Ex-Beatle Ringo Starr once released ‘I’ll Still Love You’, a wonderful ballad penned by his former bandmate George Harrison, whose lyrics went:
When every song is sung
When every bell’s been rung
When every picture’s hung up
I’ll still love you
When every wind has blown
When every seed is sown
When everything is known
Then I’ll still love you
You know I’ll love you, yes I will
You know I’ll love you, love you, love you
Always will, until
When every soul is free
When every eye can see
When people all agree
Then I’ll still love you
You know I love you, yes I do
When times get so hard, you know
I’ll be there loving you
You know I’ll love you, yes, I will
Yes I’m gonna hold you, need you, love you
Always will, love you still
When every note’s been sung
When every bell’s been rung
When every picture’s hung
I’ll still love you
I really love you
Courtesy of Gustave Klimt, “The Kiss”
The words conjure up the survival and endurance of life, love, and the human spirit beyond both the end of time and the demise of the material universe. It prompts us to wonder—is there a fundamental, irreducible nature of reality, something that will continue to persist and endure when everything else, everything that can possibly be stripped away, is gone? Something which, perhaps, has always been there, even before our universe came into existence? Is it, as the song says, the human spirit, or could it rather be some physical feature or property of the universe, such as time, or space, or some perhaps some particle or particles, or alternatively something more exotic or abstract, like mathematics or some God, or something else entirely? Could it even be that there is no fundamental feature of reality at all, and that in the end, at some end, all winks out into nothingness, and nothing remains?
No consensus has ever emerged on just what reality exactly is, and to this day different communities swear by starkly disparate and incompatible views of what ultimately makes the universe, and life itself tick. According to some, we live in a meaningless, largely mechanistic and material universe where we put in brief, fleeting appearances before we disappear again for good, never to be seen nor exist again. For others, the universe is imbued with meaning, although there is little agreement on what this meaning might be. Is there any objective way we can tease out, from the many options of what reality could possibly be, a likeliest scenario of what it actually is?
Einstein famously once opined that ‘imagination is more important than knowledge’, and indeed, much of mankind’s quest for understanding the nature of reality seems to have been plagued by stark cognitive bias and failures of imagination. In war for instance, it has become a cliché that generals always tend to prepare to fight the last war—despite the unparalleled criticality of what is at stake. Even in science, it takes for example the likes of Roger Penrose to propose, on the strength of pure mathematics, a totally different nature of what Dark Matter could possibly be, away from the common but unimaginative view that unseen matter is somehow made of weighty particles. And many religions, which by their very nature ought to be the abode of the disruptively imaginative, tend to exhibit woeful failures of imagination, whereby the Gods they describe typically seem to be starkly anthropomorphic, often hopelessly human-like in both their attributed qualities and their alleged failures of character. The examples are endless. We need to imagine more.
The very first order of business when attempting to probe the mysteries of the universe is therefore to let go of our instincts, and sideline in the first instance the common-sense notions that our minds insist on proffering. Any gut feelings we may have for what is ‘true’ do not take their source in what is factual, but from what, in the course of evolution, helped keep us alive long enough to pass on genes to the next generation. Nature emphatically doesn’t do priggish: it will use whatever techniques happen to work to keep living organisms alive for yet another day, and it does not matter a whit if such are made out of false beliefs, misapprehensions or outright lies (such as, say, the passive lie of a predator’s coat camouflage, or the active lie of built-in prey decoys in some species of deep-sea fish), or even, devastatingly enough, of curbs on freewill or intelligence and/or, as the case may be, limits on character—as long as such properties enable their owners to live another day.
