Galileo learned a very important lesson from Giordano Bruno – namely, to be very careful when questioning dogmas, especially when the dogma is set forth by the leading institution of Galileo and Bruno’s day, the Catholic Church.
Bruno, a 16th century Renaissance-era philosopher and poet, believed in the infinitude of space, and that stars and planets are more or less randomly mixed together in infinite space. He was the principal representative of the doctrine of the decentralized, infinite, and infinitely populous universe. He strongly advocated such viewpoints in his writings, especially in his dialogue of 1584, “On the Infinite Universe and Worlds.”
These and other writings were influential enough that Bruno is considered a forerunner of modern philosophy, because of his influence on the Dutch philosopher Baruch Spinoza, and his anticipation of theories of 17th century monism.
His theories caught the attention of the Church, and in 1591, a trap was sprung, and Bruno was arrested and turned over to the Inquisition, on charges of being a heretic. For nine years, Bruno was interrogated, tortured and tried; yet he refused to change his beliefs. Finally, in 1600, he was burned at the stake.
Spinoza, himself, had a less horrific fate than Bruno did; yet his community also turned him out. His unorthodox views caused his expulsion from the Jewish community and exile from Amsterdam. He lived and wrote in obscurity, earning his living as a lens grinder. His work was ignored for a century after his death; now he is considered one of the most original and influential of modern philosophers.
And so, Bruno’s example caused Galileo to express himself a good deal more cautiously on scientific questions in which the Church had a vested interest. By the early 17th century, Galileo was a world-famous scientist, thanks to such developments as his refinement of the telescope, which allowed him to peer into the cosmos and announce Copernicus was right, that the Earth was not the center of the universe. In 1629, he wrote a best-selling book, Dialogue Concerning the Two Chief World Systems. In his book, Galileo tried to be fair to both perspectives, and not ruffle too many feathers.
Ultimately, Galileo’s enemies within the Inquisition brought charges against him. In 1633, in Rome, he stood to face trial by the Inquisition. As opposed to Bruno, when Galileo was threatened with torture if he did not recant his theories, he acquiesced. For doing so, Galileo’s death sentence was commuted to house arrest for the rest of his life.
The incident of the Inquisition represents one of the worst examples of dogmatism within recorded history. In fact, it wasn’t until 1992, at the 350th anniversary of Galileo’s death, that Pope John Paul II finally apologized to Galileo for his treatment by the Inquisition. In regards to Bruno, in the late 19th century, a statue was erected in honor of the cause of free thought at the site of his death.
History is littered with Inquisitions, be they Salem witch hunts, McCarthyism, or Islamic jihads. All point to the same thing: a desire to stop the free flow of thinking.
Dogmas are the enemies of a Godelian universe, because they attempt to end all discussions and tests of truth; they are totalitarian viruses for the mind, preventing the creative growth that Godel’s proof implies is possible. Godel’s universe is not totalitarian, yet it does not deny our need for order and explanation. The universe he predicted and showed we live in is an open-ended one, not a clockwork one.
In the book Chaos: Making a New Science, by James Gleick, are many descriptions and insights that can be expected of Godel’s universe, such as:
The vogue for geometrical architecture and painting came and went. Architects no longer care to build blockish skyscrapers like the Seagram Building in New York, once much hailed and copied. To Mandelbrot and his followers, the reason is clear: Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world. In the words of Gert Eilenberg, a German physicist who took up nonlinear science after specializing in superconductivity: “Why is it that the silhouette of a storm-bent, leafless tree against an evening sky in winter is perceived as beautiful, but the corresponding silhouette of any multipurpose university building is not, in spite of all the efforts of the architect? The answer seems to me, even if somewhat speculative, to follow from the new insights into dynamical systems. Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects – in clouds, trees, mountain ranges, or snow crystals. The shapes of all these are dynamical processes, jelled into physical forms, and particular combinations of order and disorder are typical for them.
Einstein was once asked what he would have done if a physical experiment had contradicted his mathematical prediction, and he answered by saying that he would have felt sorry for the Lord. Throughout his scientific life, he always stood up for intuitive imagination as being superior to physical experiment, although not independent of it.
It’s not just Inquisitions, nor religious or political intolerance, that is the sole purveyor of dogmatism. Any type of thinking that is antithetical to an open-ended universe is, at its core, dogmatic. To live in Godel’s universe is to be able to grow, to move from lesser to greater states of knowledge, and to develop; in other words, to become a polymath, a person with a wide range of knowledge, broadly educated in the sciences and humanities, capable of understanding how one area connects to another.
And when we extrapolate this to the largest degree, we can realize that we are amenable to and interconnected with the infinite aspects of the universe, and that there are and will always be new and emergent aspects of the universe to be uncovered. In other words, we are on a slow and indelible march towards infinity.
