a happening that can’t be reduced to a singular datum. To put it simply, is mathematical thinking algorithmic? If yes, what it implies is, mathematical thinking is a discrete computational process that can be reduced to finite mathematical steps. This is a very fundamental issue, as it forms the basic premise of a school of thought called Strong Artificial Intelligence, which promulgates consciousness to be a computational process, hence algorithmic. However, it was brilliantly depicted by Roger Penrose that mathematical thinking itself is nonalgorithmic. The argument is, if the most clinical of all thought processes (mathematical thinking) is not amenable to computation, how Strong AI can claim the computability of infinitely huge panorama of complex human thoughtprocesses, which may vary from Poetic ecstasy, mushroom trips, depression, sense of existential meaninglessness, to a Schizophrenic Godtalk? We will continue our argument based on this particular premise.
Strong AI basically presumes the following:

Thought is the function of brain machine;

For everything happening in mindmachine, there is a strict neurological correlate in Brainmachine;

There is a strict causal connection between brainmachine and mindmachine;

Mindmachine is the aggregate of algorithmic computations carried out in brain machine.
Are these assumptions tenable for the computational school of thought concerning consciousness to be a valid theory? What do we mean when we use mind as a totally defined category? For instance when we use the term “I am losing my mind”, are we referring to the brain itself or the sum total of all the algorithms being carried out in the brain? Or is it a small atomistic soul that resides inside the brain? A little bit of ruminations and we can see that mind is quite an arbitrary assumption. “Mind” is just a symbol that we have collectively agreed to represent the totality of our thoughts. What we are constantly aware of, is our thoughts, not our mind. When we are thinking, there is absolutely no guarantee in scientific sense that it is something happening exactly in our head. Thought is a process, a becoming, and it may be the case that it is actually totally identical with our whole psychosomatic matrix, or maybe not.
Thought is not an atom, it is a sandpile; it is not a matchstick but the whole fire; constantly changing, constructing, dissolving, dissipating, yet remaining an irreducible organic whole. A fire never exists in isolation; it is a dynamism that permeates the whole matrix of chemicalcompounds making the matchsticks, the fuel, the oxygen that I am breathing at the moment and all the inorganic and organic things it is consuming.
In the light of strong AI’s claim, if consciousness is dependent on the mechanics of brain, we certainly need to sort out many burning issues. First, we need to identify each and every type of thought and secondly, we need to find their exact neurological correlates. Thirdly, we need to identify the underlying algorithms that are implicitly actuated to generate them. And still we will be missing,

The exact causal connection between the actualization of these algorithms and their neurological correlates

The exact causal connection between the corresponding neurological events and their behavioral correlates
A certain pattern of neuronsfiring in the brain will generate a certain level of consciousness in the mind which will generate a particular feeling and which will be expressed through a particular behavioral response by the subject!
These are some strikingly preposterous assumptions which fundamentally express nothing but a shitload of hypotheses, and baseless assumptions.
Edward Titchener counted 44, 435 numbers of elementary sensations, including 32, 820 for vision, 11, 600 for audition and 1 for sex. And they don’t even cover the smallest portion of the spectrum of consciousness [At the moment we are totally unaware of its size]. As we move towards higher psychological states which encompass perception, reflection, contemplation, awareness, understanding and selfawareness, our atomization is bound to fail miserably.
Problem with intentionality, agency and action: If the algorithmic nature of consciousness is a valid assumption, it implies infinite computation which is beyond our current level of material progress to understand. And there is always an inevitable leap to agency and action that we can never not consider. We may well be computer as per strong AI’s claim, but we still show response and act on our volitions. Then how the computation begets intentionality? Consciousness is a vectorial relational field; a consciousness of something implies an intention to action. And the “Intention to action” is based on the meaningsystem created by the subject, which is further based on his selfreflection on his existence and its dynamics with the adjoining cultural milieu. For instance, if the feeling we collectively agree to be named as “anger” is associated with the operation of certain algorithm in our brain, where is the link connecting this sensation with its behavioral and intentional unfoldment? When I am angry, I may possibly turn red, I may clinch my teeth and scream at my loudest possible voice.
If we posit actuation of certain algorithm to beget such responses, then we possibly need to admit the presence of another different algorithm to actuate that particular algorithm. If we adhere to strong AI’s position of computational consciousness, we have to face the chimera of infinite regress to admit any causal connection between a particular computation in brain and the consequent intentionality. Intentionality by its very nature posits the presence of “Agency” which is by our argument beyond algorithmic computation. The “Agency” and “Intentionality” are still epiphenomenon, the “Ghosts in the computing machine” if we adhere to strong AI’s claim. Is my “Anger” the result of running some algorithm in my brain machine or is it my anger that actuates certain other algorithm resulting in certain biochemistry of my brain machine to yield some particular behavioral response?
If my brain machine at the beginning is just a “Neuroidal Tabula Rasa”, what actuates the first ever algorithm to ensure intentionality and agency?
The whole claim of the school of strong AI can thus be seen as a mere tautology based on an unfounded assumption of arbitrary causal connection between brain and consciousness. As we discussed above, we can’t physically detect the abstraction called “Mind” and we certainly don’t have sufficient science to establish the causal connection between brain and consciousness. We have created this erroneous dualism of brainmachine and so called “Mindmachine” based on our ancient habits of reductionism, linearization and equilibration. One of the Greek philosophers (Hippocrates or one of his followers, contemporaneous with Plato) wrote “From the brain and from the brain only, arise our pleasures, joys, laughter and jests, as well as our sorrows, pains, grief and tears“. And 2 millennia later, we are still operating on the same paradigm without any formidable ground and basis.
L.G. Valiant, a computer scientist who has worked on the algorithmic and programmable model of brain function, presupposed a model of neuronnetwork called Neuroidal net which can be computationally programmed. The author has proposed that NTR model can be algorithmically trained to learn by basic mechanical procedures of memorization and deductive reasoning. He has asserted that memorization can be computationally viewed as a process of forming Boolean conjunctions. Fair enough Sir! But how much of my mental exercise is involved in memorization and deductive reasoning to come up with an actionable intentionality? I can memorize my national anthem through a mental process that can be modeled as the formation of Boolean conjunctions, but how can it model my innate sense of responsibility to my country, to the whole planet earth, and to humanity, which I feel with complete certitude?
The author states “It is the internal computations of these kind, that pull together a novel combination of pieces of information already known, that we consider here to characterize reasoning”. However, he further states that, “The algorithm is already a weakness when it comes to the “commonsense reasoning” that is done subconsciously”. He admits the inadequacy of the computational model to encompass higher level reasoning which keeps on getting blurred as we move to deeper psychological levels. In the meantime, he has admitted a psychological state that we all collectively agreed to be named as “Subconscious”, which total mechanics is still an unknown.
Unless we know the physics of the problem, we can’t develop its adequate mathematical model, and unless we have an adequate mathematical model, the resulting algorithm tends to be more fallacious, arbitrary and without any tenable substructure. As already said, thought or consciousness resides in the plane of complete indivisibility and relational interconnections, which exact material model we are still unaware of. Unless we have the complete scientific theory of consciousness (if there is any), we will never be able to comprehend the multidimensionality of humanpsyche in quantitative terms. Hence, to admit the computability of consciousness, we need to know consciousness, its genealogy and its mechanics and its relevance to brain machine, if there is any.
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