The number pi (π) is known as the ratio of the circumference of a circle to its diameter. In Euclidean geometry, π is defined as an irrational number, which represents the circumference C of a circle divided by its diameter D, that is, π=C/D​. Additionally, since D=2R (where R is the radius of the circle), the circumference can be expressed as C=2Rπ.

However, when we consider discrete geometry, in which points have non-zero dimension d, corresponding to the limits of our material world, the relationship becomes more complex. In reality, multiplying the radius R by 2 on a circle is equivalent to counting the central point c, of dimension d, twice. This means that the correct expression for diameter in terms of radius would be D=2R−d.

Consequently, the relation π=C/2R​ is only valid if d is zero, that is to say in a purely theoretical context where the points have no dimension.

Introduction

The square root of 2 is known to be an irrational number, meaning that it cannot be expressed as an exact fraction of two integers. However, the difference between the abstract world of mathematics and physical reality introduces important nuances in our understanding of the square root of 2. This article explores these differences and offers an alternative perspective on the nature of this square root, which extends to other square roots considered "irrational."

We generally conceive that our present is situated on a single timeline that stems from the past and runs towards the future in an eternal journey. Even though we can only experience the present, we freely fantasize about the possibility of moving backward or forward in space-time, and it has even been mathematically proven that there are no theoretical obstacles to such a feat. Thus, we accept the paradigm, we strive to understand the notion of relativity, the influence of speed and gravitational fields that might disrupt the synchronization of our earthly clocks. However, there are other ways to view time, one of which determines that it might simply be an illusion of the mind or an extreme simplification.

Before diving into these dizzying concepts, it is essential to arm our minds with some conceptual tools. Let's start with infinity: an indispensable concept when talking about eternity. Infinity, by definition, exceeds any measure or limit that our mind can comprehend – this is a testimony to the reach, but also the limits, of our human cognition. Secondly, there is the still quite metaphysical concept of a quantum reality that materializes when observed and remains undetermined or in a state of probability when it is not. If you are not familiar with these notions, you can start by looking at the double-slit experiments or reading about Schrödinger's cat. Brace yourselves for what follows: let's imagine there exists a "quantum soup" where all particles float freely without representing anything but are ready to create a single reality when observed by a consciousness, that is, among an infinity of probable combinations, a observing consciousness only fixes one. If the "quantum soup" were observed by another consciousness, its materialization would be ipso facto different. Finally, the "quantum soup" itself would stem from an energy that could be called the Consciousness of Being, contained in a Singularity, which the Bible describes as God in Genesis, when He presents Himself by saying "I am who I am." This Consciousness of Being needs nothing since it is aware of its own Being, which is the maximum state of consciousness one can aspire to. The Energy of Being, however, can manifest the All, that is, everything that can be and the All would be nothing more than the Singularity of the Consciousness of Being expanded and explained, but without adding anything to what Being is.

It's a long detour to come back to our notion of time. In the All, everything that is possible exists in the present moment, simultaneously, there can be no reality either in the past or in the future, everything is in the present. It is worth mentioning that the Present in which we live is not the materialization of a single possible line but rather an observed point on a line of possibilities. To visualize this concept, imagine time as a network of rails, each rail symbolizing a distinct temporal sequence. We experience the present as if we were on a train moving along one of these rails. However, it is possible to consider a 'jump' to a parallel rail, and thus from rail to rail, each change of rail corresponding to another temporal sequence that remains coherent with the previous one at the moment of the jump. Each rail encapsulates the entirety of the past and future of that trajectory. Nevertheless, our experience is strictly limited to the current point on the rail where our train is located. Time travel would therefore not amount to moving forward or backward on a fixed line but rather to jumping to another, more distant line where our present would unfold at another time, non-sequential with the previous one. It would be like making a quantum leap to a parallel reality. The first difference from what we usually conceive is that there would be no temporal paradox - the typical question of what would happen if we killed our future grandfather - but rather that we would be on another coherent trajectory without being aware of what happened before the jump. Even if this were possible on a quantum level, it would likely not be very appealing because we would probably have no memory of a previous physical plane and could not coexist with a past or future self in any case. The present is the only possible reality for consciousness, and the memory of the past, which is information, normally depends on our physical being, our brain, without excluding the possibility of eventually recapturing that information which is never lost.

Why create a different temporal model from the conventional model? The idea is to unify the notion of the Singularity of the Consciousness of Being and the All, which is the same Singularity explained by Information. Everything is everything, nothing can be missing. On a single Time line, there would be only one version excluding an infinity that should coexist in the Present and the others could therefore not exist. Thus, the All, in its essence, would remain purely potential, never manifesting concretely. This allows us to conceive of the multiverse, also infinite, not as bubbles floating each in a sort of ultra-cosmic megavoid but as a cosmic matrix of all potentialities that coexist at the same time and that effectively materialize into one under the observation of a consciousness without excluding the others.

