This solitary hill has always been dear to me
And this hedge, which prevents me from seeing most of
The endless horizon.
But when I sit and gaze, I imagine, in my thoughts,
Endless spaces beyond the hedge,
An all encompassing silence and a deeply profound quiet,
To the point that my heart is quite overwhelmed.
And when I hear the wind rustling through the trees
I compare its voice to the infinite silence.
And eternity occurs to me, and all the ages past,
And the present time, and its sound.
Amidst this immensity my thought drowns:
And to flounder in this sea is sweet to me.
The Italian poet Giacomo Leo Bardi stood one day on the highest hill in his hometown and then imagined a limitless space, deep silence, and absolute peace, as if he had disappeared into nothingness, a nothingness that made him feel frightened, but the shaking of the wind brought him back to reality. He noticed a speculative philosophical infinity that combined the contradiction between the desire for infinity and the failure to achieve it. Leo Bardi’s infinity is one of those infinities that hid in humanity’s scientific, literary, philosophical, and artistic ideas, emerging from an abstract mathematical concept into an idea that holds many secrets in the universe.
Infinity and the Symbol of Eternity
“Mystery is the Basic Element of all Works of Art.”
The artist Bosco portrayed the concept of eternal spring and perpetual youthfulness, after drinking from the River of Life, in his famous painting, The Garden of Earthly Delights. This work provided a glance at the legendary spring of endless pleasures and immortality, which was a recurring theme in ancient myths and diverse cultures. The narratives surrounding this idea expanded with the explorations of Alexander the Great.
As for the ancient Egyptian god, “the god of millions of years,” in her masculine form, “Heh,” and in her feminine form, “Hauhet,” which carried the meaning of infinity, the form of the divine embodiment of the finite in the temporal aspect of eternity. In this formation, the rings indicated infinity, and the curved cross on the arm indicated the number one million in ancient Egyptian mathematics, which is the number that equates to infinity. Just as the golden ring symbolized an intense image of infinity, the formality of the ring in its circular shape remained a symbol of completeness and idealism, while eternity was linked to the symbolism of the rare metal gold with its properties that are difficult to change, so that these two concepts constitute the embodiment of eternity in life after death.
Infinity in Philosophy
“The Human Mind is a Part of the Infinite Intellect of God.”
The Greek philosopher Zeno of Elea was the first to present infinity as a philosophical idea. Zeno’s infinity is known philosophically as the dilemma of “Achilles Paradox.” In order for Achilles to complete the race, he must first cover half the distance, and in order to cover halfway, he must cover a quarter of the distance, and in order to cover a quarter of the distance, he must cover one-eighth of the distance… and so on to infinity. Accordingly, the runner cannot reach the finish line, but in reality, Achilles finishes the race. Zeno’s division of space and time made him believe in the illusion of movement and the lack of trust in the senses. But this division is a mature idea for what would later be known mathematically, at the hands of the scientists Leibniz and Newton, as calculus.
René Descartes presented an infinity that stems from a first rule that precedes thought and consciousness, “I think, therefore I exist.” Then infinity comes as a symbol of precision and perfection (an ideal nature governed by infinite precision). According to Descartes, self-reflection is not ideal, because perfection does not come from a self that is overcome by its own defects or self-incompleteness, but rather it comes from an existence that has the characteristics of ideality and perfection (God). This existence is represented by an eternal, unchangeable, independent entity that has absolute knowledge and absolute power. The third rule is extension, represented by material things governed by physical laws such as movement, position, and form.
In “Critique of Pure Reason,” Immanuel Kant presented a contradiction about the infinite universe, a contradiction that supports the hypothesis that the universe has a beginning in time and is limited in space, and another that says that the universe has no beginning or limits because it is infinite in time and space. Infinity is suspended between existence and limits. A universe that is not limited is a universe that does not exist because everything that exists has a beginning and an end. As for a universe with unlimited space, it is a universe that is not defined by the boundaries of time and space. While Hegel considers infinity a definition of the absolute, as he rejects the concept of infinity with unlimited progress, true infinity in his philosophy is the totality of moments of existence that are contained in each of the comprehensive cosmic boundaries. As for Nietzsche’s infinity, it is in the idea of eternal return, which is the endless repetition of the theater of the universe and human life, thoughts, and feelings. Nietzsche’s infinity is the struggle to deal with time as an eternal concept separate from movement.
