Infinity

The term “infinity” as it relates in the discussion of metaphysical and esoteric has to do with the fundamental nature of all existence.  Quite a broad concept, but a definition at the outset of this discussion is necessary so the reader understands in what context the term is used.  In this essay the aforementioned term may be interchanged with words like “the infinite,” or the “unknowable” or the “incomprehensible” but they are meant to describe the same idea: that knowing “infinity” implies understanding of the true nature of reality, with no truths hidden.  Understanding my meaning behind the concept helps the reader understand how the words are interchangeable and not just vague terms that can confuse.

Contemplating infinity implies contemplating the incomprehensible.  It passes through thoughts in fleeting grasps but the ultimate answers never become retained knowledge as knowing infinity is unattainable by definition.  Yet striving for hints or aspects on the nature of infinity can enrich one’s life by enhancing thought processes and contemplation techniques.  Understanding these advancing grasps puts one in a better frame of mind to function in everyday life by putting things into perspective no matter how limited the advancement in understanding may be.  Infinity can be conceptualized and approached from different angles – philosophically, scientifically, and religiously.

Those of us not able to approach infinity or are unable to be a part of the infinite, in other words, all of us, spend our spiritual lives striving towards attaining infinity.  If we do not strive towards it, what is there to strive for?  If we are not striving towards the infinite are we not marching blindly to our deaths?  It is within human nature as thinking beings to strive for knowledge and to know truths no matter how vague or vast the concepts may be.

We may spend our days working our day jobs day in and day out; largely living a compartmentalized existence yet somewhere within all of us we know that we are part of something greater, or that there is something greater, within us and around us – encompassing us.  We can sense it, and at certain times we are more perceptive of this infinite nature than at other times but if we never take the time away from our modern, mandated existence we can never attain knowledge of the infinite that we innately know to exist.  If we spend our lives going to work, returning home, and going back to work in a never-ending cycle with no time for contemplation we are ignoring that intuition within ourselves to attain higher knowledge. 

Throughout history many great men have made vast strides on their own individual paths to knowing the nature of what is not finite.  Many of these men we know by name for their immense accomplishments in brightening the path for the rest of humankind.  It is important we observe some of these paths and understand the similarities of how some of the fundamental aspects of infinity are conceptualized.

One such man well along the path to understanding the incomprehensible was Isaac Newton.  Newton’s contributions to science and philosophy serve as bright paths for all of mankind and provided advancements for all of us.  One can speak for days in describing Newton’s contributions.  However, in this context Newton’s contributions to mathematics were the first to provide a symbol and a method for working with the innumerable.  As described in Newton’s calculus, infinity  can be expressed as an unbounded limit.  A limit that has no bounds can never be reached no matter how much is added to it.  Numbers can approach infinity, but never reach it.  Mathematicians in successive generations provided different methods for describing infinite numerations.  Another way mathematics describes infinity was first expressed by German mathematician Richard Dedekind in his Dedekind Infinite Set described as a relationship between a set of numbers and a subset of numbers where a relationship exists that is both injective (a one-to-one relationship) and surjective (onto relationship) or, more specifically, is described as the one-to-one (injective) relationship set of all natural numbers (positive integers) into a subset. This relationship would have to be infinite, or would it?

While Newton’s definition of infinity as a symbol in calculus and Dedekind’s definition of infinity in terms of number sets have served their purposes, they do not define infinity even in the mathematical sense as philosopher Bertrand Russell came to prove in 1901.  Defined as the “set of all sets that are not members of themselves” the statement implies that a subset is both a member of itself and not a member at the same time.  So, inherently, trying to describe infinity as a symbol or a set loses all meaning because infinity would have to include all members of the set that are not members.  Bertrand Russell provides proof that even describing never ending quantities is an impossible task.  Newton’s description admits this.

As we can see already, contemplating infinity is exhausting.  Any attempt to quantifying infinity is ultimately a losing battle, but obviously a worthwhile experience for all involved.  How can the infinite possibly be quantified?   It’s easy to see from these mathematical concepts that contemplating infinity requires a lot of work.  Nobody in all of history came up with even a mathematical symbol useful in equations to denote infinity before Isaac Newton did with his calculus and we are all in gratitude for him having done so.

Philosophy takes on different approaches to contemplating infinity from attempting to quantify it.  Philosophy really tries to define infinity by asking questions about it.  Since infinity is incomprehensible, that’s really all we can do.  One philosophical approach is to think of infinity in terms of causality or how cause relates to effects.  What was the first cause and what is the last effect?  Of course, there is no answer to this question but it does paint a picture, however faint, of the infinite.  Asking questions about causality also shows our finite minds the faint grasp of infinity we can understand by thinking about the causes and effects we can put together in a stream.  For example, if you thought Big Bang to be the first cause and your current breath to be the most recent effect, than that is your own personal grasp of the infinite, but definitely not all that is infinite.   