Finally, it is about showing that our time paradigm is neither unique nor certain, and that philosophical research can bring us closer to different ways of perceiving what our reality is. Beyond the complexity of what is exposed above, we find the undeniable fact that Time is an illusion of our mind, it is neither defined nor absolute, but above all, the past only exists in our memory and the future is just an unrealized probable projection. Therefore, there is only the present point in an immeasurable All, but this point, which is our conscious life, is unique, indispensable, and irreplaceable. It cannot not exist and must therefore be lived. The way in which we live our present moment is the subject of philosophy and Pointfulness.

A friend of mine, who studies cosmology, shared a quote from an expert in the field: "It cannot be that the entire evolution of the cosmos over 13.5 billion years since the Big Bang was just so we could shop at a mall over the weekend." This reflection leads me to think of Nietzsche's concept of eternal recurrence, which challenges us to value our lives under the perspective of having to live them over and over again, eternally.

Teleological perspectives in philosophy, which analyze the purpose of things, often resort to absurdity to make their point. This concept is reflected in the question: Why embark on an eternal journey in search of the All and the fullness of the Consciousness of Being, if that same fullness is found in the singularity of the present moment? We embark on a journey whose purpose seems to require an eternity, when that purpose is accessible here and now, if only we elevate our consciousness.

I am tempted to unite these three thoughts: The affirmation of our being through our acts has been the result of an evolution of 13.5 billion years in a vast and complex universe, which might just be one iteration among countless others. All this, for what?

From this perspective, the nihilistic stance is understandable: everything is so insignificant that it seems to lack importance. However, one can also adopt the opposite view, that everything has collaborated so that we can enjoy these precise moments, that we possess an immense fortune to spend on what life offers us, even if it were just breathing.

When I suggest along with others that the fullness of the Consciousness of Being is our greatest longing, it sounds abstract because we prefer to experience Being with small flashes of happiness, through possession, love limited to what pleases us, in short, collecting grains of sand hoping to make a beach instead of enjoying the beach that is already before us. To achieve this, it almost suffices to raise our gaze and our level of consciousness, ceasing to focus on the grains of sand.

Nearly twenty years ago, when I experienced depression, I often described it, like others, as a constant, diffuse physical pain caused by a feeling of emptiness in my chest. This painful sensation remains difficult to explain because it isn't associated with a specific organ or nerve that can be numbed, and appears to originate, until proven otherwise, in the mental realm.

However, one doesn't need to reach a state of depression to experience emotional pain that, at times, resembles physical pain so closely that some individuals resort to self-infliction to materialize what cannot otherwise be expressed.

Well-being, or the absence of pain, is our normal condition, and naturally, we strive to maintain it, whether by avoiding harmful causes or restoring balance as quickly as possible by any means available. Yet, deep and prolonged pain prompts us to question the very meaning of our existence, whether our own or that of another, and is therefore often at the center of philosophical debate.

As I discuss in my book The Singular Life and the Triangle of Illusions, our brain functions like a powerful calculator designed to ensure our survival and, whenever possible, our well-being. Physical pain, signaled by our nerves, demands an immediate solution. If the intensity remains unbearable and without relief, the "calculator" spins until you faint, or, without going to that extreme, thoughts about this seemingly insurmountable problem invade our mind. The pain then transforms into suffering, i.e., into a virtual, mental form that constantly reminds us that the problem persists. And since we have the ability to remember the past and project into the future, this immaterial form can draw on what no longer exists or has yet to occur.

But let's return to pain itself, which is part of our vital experience. As I've stated elsewhere, living in the present is inseparable from having unconditional love for one’s own life and, consequently, for our own pains as they arise. Thus, “living in the present” is not just a trendy mantra, but quite the opposite: it is a state of mind achieved through discipline, understanding, forgiveness, compassion, and kindness, allowing us to live peacefully, free from illusions. Very often, the first obstacle on the spiritual path is pain, as it manifests as a piece of hell while we seek paradise.

The Pointfulness philosophy addresses pain as it truly is: very real, but also as a powerful generator of illusions that can intensify and magnify it with suffering. Promises to reduce or eliminate pain are the most compelling sales pitches, especially if they are easy and free. There are thousands of websites and recipes dedicated to all sorts of ailments, known and even imagined. Pointfulness, through the deconstruction of illusions, attempts to return pain to the perceived reality of life, accepting it as it is and not as what we make of it. Only in this way will it be possible to accept it unconditionally in the present moment and not mentally flee from it down paths of illusions.

