Infinity and The Big Picture

Infinity versus Infinity
Infinity, as illuminated by mathematicians,* applies to not only a succession of moments but also to an infinity in each moment. Resultantly, there are no more or less moments in a moment than there are moments in succession of moments. Infinities cannot be made bigger by adding to them or stretching them out. Meaning: infinity is not a property of space and time, and space and time are not properties of infinity.

Remember, we do not see infinity when we look out into space. We see only emptiness between things and suppose it is something in its own right. Like our nesting problem, infinity cannot be gathered up and placed in a picture frame. It is transcendental. That space flows without end is a seeming truth to us, albeit a paradoxical truth. We may seek to resolve paradox with mathematics, but in experience we cannot see beyond space to see its end.

Succinctly, saying infinity is in some sense physical, and then leaping to mathematics to argue infinity is also logical, does not make the logical and the physical the same thing. These are two different types of description that cannot be shown to converge. The paradox of time being either finite or infinite is a separate question from either logic or experience since neither resolves it. The Noumenon is posited in a kind of philosophical perturbation to resolve the paradox, and it does so by divorcing time from infinity.

Nevertheless, some cosmologists believe it is possible for time to be infinite, simply because infinity makes more sense than saying time has a beginning. This only makes sense if you divorce direction (flow) from time and are left with subatomic symmetry at the smallest scale. However, for us to reach this conclusion, we must observe particle collisions for some duration to determine their interactions are reversible; and this requires an observer’s compass of direction to determine that subatomic particles adhere to it. Moreover, we may witness numerous examples of these reversals, and reasonably assume they will continue ad infinitum, but it is only the witnessing that makes time real. The assumption of infinite continuity is inescapable, but it is not had in the witnessing.

Science may displace infinity, or use it as a diversion for the sake of making one believe that an infinite universe or an infinite number of universes are somehow accounted for as objects of sense with numbers, but Kant draws a hard distinction between the appearance of things and things as they exist in themselves. Mathematics, which may engineer around infinity by grasping how it and the finite can be made equivalent, demonstrates little with its equal signs: Equivalency is only equivalency. It is not the thing-in-itself!

(*In much the way we assume the universe to be flat, unbounded, and infinite, we do the same with mathematics. Without the presupposition of infinity, there can be no succession of numbers [n+1, etc...], and therefore no mathematics.)

Infinitude versus Finitude
Other cosmologists do believe time is finite, and precisely because they propose the Universe (and time) emerged from an infinitely small singularity. The Universe, if the Big Bang is to be believed, clearly had a “beginning time” by the measure of cosmological time.

Cosmologists attempt to get around paradox by claiming time only exists within each universe as it emerges, but this limiting concept does not negate the implied sequence of infinitely regressive time bubbles for each universe. This in effect constitutes a temporal sequence of “times” punctuated by boundaries between them. Even if we say all-possible universes exist simultaneously to get around the time sequence problem, there would still be a sequence of spaces. The enigma of infinity stills lurks in the margins.

Infinity versus Space/Time
Sidestepping such impossible tasks, we turn instead to impossible objects: Einstein gives us another possible solution to the paradox of an infinite universe via curved space/time. (This is the hypersphere model already discussed.) Here too the model relies on mathematics to convince us we are somehow accomplishing something that in no other way makes sense. Infinity, beyond the language of mathematics constructed to limit it, must be noumenal. Finite space and time are phenomenal. As Schopenhauer taught, the noumenal and the phenomenal are double aspects of one another in their respective spheres, which means the former can never be quantified contigent on the latter. Quantity is reserved for the realm of phenomena.

Space/time, as a scientific notion, does not concern itself with infinity per se. This is not simply an issue for boundless space and time (which physicists believe aptly describes our Universe) but for causation itself, as well as the very beginning of the Universe. General Relativity, for example, cannot predict what the geometry of a black hole would look like at the point of gravitational singularity, where the curvature of space/time becomes infinite. Similarly, the singularity supposed at the staring point of the Big Bang cannot be adequately described by physics.

