I believe that infinity is an either/or, all or nothing proposition. If it exists, there are no degrees of infinity, though there are, of necessity, degrees of finitude. The world of the finite is necessarily a comparative one. Yet if any aspect or entity is infinite then, by definition, it is beyond compare.
If anything is infinite, then everything is, in a way, infinite because it is included within the infinite subset. Everything that is must exist within the infinite, and must be connected to limitlessness. We may not be infinite, but the infinite is us. It operates through us.
I hold that infinity does exist. Probably. From our standpoint in the universe, as finite beings, I can offer no definitive proof, but I can argue the probabilities. Infinity is more likely than not.
I must start from a position of ignorance rather than knowledge; of not knowing rather than knowing. I operate from an assumption, for that is all I can do. Any proof moves out from initial assumptions. The only certainty is ignorance.
We humans are the only creatures which ask—
- Who am I?
- From where did I come?
- Where am I going?
We are the only organisms, to our knowledge, which wonder what, if anything, we were before we were born. We remain alone in asking this: What, if anything, are we when we die? We just don’t know. And when we don’t know that we don’t know, we remain encased in the amnion of an everlasting ignorance. When we know that we don’t know the answers to these questions, we arrive at the beginning of the answers.
For answers to these questions, we sometimes look to the miraculous, rather than to the commonplace. Yet the answers may be all around us, in the signature of spacetime itself. For that which is infinitely divisible is infinite. It is immeasurable, and this immeasurability is the very ‘measure’ of the infinite.
Even if there was a ‘wall’ at the boundaries of space, the simple fact that any ‘amount’ of space can be divided forever means that any small cross section of its volume, carved out from the rest, is endless. Therefore, the infinite does exist. It is the smallest space imaginable, which may be further carved up without limit. Since we are composed of such units, of such ‘spaces,’ we, too, must be infinite.
The Copernican Principle holds that we are not privileged observers of and in spacetime. We do not occupy a unique perch within the dimension we inhabit. We are not especially ‘big’ or ‘small.’ We are not specially chosen witnesses to reality, not elect watchers of the universe. Therefore, it is unlikely that we are organized or operating at the larger end of spacetime in either direction – from the universal to the quantum scale. It is, therefore, more likely than not that spacetime continues out beyond us in the macroscale direction to an illimited extent. We are merely a rung on this ladder of scale. We are probably an intermediate stage in an infinite series which extends in both directions of size.
The infinite cannot be proved, understood or defined, but it can be alluded to. Our imaginations point to it. We can imagine, though we cannot truly comprehend, an infinite series, whether that series is numbers, moments or parsecs of space. We devise mathematics with an infinite set of discrete values. We can envision the infinite both in space and in time.
When we say that the infinite cannot be understood, we mean that it cannot be comprehended by the intellect alone. Though intelligent grasp of the endless is part of a holistic knowledge of it, infinitude cannot be wholly understood by intelligent means. This means that the infinite cannot be proved. If it cannot be proved, comprehended or defined, the intellect concludes that the endless either is not, or else that since the infinite is unverifiable, it is not amenable to rational understanding. For this reason, it is often ignored, discounted as irrelevant, or otherwise not seriously considered as a variable in an intelligent understanding of reality.
It is unlikely, we hold, that an entity could imagine the concept of endlessness unless the illimitable was a feature of reality. Why else would we have this a prior capacity to speculate about it? In the late 17th century, mathematicians and scientists were able to derive abstract principles which corresponded to real world phenomena through equations which describe and explained phenomena in the natural world. If these preexisting forms of rational and mathematical knowledge in the mind corresponded to the physical world, why shouldn’t imagination -which points towards the possibility of the infinite – also provide analogues of external reality when they envision limitlessness? To these, we can add spiritual and mystical understanding, which most often postulate an infinite quality which describes the penultimate reality. Thus, we have several ways of knowing which allude to inferential evidence of the limitless. Though it cannot be directly proved, infinitude can be inferred indirectly, and the very fact that it can be surmised circumstantially makes its existence more probable.