Perhaps the greatest milestone reached by philosophy concerning a conceptualization of the infinite was those penned by G.W. Leibniz in his Monadology in 1714.  Within Leibniz’s theorizations, which resemble a remarkable precursor to modern subatomic particle theory, a monad is defined as that simplest bit of reality that cannot be divided into parts.  It is the smallest amount of a substance that can be divided no further.  But, this simplest part that can be divided no further contains all potential of what that monad can become compounded with everything it had been in the past.  This statement brings the concept of causality into the nature of the infinite.  What was the first action?  What will be the last?  Understanding that there is no first action and will be no last provides a fundamental concept on the nature of the infinite.  These concepts present an excellent analogy of how all components of reality, including actions causing actions and reactions among other aspects within reality, are finite yet, as a whole, compose the infinite.  Leibniz, of course, states this best himself:

            “So if I were capable of considering distinctly everything which is happening or  appearing to me now, I would be able to see in it everything which will ever happen or  appear to me for all time. And it would not be prevented, and would still happen to me,  even if everything outside me were destroyed, so long as there remained only God and  me.” – G. W. Leibniz – Discourse on Metaphysics

According to Leibniz’ concepts, causality in the most broadest sense is unfounded and cannot be determined since potential and history are contained within the subject at the most fundamental level.  The fact that there is unity in the “action” of monads and order in the world can only be explained by the will of God (the Infinite) to create a harmonious universe, according to Leibniz.  As stated earlier that each of us (the finite) strive towards unity with the infinite, Leibniz expresses this concept within his monads as each having properties of the infinite whole.

Back to the world of science, as briefly mentioned previously modern particle theories also fit in nicely with Leibniz and provide good conceptualization as to the complexity of the infinite.  Particle theory remains a long way from fully explaining the infinite and the relationship between the finite and the infinite and leaves a whole lot of unanswered questions.  Particle theory leaves a lot of questions unanswered within the context of the theory.  That is what theories are, by definition they are backed with facts but not all the facts.  According to particle theory, subatomic particles are thought to be the simplest bits of matter, and behave very oddly at the miniscule spectrum of quantum mechanics.  Perhaps they behave so oddly at these miniscule levels because they contain fundamental causality, as Leibniz described in his monads.  According to the standard particle model, all of reality is composed of six types of quarks and six types of leptons which will interact differently with each other according to how the four types of forces are applied.  The four forces are strong, electromagnetic, weak, and gravity.  However, as said, these four forces do not explain the extremely odd behaviors of the particles.  For example, the lepton type known as a muon “spontaneously disintegrates” into an electron.  Exactly what forces are at work here are obviously unknown.  Yet nuclear physicists remain unfazed and continue along the trailblazing path created by previous generations of nuclear physicists in an attempt to understand the incomprehensible. 

Causality again comes up within quantum physics.  According to particle theory, for every tiniest bit of matter or particle, there is an opposite bit called antimatter or an antiparticle.  Within this concept we can contemplate causality once again and see there is no ultimate causality – matter does not cause antimatter and neither does antimatter cause matter.  Yet, somehow all these tiniest bits of matter, and tiniest bits of antimatter, make up a whole, the infinite…and somehow all these tiny bits, with their interactions and interrelationships have aspects of the whole, the infinite.  Once again, we can see that even on the most fundamental level, there is a striving towards the infinite. 

Interesting concepts about the infinite have also been expressed by commentators within a religious context.  Blaise Pascal, the French physicist and philosopher, also had some interesting ideas about God implying the infinite and we, in our finite nature, cannot possibly comprehend the infinite nature of God, yet we strive to do so.   

            “If there is a God, He is infinitely incomprehensible, since, having neither parts nor  limits,   He has no affinity to us. We are then incapable of knowing either what He is or if He is” – Blaise Pascal – Pensées

It is quite interesting to see science, philosophy, and religion conceptualizing so similarly on such a fundamental level.  It’s not only religious thinkers from the Western world with these conceptualizations, either.  Even more remarkably some 2500 years ago the Indian teacher Pakudha Kaccāyana taught that there were fundamental bits of matter and fundamental forces that influenced matter.  For Kaccāyana, the most fundamental bits of finite matter were seven “substances” – earth, water, fire, air, joy, sorrow, and life.  Interestingly enough, relating these ancient teachings to modern particle theory, Kaccāyana’s “substances” could be grouped as bits of matter – earth, water, fire, air, and as “forces” – joy, sorrow, and life.  Kaccāyana did state that these seven states of matter never alter, never change and are incapable of causality – once again we have the concept of no beginning and no end and we have a record of mankind striving to contemplate the infinite over 2500 years ago.

No matter the path taken towards the infinite, it seems the goal is uniform in its nature somehow.  Mathematical solutions, philosophical solutions, scientific solutions all are congruent on the most fundamental level.  Individuals must find their own paths towards the infinite, and those paths vary greatly, as we can see. Individuals on the path to understand the infinite may not work through detailed mathematical equations or contemplate broad philosophical concepts or study quantum physics but, in each their own way aspects of the infinite are grasped.

Inspiration can come from many sources.  Perhaps it can come from a camping trip in a solitary location or from words spoken by one who has a higher understanding of the infinite like a pastor or a yogi or a wise elder relative.  Perhaps encouragement along the individual path can come from the situation of another – a near death experience, or a triumph in the face of adversity, for example.  Inspiration to know the unknowable can come from many sources and this inspiration, in itself, furthers one along the individual path.  Understanding comes in small steps that are immense advancements.  All steps taken are quantum leaps forward from where the individual had been in their quest before.  Seeking out these sources of inspiration and staying on the path to wisdom and knowledge will keep one on the path to the unattainable in an interminable quest.

It is obvious this separation from the infinite makes us strive towards it.  As thinking, rational, aware beings striving towards the infinite nature that is within us all is a natural tendency.  We can sense it within ourselves, yet we can never know the true meaning within our limited capability to understand.  Since we all work individually to grasp the unknowable as a whole the human race makes a collective effort to understand the infinite.  Proof of this lies in the steps mankind has made throughout history in his ability to understand the nature of things that were previously incomprehensible.  Newton, Dedekind, Leibniz, and the quantum theorists all provide human examples of these immeasurable leaps in knowledge for the collective human race. 

You can see an expanded lens on Infinity at my squiddo page.