(*This infinity enigma is also reproduced when we try to measure the circumference of a circle and get pi, a real and irrational number of infinite length.)

Infinity versus The Big Bang
“Infinity, again, is something else. Science and mathematics have found ways to paper-over the enigma with limits, but such serviceable fixes should not be confused with demystification. Simply put: causation breaks down at the level of quanta, and no proposed number of preceding Big Bangs would ever explain a first Big Bang.” ~from Omar's letter, Chapter Six of Icarus Transfigured

We are told nothing existed before the Big Bang. And still, inexplicably, something the size of a proton existed the split second before space and time exploded into existence. Does this something-from-nothing* argument satisfy the intellect in positing a first cause to our reality? Can we be assured there were no Big Bangs prior to the one that began our Universe? If not, do these Big Bangs extend infinitely into the past?* As Schopenhauer was fond of saying, if the past were infinite, then it would be impossible we should exist, for an infinite amount of time would need to have lapsed for us to get to a present moment.

(*Where physicists try to get around the something-from-nothing argument, and try to avoid a Russell-like paradox, they do not propose a true nothing for starters. They begin with an expanding but boundless space [like a 4-D hypersphere], which is made interchangeable with an energy field. Here they have changed the definition of nothing to something before that something can be posited as a nothing to set things off.

Obviously, a physical reality requires physical means and ends, which means beginnings and endings. “Something” can come from “nothing”, but only if by nothing you do not feebly refer to virtual particles or energy fields whose sole purpose is to “appear” on cue. The only way to make sense of a world of appearance is, by the logic of opposition, posit “something” that itself does not have appearance.)

(*Many in cosmology believe exactly this, and in no small part because they want to explain the extraordinary, life-supportive fine-tuning of our Universe’s physics by statistical chance alone and not by exceptional circumstance: This is to say, if our Universe is only one in a long line of universes, then whether it is one in a hundred, or one in a million, at some point the dice must come up double-sixes for a universe conducive to us. If there are an innumerable number of rolls of the dice preceding ours, then our special universe does not appear so special, only inevitable. For someone to believe they are witnessing a special roll of the dice, they are [it is alleged] committing the inverse gambler’s fallacy. However, this argument not only assumes previous badly tuned universes, but the fallacy itself, as pointed out by John Leslie, is not applicable to the observer in question: He does not witness innumerable rolls of dice at random, but is only allowed to witness a double-six, since his experience of a double-six requires no less than a fine-tuned universe for him to observe it. Regardless, the multiverse hypothesis is clearly a mathematical fix devised to undermine the mathematical improbability of us being here, and so is more argumentative than scientific.)

The Big Bang versus The Big Collision
With some cosmologists, getting back to a trillionth of a second after the Big Bang is close enough, but the “what came before” question remains. Superstringers, pained by this camel’s nose under the tent, replace Big Bangs with periodic collisions of proposed “branes” that float independently of one another, thus getting around the something-from-nothing conundrum. (This, of course, is only displacement of the ontological problem since Big Collisions neither explain where branes come from nor where the “something” in branes comes from.)

One virtue of this brane model is, you could say, “spiritual”. As the Universe flies apart, and apparently at an ever increasing rate of speed, the spiritually repugnant prospect of its dissolution into abysmal nothingness is here negated by the idea that the Universe is simply expanding to fill a membrane; and with the hope that another brane collision will come along to turn the lights back on somewhere else. I argue in a different direction: The more demonstrable the void is to the circle-closing mind, the more the heart can take comfort in its nonexistence.)

Infinity versus Quantum Mechanics
“There is a concept that is the corrupter and destroyer of all others. I speak not of Evil, whose limited empire is that of ethics; I speak of the infinite.” ~Jorge Luis Borges

In the development of quantum mechanics, infinity presented problems when taking precise atomic measurements in a space/time continuum. With the practice of renormalization, infinities encountered in quantum calculations were absorbed by corrections to mass and charge, where the result would be finite and physical rather than adhering strictly to quantum theory. Though renormalization made special relativity and quantum mechanics work within a framework of quantum electrodynamics, Richard Feynman, who received a Nobel Prize for his work in the field, characterized the ad hoc fix as “hocus pocus”.