Letting go of instinctive common sense leaves us in unchartered territory, where the wonted landmarks and frames of reference of reality have vanished, replaced by none others. Our only remaining anchorage has now become unprejudiced mathematics—or rather, more narrowly, numbers—i.e., a set of totally objective tools allowing for reality checks whenever reality is amenable to numbers-based analysis, which luckily will happen to quite very often be the case. Numbers are not based on any prior hypotheses in the form of unverifiable axioms or assumptions about reality, but on mere vocabulary definitions describing straightforward items of external reality observed at face value—ultimately, on the sole predicate that we are entitled to naming what, say, 1 and 1 put together shall be known as, without having to thereby formulate any hypothesis about any deeper reality or its meaning, and that by convention, we choose to call it two.
Armed with numbers, our next order of business will be to sift through various possible ultimate components of reality, eliminate those which can neither be fundamental nor irreducible, test those that remain, and explore whether there just might exist other building blocks which we may have overlooked. For instance, it is obvious that, say, human-designed architecture cannot be a fundamental component of reality—but what of geometry, which underlies most of it? Fields medalist and geometer Shing-Tung Yau makes a solid case that geometry is a fundamental constituent of ultimate reality. Since geometry is a part of mathematics, we will subsume ‘geometry’ into the general overarching concept of mathematics, and investigate whether mathematics itself can be a or the ultimate constituent of reality. Bearing in mind that we might inadvertently overlook some candidates for the role—something we will go back to in the course of this investigation—we begin by looking at some possible contenders for ultimate reality.
A growing trend in modern science sees the universe as ultimately purely and only mathematical and although this view is controversial, the evidence in its favor is strong.
To begin with, there is indirect evidence. The perhaps strongest first hint, hardly recognized at the time, appeared in 1905 with the publication of Einstein’s e=mc² equation, which demonstrated that unforeseen, very-real life effects happen just so that a valid, purely mathematical equation not be violated. Further clues kept popping up right and left across the physical sciences, leading in 1960 to Nobel prizewinner Eugene Wigner’s celebrated paper on ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’.
If anything, the body of direct evidence is even more compelling. Further to the 2012 discovery of the Higgs boson, the last ramparts of old-style matter-based, math-free, so-called Aristotelian materialism came crumbling down (science journalist Stephen Battersby, anticipating its discovery, had earlier jumped the gun and stated, in a famous 2008 NewScientist piece, ‘It’s Confirmed: Matter is Merely Vacuum Fluctuations’.) Separately, mathematicians from a number of narrow mathematical disciplines kept reinforcing this view. Shing-Tung Yau, whom we encountered above, confirmed some of Einstein’s insights and showed how pure geometry can under certain circumstances give rise to gravity, and thence to mass itself.
Reinforcing this view from a different angle, if we take a physical chemistry view of all there is—of materiality itself—we soon find that all of the properties of any collection of material elements, the electrons, protons, neutrons and other building blocks of materiality, can be wholly described by purely mathematical objects: their wave functions.
Therefore, we must in the first instance accept mathematics as a possible contender for being a or the component of ‘Ultimate Reality’.
But what is mathematics? As mathematician Keith Devlin once put it, math is, at its core, the expression of relationships—between things, whatever such may be, be they material objects or even imponderables, such as numbers, waves, and also mindstuff (something which of course will have to be further defined.) The envelopes encompassing these relationships give rise to patterns, which in turn become the subjects of the different branches of mathematics. With math playing a key part everywhere—although it’s not yet clear whether that part will turn out to be the essential part, or not—if we are to make any progress towards properly analyzing and apprehending reality, we need to be reasonably good at it. The sad reality however is that we are generally, as a species, not very good at math, which sometimes leads eminent scientists to cast withering doubt on parts of our mathematical edifice, and above all its applications in physics and in understanding reality. However, those who fear that modern physics has become unmoored from reality through its reliance on overly fanciful mathematics are probably barking up the wrong tree: there is ample evidence that at least most of the many issues in contemporary physics which can be traced to dubious interpretations of math can most likely be solved by more, not less mathematics. Mathematician Michael Monatstyrsky had commented in his 1998 monograph ‘Modern Mathematics in the Light of the Field Medals’, obviously puzzled, on how extremely arcane and abstract mathematics (such as non-commutative algebraicgeometry) routinely keeps yielding up totally unforeseen real-world applications in diverse fields (such as solid state physics), reinforcing a suspicion that mathematics underlies all of reality in often unforeseeable ways.