Einstein described space as curved. Ancient Hindu philosophy characterizes time and the material universe as existing in endless pulsing cycles, which is similar in some ways to the behavior of certain stellar objects. With this understanding, space is curved and time is represented by a recursive, cyclical loop. A curved structure may be so recursive that it ends within itself, that it ends where it begins. A circle is infinite. It has no beginning and no end. Therefore, a circular or cyclical description of spacetime brings us back to the idea of infinity.
Along its time axis, infinity, is, of course, the eternal. Illimitability is therefore transferable as a concept to aspects other than the three dimensions of space. We tend to think of the illimitable as that which exists in spacetime, as applying to either or both space and time. Yet this does not preclude the quality of limitlessness as applying to other physical aspects, such as energy or matter.
Some astrophysicists have postulated that a blackhole exists at the center of our galaxy, and at the center of every galaxy. Some cosmologists have likened the entire cosmos to a blackhole. Blackholes have singularities which represent points of infinite density. Infinity is again our measure, or lack of measure, if you will.
Some have called blackholes wormholes – apertures into other dimensions. Others have stated that there exists a megaverse with an infinite number of galaxies blowing up like bubbles in each moment. In these hypotheses, the concept of illimitability is used to describe the nature and structure of reality.
No matter the discipline applied, or the way we approach to investigate this issue, we come to the conclusion that infinity may exist, and that it probably does. Allusions to it may be found in science, in philosophy, in religion, and in the realm of imagination.
Endlessness can be a troublesome topic for us, since it implies the existence of a God, which is here conceived of as an endless force. For this reason, many relegate the infinite to the graveyard of the impractical, the irrelevant, the impossible or the improbable. Those who espouse a materialist philosophy may regard infinitude as possessing a purely unconscious quality. This obviates the need for theological speculation. Yet we have shown how consciousness, even if confined purely to human and other sentient beings, subsists within a subset of the infinite (if infinity exists) and that it is therefore part of the limitless. We simply ask: If there is infinity, what is the difference between this endlessness and our conceptions of God? Obviously, something within the cosmos and within reality is conscious, or we could not be writing this, and you couldn’t be reading it. If this reality in which we exist is limitless and we are conscious of the fact of its illimitability, then this consciousness extends without limit simply by virtue of our envisioning of it. Infinite consciousness is God.
Yet there are those who argue for finitude and for an explanation of reality which has as its underpinnings purely unconscious forces. The ferocity with which this conclusion is defended cannot be underestimated. Many of us would rather be limited creatures inhabiting a limited dimension, on the condition that we remain in control of our own destinies. I shall return to the reasons for this vociferous defense at the conclusion of this essay.
Could infinity also be ascribed to nonphysical aspects of reality, such as power in its abstract sense, to being, or to consciousness? What about infinite intelligence, infinite goodness, or infinite evil?
With qualities like power, being, consciousness and intelligence, an infinite capacity may be ascribed. Yet with good and evil, normative attributions come into play. What is good? And what is evil?
Anything which is already infinite can have no opposite. It is omnipresent and omnipotent. It can only be of one quality, and not two. The concept of duality is perhaps one invented by human consciousness and projected outward onto the vast scape of reality. Therefore, if it is endless, then whatever reality is can only be unified, and not dual.
From this, we know that if it is real, then one of the qualities of the infinite is that it stands unopposed. As a result of its unrestricted nature, it must also be unified. That which is unopposed has no opposing force which contends with it. It is beyond human concepts of good and evil and transcends any of the many dualities which we find in the physical universe or the human world: positive/negative; creative/destructive; good/evil; matter/energy.
Being unified and unopposed, it is also like itself throughout. It is fungible. There is nothing which is unlike itself. This, as we have concluded, means that humans are identical to it. They have their identity in it.
Since it is unrestricted, it must also be unconditioned. It transcends the conditioned reality which humans seem to perceive and to which they seem subject. A thing unconditioned is unlimited. It is not subject to any boundary value or boundary requirement.