Probabilistic Quantum Mechanics versus Deterministic Reality
Regarding quantum mechanics, we have observations that run counter to the foundation of causal science:

With the double slit experiment, we have one photon of light being directed toward two slits in a barrier, which produces a wave interference pattern on a screen beyond the barrier. However, if we insert the observer by one slit or the other, then we produce no interference pattern on the screen because the observer forces the photon to choose a given path. If, allowing for the speed of light, we close one slit after the photon has theoretically passed through the slits unobserved, yet before it has time to reach the screen, the photon still does not produces an interference pattern. The observer effectively influences the photon’s behavior after the fact!

Another example of the observer’s influence can be seen in The Quantum Zeno Effect, where in measuring a decaying particle, the decay is arrested on being observed. In theory, a particle would never decay if watched it continuously.

Spooky Action at a Distance
“The world of matter appears less muddled to us than our thinking about space/time, though, at the molecular level, it is Heraclites’ river that always looks the same even as its water of whirling atoms changes each time we put a foot in it. As quantum physicists, Bohr and Heisenberg, argued in their ‘Copenhagen Interpretation’, subatomic particles such as electrons have no real existence, only probability, until the act of observation forces them into a single state. In Kantian terms, there is no actual “there” there until one is posited in perception. ” ~from Omar's letter, Chapter Seven of Icarus Transfigured

Given the disconnection between quantum mechanics and the Theory of Relativity, one can readily grasp why the former gave Einstein fits. For example, with quantum entanglement, subatomic particles can become entangled and share properties; and regardless how much space may come to separate them, when one is collapsed and disentangled by an act of observation, its pair collapses too. This, in simultaneity, is a clear violation of the speed of light, which is the only absolute constant in Einstein’s scheme. If this is true, and not an error in calculations as Einstein believed,* then it casts doubt on the reality of space and time as anything that separate matter in a metaphysical sense.

Schopenhauer, building from Kant, argued this was indeed the case in the century before quantum entanglement was proposed. Because space and time have no reality-in-themselves, they constitute no barrier in the underlying ontology of all phenomena. (This idea is similarly illustrated in Heisenberg’s Uncertainty Principle, where electrons, when considered as particles and not waves, change location within their shells instantaneously without passing through an intervening space.)

(*Einstein regarded the idea that atoms were more ghost than real paradoxical, so helped devise an experiment whereby the hypothesis could be challenged by showing how split particles could not cooperate over distance without communication. Bohr, as though channeling Schopenhauer, said that until a measurement could be taken, the split particles could not be regarded as separate. They must be regarded as a single entity, even if light-years apart. Subsequent scientific tests have sided with Bohr.)

Space/Time versus Gravity
As space and time are integrally linked with matter/energy, and as space and time are synonymous with the force of gravity (according to Einstein), then what are space and time? What is gravity, for that matter? If space/time/gravity is a form of energy, then this energy is playing by a different set of rules than other physical forces. Since energy can neither be created nor destroyed, only conserved as it changes states, then where is the space/time energy coming from as the Universe flies apart? Gravity’s existence is based on anticipated results consistent with the presumption of its existence; this, once more, is an instrumentalist proof, not a realist proof.

Adding to the mystery, why is gravity many billions of times weaker than electromagnetism? The gravity of a planet many orders of magnitude bigger than me cannot overcome electromagnetism and pull a pen from my hand. The gap that separates the physics of the very large (gravity) from the physics of the very small (electromagnetism, strong nuclear force, weak nuclear force) is the primary problem that confronts modern physics. A hypothetical graviton* particle is advanced as a way of beefing up gravity and connecting it to the other quantum forces. Advantageously, gravitons, being the force carrier for gravity, would also lend physical reality to space and time, since space and time are—again—identical to gravity in General Relativity. Yet where is this validating graviton to be found? Why in other proposed dimensions of space, of course. (This is a little like trying to prove the existence of a flashlight by illuminating it with a flashlight. The yogi cannot bend himself into a pretzel to escape his dilemma.)

