The Destiny of Free Will
Few questions have persisted as much as the timeless debate of destiny versus free will. This intellectual odyssey weaves through the annals of philosophy and physics, forming a rich and complex narrative that has captivated the minds of scholars and thinkers for centuries.
The great philosopher Aristotle pondered the concept of voluntariness and the extent to which human actions were governed by choice rather than external forces. His ideas laid the groundwork for the nuanced discussions on free will that would follow.
Fast forward to the age of Augustine, the early Christian theologian and philosopher who grappled with the implications of divine predestination and human free will. His theological musings resonated with the enduring tension between the human capacity for choice and the notion of a predetermined divine plan.
Medieval Europe saw the emergence of Thomas Aquinas, who introduced the idea of compatibilism, suggesting that free will and determinism could coexist harmoniously. His synthesis of Aristotelian thought and Christian theology offered a fresh perspective on this age-old debate.
The Enlightenment brought forth David Hume, whose skepticism challenged conventional notions of causality and determinism. Hume’s empiricist approach questioned whether our sense of necessity was rooted in objective reality or simply a product of human experience.
Enter Immanuel Kant, whose philosophical brilliance illuminated the concept of moral autonomy. Kant’s notion of categorical imperatives and the moral law within us ignited a renewed interest in free will as a necessary condition for genuine moral responsibility.
As the 18th century gave way to the 19th, Jean-Jacques Rousseau’s writings delved into the essence of human freedom within the confines of society. His explorations laid bare the tension between individual liberty and societal constraints.
Meanwhile, Arthur Schopenhauer offered a somber perspective, suggesting that true freedom could only be found through transcending one’s individual will, which he believed to be inherently driven by desires and motives.
The 19th century witnessed Friedrich Nietzsche challenging traditional moral values and extolling the virtues of individual agency. Nietzsche’s philosophy laid the groundwork for existentialist thinkers like Jean-Paul Sartre, who proclaimed the existential dilemma of human existence: the burden of absolute freedom and responsibility.
In the 20th century, philosophers and physicists alike engaged in debates on determinism and indeterminism, with figures like Albert Einstein, Werner Heisenberg, and Erwin Schrödinger exploring the implications of quantum mechanics for the concept of free will.
Albert Einstein, renowned for his contributions to physics, had philosophical discussions with figures like Niels Bohr about the nature of quantum mechanics and determinism. He famously said, “God does not play dice with the universe,” expressing his discomfort with the probabilistic nature of quantum mechanics.
Werner Heisenberg, one of the pioneers of quantum mechanics, introduced the uncertainty principle, which highlighted the inherent limits to our ability to simultaneously measure certain properties of particles, introducing an element of indeterminacy into physics.
Erwin Schrödinger, another key figure in quantum mechanics, proposed the famous thought experiment known as Schrödinger’s cat to highlight the strange and counterintuitive nature of quantum superposition and wavefunction collapse.
Today, the discourse continues, with contemporary philosophers like Daniel Dennett defending compatibilism and addressing the complexities of free will in a world increasingly shaped by scientific understanding.
Consider the following great summary of some of the current discussions by Sabine Hossenfelder:
There is nonetheless another physicist to which I want to turn our attention, one that was briefly portrayed in “Oppenheimer” movie, that is Kurt Gödel.
Born in Brünn, Austria-Hungary (now Brno, Czech Republic), he made profound and lasting contributions to both fields during his relatively short life. Best known for his incompleteness theorems, which revolutionized mathematical logic and challenged the foundations of mathematics, Gödel’s work had a profound and enduring impact on the way we understand the limits of formal systems and the nature of mathematical truth.
In 1931, Gödel published his best known work, his two incompleteness theorems. These theorems demonstrated that within any consistent formal mathematical system that is capable of expressing basic arithmetic, there are true mathematical statements that cannot be proven or disproven within the system itself. This revelation shattered the hope of finding a complete and self-contained set of axioms for all of mathematics and forever altered the landscape of mathematical logic.
A much less known work is his solution to Einstein’s field equations in general relativity that suggests the possibility of closed timelike curves (CTCs) within certain spacetime configurations. CTCs are paths through spacetime that loop back on themselves, potentially allowing for time travel to the past. Gödel’s solution is often referred to as the “Gödel metric.”
The most intriguing aspect of Gödel’s solution is that it contains closed timelike curves. These are paths through spacetime that, if followed, could allow an observer to return to an earlier moment in their own past. This suggests the possibility of time travel within this hypothetical universe.
It’s important to note several significant caveats and consideration. Gödel’s solution is a highly theoretical and non-physical model. It doesn’t describe our observed universe, which appears to be expanding rather than rotating as assumed in the solution.