These qualities may be difficult for the human mind to accept, since that mind sees itself enveloped in boundaries, subject to conditions, opposed by various forces, interactions and entities, and part of a fragmented existence. Arguments seem to arise naturally in opposition to my statements and conclusions, and this opposition is the reason why a unified reality is not experienced as a ubiquity.
And why isn’t a unified, unopposed, unbounded reality experienced? I believe the reasons for this lack of experience have psychological causes.
Created beings have chosen for themselves a unique power: the ability to suppress awareness of a unified reality. What makes this power all the more remarkable is that atop the void created by this suppression, an illusion – or rather a series of illusions – is projected as a substitute reality.
Let’s look at the first step: the suppression of reality. The description here is of a void. Emptiness characterizes this apophatic spiritual tradition. Ultimate reality has been described as a divine darkness, as a void or as an abyss. This represents the vacuum left over when reality is suppressed.
Yet no vacuum exists, even in the physical world. If the ultimate is, as we have described, unopposed and omnipresent, then it will infill the void left after the suppression of reality is withdrawn. the psychiatrist, C.G. Jung, wrote about the withdrawal of projections as a necessary stage in human psychological evolution. Once humanity withdraws its final projection – which in the collective is an amalgam of all individual projections known as the universal projection – unified reality will take its place.
What about the projection of multiplicity which sits atop the original suppression and which constitutes the phenomenal universe? This reality is composed of a series of concentric boundaries, or boundary conditions. These boundaries obscure spacetime infinity in a physical sense, and the idea of the infinite in an abstract sense. It is clear that an individual brain housed in an individual body, which are both defined by their boundary states, cannot truly grasp the concept of the infinite or the qualities of the illimitable: unity, ubiquity, fungibility, unconditionality, and lack of opposites.
Standing behind and beyond the mask of a limited physical reality, there is no void in the sense of absence. The abyss, the void experienced in the apophatic mystical traditions, is simply the first stage of the absence of reality. It is the attempted suppression of the infinite.
Yet neither is the endless reality equivalent to the somethingness of the phenomenal universe which is projected by the mind onto the suppression. The somethingness of phenomenal reality is defined by limits, by boundaries. We know the nature of a thing by its boundary. This is how we define it. We also know its nature by its relationship with another entity, which is defined by yet another boundary.
According to the International Astronomical Union, a planet is defined as a celestial body which orbits around the sun. It has attained hydrostatic equilibrium (a fluid or plastic solid at rest) in which the force of gravity is balanced against a pressure-gradient force. Gravity pushes against this force and precents the atmosphere from dissipating into space. In short, the planet has a boundary. A planet may have several boundary definitions, as earth is defined: a surface, an inner atmosphere, and several shells of outer atmosphere, in addition to a magnetosphere. Similarly, the sun exhibits several boundary conditions by which it may be defined. Each celestial body can be defined, in part, in relation to other celestial objects, and each is also defined by its boundaries.
The somethingness of this universe and of all entities and interactions within its spacetime substrate are each defined by limits. Thus, finitude is a necessary condition if an observer is to conceive of a cosmos of somethingness.
A boundaryless condition is no condition at all. Having no conditions, it cannot be defined. It can exist in relation to no other thing, and so it is noncomparative. Since it cannot be defined, it cannot be understood.
I conclude that the mind – the human mind – is heavily invested in the suppression of ultimate reality and the projection of a cataphatic somethingness in its place. Therefore, it must conceive and perceive in the lexicon of boundaries and describe reality terms of a limited nature. The intellect has become so inured to its definitions and to its somethingness that it finds it difficult to envision a limitless nature in anything. And so, it denies the existence of the illimitable, and attempts to convince others of the impossibility, the improbability or the irrelevance of the infinite. For any organism sees in its boundary proof of its own existence. Take away the boundary which defines a thing, and you take away the basis for that entity’s very identity. You remove the source of and the rationale for its own existence.
There is a reason why we neither see nor comprehend the infinite. We really don’t want to. Many of us make claims to believe in or to head toward the endless, but few really desire it.
© 2023 by Michael C. Just