(*The truth of science, as Wittgenstein reasoned, lies in the relational realm of logical statements. Outside this logic, the world can only be regarded as a collection of “accidents” from which no inductive proofs can be drawn. We may have a serviceable set of facts that describe, for example, gravity by way of relation, and claim for it logical consistency where it does not contradict observations or fail to make predictions. Yet these are logical proofs only. They cannot be offered as proofs for the existence of gravity.)

(*As the photon is the force carrier for electromagnetism, and the W and Z bosons are the force carrier for the weak nuclear force, and the gluon is the force carrier for the strong nuclear force, what is the force carrier for gravity?)

The Center of The Universe After All
Our ability to gaze back to the earliest visible events in the Universe has been improved by the launch of the aforementioned WMAP satellite, whose primary mission is making the most accurate map of the early Universe to date.

WMAP’s findings have strengthened the flat universe model of the Universe. In fact, the Universe is so flat its critical density is described as having the “special value” of N=1, and this “fine-tuned” status has been maintained since shortly after the Universe’s violet inception. A Theory of Inflation, where there is a sudden expansion in the size of the early Universe, was devised to account for this unusual equilibrium and flatness. General Relativity, if not Special Relativity, allows particles to travel faster than the speed of light, and this is the foundation of an inflationary theory that addresses a host of problems engendered by the Big Bang model:

Why did the early Universe give rise to dispersed gas and not a crowded field of black holes, which would have eaten the Universe alive? Why is there a horizon problem where, in pushing back our visible horizon to the time when the background radiation began to cool and become homogeneous, we see celestial features that are too far apart to see each other? (The Universe is too large for emitted light from these remote sources to connect causally.) Finally, why is there a lack of exotic relics that should have been present in an earlier, hotter Universe?*

Some in the scientific community, however, are not sold on inflation’s multi-tasked fix. Truly, there are cosmologists who have never been comfortable with the Big Bang model of the Universe; and its theological overtones can be no small part of their misgivings. More to this point, the WMAP data has emboldened advocates of Intelligent Design to explain the creation of our “special” Universe. Indeed, the most extraordinary discovery of WMAP has come from looking at the cosmic microwave background itself, for if the “boundary” of the observable universe is equal to the entire universe, then this has profound ramifications for our place in it:

“Results from Wilkinson Microwave Anisotropy Probe (WMAP) appear to run counter to Copernican expectations. The motion of the solar system, and the orientation of the plane of the ecliptic are aligned with features of the microwave sky, which on conventional thinking are caused by structure at the edge of the observable universe. [6][7]

Lawrence Krauss is quoted as follows in the referenced Edge.org article:[8]   ‘But when you look at CMB map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of structure with our motion of the earth around the sun — the plane of the earth around the sun — the ecliptic. That would say we are truly the center of the universe.’” ~Quoted from The Copernican Principle in Wikipedia* 

#To reestablish the validity of The Copernican Principle, scientists proposed another fix, namely, dark energy:

“When the universe was just 400,000 years old, matter and radiation decoupled and left a remnant radiation that still pervades the entire universe today. By measuring the tiny temperature fluctuations of this CMB radiation, scientists can learn things about the universe such as its shape, size, and rate of expansion. In the latter case, the observations show that the universe is expanding at an ever-accelerating rate, leading scientists to speculate about the existence of dark energy, new laws of gravity, and other possible – and often exotic – theories.