Let’s keep in mind that Gödel’s solution is primarily a mathematical result, and it remains unclear whether such a universe could exist in reality. It’s considered more of an intriguing curiosity in the realm of theoretical physics and mathematics rather than a concrete prediction of time travel.
Nevertheless, let’s consider, leaving apart the technological problem of making a time travel, that his solution is really possible. The presence of closed timelike curves raises questions about causality and the potential for paradoxes. If time travel to the past were possible in such a universe, it could lead to situations like the famous “grandfather paradox,” where a time traveler could prevent their own existence.
So if a time traveler goes to the past then in order to obey the principle of causality he should not be able to change anything, but her or his sole presence would make a change, avery decision no matter how small (just breathing for example) would provoke a change. So how could this be compatible?
Events Matrix Eigenvectors Hypothesis (EMEH)
Lets suppose we have technological capacity to determine (even if only up to a probability distribution) the position and momentum of every particle in the universe and we write them down in what we may call the Events Matrix.
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used in mathematics, physics, computer science, and many other fields to represent and manipulate data, perform transformations, and solve equations.
Here’s an example of a simple 2x3 matrix:
| 1 2 3 |
| 4 5 6 |
In this matrix, there are two rows and three columns. Each entry in the matrix is called an element, and it can be identified by its row and column position. For instance, the element in the first row and second column is “2,” and the element in the second row and third column is “6.” Matrices can be used for various mathematical operations like addition, subtraction, multiplication, and more, making them versatile tools in various applications.
Now we can transform the information coded into a matrix using a matrix transformation. A matrix transformation, also known as a linear transformation or a matrix operation, is a mathematical operation that takes a matrix as input and produces another matrix as output. It involves multiplying a given matrix by another matrix, often referred to as the transformation matrix, to map points or vectors from one space to another. Matrix transformations are used extensively in linear algebra, computer graphics, and various scientific and engineering applications.
Here’s a brief example of a 2D rotation matrix transformation:
Suppose you have a point (x, y) in a 2D plane, and you want to rotate it counterclockwise by an angle θ. You can achieve this using a rotation matrix:
| cos(θ) -sin(θ) |
| sin(θ) cos(θ) |
To apply this transformation, you multiply the original point (x, y) by the rotation matrix:
|x’ | | cos(θ) -sin(θ) | |x|
|y’ | = | sin(θ) cos(θ) | * |y|
The resulting (x’, y’) will be the coordinates of the point (x, y) after it has been rotated counterclockwise by an angle θ around the origin. This is a fundamental example of a matrix transformation in which the transformation matrix describes the rotation operation. Matrix transformations can represent various operations beyond rotation, such as scaling, translation, and shear, making them powerful tools in geometry and linear algebra.
Now we could think that the Events Matrix at a time t, denoted by EMt transform into a new EM on a subsequent time t’ by applying a transformation A that codes the effect of following the laws of the universe (in the most broad sense imaginable), so we get EMt’ =AMt
Now what is very interesting is that for every matrix there are some special vectors called eigenvectors. An eigenvector (also spelled “eigen vector”) of a square matrix is a non-zero vector that remains in the same direction after the matrix transformation. In other words, when you multiply the matrix by an eigenvector, the resulting vector is a scaled version of the original eigenvector, and the scaling factor is called the eigenvalue corresponding to that eigenvector.
Eigenvalues and eigenvectors have physical significance and provide valuable insights into the behavior and characteristics of that system.
For example, in mechanical engineering, if we describe the behavior of physical systems in terms of matrices then these matrices will represent systems of linear equations that gover the mechanical structure and dynamics of the system. Eigenvectors in this context represent the modes of vibration or deformation of the system, while the corresponding eigenvalues indicate the frequencies or natural frequencies at which the system vibrates or oscillates. Engineers use this information to study structural stability, resonance, and dynamic behavior.
The study of natural frequencies are now considered one of the more important topic in big constructions design, a lesson learned by the famous case of the Tacoma bridge.
In the early 1940s, as the world was reeling from the impacts of war, the bustling city of Tacoma, Washington, found itself at the precipice of a different kind of monumental endeavor — the construction of a bridge that would come to symbolize both engineering ambition and the irresistible forces of nature.
The Tacoma Narrows Bridge, fondly dubbed “Galloping Gertie,” was envisioned as a soaring testament to human innovation. Stretching gracefully across the Tacoma Narrows strait, it aimed to connect the city to the Kitsap Peninsula, promising enhanced connectivity and economic opportunities for the region.
Guided by the hand of esteemed engineer Leon Moisseiff, the bridge was conceived with aesthetics in mind. Its slender, streamlined profile was a marriage of architectural grace and engineering brilliance, resonating with the aspirations of an era.