My central argument is simple yet profound: the diameter of a circle is not exactly equal to twice the radius. This claim is based on an observation about the parity of points: a diameter, including the central point, consists of an odd number of points, whereas two radii, added together, always result in an even number of points. Although the difference is minimal – just one point – this small discrepancy prevents the equality from being absolute.

This observation leads us to wonder: is it possible to form a circle from a segment that has an odd number of points? While the answer might be affirmative, the absence of a defined central point introduces an undefined aspect into our geometric construction. Delving deeper into this reflection, we might suggest that this duality of odd and even diameters introduces an indefiniteness at the central point, which could offer an explanation for why the number Pi is irrational. Pi represents the relationship between the circumference and its diameter in a perfectly closed circle, though conceptually the diameter might present these peculiarities.

I use this analysis to emphasize the importance of the "central point" in my Point Theory, which I explore on my blog. This concept is not only crucial in personal life but also has significant implications in mathematical calculation, such as in determining square roots, where the intersection point of two segments is counted twice.

Furthermore, I propose a corollary related to the theoretical versus practical nature of mathematics. Although mathematically we can calculate the decimals of Pi ad infinitum, physically it makes no sense to do so beyond the smallest possible physical distance. This is because a circle must close perfectly for any defined diameter with an integer number of points. Therefore, the decimals of Pi could theoretically be limited to those corresponding to the smallest possible distance and the nearest odd diameter as a conceptual limit.

This approach invites us to reconsider not only the foundations of geometry and calculation but also how we interpret and apply mathematical principles in the physical world. I am very interested in discussing these ideas further and receiving feedback that could enrich or challenge this perspective.

Welcome to Pointfulness. In one of his talks, Eckhart Tolle says that he does not like the word “Mindfulness” because it means “Full of mind” when one seeks precisely to get rid of the empire of the mind over our life. Pointfulness attempts to correct the original word, placing emphasis on the singularity of the point, in the Here and Now.

A friend of mine, referring to my book during a conversation, said to me, "And to think that it all started with a point..." Whether consciously or not, his comment was very precise. If someone were to remember only one thing from my book, it would be about the importance of the point, of Singularity.

The "Theory of Everything," which aims to unify quantum mechanics and relativity to explain our Universe, is widely discussed. However, I also find it relevant, from a metaphysical standpoint, to discuss the "Theory of the Point." This small point that is the Consciousness of Being. Imagine I want to describe a circle and, after extensive research, I discover that the circumference equals twice the radius multiplied by Pi (an irrational number). This formula implies that my circle could be located anywhere in the Universe, provided we know where it is centered. A similar problem arises with the Theory of Everything that tries to find a universal formula without knowing the point of observation, here the Consciousness.

In our everyday lives, we need a center to locate ourselves, and this center is the point of our consciousness of Being. Everything else is just information, and information can create illusion if we do not have an absolute reference. First, our consciousness of Being is unequivocally in the Present; I cannot exist in the past or the future. Secondly, the consciousness of Being is pure and complete, meaning that Being admits no attributes or complements. This is what Eckhart Tolle defines as "Presence."

The Point Theory also emphasizes the role of the observer in quantum mechanics. Without an observer, everything seems chaotic, but when someone observes, the chaos actually reveals itself as ordered. And behind an observer, there must be Consciousness. My personal point of consciousness establishes the center of my universe and defines what is my Everything, just as the center of a circle determines its position and extent. Determining the point of observation from the Consciousness of Being organizes all the information around me and becomes my reality. Since no reality can be greater than that encompassed by Being, we understand that the singular Being of the point equals the Everything, or that the Everything is the Singularity explained by virtually infinite information.

Even if I extend the radius of a circle infinitely, I will know nothing more about the point of its center, and there will be no more information than what is already contained in the number Pi. Similarly, the Fullness of the Consciousness of Being is fully present in the singularity of the moment, in the Present, and any additional information you might seek will not better explain Being, even if you devote an eternal life to it. Everything comes back to the Point.

One of the things I pursue with Pointfulness is to practice an engineer's philosophy, that is, to find ideas that work based on reason and common sense, with more emphasis on the substance than on the form. The reason why I wrote my book in Spanish and not in French, which is my mother tongue, was to limit myself in the literary sophistication to which the French language almost inevitably invites. Living in a Spanish-speaking country was obviously the other motivation. That said, there are concepts that need to be described and explained carefully and the first, fundamental among all, is the Fullness of Being.

I have two good news: the Present is still there and the Future is not written.