Let’s start this section with a quick review of the key terms we’ve covered.
The three kinds of infinity:
Immanent (aka countable) — a set of integers with no beginning or end, but with an established pattern of relationships that defines the integers, and makes knowable the value of any given member of the set.
Transcendent — an infinite set created by the relationship between any two numbers. It is not countable because it includes decimal numbers, which do not progress horizontally in linear fashion, but create their own vertically infinite set of numbers in relation to each other
Absolute — the infinite set of all infinite sets and all possible numbers. Numerality itself.
The two metaphysical terms by which we will examine the real-world meaning of these mathematical terms are:
Isness — the qualities of a phenomenon or physical entity that define it, and make it a distinct and knowable thing. Isness is always a finite set of information.
Suchness — the relational context between a thing and its environment. It is not an objective property of the thing itself, but of the information shared between the object and its surroundings. Suchness is always an infinite set of information.
Now we can apply our metaphysical concepts to the properties of numerality and its various infinitudes, and make of them demonstrable models for our mythopoetic ideas about God. Let’s start with immanent infinity:
Does an immanent infinity have a “first number?”
Immanent infinity, the set of all possible integers, is an endless series of little packets of isness. Each integer is defined by its relationship to all other integers, and that in itself is a daunting concept to wrap one’s head around because “all” has no natural boundary.
This illustrates a principle we will see repeating itself throughout: any finite thing (isness) is defined by its relationship to the infinite (suchness)— in this case, to the countable infinity of things that can be known, or Consciousness itself (“Mind” is sometimes used synonymously, or “thought” in Spinozan terms). Though the scale of relational properties involved in suchness is beyond our comprehension, the foundational premise is simple and uncontroversial: We only know what something is in contrast to what it isn’t. No matter what isness we choose to analyze, almost all of what can be said about it pertains to the relationship of contrast, to what it isn’t rather than what it is. The isness of the number 3 is finite, while the set of knowable numbers that are “not 3” is infinite. Pretty straight-forward, right?
So let’s make it more complicated…the integers of an immanent infinity seem to progress and regress horizontally along a line, one finite number following the previous one, just as we experience the progression of time when we are tracking it.
But where does the line begin?
The most common point of reference is 0, but that’s all it is: a convenient position of orientation that divides negative numbers from positive. It is not in any way a terminus for a linear immanent infinity of integers.
So what is the meaning of a linear progression that has neither beginning nor end? Can the integers in a countable infinity have any absolute value in relation to that infinite set if the set contains no absolute parameters?
Without a “first number,” is there any reason to call any others the second, third, and so forth?
Seems a little counterintuitive, doesn’t it?
That’s because it is. And this is how we are going to kill the concept of linear time as an absolute. Linear time exists only as a measure of isness for a specific event or series thereof. It is not a quality of an immanent infinity of time.
If 0 is proposed as the starting point of immanent infinity, and progress means counting the positive integers in a manner analogous to the progression of time, what to make of the negative integers? Can time move in two opposite directions at once? Similarly, if we start at 0 and progress infinitely in one direction, that starting point has no definitive value, no isness of its own, because its relative position has not been fully established– it could be 0, or it could be 100 billion, and the abstract infinity would still both contain and exclude “almost all” of the possible integers, hardly a useful measuring tool for time-space phenomena.
In order to have any practical meaning, in other words, linear time must have a beginning and an end. Any apparent progress along a spectrum of linear time is like the counting of elements in any finite set: it implies the choice of parameters by an observer. These parameters form the beginning and end of a segment of an immanent infinity that is itself without beginning or end. Without the perspective of finite parameters established for the purpose of measurement, there is no “first moment in time,” just as there is no first number.
Difficult as it may be to visualize in four dimensional time-space, a temporal or spatial expression of infinity thus cannot be represented by a horizontal line centered at 0 and running indefinitely to the left and the right. It must curve back upon itself and form a circle. There is no definitive starting point on a circle, nor any relative locations other than those arbitrarily chosen (like the locations of degree markers), and progress along a circle is only relative to itself, not to any absolute location as it is in linear time.
This is the basis for the concept of cyclical time, the closest we can come to imagining eternity from our finite perspective. In cyclical time, any notion of progress involves a return to a point where one has been before— or, more precisely, there is no progress, only timeless moments that are always equidistant from the center. The Hindu concept of time is cyclical, as are those of many aboriginal cultures.