But what if the universe’s accelerating expansion is just an illusion? As Caldwell and Stebbins explained, this scenario is entirely plausible if the Copernican principle is loosened a bit. If, instead of the universe being homogenous and isotropic as the Cosmological Principle states, there is rather ‘a peculiar distribution of matter centered upon our location,’ then the universe would be centered on a low-density, matter-dominated void. Such a universe would be non-accelerating, and there would be no need for dark energy or other similar theories.” ~A Test of the Copernican Principle From Physorg.com

“Although dark energy may seem a bit contrived to some, the Oxford theorists are proposing an even more outrageous alternative. They point out that it's possible that we simply live in a very special place in the universe - specifically, we're in a huge void where the density of matter is particularly low. The suggestion flies in the face of the Copernican Principle, which is one of the most useful and widely held tenants in physics…” ~Dark Energy v. The Void: What if Copernicus was Wrong? From Physorg.com

(*A flat universe would be both unbounded and infinite, so one could ask in what sense does it have a “shape”?)

(*Martin Rees wrote, “Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn’t exist!” This is not only a paradox of fine-tuning requiring fine-tuning, but an example of a theory that can explain any result thrown at it, even contradictory results.)

(*Jung’s concept of synchronicity, which we briefly discuss in our next section on Design and Evolution, regards extraordinary coincidence of critical importance in understanding the nature of reality. Though we cannot see direct causal correlation between exceptional events and our acausal interpretation of them, our finding “special meaning” in improbable coincidence can be no accident.)

Space, Time, and Analogy
“The speed of light may be the one absolute constant in our physical universe, but it is truer to say that light, like a road, goes nowhere, and it is only we, having taken incarnate form, who have wandered off its path to create so vast, lonely, and treacherous a place. ” ~from Omar's letter, Chapter Twenty-seven of Icarus Transfigured

By converting a theoretical fourth dimension of space into the dimension of time, Minkowski represented the whole Universe—past, present, and future—in a two-dimensional diagram. This “hypersurface of the present” is where the observer resides as a point, and he can only be considered in reference to a past light cone that intersects him on this grid, for everywhere he looks he is bombarded by light from the past, and to which he must consider even his body as being something lapsed. The future light cone can only be a projection, which like the past light cone, is visualized in widening concentric circles out from the observer. Whatever lies beyond these circles, in the past or future, is not causally connected to the observer and must be unknowable.

When we look up into the night sky, we are looking back into time. And yet, if the Universe was smaller at its beginning, then everything in that early Universe should be, by logic’s reckoning, close together. Instead, we see the most distant objects in the Universe everywhere we gaze in the heavens. They are not converging on a Big Bang event in a funnel, but appear far flung to the outermost frontier of our expanding Universe. The paradox, as in so many cases, comes down to the inscrutable observer and their point of view.

First, things closest to us in space are also closer to us is time. For example, a comet breaking up in Jupiter’s atmosphere happens closer to our timeframe because Jupiter is not very far away. The same idea can be extended outward, moving from near-time events within our solar system to far-time events occurring on the other side of the Milky Way, as with supernovae. Since we remain in place in our present moment and see further into space, our horizon line widens with our penetration deeper into time. Consequently, we see more things, and by the time we get to the furthest events in the Universe’s past, the horizon becomes a panoramic view of the entire history of the observable Universe. The funnel effect is the reverse of what logic would suppose: I, as a stationary observer, am at the narrow end of the funnel looking out.

In one sense we do not understand what we see, since we objectify the Universe as a picture and ascertain a narrative from an order and sequence of light energy.* And yet, we imagine the Universe whole, even as we imagine ourselves whole. Resultantly, our understanding is analogous. Space, time and causation enable this appearance of reality, though, in lacking objective reality in themselves, they are fictions, and therefore the first analogies and first mythologies.

(*When we look into the night sky, we see the whole history of the Universe laid out before us as a continuous visual record. Our point of individuated consciousness, which here at a planetary scale can almost be characterized as a single point, apprehends that no part of this “temporal record” is separated from us in point of fact in experience. We impose time where it cannot exist, onto stars and other celestial events long vanished. It is our time that sees and seeks time.)