Mathematics within the Universe
Mathematics can only function as a fundamental component of ultimate reality if it holds up—i.e. does not break down or somehow unravel. It fully holds its own within finite environments, but in the case of infinite environments, however, mathematics cannot be a or the fundamental constituent—because it breaks down. Mathematics ceases to function properly at infinity: Georg Cantor demonstrated that an intractable self-contradiction arises within mathematics at infinity: the so-called Cantor antinomy.
As it happens—and as could be expected—this antinomy also fully shows up within the physical, material make-up of an infinite universe, should such exist. To understand how, we need to look anew at the wave functions we briefly encountered earlier: every bit of materiality in our universe, be it an individual particle or some collection thereof of any size, carries with it a mathematical signature, in the form of a wave function.7
There is a pivotal question however, which does not meet with consensus: is there such a thing as the wave function of the universe itself? At first blush, it would seem obvious that it must exist: under the hierarchically ascending way whereby wave functions build up and complexify to be able to encompass more variables when such are brought in (more variables corresponding to more material elements, such as particles, becoming subsumed into a bigger material collection aka system, capable of including ever more constituents and collectively governed by the wave function in question), there is no reason why a growing taking-in of ever more elements would ever stop, all the way up to and eventually encompassing the whole universe.
This is where, unexpectedly, we hit a wall. To cut a long story short, one of the properties of the wave function is that if we perform a simple mathematical operation on it, an operation we’ll call twist, this operation yields up the odds of presence of the physical object it represents within that volume of space. Hence, although the actual mathematical expression of the wave function of some object (i.e., a collection of particles) can be horrendously complicated and incalculable, we nevertheless know that if that object actually exists somewhere in the universe, then its probability of presence in the universe is 100% (or, equivalently, 1) and therefore that the result of the above-cited twist operation, carried out on that no matter how complicated wave function, must yield 1.
This is where the concept of a wave function of the universe seems to break down. If our universe is all there is, then the very concept of the probability of its presence becomes meaningless: presence where? There is no ‘out there’ within which a probability of presence of the universe would be in any way make sense or be meaningful.
From these simple bare facts, it all now becomes a matter of interpretation. Some sweep the issue under the proverbial rug by asserting with no further ado that there is simply ‘no such thing’ as a wave function of the universe, period. End of discussion? A bit of analysis however throws up extremely difficult questions as to how this could be the case. First, all of the physical forerunners of everything that now exists within the universe were closely associated in some form of contact at the Big Bang onset of the universe, and therefore were bound up or entangled in some way. The mechanism whereby variables which were once bound up within some wave function become disassociated from one another is called ‘decoherence’, but decoherence can never be total: there is no known mechanism whereby the extremely tenuous leftover mathematical remnants of formerly existing entanglements can somehow become fully obliterated from the scene. In technical terms, absolute decoherence never happens – there will always exist a vanishingly small, forever fading residual association with former mates. Second, neither is there any known or even imaginable mathematical mechanism whereby the existing wave function up to that point (i.e., the whole universe minus one particle) could suddenly just disappear in some magical poof! by the simple agency of adding in one last particle to its set of its variables. This is why many theoretical physicists, who call themselves wave function realists or monists, take the view that the wave function of the universe is for real.
But the issue nevertheless remains that the physical meaning attached with performing the twist operation on this final wave function seems to have vanished: whereas it is possible to mathematically twist this ultimate wave function, the operation’s physical meaning has, along with the ‘probability of presence’ that the math thus calculates, suddenly become nonsense.
Two things can however alter this conclusion.
A first possibility is that the universe is not all there is, and our known universe is actually located in some corner of a greater universe—a second universe out there which somehow encompasses ours. In that case, and only in that case, the meaning of the phrase ‘probability of presence of the universe’ has become meaningful again.