Infinity in Mathematics
“Nature is the source of all true knowledge. She has her own logic, her own laws, she has no effect without cause nor invention without necessity.”
Georg Cantor presented infinity as a mathematical concept and not a real number, because if infinity is treated as a number, it means stripping infinity of its “infinite” meaning. This concept can be dealt with mathematically in algebra, known as set theory. For example, the natural numbers contain the set of even numbers, since the even numbers are an infinite set, and likewise the natural numbers are an infinite set, but the infinity of the natural numbers cannot be equal to the infinity of the even numbers, because the even numbers are a partial set of the natural numbers. Hence, the infinity of any set of numbers is different from the infinity of another set, and this is what makes adding or subtracting any value from infinity to be infinity. Infinity cannot be treated as a fixed value, but rather as a concept that means unlimited extension. Every infinity may be greater than another infinity or smaller than a third infinity, in fact, there is an infinity of infinity. Unfortunately, the idea of different infinities drove Cantor crazy, and fortunately it served many branches of mathematics and physics.
But mathematical infinity does not stop there. Rather, the physicist Isaac Newton and the mathematical philosopher Leibniz realized that there is a problem in finding the value of square functions (determining the length or area of curves) by dividing the areas or curves resulting from the movement of bodies into infinitesimal sections. This science is known as calculus, and the symbols used mathematically go back to the scientist Leibniz. This is because the physicist Newton worked on infinity geometrically to study the movement of bodies and the forces affecting them, while the mathematician Leibniz dealt logically with what is known as “Symbolic Mathematics.”
Infinity in Physics
“Within us there is a strong, true purpose, and if we fail in this purpose we will be forever lost.”
Quantum vacuum:
For centuries, science and philosophy have been wrestling over the issue of emptiness. It was believed that nature abhors emptiness and tends to fill space with something, whether this thing is air, ether, or something else. However, linguistic considerations do not present emptiness unless it is devoid of matter. Today (within a century) theoretical physics in the concepts of quantum mechanics deals with the vacuum as a potential space for the creation of particles from nothing. The vacuum is not a vacuum in itself, but rather every point is a possibility for the particle to exist instantaneously for a time within the limits of the Planck time (h/mc2) and then for it to disappear. The vacuum contains infinite energy that creates these particles that we cannot detect, according to Heisenberg’s uncertainty principle.
Dirac Sea:
In the Dirac Sea, infinity was hidden in the famous equation of the genius physicist Paul Dirac, which most physicists call (the most beautiful equation in the universe). Dirac assumed that the universe contains a deep, infinite sea of electrons with negative energy levels that fill all possible spaces. Experimentally, the Dirac Sea is the positively charged holes (vacuum of electrons) in electrical conductivity in photoelectric theory. The Dirac Sea also predicted that Einstein’s famous equation E=mc2 is not only an equation for a visible physical universe, but also a mirror image of a universe in which there are elementary particles that have the same mass as the known elementary particles (electron, proton, and neutron), but with opposite charges. These particles are known as antiparticles.
Infinity in Literature
“The beginning is the end itself, and if you search for something, you will find it in something else, not in itself.”
While infinity was mathematically linked to the unattainable extension of numbers, for the writer Jorge Borges it was more than that. Borges’ infinity is a chaotic, uncertain concept that rebels against the system. In his book El Libro de Arena, his true character shook hands with a stranger whose selves met in two different places and times. In this book, whose name means the Book of Sands, Borges intended a mysterious book that had no beginning or end. Its page numbers were as infinite as sand. As for infinity according to Umberto Eco in his novel The Name of the Rose, it is a cognitive concept embodied in the great library, which may be a tool for spreading the truth or a tool for postponing it, which contained an unknown number of books to reveal secrets hidden in its pages, just as a rose opens from its petals.
Infinity in Cinema and the Arts
“An idea. Resilient… highly contagious. Once an idea has taken hold of the brain it’s almost impossible to eradicate.”
