Although it is not something we usually think about during the course of our lives, the fact of the matter is that humans exist in and experience only a tiny snippet of reality. This is not just in the sense of everyday constraints to our travel and psychological experiences - for instance, the difficulty of riding on an asteroid or putting one's self in the position of another enduring the hardships of living in a third world country. Although awareness of these constraints and an effort to overcome them are just as important to living a mindful and enriching life, the universe limits the human experience in a more profound and fundamental way - one necessitating a diligent open-mindedness just to recognize and appreciate, and a boundless, indefatigable passion to truly escape from.
Everything we are capable of thinking and visualizing is rooted in our experiences. To quote Aristotle, "nothing exists in consciousness that has not first been experienced by the senses". Even if we've never actually experienced a specific thing or event, we can combine knowledge of related experiences to imagine, through extrapolative thought and visualization, what a new experience might be like to a decent degree of accuracy. For example, even if you've never seen a group of 50 lions with ducks' heads running around on a purple football field, you've seen 50 of something, a lion's body, a duck's head, the color purple, and a football field before, so you are still able to imagine the scene. However, if you wish to imagine something that you lack the experience-grounded components for, the imagination will be a gross misrepresentation of the real thing, and will often be utterly inconceivable. Try imagining circling the Earth at the speed of light, 671,000,000 mph. You simply cannot; you have not the slightest sense of what it would be like, because the order of magnitude of speed incomprehensibly surpasses that of even the greatest speeds attained in the human experience - perhaps a plane ride at 600 mph.
An intimately related conundrum is that of trying to verbalize the sensation of love. For thousands of years humans have attempted the task, invariably realizing the inability of spoken language to perfectly capture and translate the feeling. In general, we have delegated words to burden unappreciated beneath a most futile endeavor: try to describe, standardize and communicate the indescribable sensations of our mind and body. To be sure, sensations refer not just to the "tingling’s" of affection or the "euphoria" of happiness, but also to the tangible things that we can sense from the physical world. What we see, smell, feel, taste and hear is equally indescribable if you think about it. What if you were asked to really describe what the color green looks like? You might list objects that are green, say what combination of other colors make up green, or scientifically define the process that creates the wavelength corresponding to phenomenon our brain interprets as green. But there are no words at your disposal to truly encapsulate what it "is", and not because our language lacks sufficient adjectives, but because it is simply impossible to translate the sensation into words. And so, we just verbally sum up and standardize this particular visual sensation as "green".
What must be realized is that human language is an abstraction of human sensation. It is a useful and understandable, yet contracted and inexact, embodiment of something more intricate - an imperfect attempt to recreate something complex in a simple form. Taking this a step further, if words are an abstraction used to externally convey the internal world of human consciousness, what we will come to see is that mathematics is a further abstraction of words used to meaningfully convey the physical world to the mental world. Just as words embody and compact sensations, symbols in mathematics embody and compact words. For the math geeks out there, it’s almost like words are the first derivative of sensations, and math symbols the second derivative.
Philosophers of mathematics fall into two camps: those who believe math is the pure, unwritten language of nature discovered by humans, and those who believe math is a human creation resembling nature to a very precise, yet ultimately imperfect degree. But even if the totality of the mathematical framework cannot be precisely superimposed over physical reality, the indisputable fact remains that it asymptotes unbelievably, incredibly, uncannily close to an exact fit. Before finally unveiling where this entire discussion is leading us to, let's briefly return to the analogy of abstractions and derivatives. Just as each successive derivative provides unique information about a system (velocity and acceleration, respectively, for example), each successive abstraction from language to mathematics does the same - words (the first derivative) describe the world of human sensations, while math (the second derivative) describes the physical world. However, mathematics possesses a unique power. Unlike our human sensations, and thus our words, which are inherently tied down to our experiences (remember Aristotle), the physical world, and thus mathematics, exists in all its grandeur and intricacy without regard for our ability to understand it. Even if math is a human creation, like Frankenstein's monster, it has the ability to escape us. Math journeys beyond the human experience and can be wielded as a transcendental tool to gain insight into secrets of reality otherwise unreachable by the limited grasp of our human biology and consciousness.
For a simple illustration of how mathematics can allow us to learn things about physical reality that are hidden from us by the mask of our faculties, let's consider the hypothetical situation of two, two-dimensional bugs that know geometry. One bug lives on a flat, two-dimensional plane and the other bug lives on the surface of a three-dimensional sphere. However, being two-dimensional creatures, both bugs experience their worlds' as being two-dimensional, and both even go to school and learn about the geometrical laws of two-dimensional realities. One day both bugs decide to draw a big triangle on the surface of their respective worlds and measure the sum of the angles. Both know from their studies that this sum should be exactly 180 degrees. Sure enough, the bug on the two-dimensional plane calculates this number for his triangle and goes home reaffirmed of his convictions about reality. But the bug on the three-dimensional sphere, no matter how many times he tries, always calculates the sum of the angles to be greater than 180 degrees. Bewildered, but convinced of his findings, the bug goes home to his textbook and furiously tries to find a kink in the axioms that has led him to his inconsistent and startling observation. These efforts lead him to an even more startling conclusion. The bug finds absolutely nothing wrong with the geometry he learned - it is a completely self-consistent theory. But what he realizes is that it only applies to two-dimensional surfaces! Being a well versed mathematician, the bug is able to find a suitable geometrical framework for three-dimensional surfaces, and sees that it matches perfectly with his mathematical observations. Even without being able to directly experience it, the two-dimensional bug is able to conclude that he is actually living in a three-dimensional world.