Infinity itself has always maintained a certain aura, a certain connection to the Absolute. The symbol for infinity, the lazy eight curve known as the lemniscate, has come to connote endlessness. Yet, for some, infinity is a scary concept, because it represents a world that is not finite and knowable, that cannot be controlled and is ultimately unknowable. Even in mathematics, no other subject has led to more polemics than the issue of the existence or nonexistence of mathematical infinities. It was Georg Cantor, who in the late 1800’s finally created a theory of the actual infinite, which by its apparent consistency, lay to rest the proofs that no such theory could be found, who said:
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
And it was the short story fiction writer, Jorge Luis Borges, who wrote in his essay, “Avatars of the Tortoise”: “There is a concept which corrupts and upsets all others. I refer not to Evil, whose limited realm is that of ethics, I refer to the infinite.”
Infinity was first uncovered somewhere between the 5th and 6th centuries B.C., by the Greeks. The concept was so overwhelming, so bizarre, and so contrary to every intuition, that it confounded the ancient philosophers and mathematicians who discovered it.
The first evidence that the Greeks were the first to stumble upon it came from the philosopher Zeno, and what are known as Zeno’s paradoxes. One of the paradoxes described a race between Achilles, the fastest runner of antiquity, and a tortoise. Because he is much slower, the tortoise is given a head start. Zeno reasoned that by the time Achilles reaches the point at which the tortoise began the race, the tortoise will have advanced some distance. Then by the time Achilles travels that new distance to the tortoise, the tortoise will have advanced farther yet. And it continues like this ad infinitum. Therefore, according to Zeno, Achilles could never beat the slow tortoise. There are a number of Zeno’s paradoxes, all pointing to the fact that space and time can be subdivided infinitely many times.
Current cosmological discussions have debated the concept of an endless universe, and whether the universe will continue to expand infinitely and endlessly, or whether at some point, it will begin to contract. Most are in agreement that at some point the universe will begin to contract, until it reaches a singularity, at which point it will either contract into nothingness, or else create an entirely new universe. Yet, whatever the universe might do, even if it contracts to a singularity, this does not negate the infiniteness of the universe, because there are spatial infinities: infinities of both the large and small. The universe can still be immersed in infinity even when it has contracted to the size of a ball.
Some would think that a large infinity is greater than a small infinity, but this is not the case. For instance, if you count between one and infinity, you will never end, because of the vastness of this large infinity. Yet, if you count between one and two, you will also never end, because of the vastness of this small infinity – there are an infinite amount of numbers between one and two.
It was Galileo, in the early 1600’s, who felt problems contemplating infinity only arise:
When we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this I think is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
It was Cantor who was able to show that infinity is not an all or nothing concept: there are degrees of infinity. This fact runs counter to the notion that there is just one infinity and this infinity is unattainable and not quite real. Cantor maintained this infinity, what he called the Absolute Infinite, but he allowed for many intermediate levels between the finite and the Absolute Infinite. These intermediate stages correspond to his transfinite numbers, numbers that are infinite, but none the less conceivable. Ultimately, Cantor realized three basic levels of infinity: the absolute infinities, the physical infinities, and the mental infinities.
The mental infinities are the things that are not physical: minds, thoughts, ideas, and forms. Consciousness, also, can fit into this category. The brain itself is part of the physical realm, and is not a part of the mental infinities – brain does not equal mind. For instance, every seven years every cell in the body changes. If brain equaled mind, then our memories would have a life span of seven years. Yet, memories continue to exist even after the brain cells that hold the memories have changed and been replaced by new brain cells that have never been exposed to the memories.
Memories are part of mind, and last indefinitely. Indeed, it may be more accurate to say that memories can last infinitely, for they are part of the mental infinities. And if memories last infinitely, can we say the same about consciousness – that it also lasts forever? We could say that attempts to analyze the phenomenon of consciousness and self-awareness rationally appear to lead to infinite regresses – when we do so, we are thinking about thinking about thinking about thinking about thinking…
One mathematician reasoned that when one images one’s own mind, their own mind becomes an item present in the mind. So the image includes an image that includes an image that includes an image, and so on. All of this seems to indicate that consciousness is essentially infinite.
There are a growing number of scientists who believe that there are three fundamental aspects to our universe: matter, energy, and information, which we can also call consciousness, and/or mind. Matter and energy are considered local and finite; information is considered non-local and infinite.
If it is non-local and infinite, where does it exist, and where does it emanate from? Are we a part of it, or is it a part of us? Are there stages to the mental infinities, just as Cantor realized that there were stages to all of infinity? Are these mental infinities continually evolving towards a greater whole? And do mental infinities have emergent properties, as do molecules and atoms?
These questions and more I will answer in my final paper, in which I explore the role of the mind and consciousness in the field of health and human development, and how it relates on a practical level to a Quantum-Integral Medicine.