Copyright 2011, John Manimas Medeiros

As a young child I wondered why does something exist instead of nothing. Through a lifetime of contemplation and geometry, I found the answer. This I believe is the correct and proper description of the real, physical universe, and I predict, and prophesy, that the description that I present here will be acknowledged, defended and generally accepted by the year 2030.

First, the most fundamental reality of the universe, the reality that determines all physical laws that follow, is that the universe is infinite in one direction: outward. This is the answer to the question "Why does something exist instead of nothing?" I conceived of this possibility early, but confirmed it over three decades of research around the riddle about squaring the circle. The resolution of this riddle is actually simple, and yet profound, and serves as the door that opens to let one enter into the real universe.

The original riddle was not a riddle, I contend, but a statement: "Using only a compass and straightedge we can construct a circle that has exactly the same area as a given square." How could this be true? It is true because a real circle in the real, physical universe cannot be the Euclidean circle that mathematicians have accepted and defended since the middle ages. The mathematical commitment to the Euclidean definition of a circle is obviously irrational and represents an "ideal form" that belongs to an ancient Greek philosophy, but is not a description of reality.

The Euclidean or "ideal form" circle is, and has been for centuries, as follows: "A circle is the curved line that is comprised of an infinite number of points, each point having no dimensions, and each point being the same equal distance from a given central point." Why the institution of mathematicians persist in defending this joke is the true puzzle, and I attribute it to a common psychological problem of mathematicians. Most mathematicians are semi-autistic and they long to be seen as having emotions and imagination, and they fall prey to the popular stereotype that they are geniuses and that they alone can understand the universe. However, everyone can understand the universe, because our brains evolved in it and our brains are designed to understand the universe, by adapting to experience.

If the circle is assigned the definition that is physically correct, for a physical circle and a physical sphere in the real, physical universe, it cannot have the Euclidean qualities, because the length of an infinite number of points, each point having no dimensions, is zero. That would make the value of pi equal to zero. Further, if each of the points are assigned a dimension, however small, that modification of the definition does not resolve its problems, because the length of an infinite number of points, each having some very small dimension, is infinity. That would make the value of pi equal to infinity. The correct solution to this problem and the square-the-circle riddle is to adopt the definition of a physical circle, based upon the doctrine that there is a smallest possible particle, and thereby every circle and every sphere has a circumference that is comprised of a finite number of particle lengths, each particle being the same equal distance from a central point or particle. This then gives pi a variable value, depending on the number of particle sides, odd or even, regular polygon or irregular polygon respectively, and the actual finite circumference being the number of particle sides times the length of each particle in the finite, physical circumference. This always approximates 3.141592653589..., but somewhere out there to the right, at the 50th or the 500th or the 5,001st decimal place, it varies from the actual length of the circumference of a different physical circle, because all physical circles are and must be polygons.

The secret to finding this solution, and the key principle of why the physical universe exists, is not to solve the riddle as a riddle of geometry, but rather as a riddle of history. Why did the original statement become a question and a geometric problem? Because that is what happens with history, things change, interpretations change. And because those who tried to construct a Euclidean circle exactly equal in area to a given square could not do it. And so they changed the statement to a question: "Using only the compass and straightedge, can we construct a circle exactly equal in area to a given square." This then became interpreted as a strictly geometric puzzle, to be tested only by geometers, and later on this riddle was derided and discredited as being only evidence that the understanding of the ancient Pythagoreans was primitive and simple. But, in reality, their understanding was advanced and correct and possibly complete.

