Narrating Consciousness - II

Matrix IIT Guwahati
5 min readSep 11, 2021

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Continuing the discussion on Consciousness from where we left…

What would the equation look like? Can it be a trigonometric function or an exponential function, or a recursion as they are notoriously so common in many of the physical phenomena around us? Or a combination of all of this?

We can talk about one such equation proposed by Lucas Roy Lehman that claims to determine consciousness! Even though it is too pretentious, let me explain it :

C = P * B * I,
Where C=consciousness ;
P = presence ;
B = breath ;
I = intention.

That is, if I am not conscious, I am thinking about the past or projecting about the future, so the first thing about being conscious is to be present at the moment.

Once I am present, what I am feeling and what I am thinking can be expanded with breath. And once I have had that expansion, what I can create from this expanded presence is of importance.

One might argue that it is very bold to state such a simple equation to determine something so complex and abstract! But then again, the factors used in the equation are very notional themselves. Furthermore, as we require perfect knowledge to calculate consciousness, is it fair to say that consciousness is computable even after using these equations? For an ideal observer bearing a complete understanding of the brain and its functioning, it might be computable, but it is incredible for humans with their imperfect knowledge.

Another interpretation of consciousness revolves around the analogy between the neural binding in the brain and the workings of a digital computer; a quest to mechanise minds i.e. our pursuit for modelling consciousness in a machine that works on mathematical terms. The coming of Godel’s theorem introduced new paths to mathematical philosophy and finally in 1961 JR Lucas stated that Godel’s incompleteness theorem proves that Mechanism is false, that is, that mind and its extension, consciousness, can’t be explained as machines.

The framework of consciousness works on models that our brain projects based on past experiences, intelligence, and the natural ability of the species to work for their survival. These models come out of complex neural wiring and lay out an algorithm on how to respond and what to ignore, called the behavioral aspect of consciousness.

But the fluke is, our conscious mind is also aware of the self; hence the brain is projecting a model to know about consciousness out of which our very thoughts about knowing it are popping up. Intriguing, right? This is where mathematics finds itself at a halt. The idea that everything is provable as true or false was at the core of math until Godel, who then shook the beliefs math had been progressing on. Any consistent (if there is no statement such that the statement itself and its negation are both derivable in the system) and formal system (equipped with finite decidable axioms) is incomplete. In layman’s language, all the statements said within and using the system can not be proven or disproven within the same system. And one such statement comes in the Second incompleteness theorem, for any consistent system F, the consistency of F cannot be proven in F itself. The undecidability of truthfulness or falseness of such statements in a given system is Godel’s claim. The statement acts as the dividing front between reasoning mind(even within the realm of pure mathematics) and algorithmic contemplations of math; as the consciousness we have developed is capable of knowing outside parameters and the very self unlike any formal system of mathematics.

“The human mind infinitely surpasses the power of any finite machine, or else there exist absolutely unsolvable diophantine problems,’’ said Gibbs in 1951.

I, call myself P, am conscious. And suppose one day P uploaded his consciousness on a machine/algorithm/system S. Given this assumption, “consider the class of statements P knows to be true.” Since P knows P is conscious and all his reasoning is in S, therefore S is also conscious. But this also gives rise to a new system S° which includes all the consciousness P has in S plus the assumption that “P transferred all his consciousness to S”. The latter statement cannot be proven in S but only in S°. But by Godel’s theorem, G(S°) is also true. However, S° could not prove that G(S°) is true.

But we can infer that P is S°(as S° is S plus the assumption that P knows that P is S), and P can also see the truthiness of Godel’s sentence G(S°) and therefore given that P is So, So can also see that G(S°) is true which contradicts the previous statement that S° cannot see the truthfulness of G(S°). Hence our assumption that must be wrong and consciousness of P cannot be implemented in any formal system.

The similarities between the action of a significant number of interconnected neurons and the internal workings of a computer are uncanny!

To make it clear, let’s take a comparison. The framework of a computer works on logic gates and the output it receives. To keep it simple, let the computer be a function of a series of logic gates and work on how each input transcends into a particular output sequence after passing through all of them. But one obvious flaw in computers is that logic gates work on the output-input basis with very few wires while neurons can have tons of synapses. The total number of neurons also takes the lead, as their number still is more than the number of transistors in the largest computer. But it comes with a ray of hope that if numbers set the experience of being conscious, then maybe in the future, supercomputers can model consciousness that present-day computers fail to.

But the human tendency to thrive for success has laid the idea for the development of parallel computers. A parallel computer, unlike the regular, carries out tons of calculations at an instant that are intermittently combined to the overall calculation. A conscious form uses past experience and memory, and thought to rationalize things; hence the idea of parallel computers is seen as an imitation to mark every action of the brain on a different computer.

In particular, a conclusion from the argument, particularly concerning Godel’s theorem, was that, at least in mathematics, conscious contemplation could sometimes enable one to ascertain the truth of a statement in a way that no algorithm could.

It is fascinating how many different interpretations a phenomenon can have! For example, throughout the blog, we have conveniently associated consciousness only with the living even though ancient Indian texts state that the universe is conscious, and so is every part of it! There is no way to prove anything, for we deal with abstract factors way beyond our knowledge or intellect. Many equations have been suggested; however, the issue remains as the parameters of these equations are abstract.

Many theories revolve around this theme; we could include only so many, now it is on you to choose!

By,
Swati Jhawar, Arti Sahu

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Matrix IIT Guwahati
Matrix IIT Guwahati

Written by Matrix IIT Guwahati

The student body of Department of Mathematics, IIT Guwahati. It exists to provide a channel of interaction between students and the outside world

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