Visualizations and Extrapolations 1

What is the Popular Understanding of Infinity?

Infinity is a pretty humongous concept. While being one of the most difficult concepts to grasp, everyone has personally significant intuitive understanding about infinity, even the most nonchalant observer. Nominally there are Three Realms of Infinity: Mathematical, Philosophical and Physical. These are the typical classifications made by intellectual analysis and rationalization as reported in textbooks, encyclopedias and scholarly treatises. Never mind these highfalutin categorical displays of intelligentsia, what does the average person on the street think about infinity and how do they comprehend it? What is the Everyday Popular Understanding of Infinity? What practical knowledge can possibly be ascertained from something that is without limits? How does Infinity affect our personal lives?

But what about the fact that Infinity as a general topic defies human comprehension by virtue of its very definition? Add to this the cognitive psychological and perceptual conditions which are pervasive in affecting human understanding of something that is not meant to be understood. Is it not the case that there are as many ways to find meaning in the concept of infinity as there are individuals to express their intuitions of meaningfulness? Would it not be that understanding the meaning of infinity comes down to comprehending the infinity concept in all its various forms in consideration of the cognitive psychology of human perception and all the inter-subjective agreements that are implied?

There is theoretical knowledge and there are practical applications of that knowledge. What would the practical applications of understanding the concept of infinity possibly be? After all, in everyday life, it does not matter whether the Universe is infinite in dimension, if there are an infinite number of stars, or if the universe expands forever. However, the human mind is inquisitive, and the quest to comprehend infinity has been ongoing since the dawn of recorded history.

The onto-genesis of the infinity concept is cross cultural: East and West. A list of contributors to the Mathematical and Scientific Realm alone reads like a Who-s Who of the greatest thinkers of all time. There is an equally salubrious contingency of authors, artists and creative visionaries from diverse Realms such as Philosophy, Psychology, Literature, Fine Arts, Mysticism and Spirituality who have devoted lifetimes to sorting out the many Paradoxes of Infinity.

While recognizing the magnificence of precise and axiomatic Mathematic-Scientific expressions of infinity, this essay is about an inquiry into the Popular Understanding of that concept in relation to Practical Application of somewhat Theoretical yet Intuitive Knowledge. With the goal of practical, comprehensive expression of infinity in everyday life, predisposing a Meta-Realm might be in order. Conceptual and Theoretical Infinity is a Metaphor for a property of experience in perceiving Facts of Reality. It is safe to say that this experiential and intuitive metaphor can and should be extrapolated as an underlying universal principle for the Mathematical, Philosophical and Physical Realms.

We do not have to go back to ancient Greek, Vedic and Hindu texts to find out how humans learn to count. We could look at how infant children learn; we could send an expedition to some indigenous culture that has had no contact with modern civilization. Primordial counting starts with observing your own hands: One – Two. Next comes observing the hands of others in the family or tribe, and finding the Many. So, from One-Two-Many it is not a far reaching leap to conceive of a limitless amount of people or stars or fish in the sea for all that matters. In the teachings of the Tao, the Yin and the yang are opposite forces of spirit which combine such that the Many become One. The Infinity concept may logically precede numerical counting of digits to fill in the void between One and Many.

Without a doubt the most common understanding of Infinity in Modern Popular Culture is knowing about the infinite sequence of natural numbers like 1,2,3… . There is an intuitive understanding that this sequence “goes on forever” and “has no limit”. Nothing mind boggling about this kind of infinity, yet the practical applications are like the concept implies: Limitless and Eternal. This kind of infinity is associated with God, Brahma, Vishnu and The Absolute of all cultures. Equally important for the fulfilling a basic human need and striving is the concept of eternal, unbounded and limitless Love.

The next most prevalent Popular Conception of Infinity is probably from the Physical Realm: the infinity of the Universe. While the question about whether the Universe is finite or not in dimensions of space and time may never be solvable, it does appear that the Universe has a flat topology, yet it is expanding at an accelerating rate. These contentions are compatible with a universe of infinite space-time dimensions. The conclusion implies that “all that is” constitutes an infinity which can be referred to as “the ultimate totality”. So, not only is there a sequential infinity, it is included in a totality which is also infinite. Now we are getting into some paradoxes. Only by understanding infinity as metaphor can something which is “unbounded and never-ending” be included in a “totality of everything there ever was”!