The difficulty of conceptualizing the co-existence of infinite temporal cycles that don’t actually follow one another in linear succession (in other words, cycle #2 doesn’t follow cycle #1 in any discernible way, for this is just shoehorning linear time back into the concept) I believe is what leads us to the multiverse idea. I am neither for nor against the popular multiverse hypotheses, I just prefer to look at something closer to home: the innumerable life cycles occurring like fractals on innumerable levels of scale within each other, all within our “known universe” that is in its own life cycle– and there is no reason to think this universe is the outermost limit of possible scale.
What does all this mean in terms of God? The most important thing is that it releases us from the fools’ errand of searching for an objective “first cause,” either natural or supernatural. As soon as we perceive one moment or one event as following or being caused by another, we should know that we are observing a segment of time that may look linear to us but in an absolute sense is part of a timeless cycle. Any event that is the first cause in that segment could just as well be caused by the last event in a different segment, so on and so on; at some point we have to acknowledge that we are forcing objective linearity of causation onto something that isn’t linear. Like everything else in the observable realm of Nature, immanent infinity suggests a cosmology of circles, of birth and death and rebirth as events within a singular process. We have all been here before.
The lynchpin of the philosophical theists’ argument for a fully transcendent God completely outside of time-space is the supposed need for a supernatural cause of the first natural event in time-space. This argument suffers the fatal flaw of assuming that linear time is absolute, and not simply the chosen observable segment of an eternal cycle.
(The perception that God is one and unmoving and unchanging is even more easily explained: like meditating Buddhists or Vedantist yogis, their attention is being drawn to the ever-still center point of the cycle, where even relative motion conceived by the observer is nullified.)
Martin Luther King Jr. famously said, “The arc of the moral universe is long, but it bends toward justice.” In the same light, we could say that the arc of cyclical time is long –much, much longer than we could hope to perceive from a point within it– but it bends toward wholeness, return to source, completion of the circle. But that too is just a trick of perspective. Just as no number is “closer to infinity” than another, no point in cyclical time is “closer to the source” or “closer to the beginning/end” than another. Each event is a unique “causeeffect” of all others, a microcosmic finite expression of the infinite macrocosm.
The only true cause of any event in time, then, is the potential for any moment to exist– Temporality itself. We will continue to see this pattern manifest as our three infinities nestle together as One.
In conclusion, immanent infinity suggests the Pantheist notion of God. The eternal Divine is the unitive substance of existence, manifesting as two matrices —the material world of isness and the web of suchness (Consciousness) in which all things are connected— that are mutually coarising and interdependent.
Contrary to both philosophical materialism and idealism, pantheism holds neither matter nor mind as primary to the other, but rather God is omnipresent as the substance of both, fully integral with and concurrent to both, with no piecemeal stratification or separation from which to discern primacy. This will not be immediately apparent as one explores the modern iteration of the philosophy that calls itself “scientific pantheism.” (See the introduction to this series, “The Pantheist Problem.”) But it is a logical necessity that will become clearer as we move further along with the three kinds of infinity.
In contemplating the pantheist concept of God, it is also important to avoid the pitfall of projecting onto it our experience of linear time, and reverse engineering it into some kind of force that stitches together all these loose parts and, at some point in the future, will unite our fragmented existence into a harmonious Oneness. Imagine if all the numbers in the immanent infinity became 1– not so much a unity as the annihilation of numerality.
In addition to confusing unity for uniformity, this kind of “evangelical pantheism” misses the whole point: the all-togetherness of this physical world bound together by suchness is what existence is, always has been, and always will be. There is no “becoming” One or achieving union with God, because God is already this. The universe is a unity of contrasts, a whirling dynamic of polar opposites connected as a single body, in which each individual isness already has its place. Pantheists see no greater unity than this, which they find expressed most fluently in nature— specifically, outside the manufactured realm of civilization where the slow work of evolution is most clearly evident and the indwelling intelligence in nature is best revealed.
Specific personal traits and anthropomorphic form are absent from this concept of God, because God assumes all traits and forms. Likewise, there is no symbology associated with the pantheist God to make it more tangible, because it already is the tangible world in its natural state.
If anything, pantheism requires a deliberately diffuse mindset to draw its attention away from the isness of “the body of God” and accentuate its suchness, so as to avoid the idolatry of materialism that would make it hardly different than the atomized, secular ontology of isolation that we turn to pantheism to unlearn.
So how do we get into that mental state of diffusion in order to see the suchness of things concurrently with their isness?
We open the mind to transcendent infinity. This is where theism will have its day….just not the first day.
GOD BETWEEN THE NUMBERS
PART 3: WE HAVE ALL BEEN HERE BEFORE–IMMANENT INFINITY AND CYCLICAL TIME