But if we now consider the ensemble of our universe together with this second universe, the same reasoning leads to the necessary presence of a third universe, and then to never ending recurrence, i.e. a fourth, a fifth, and soon to an infinite number of other universes which all become necessary to provide the scope within which the wave function of the universe can exist.
This wave function thus acquires an infinity of variables. Looking back, we see that at every step of the way towards infinity—corresponding to every new universe encompassing the previous set of universes—the resulting wave function could safely be ‘twisted’ to yield a probability of presence of that universe at 100%. The issue arises when we reach infinity: we can still safely twist the ultimate wave function of the now-infinite universe (which now has an infinity of variables), and we still find 100%, a result which however has now again become nonsensical, because what this result would physically mean is that the resulting infinite universe must both strictly contain itself (by ‘strictly’ is meant that it would be strictly bigger than itself, not ‘bigger or equal’) and must also be strictly smaller than itself, so as to be able to be strictly contained within itself: via a roundabout way, we have just discovered a physical rendition of Cantor’s antinomy. In other words, when mathematical infinity incarnates into the real universe, mathematics breaks down the very selfsame way it does with abstract infinite number sets, underscoring its inability to describe or undergird material infinity.
But there is a second possibility that could invalidate the above conclusion that mathematics cannot possibly be a key constituent of reality within an infinite universe. Remember that the foundational reason why we are entitled to surmise the existence of a wave function of the universe is that, first, all of the universe’s current constituents are descended from their physical Big Bang forerunners, which were tightly associated at the onset of the universe, and second, that past such associations never fully mathematically decohere.
But what if there were Big Bang, and our current cosmological model is wrong? Then, depending on which alternative mechanism for the birth of the universe holds, it could be that separate constituents within our universe have never been (and shall never be) bound by any form of past nor future contact or association, and therefore there cannot be any such thing as a unique wave function of the universe, but there are instead a number of separate wave functions, which will never coalesce. The infinite wider universe – the multiverse – would then be made up of a number of finite universes that have never been in contact, and mathematics would never break down. Another possibility, of course, would be that the multiverse is made up of several disjoint multiverses. some of which could be finite and some others infinite (in which case math would break down again.
The eventuality of the Big Bang being a faulty picture of our reality has generated much discussion over the last few decades. A number of scenarios have been mooted to replace the Big Bang picture, some of which would lead to separate wave functions merging and therefore would not essentially invalidate the above discussion, whereas some others would not and hence invalidate the discussion. In the first instance, we shall accept, with the overwhelming majority of physicists out there, that the Big Bang or something very similar happened, which owing to the above considerations leaves us with a provisional conclusion that pure, mindless mathematics cannot be the fundamental component of reality in an infinite universe.
But what if the universe is finite?
Let us assume that the universe is in fact finite, as in fact our own known universe is. As the above reasoning showed, a finite universe can only work if we accept the demolition of any picture of reality predicated on wave functions (as we have seen, the many physicists who are not ‘wave function realists’ subscribe to this view of reality). But since mathematics fully underlies the wave function picture of reality, we must conclude that mathematics also somehow breaks down in a finite universe.
Mathematics therefore cannot be the ultimate core component of the universe, whether finite or infinite. It is worth noting though that irrespective of what the ultimate component of reality may turn out to be, the overwhelming balance of evidence however shows that mathematics is the vehicle whereby any ultimate reality intermediates itself into the world.
Is there such a thing as a rock-bottom, irreducible, ultimate component of reality at all? Maybe all of reality is only an illusion, with no fundamental reality to it, and a quest for its ultimate essence is but a fool’s errand?
