Oneness Vs. Duality Part 2 of 3: Kurt Gödel, Camus, and the Never-Ending Proof
Continued from: Overcoming the Madness of Infinities
Austrian Mathematician Kurt Gödel (1906-1978) (pronounced like girdle) came up with what is called the Incompleteness Theorem. And while most people have never heard of Gödel’s Incompleteness Theorem, it is nonetheless one of the most important discoveries in human history. What Gödel’s Incompleteness Theorem demonstrates is that in any formal system (a system consisting of a formal language and a set of inference or transformation rules) there are true statements that are not provable within the confines of that system. In other words, formal systems are doomed to incompleteness; there are always dark spots that are true but not provable.
What this means to a formal enterprise like science, is that such an enterprise is perpetual: no matter what you find out or what models you make, there will still be missing elements and so new things to discover and new models to make. A few years ago, famed physicist Stephen Hawking gave a lecture titled Gödel and the End of Physics. In the lecture, Hawking, referencing Gödel’s Incompleteness Theorem, described why the Holy Grail of science, the Theory of Everything, will never be fully realized. There will always be things that are not predicted. Therefore, science is in effect never-ending.
As was discussed in the previous article, multiplicity leads to infinities and infinities lead to madness (both figuratively and literally). If we are to attempt to merely understand the universe on its own multiplistic terms, we are doomed to live like the mythical Sisyphus, perpetually pushing a rock up a mountain only to let it roll back down again. Which is to say, we are doomed to chase infinities.
The mythical rock rolling Sisyphus is a great example of the plight of the infinity chaser. And that plight was explored thoroughly in the essay “The Myth of Sisyphus,” by the French author and philosopher Albert Camus (1913-1960) (pronounced like cam-ue). In the essay, Camus concludes that happiness comes from the recognition of the undeniable futility of the perpetual task: a contended acceptance. Thus Camus says that “The struggle itself is enough to fill a man’s heart” and so “One must imagine Sisyphus happy.”
However, while Camus’ attempt to come to terms with chasing infinities is noble, it is nonetheless simply a classic case of “turd polishing.” Consequently, I do not quite hold the same sentiment as Mr. Camus. I would instead say that “The struggle itself is enough to keep a man temporarily blind (psychologically asleep)” and so “One must imagine Sisyphus as complacently mad (chasing infinities).” No one is ever doomed to the impossible (chasing infinities) unless he continues to accept it so.
Chasing infinities is an act of war/conflict; it is an external struggle to find fulfillment that is doomed to incompleteness. The plight of the playboy (or girl) ever unfulfilled by his extravagant excesses, is the same plight of the intellectual attempting to understand the universe on its own terms. Satisfaction is always elusive when chasing infinities; it is an exercise in futility.
While a person can attempt to simply revel in the futile absurdity of chasing infinities–like Camus, existentialists, and scientists like Stephen Hawking try to do–or justify chasing infinities–like many mystics, religious, and new-ager-types try to do–it is not until a person inverts the multiplistic thinking of the world that any true, un-fleeting satisfaction can be found. To invert the thinking of the world is to flip multiplicity around from being a road to infinity to a road to oneness (singular Infinity). (Note: Don’t confuse singular Infinity with the idea of singularities. Singularities are another form of infinities, not oneness.)
Infinities (plural) are as much related to spacetime as Infinity (singular) is related to eternity. The spacetime world we see with our bodily eyeballs is an artifact of a pervasive idea…the idea of multiplicity…duality…separation…splitting. Devoid of the concept of multiplicity, there is no world, only the eternal, only oneness, only the sublime.
It is just as imprudent for the materialist-rationalist to dismiss concepts like eternity, as it is for the mystical non-materialist to mix eternity with multiplicity (infinities). Such is an example of confusion of levels…confusion of mind and matter…confusion of cause and effect. Such is the confusion that keeps man chasing infinities. And that confusion is what we will explore in the next article: Level Confusion Dreamtime
Oneness Vs. Duality Part 1 of 3: Overcoming the Madness of Infinities
German mathematician Georg Cantor (1845-1918) spent much of his lifetime trying to wrap his mind around the concept of infinities. As a result, he went mad. Which doesn’t surprise me. There is no concept I have found more consistently disturbing in my lifetime than the concept of infinities. My dreams as a child were often riddled with immensely frustrating themes of ungraspable infinities. Treadmill effects, exponential growth curves, and perpetual splitting were ideas that would often turn my nighttime slumbers into nightmares.
My distress over infinities peaked at around age eight and then progressively subsided. Today, infinities only manage to take hold and haunt my mind during times of illness (flu), which fortunately has been very rare since my childhood.
Although my lifelong relationship with infinities has been distressing, it has taught me an important lesson: There is no difference between madness and infinities. Entertaining the idea of infinities is itself madness. As a result, I have come to be very weary of all thought systems that require an acceptance of infinities. And to put it simply, any thought system that accepts multiplicity as a reality necessarily accepts infinities. Thus, whether the thought system comes from science, religion, philosophy or wherever, if it accepts multiplicity as reality, it accepts inescapable infinities, and so is just a variety of madness.
It must be noted though, that there is a difference between infinities (plural) and Infinity (singular). However, in the normal everyday use of the word infinity, this difference is not recognized. Notice that thus far in this article, I have said only that the concept of infinities (plural) is equivalent to madness. I have not said anything about the word Infinity (singular). Infinity (singular) is not madness; it is in fact sanity.
Our analytical brains are only capable of grasping (running with) the concept of infinities (plural) not Infinity (singular). Analysis is in itself the act of breaking things down into smaller, more manageable parts, which are then assessed by an observer that is treated separate from the thing being analyzed. In other words, analysis is all about multiplicity, which when carried out indefinitely leads to infinities. Infinity (singular) cannot be analyzed. Thus, Infinity is incomprehensible to the analytical. Analysis turns Infinity (singular) upside down and splits it apart into infinities. What all this means is that one cannot grasp Infinity (singular) without actually being it in experience. Any thought of separation (multiplicity) renders Infinity (singular) incomprehensible, and so it cannot be understood by an outside observer (perceiver).
This understanding of Infinity versus infinities is why I find thought systems like atheism/materialism just as limited and grounded in multiplicity as most religious/spiritual doctrine. The arena of human thought systems is for the most part a spectacle of blind people arguing over the colors of nothing. What unites almost all human thought systems is a mutual attempt to justify multiplicity and thus justify infinities. Human thought systems are sometimes useful for getting things done in the world of multiplicity, and for sometimes providing glimpses of truth, but they are always incomplete and self-blinded. There are just as many potential thought systems for attempting to justify infinities (multiplicities) as there are infinities (potential multiplicities)…and all of those thought systems are doomed to incompleteness due to their inherent reliance on multiplicity (non-oneness).
In the next article, we will look at incompleteness as it relates to truth in: Kurt Gödel and the Never-Ending Proof