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Sometimes regarded as the queen of all sciences, mathematics finds application in almost all endeavors of our lives, it is applied in the commercial world, the scientific world, the world of humanities and in our daily lives. We seem not to do without it, even if one is not formally educated somehow he/she manages to have knowledge about it probably because it seems not to lie and also has a way of bringing balance and optimization to our daily lives and activities. In fact this was a very beautiful poetic quote about mathematics from the notable philosopher and mathematician Bertrand Russell.

" Mathematics, rightly viewed, possesses not only truth, but supreme beauty cold and austre, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a Stern perfection such as only the greatest art can show. The true spirit of delight, the exaltion, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry ".

However whether nature is fundamentally mathematical or not is still a matter of philosophical debate. In the sciences, especially in the natural sciences mathematics is a very invaluable tool, as it is used to simplify physical laws, develop and predict physical laws (theories), no wonder in our various formal institutions it is one of the basic subjects being taught, especially for those of us that would eventually become scientists and engineers.

Despite the beauty, predictive power and success of mathematics, there appears to be a common phenomenon in the field of science that it fails to handle, not only that, the basic understanding of this phenomenon despite being common is still inconclusive. What then is this phenomenon ?.

Consciousness

You must have guessed right, it is consciousness, nobody really knows what consciousness actually is. Several attempts even from the greatest minds since antiquity, has been made to pin it down especially from a philosophical perspective, up until now the result is still inconclusive and sometimes arguments among Philosophers and Scientists leads to heated disputes and has led to different philosophical schools of thought. Some say it's an attribute of only human beings, some say it's an attribute of only living things

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and some say it's an attribute of intelligent agents - artificial intelligent agents included.
A simple and generally accepted definition of consciousness is awareness of the environment, but wait a minute, if this general definition is actually true, then can't everything be said to be conscious - a view/belief that is accepted by the panpsychists (Philosophers that believe everything in the universe possesses a mind in addition to the body and therefore be said to be conscious). Take a simple and common scenario such as change in state, for example ice to water.

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When ice is in a hot environment, it interacts with it and gives a response by changing state to water, implying that it is aware of it's environment. From a technical level, assuming at normal pressure and no impurities on/in the ice, this change in state is possible if the temperature of the environment is above freezing temperature of water - 0º celsius. Looking at it from the mind perspective, the ice is aware that when the environment's temperature is above 0º celsius it should change state and from the body perspective the information is stored somewhere in the ice, however the stored information for the same ice cannot be the same for all observers, as different observers in other planets would convey different values for the normal pressure, implying that it's mind is subjective. This scenario is analogous to humans whom the mind and body is more attributed to, when i tell you to come to my house tomorrow, you would, provided it interests you, it interesting you is an attribute of free will of the mind but you coming tomorrow implies that the information was stored in your brain.

There are disciplines in the natural sciences that are very interested in understanding consciousness and a well established understanding of consciousness can take this disciplines to their prime and further improve our technologies.

Neuroscience/Cognitive Science

Consciousness and intelligence is often considered/believed to be an aspect of the mind and the mind is mostly localised in the brain (body).

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This aspect of science seeks to understand consciousness from a physical perspective - how it arose from biological neural networks/nervous system.

Computer Science

Sometimes consciousness and intelligence are interchanged, understanding consciousness is crucial in the field of artificial intelligence - a branch of computer science. There are two kinds of AI which are the strong AI and the weak AI, the former is capable of doing everything the human brain can do, while the latter does specific purposes and is in current use, especially in industries.

Physics

When @juecoree posted his article in this community titled "Why do we dream?: A defense mechanism, what-if simulation or to ease painful memories" which talked about the possible reasons of dreaming during sleep, I posted a comment that suggested that dreams might be a manifestation of quantum mechanics with indirect proofs and also suggested the possibility of everything in the universe dreaming including subatomic particles, indirectly what it tells us is that everything could be conscious, we shall see why it points to that direction.

Surely we should all be surprised that physics is now interested in consciousness, after all the philosophy of physics(classical) does not basically include consciousness, it's main aim is investigating the fundamentals of matter and energy, and interactions in space and time, consciousness is considered a secondary concept/concept beyond physicality. This idea began to crumble in the early 20th century with the inception of quantum mechanics and originally began with the work of Max Planck that attempted to explain the black body radiation curve to be a consequence of energy quantization, it was eventually verified experimentally. When quantum mechanics was fully developed the philosophy of physics changed and what is most striking is that we are yet to reconcile quantum physics with classical physics.

Consciousness in quantum mechanics comes in two forms, back to back

1. A single particle is always first in superposition of states e.g an electron can be in multiple places at a single time ( an idea that is impossible in classical physics), when measurement is made only a single state is observed (an idea also impossible in classical physics), in the case of the electron, you would see it in a particular place not in multiple places anymore - double slit experiment confirms it, how it happens is still a matter of philosophical debate. The measurement is always made by we humans the often attributed conscious entity, in fact even if animals or non living entities interacts with the quantum system, we would still get involved, as we would need to get information about the system, for the fact that we must always get involved, then consciousness must be involved in describing the physics of the quantum world.

2. The particles/universe appears to be conscious, they/it can sense our involvement in trying to get information about them and somehow able to counter-trick us when we try to trick it, for better understanding see delayed choice experiment - an extension of the double slit experiment.

In fact when you compare quantum physics and classical physics you would observe that that the universe is contradicting itself, see Schrodinger's cat experiment.

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A generally accepted but absurd view is that the physical reality we observe is brought into existence by our observation, this view has kept scientists worried up till this moment, even Einstein one of the early founders of quantum physics disliked the quantum mechanical principles, even till he died, he said quantum mechanics was not complete and once asked one of his colleague if he truly believed that the moon wasn't there when no one was looking.

From the change in state scenario (ice to water) and quantum physics, you might be forced to believe that everything is conscious and that consciousness is a fundamental property of the universe. However you don't need to worry as you are not alone in this, in fact some Scientists went further in believing that consciousness itself might have quantum mechanical origins, this idea was first proposed by the renowned British mathematician and 2020 physics Noble laureate Roger Penrose, back in the 1980's in his book titled "The Emperor's New Mind" and was called Orch-OR hypothesis(orchestrated objective reduction).

Mathematical Description Of Consciousness

Assuming the panpsychists approach to consciousness were to be a true fact, then consciousness can be described mathematically and this is what some Scientists are currently working on. The corresponding theory is called IIT (integrated information theory), this theory follows Penrose's quantum mechanical approach and according to two researchers from the Munich center for mathematical philosophy and University of Oxford, the theory predicts that consciousness is everywhere and is quantifiable - it can be calculated, and it's quantified form is called Phi.

This however is only in theory, science requires experimentation to establish any theory as facts/laws. All we can do now is wait and watch, if it indeed comes out positive, then it would revolutionize what we know about the universe. Imagine being able to predict your friends next moves with equations, probably he/she might not be the friend he/she claims to be, probably he/she wants to kill you, take your money or your hot babe, hmm sounds fun right, I just can't wait to whoop somebody's ass. I bet some of you are praying this research doesn't turn out positive, well keep it up, we shall eventually find out.

For further reading
Some Scientists Believe the Universe Is Conscious

The Strange Link Between The Human Mind and Quantum Physics

I would like to thank you all for stopping by to read my jargons and also would like to thank the @OCD team for their valuable support.
Lastly don't forget to do the needful,
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