A look at vacuum will provide an answer. There are two kinds of vacuums, so-called false and true.1 In essence, false vacuums are vacuums that contain some faint residual energy, in the form of fields and/or wraithlike matter, such as (exotic) particles. Cutting a long story short, there is an infinity of possible renditions of the false vacuum, ranging through an infinite range of possible vacuum energies. All false vacuums are potentially unstable and can theoretically decay into a lower-energy vacuum, much like a football stuck somewhere on a house roof can potentially roll down from its location and fall to the ground. Because any false vacuum can always decay to another, lower-energy new false vacuum, it ensues that false vacuums cannot be a fundamental feature of reality. Furthermore, whereas any existing false vacuum can decay to energetically lower ranking vacuums, it can never reach the status of true vacuum—for the simple reason that it’s too late for that. Since something, somewhere in the universe (matter, energy) already exists, that something can well morph and transform into something else, but cannot wholly disappear into nothingness.
If a true vacuum were possible, it would mean that reality itself would not be fundamental, let alone then have fundamental, irreducible components or features. But it does not exist (or at least, as we shall see, it no longer exists), and our quest for the fundamental constituent(s) of reality continues.
Luckily, there are other contenders other than mathematics to what may constitute ultimate reality—Time, Space, a form of mindstuff which some may want to call Godhood, even life itself all spring to mind, and there may be other as-of-yet unknown or hidden elements—things we simply don’t happen to know of nor perceive (such as perhaps some unknown particle, hidden variables, or other), all of which could conceivably belong to fundamental, irreducible reality.
Having no direct means of evaluating any possible hidden components, one way to eliminate any such from consideration would be to establish that some other, known component would be fundamental on its own—which would thereby eliminate the eventuality that some hidden component would play a significant part in building reality (which is precisely what we will discover, thereby eliminating any ‘hidden’ components from further consideration.)
Roger Penrose describes the situation when, in the very far future, the universe has become inconceivably immense in its space extension, its every last Black Hole has long since evaporated through Hawking radiation, and matter itself has diluted to the extent that only massless particles (such as photons) remain.
In this far-future corpse of our universe, time as we know it has ceased to exist, and yet, a form of reality still exists: therefore, time cannot be a fundamental component of irreducible reality.
From a wholly different angle, it has been argued (in ‘The Far Horizons of Time‘) that time cannot possibly be fundamental. A brief part of the argument bears repeating here: simple relativistic mathematics—the Lorentz transformation—shows that time, speed, and distance cannot be considered independently of one another but are inextricably bound together. The way this interdependence works out in the real world can be described thus: stay put and look towards some star light years away. You happen to be, as you contemplate deep space towards that star from your fixed position, simultaneous with some event A on it. But now walk towards it: you have now become simultaneous with some other event B on that star, that happened (depending on your walking speed and the distance to the particular star) hours or even days earlier than the event A you were simultaneous with mere seconds ago when youwere standing still.
Now turn on your heels and walk away from the star: you have now become simultaneous with yet another event C, which took place hours or days later than A, and twice as long later than B.
So far so good, it’s simple math. But what happens if you start spinning, dervish-like, around your body axis? Then the right half of your brains becomes instantly and continuously simultaneous with events on that distant star that are separate by hours or days from the events your brain’s left side is simultaneous with, although both your brain halves are closely, if not perfectly, simultaneous with each other: the whole concept of time has just irremediably broken down. Time cannot possibly be a fundamental constituent of reality.
The above-cited work went on to analyze the issue, eventually concluding that the only possible way out of the conundrum consisted in time not being a fundamental variable of a mathematical universe, but a side effect of something more fundamental. That more essential something turned out to have to be, in some form or other, mindstuff. (Note that this analysis only shows that mindstuff has to be a more fundamental property of the universe than time, not that there may not exist something else, deeper still than mindstuff.)
Mindstuff, which have to be defined more in-depth, has therefore become a contender.
Although we live in it, there is much that we don’t know about geometrical space: we are not even sure of its true dimensionality. Is space only really 3-D, as our ordinary senses tell us, or are there more dimensions, perhaps so small and tucked away and curled up in such a way that we do not perceive them?