The historical solution, therefore is this: The real reason this riddle was presented to students of geometry is because in the world of the Pythagoreans a student of geometry was a student of reality, a student of mathematics and reason and logic and of the real, physical universe. And, this riddle is a pointer, a pharaoh or lighthouse or guiding light that points the way to understanding. What is the understanding that this riddle points to? The understanding that the ancient "square-the-circle" riddle points to is that a universe in which there is no smallest possible particle is dramatically and devastatingly different from the universe we live in, the universe where there is a smallest possible particle. In a universe with no smallest possible particle, physical reality would diminish gradually to nothing, to zero, and that would mean the ultimate reality -- in the real, physical universe -- is void, null, nothing, emptiness. How could we then measure and manipulate nothing? The correct answer to the riddle is not a geometric trick or hidden constant quantity, but instead is the discovery and conclusion that because there is a smallest possible particle, we can square the circle exactly, we can construct a regular or irregular polygon using only a compass and straightedge that has exactly the same area as a given square. The mathematicians will roar, or cry out, that this solution is trivial. But it is trivial only if it is designated as a strictly geometric construction, which it is not. It is instead the construction of the universe. The real discovery is as I have stated here, the discovery of the immense and cosmic difference between a universe with no smallest possible particle and the real universe with a smallest possible particle. The ancient Pythagoreans were not presenting the riddle in order to make students busily play with their compass and straightedge long into candle-lit nights, but rather to discredit the Euclidean circle and ideal forms in general and impress upon serious students of the universe that if one wants to understand the real, physical universe, the first step is to see that the universe is infinite in one direction: outward. The universe is not infinite in the other direction: inward. There is no outer boundary to the stars and galaxies and clumps of matter that we detect with our visual and electromagnetic telescopes.

Each time our instrumentation improves, we find a "new" outer reach of the real universe. In other words, the more we see, the bigger the universe gets. It is very much the same thing as saying that we envision the world differently after we accept with certainty that there is another continent on the opposite side of the ocean. Before we knew that the other continent existed, for certain, the entire world was just our continent.

Although the mathematicians and physicists will still insist that this explanation is trivial, it is not; it is profound. All of mathematics and geometry and physics must and will adjust to the fact that pi is variable, and rational (equal to a whole number divided by a whole number).

Second, time is a fiction of consciousness. I have several essays posted on my website endeavoring to defend this view of reality. It is again not trivial, but profoundly important, and represents the real universe as vastly different from a universe where time is a real, separate entity that is independent of all other entities or other dimensions. All of twentieth-century physics will soon be revised to adapt to this concrete reality of the universe that encloses us and that we measure. Much can be said in defense of this view of time as a fiction of consciousness, but the best and simplest explanation is to see time for what it really is: counting the repeated occurrences of a cyclical event. There are many cyclical events in our real universe. In fact, any physicist who has taken the time to contemplate reality, without shame, cannot help but notice that most, and possibly ALL events that occur in the universe are cyclical. This is a challenge to human understanding, because it raises the question as to whether there are any events that have occurred only once. Or, are there any events that we might imagine or anticipate that might occur in the future, but occur only once? The paradox here is that time exists only in our brains because we must be able to count cyclical events and formulate concepts of past, present and future in order to be able to observe and deduce cause and effect. And, further, even more profound and ironic, we must live in a determined universe, a universe that is comprised of causal chains of events that produce following events, or process, in order for us to have free will. Because, in order to have free will, we must be able to plan to achieve a goal and complete the steps that lead to achievement of that goal. And, in order to execute a plan successfully, the steps we take must yield the results we expect. And in order for the steps we take to yield the results we expect, the universe must consistently produce events that are caused by events that precede them: cause and effect. Exhaustingly, we cannot choose anything unless we live in the universe we do live in, where precise causes yield precise effects -- a universe that is determined, and the only kind of universe in which rational and conscious beings can make effective choices. And that is what free will is, the capacity to make an effective choice. If one could not choose to throw a stone at a rat, and then throw it and hit the rat, then there would be no free will. Without cause and effect, there could be no free will. Therefore, again, the reason that our brains count time, is because we must be able to count time in order to conceive of cause and effect. However, it is only we, and our brains, who need to count time in order to conceive of cause and effect. Nature does not need to count time in order to do what it does, because Nature simply executes process according to the physical laws. It does not need to record what it does or possess a view of a past or of a future. It just goes, flows like a river, moves like the wind or a tide, but does not need to count "how long" it takes to complete a process or a cycle or an event. Time is duration, and all events possess a duration, but an event possesses a duration according to the cyclical events that we choose to count in order to render a measurement of "time." However, as you can see, if you will look, by counting the occurrences of any cyclical event, we have not measured anything concrete. We have just counted and created, in our brains or on some chosen medium -- such as paper -- a representation of the duration of that event, in terms of the chosen cyclical event (sunrises, seconds, or moons, or cricket chirps at 80 degrees Fahrenheit). We create records, describe the past and project the future, but Nature does not need to do either, and Nature does not do anything that it is not required to do. That is the second revolution in physics that must come in order for human civilization to move forward in its understanding of the universe and itself.