Construction began in 1938, marking the realization of Tacoma’s dreams. The Tacoma Narrows Bridge opened to the public on July 1, 1940, emerging as the third-longest suspension bridge in the world and a symbol of local pride.
Yet, mere months after its grand debut, on November 7, 1940, the bridge bore witness to a climactic encounter with the elements. Strong winds descended upon Galloping Gertie, and the bridge responded with eerie, undulating motions. Passersby watched in awe as the bridge seemed to take on a life of its own.
As the winds gathered force, the bridge’s majestic symphony of oscillation reached a crescendo. Nature’s forces ultimately overpowered the bridge’s structural resilience. With a deafening roar that echoed across the Tacoma Narrows, Galloping Gertie surrendered to the relentless wind, collapsing into the frigid waters below.
In the aftermath of the disaster, the world of engineering was forever changed. The collapse of the Tacoma Narrows Bridge served as a stark reminder of the importance of understanding the harmonious interplay between structure and nature’s rhythms.
In electromagnetic field theory, matrices can describe the behavior of electromagnetic waves in different media. Eigenvectors represent the polarization states of the waves, while the eigenvalues correspond to the propagation constants or refractive indices. This is crucial in understanding how light interacts with materials and how optical devices work.
In all these cases, eigenvectors provide insight into the fundamental modes or states of the system, while eigenvalues represent important physical quantities, such as energy levels, frequencies, or stability properties. Analyzing these eigenvectors and eigenvalues helps scientists and engineers gain a deeper understanding of the behavior of physical systems and make informed decisions in various fields of study and application.
In this way it would be natural to ask ourselves about what could be the meaning of the EM eigenvectors. My hypothesis is that the structure of interactions and cross casualties in the EM of the universe is such that eivenvectors represents a set of events or events trajectories that are preserved, meaning that in terms of our time traveler, no matter what she or he do, these events would still happening.
Let us imagine for a moment that Claus von Stauffenberg was a time traveler trying to change history by killing Hitler. The historic von Stauffenberg was German officer and key figure in the failed plot to assassinate Adolf Hitler during World War II. He was born on November 15, 1907, into an aristocratic family in Jettingen, Germany, and he came from a long line of military tradition.
Stauffenberg initially supported Hitler’s rise to power, but his views changed as he witnessed the atrocities committed by the Nazi regime and realized the destructive path on which Germany was headed. He became deeply involved in the German Resistance, a network of individuals who opposed Hitler’s dictatorship and sought to overthrow the Nazi regime.
On July 20, 1944, during operation Valkyrie von Stauffenberg, carried a briefcase containing a bomb with a time-delayed fuse and managed to place the bomb inside the briefing room and left the scene, believing that he had successfully killed Hitler. However, the bomb only partially detonated, as the briefcase had been moved slightly. This stroke of bad luck spared Hitler from the assassination attempt. The blast killed several people and wounded others but left Hitler with only minor injuries.
Realizing that the attempt had failed, von Stauffenberg and his fellow conspirators in the Resistance quickly launched Operation Valkyrie, a plan to take control of key government offices in Berlin and arrest high-ranking Nazi officials. However, the plot unraveled, and Stauffenberg was arrested the same day.
So if von Stauffenberg would have been a time traveler, his failure would be a consequence of Hittler being (even if we hate to think about it as this) an eigenvector of the EM. It seems to be clear that EM eigenvectors will tend to be some of the most positive or negative set of events, or maybe even cross roads type of events.
This is what I called the Destiny component of the EM. In a complementary manner, if the von Stauffenberg time traveler decided that morning to sing his preferred opera or not; taking his morning coffee with or without sugar and so on; conform the Free Will component of the EM.
Being the universe the most possible complex system, then it would be natural that its events dynamics follow a good balance between Free Will (randomness or informational emergence) and Destiny (order or self-organization), a fingerprint of one of the universal features of complex systems the so called Criticality (see https://www.mdpi.com/journal/entropy/special_issues/dynamical_criticality).
Most interesting to me is that the (EMEH) seems to be consistent with the punctuated nature of history as pointed out by Taleb in Fooled by Randomness and because of Free Will component of the EM and considering that even local eigenvectors may change due global eigenvectors, then EMEH is also consistent with Wolfram principle of computational irreducibility.
Taken as a gedankenexperiment or even as a fictional element, the Göedel solution might as well allowed us to uncover a plausible (not just fictional) feature of the dynamics of events in the universe that makes sense with some universal principles of complex systems as well as empirical observations about history.
One last thought, if instead of considering the whole universe we take the EM for our lives, we would identify as well our own events eigenvalues, those personal set of events that (punctuated) has made us what we are, what does that makes you think?