Another well known Popular Knowledge and Understanding of the concept of Infinity dates back to ancient Greece. Xeno of Eliade presented a race between fleet-footed Achilles and a tortoise which demonstrates that there are infinities between points on a line. The tortoise gets a head start, but Achilles, by running half the distance to the tortoise, over and over and over again can never catch up.

This type of infinity presents itself in irrational numbers and brings on confusion, both mathematical and metaphysical, about infinite numbers which are nested within infinite sets of numbers of another kind. These kinds a paradoxes leave most people nonplussed. No wonder Aristotle tried to do away with them.

An ancient mathematical text from India, the Surya Prajnapti, classified all numbers into three sets: enumerable, innumerable, and infinite. In modern times Georg Cantor distinguished between different levels of infinities, countable and uncountable. Cantor found that there are different kinds of infinity and that some of them are larger than others. He was also originator of the Continuum Hypothesis. Pretty much everyone has intuitive notions about whether the continuum hypothesis is true or not. Most are in general agreement that there is universal connectivity between all things, facts and events, which includes interpersonal and social relationships all the way up to consciousness itself.

The infinities of Macrocosm and Microcosm span the whole Physical-Mathematical-Philosophical gamut. What? The Universe is expanding at rates faster than the speed of light? There is a waterfall of un-see-able reality going off the edge of the event horizon? Are the electron, the photon and the quark really the lower limit of what can exist in space-time? Surely not, if the “As Above So Below” aphorism of alchemy is true. Now we venture into realms of Mysticism and Spirituality, which has always captivated and fascinated Modern Popular Culture. Conceptions of Metaphysical infinity can take on a Mystical and Spiritual dimension when the paradoxes expressed in terms of cosmic consciousness. In In no other way does it become more apparent that extrapolation from analogy and metaphorical reasoning underlies the popular understanding of the paradoxes of infinities.

For a more sophisticated fascination with the infinity concept, David Hilbert has brought us a thought experiment: Hilbert’s Infinite Hotel. The hotel has an infinite number of rooms which are all occupied. Is there room for one more guest? In a hotel with an infinite number of rooms there is always room for one more (or even one less). Infinities are not logical, they are intuitive: and, as Hilbert demonstrates, they can be metaphorical. On such metaphors, theories of probability are constructed. What is more, in the formulation of quantum mechanics there are such conceptual things as Hilbert Spaces which are infinite not only in size but in dimension.

One commonplace highlight about infinity in Popular Culture would be the Infinite Monkey Theorem, in which the complete works of Shakespeare would be written if an infinite number of monkeys typed at random on an infinite number of typewriters for an infinite amount of time. Why stop there? Lets add all the Great Books of the Western World plus the entirety of the Library of Congress. Everybody knows that those monkeys could and most surely would type them perfectly. The whole deal depends on whether the universe is infinite or not. The “monkeys with typewriters” metaphor originated in the work of French mathematician Emile Borel in 1913. In it’s modern context, there is a lesson about probability relevant to the Large Language Models of artificial intelligence.

The most masterful logical move one can make in a debate is to demonstrate that your opponent’s position leads to an “infinite regress”. This type of argument demonstrates that a logical house of cards has been founded upon a belief that is based on a series of beliefs that are justified on still another belief which is justified on yet another belief “ad infinitum”. The concept of infinite regress has captured the imagination of every intellectual sharpshooter and is firmly ensconced in the collective psyche of popular culture. Infinity is absurdity when logical conclusions are connected in such a way that each one depends on the one before it such that there is no end to the sequence.

Einstein called the Cosmological Constant his greatest blunder. In scientific theory, “re-normalization” is a clever way of getting rid of infinities that arise in equations, effectively adjusting parameters to fit observations and make meaningful predictions. It sounds a bit deceitful doesn’t it? If the re-normalization problem is a matter of scale “coarse-graining” is probably fair game. That would be like the surface of a sphere appearing to be flat to a microscopic observer. However, according to modern science, we are supposed to accept the “double-dark” theory. Matter and energy we cannot see or interact with makes up 70 and 24 percent of the universe? Presto: No Infinities! That outcome is the result of re-normalization, to make the cosmological constant from a prevalent hypothesis of inflation compatible with observation.