In Christopher Nolan’s masterpiece (Inception), infinity was presented in the puzzle of dream and reality. The idea oscillates between a reality that plants it in a dream and a dream that creates an idea as if life were a Möbius strip, the mutual and endless transition between reality and dream. Multiple levels of dreaming were also created that go far into the depths of the mind and soul until the self is lost in the void of infinity. Because this is a maze between the existence of the dream and the absence of reality or the perception of reality and the dream’s hiding in the subconscious mind, it was exited by a physical connection in the symbol that proved the existence of infinity in continuous movement, when the mind realized reality. The design of the dream also requires the infinity maze of complex geometry between the interplay of physical dimensions and the infinite Penrose stairs.
Penrose Stairs, influenced by the artist Maurits Escher, famous for his two- and three-dimensional geometric designs of impossible worlds decorated with imagination. Escher did not rely on feelings or philosophy in his works, but rather on optical illusions, mazes, overlapping dimensions, and curved spaces that reflected his deep understanding of geometric and physical concepts. Infinity is evident in Escher’s works in his two paintings: “Waterfall/Day and Night.”
Infinity in Technology
ATMOS
It is a luxury Swiss watch brand owned by designer Antoine LeCoultre. In 1836 AD, his small workshop expanded into a global brand where he created a high-quality instrument for highly accurate measurement of time. But infinity was hidden in an endless mechanical movement developed by engineer Jean-Léon for the ATMOS pendulum, which is a clock that does not require a battery, electrical connections, or any external device. It obtains the energy needed to operate it from slight differences in atmospheric pressure and temperature, which cause the gas in the closing key to expand or contract, making it appear as if the watch is breathing. ATMOS is characterized by its efficiency, its infinite mechanism, and its consumption of the least possible energy in the universe.
QR is a system for storing information that uses a two-dimensional square dot matrix, characterized by its square shape and three frames in the corners. It was established in 1994 and was used to manage warehouses and factories. With the digital phone revolution, it expanded to include the field of communications and marketing. Infinity hides in QR, because there are an inexhaustible number of possibilities for storing information in pixels. Assuming the QR is 25 pixels wide and 25 pixels tall, its total area will be 625 pixels. Usually there are 250 pixels of fixed information, while 325 pixels change freely between black and white. This means that the number of possible possibilities for storing information is equivalent to:
That is, each person is able to create seven billion QRs of his own.
Infinity in the Universe
“Because deep down we are so alone.”
Minds in early times imagined the universe with Earth representing its center and visible bodies completing their revolutions around the Earth, and beyond that the universe extends into an infinite void and unlimited matter, which the philosopher Anaximander called Arche. Copernicus’ heliocentric theory contributed to an intellectual revolution in cosmic geometry, but within the limits of an infinite universe. Giordano Bruno, the religious philosopher, not only believed in an infinite universe, but also infinite worlds. Because God’s creative power cannot be limited to a finite universe. While a precise understanding of the foundations of geometry and continuity of motion gave Isaac Newton great respect in his theory of body mechanics, which described the laws of motion and forces, infinity for Newton is the intersection of three elements that are inseparable from each other by gravity: absolute space, absolute time, and matter.
Einstein and Parallel Universes:
When Einstein’s genius eliminated the existence of the ether, that idea of the emptiness of space that had dominated the human mind for more than two thousand years. The theory of general relativity represented a new vision of the concept of gravity, one of the most complex natural phenomena in the universe, which was later realized to be the basic structure of space-time. Space is a physical geometry in which the three-dimensional coordinates of space are related to a variable time at each axis. This geometry imposed the relativity of space and time according to gravity and the speed of light, and even more than that, the birth of black holes with infinite gravity. These holes inspired the idea of infinity hidden in the Rosen-Einstein bridge that connects two possible universes, so this idea developed into the theory of parallel universes that proves the subjectivity of time and matter and changes the course of events in multiple universes that are impossible to connect.
Infinity exists everywhere and in every thought. Indeed, infinite nature exists within us as well, in our atoms that are connected to the universe and depend on the structure of the vacuum in every billion seconds that we live. Every atom in our bodies is an enormous source of information that constitutes an endless activity in creating the universe through the exchange of energy and matter. But does the universe have a beginning and an end? This question remains stuck in the infinity of our ignorance about the universe, and what we know for certain is that it is not the primitive universe in which Bosch closed his painting “The Garden of Earthly Delights” from existence.
References:
- Antonio Lamúa; Los secretos del Infinito, (2012).
- Charles Seife; Decoding the universe. (2006).
- Freeman Dyson; Infinite in all directions, (1985).
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