Albert Einstein did something essentially similar to the bug when he proved that the three-dimensional world we thought we lived in is actually four-dimensional, in the entity of "space-time" in which mass curves 3D space. But Einstein's attempt to explain this reality in words brings us right back to the beginning of our discussion. The classic visualization used to help imagine this four-dimensional world is that of a bowling ball rolling on a sheet held up horizontally by its ends by two people, and observing how the ball causes the sheet to seep in or "bend" wherever it rolls. However, this is the curving of 2D space to make it 3D, not the curving of 3D space to make it 4D. Yet we can offer no better visualization or explanation, because our experiences are grounded in a 3D reality, and so too are our imaginations and words. For the human being, a true understanding of 4D space-time can only be accessed through a true understanding of its mathematical description. This holds for any feature of non-classical, or "non-human experienced" reality. Only an extremely well-studied individual in the mathematics of, for example, Quantum Mechanics, can access true understanding of the non-intuitive phenomena of sub-atomic reality.
To this point, our discussion has centered around the fact that humans exist inside an infinitesimal bubble of physical reality who's membrane shields us from a wholesome truth, and that only mathematics has the requisite structure to permeate the membrane and signal back this truth to those trained to interpret it. If we are willing to accept the validity of such a paradigm for physical reality, in which we readily acknowledge the existence of facets untouchable by our cognizance, what reason is there to definitively denounce an equivalent paradigm for non-physical, or spiritual reality? Whatever you might personally believe, or give potential credibility for, such a spiritual reality to be, ardent monk and fierce skeptic alike would agree on one thing. From his lack of observation of a spiritual reality in his human experiences, the skeptic would have to, at the very least, concede that if such a reality actually exists it must do so outside the human experience. From his own transcendental experiences, the monk would claim to know that most of the spiritual reality exists outside the human experience - as is the case with physical reality. The transcendental tool analogous to mathematics for accessing the truths of spiritual reality is meditation. As an aside, in a rather paradoxical way from the perspective of Western thinking, it could be argued that the mystic has a better grasp on spiritual reality than the mathematician does on physical reality. The mystic bases his understanding on actual experience and observation, whereas the mathematician's understanding is second-hand. This is paradoxical because most Westerners tend to view the foundation of mathematics, science and the other "rational" schools of thought as definitively empirical, and typically do not view mysticism in this way.
Furthermore, in the same way that the mathematician cannot accurately convey his mathematical understanding of phenomena beyond the physical "membrane" in words, neither can the mystic verbally convey the non-human experience he undergoes while passing through the spiritual "membrane" during meditation. Skeptics like to pounce on this inability to realistically describe the spiritual reality - failing to consider the equivalent quandary for the large part of physical reality - and the ostensibly inaccessible form of confounded language used in its attempt, to discredit it. Yet, sages of the various mystic traditions deliberately employ artful and creative forms of language to try to chip away at its traditional shortcomings in communicating greater entities. For instance, Hinduism speaks of the spiritual reality in colorful myths and metaphors, and Buddhism uses paradoxical statements called "koans". These are not incoherent ramblings of crazy hermits - they are in fact intelligently constructed devices designed to enhance the conveying power of language.
Some may lament that it is of unfortunate, even cruel, happenstance that we as humans seem to live in this grand delusion. If we are to put faith in the mechanics of evolution and natural selection, though, it does make sense. Our biological purpose is simple - to survive long enough to reproduce. Evolution tends to strongly select only for the traits that aid in this end, as anything extra would be energetically wasteful. We don't need the ability to see the entire range of the electromagnetic spectrum or to perceive more than three spatial dimensions in order to survive and reproduce, as a sort of twisted form of the anthropic principle proves. And so life, at least on Earth, at least that we are generally aware of, has not evolved with these faculties. Of course, the beautiful quirk of evolution is it's keenness for espousing diversity through DNA mutations and recombinations, and so maybe there have been humans scattered throughout our history with such extraordinary capabilities - though if such people ever existed, society probably vehemently and without second thought stigmatized them as insane and their claims as without credibility or as statistical flukes even if experimented upon. A little less ethereal and a little more relevant manifestation of this idea, nevertheless, comes in the form of people we may interact with every day: those who are natural math geniuses or those who seem to have the innate ability to interact with the spiritual reality, like psychics or fortunetellers. But evolution does not select for these abilities, and as such, people with them are far and few between. For the rest of us, an even more cruel and unfortunate happenstance presents itself: the tantalizing prospect of being able to penetrate our awareness to otherwise invisible realms of reality through mathematics and meditation is so incredibly difficult. To comprehensively master advanced mathematics, or to reach the high state of mindfulness necessary to achieve deep meditation, can require a lifetime of arduous study and commitment. But as we recognized from the very beginning, the veil cast by the universe over human beings is profound - one necessitating a diligent open-mindedness just to recognize and appreciate, and a boundless, indefatigable passion to truly escape from.
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