Third, the contest between religion and science is a political contrivance. It has no basis in reality. Both religion and science are methods to seek the ultimate truth. All conflicts deemed to be between religion and science are actually between democracy and theocracy. The human motives behind all such conflicts are the desires of scientists, or religionists, to control the beliefs of others. This is not necessarily strictly a nefarious motive. One might feel that the truth must prevail, and it order for the truth to prevail others must see the world as "we" see it. But in order for freedom and justice to prevail, each person must be free to see the universe as they see it. We must allow for religion and science to live together, like a marriage forced following the birth of a child of passion. The child -- being the universe -- is born to us, in our minds, and we must take care of it together, mother and father, male and female, love and knowledge, emotion and reason, work and play, rage and serenity, or perish. Without our children, we expire, gone with no one to write our history, or hear it or read it, with no one to know with certainty that we are, or ever were. And likewise, religion and science are the children of our minds, dueling siblings, each claiming that we don't love them as much as the other, and how the other is sinning and not being appropriately controlled or punished.

Religion arises from our hunger to envision the big picture, teleology, the cosmic questions and cosmic realities of existence, the how and when and why of undetectable origins. We use science to explore the causes and effects in the universe of all sizes, clearly being led to detect and discern that which is very small but yields the results that are very large, such as health, death, climate, movement, collision, creation and destruction or transformation of all things of all sizes. Thus we have felt the movement of a reasoning mind or sensed a logic to the stars we see in the sky, the secret, hidden diseases that make us sick and kill us, and the mysterious passions that move us and cause us to do things that we thought impossible either because of their sublime greatness or their incredibly dark and violent and selfish destructiveness. Out of our contemplation of undetectable origins, we invent gods and make gods in our image, and we create other worlds and then claim that we are made to be like the God that created the universe and there is a life after death of the body. And all this could be true. But the key third reality, the reality that we must face soon in order for human civilization to survive and move forward is the reality that we cannot decide, using reason, whether there is a Creator God or a life after death, but we can decide, using reason, who and what we are. And, we can do this by using all that we find useful and meaningful from all sources of information, both the scientific and the religious sources. Knowing who and what we are is in fact more important and more fundamental as to whether there is a life after death or whether the universe was created by some form of divine "person."

In order to understand who and what we are, one must set aside the presupposition that any communication from the divine to the human must be comprised of morality, or moral law, or rules for moral behavior. One must conceive of a God who provides useful information to humans in order to help them understand who and what they are and how they can best survive in the real, physical universe. Half or more than half of all ancient religious myths include stories of gods teaching technology and science to humans rather than morality. The ancient Greek myths, respected in the field of the history of Western Civilization, include the story of Prometheus stealing fire -- the birth of technology -- from Zeus and giving it to humans. It is only the Christian and Muslim religions that can become dysfunctionally fixated on moral laws and sadistic punishments. This means that all religious sources must be re-examined to discover the scientific messages hidden within allegedly moral communications. And these include most if not all of the ancient scriptures, the Old Testament and the New Testaments, and the ancient holy scriptures of the Egyptians and the Tibetan mountains and those drifting in the mists of ancient China and India, Black Africa, the Andes and the Amazon. We are so earnest to extract gold and uranium from rocks, and we do so. We need to just as diligently mine the science from the rocks of ancient scripture. The first person whom I heard make this suggestion is Erich von Daniken (Chariots of the Gods).

These are the three main principles of the new paradigm. Your children will wonder what took us so long. --- John Manimas Medeiros, November 2011.