Srinivasa Ramanujan (1887-1920), was a brilliant mathematician from India who was born into extreme dire poverty. He had no formal mathematical training. In his short life, he made many amazing discoveries about infinities in co-variant equations. He developed Ramanujan summation to assign values to divergent sets of infinities. He found a formula for the infinite series of pi. His Theta Function is the basis for positing the ten or eleven dimensions of String and M-Theory. Most importantly, Srinivasa Ramanujan formulated his mathematical discoveries on intuition only and was ultimately proven correct by other mathematicians. While not being in the forefront of Popular Understanding of the Concept of Infinity, he certainly should be.

No evaluation of the Popular Understanding of the Concept of Infinity would be credible without considering the Infinity Symbol and its meaning for everyday lifestyles in the Post-Modern World. The Infinity Symbol, a sideways figure eight, was introduced by Mathematician John Wallis in 1622, It is also known as the lemniscate, which means “ribbon” in Latin. Properly articulated, the infinity symbol should be presented as a mobius strip. The twisting, turning and indefinite boundaries of the mobius strip are appropriate representations of the many paradoxes involved in concept of infinity.

The sideways figure eight has a simple elegance that appeals to those who are metaphysically inclined as well as those who are fashion oriented. It represents thoughtful introspection while being free of the baggage of religiosity and political connotations. Wallis’ design of the infinity symbol was fortuitous. It was inspired by the Roman Numeral for 1000, which was also used to mean “Many” of “Countless”.

In popular Culture, the sideways figure eight is more than just a mathematical symbol that represents the concept of infinity. It has multiple interpretations and a long history. It has appeared in some form in many different cultures. The infinity symbol resembles Celtic Knots, which consist of never ending loops representing the eternal cycle of life, death and rebirth. It can be seen as a convoluted Egyptian Ouroboros snake or serpent eating its own tail which symbolizes the cyclic and infinite nature of the universe. From death comes life and from destruction comes creation, an infinite cycle of renewal.

There is also a strong resemblance in structure to the yin-yang figure of the Tao and Zen Buddhism. The yin-yang famously represents the unity of two opposing forces or qualities such as masculine and feminine or earthly and divine. So, in popular culture, we recognize at least four types of infinity: sequential, everlasting, cyclical and unified-totality through the sideways figure eight symbol.

These multiple associations have made the infinity symbol a popular and highly meaningful design. Most significantly, the Infinity Symbol has come to represent the concept of Infinite Love in popular understanding. The infinity symbol represents eternal and everlasting love; love that is infinite in magnitude, limitless and without end. The lemiscte combines the concepts of eternity, everlasting love and the boundless nature of the universe.

The infinity symbol also represents the fact that there is no beginning and there will be no end, it is an everlasting cycle, similar to a cycle of love which goes on forever. Endless possibilities are also implied by the concept of infinity and represented by the symbol. These can be like the endless possibilities which propel quantum events or endless possibilities in in the realm of human interaction.

In the context of relationships, the infinity symbol can signify a bond which transcends space and time.

It can be testament to undying love or friendship or visualization of a force that is enduring and unbreakable. For some, it symbolizes balance, harmony and the interconnectedness of all things and events. It can also be a personal emblem of one’s own limitless potential, resilience, perseverance, and the never ending journey of self discovery band personal development-growth.

The Infinity symbol has universal appeal, capturing the essence of something esoteric which cannot be contained within or defined by space-time and causality. The most popular understanding of Infinity would imply eternal love interconnected with universal consciousness. Whether it originates in the religious belief that God is Love, or from a New Age Awakening, or even one’s own individual spiritual yearning, there is a popular equivocation between Infinity and Love.

The popular concept of infinity offers a visualization of the everlasting and the boundless. We live in a culture of consumption, with the deceptive perception that everything of value seems to be transitory and ephemeral. The concept of Infinity represents our innermost desire for something that transcends physicality and lasts forever. The powerful Infinity Symbol represents limitless potential and endless possibilities within us, the eternal nature of love and our deep connections to the infinite universe.

Fred Jay Ross

fredjayross@gmail.com

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