Luckily, space can be fully modelled by, and subsumed within, mathematics. We are fully capable of modeling ever more extensive and involved space topologies, through a mathematics than may or may not reflect, and map, some existing reality out there, somewhere or somewhen beyond ours. Whatever space may exist anywhere in a wider multiverse can be modelled through mathematics. Hence, mathematics as an expression of ultimate reality describes every single last bit of reality that could possibly be embedded within any actual space anywhere, including every possible configuration—regardless of whether such exists or has existed or will at some point exist in some reality. It encompasses all of the information that could be embedded within any actual rendition of any possible space: we are therefore back to mathematics as a possible component of ultimate reality, embedding amongst other things all of the possible realities of geometrical space.
The ex-Beatle sings beautifully of a life enduring beyond both time and the end of the material universe, which bears the hallmarks of poetic licence—after all, we can certainly surmise that nothing was discernibly alive during the Big Bang. Life seemed to first enter the picture in the form of primitive amino acids hundreds of millions of years after the beginning of the universe, its primitive forerunners first arising from the spontaneous interactions of stray molecules, billions of years after the Big Bang. Whereas such Ur-molecules may form in space, a favorable habitat such as the Earth is needed for their further development, where they can generate ever more complex chemical compounds, eventually forming sugars, fatty acids, nitrogen bases…. to wit, the building blocks of life as we know it today.
But surprisingly, there are quite sound underpinnings to the Beatle’s idea.
What is Life?
For all our powerful science, we cannot even unequivocally say whether a simple virus qualifies or not for the status of being alive. Most of us would agree that a mechanical robot is not alive in the conventional sense, but that a person is. We must therefore in the first instance estimate, from a higher level perspective, that the one determinant higher-level difference between the robot and us is a measure of free will—the robot is a mindless and conscienceless automaton, whereas we have awareness, outwardly expressed in a measure of free will (although some people argue that we have zero free will, which we will return to shortly.) Crucially, if we do have a measure of free will, then it means that whenever we make a decision, nothing anywhere in the universe can foretell nor, crucially, foreordain, at any time prior to when the decision is made, what this decision will turn out to be. In other words, to exercise itself, free will must not have been determined by anything that has happened anywhere in the universe at any time, however short, prior to the instant when the decision is made. But we, the decision-makers, are made up of atoms! The Free Will theorem demonstrates that for free will to be able to exist at the macroscopic level of our human decision-making, then it must already exist, albeit in an elementary form, all the way down to the atomic, and indeed to the elementary particle level (technically of course under a set of conditions, which do not modify the broad argument.)
In other words, under a liberal but inescapable definition of life, if we happen to have a measure of free will then the whole universe itself must be alive. Which is just really another way of saying that some mind—some mindstuff— would be the fundamental operative element.
Viruses may be alive (barely so), lower life forms such as amoebas are definitely alive, human cells such as brain neurons are alive—but are not remotely in the same league of awareness, and potential decision-making prowess, as full-fledged humans. In a rudimentary form, life thus begins at a far more elementary level than us, but what the Free Will theorem shows is that life may begin much farther down in the scale than we ever thought—deeper than what we used to think was the ‘possibly-alive’ virus level, but squarely at the elementary particle level. Because the argument is predicated on the indispensable necessity of a form of free will, life at any level becomes indistinguishable from the source, repository, and exerciser of free will: mindstuff itself (which had already been pegged above as a possible contender for being the stuff that makes up ultimate reality).
But what if, as some claim, we lack any measure of free will? In that case, it would be safe to say that there is, ultimately, no such thing as a mindstuff. Mechanistic mathematics would then seem to have to carry the day …. which we have however proven above can hardly be the case. With mathematics proven to most likely not be the ultimate reality, and if free will does not exist, we seem to land into a stark contradiction, which can logically only be solved in either of two ways.
The first way would be that there is no such thing as an ultimate component of reality: reality itself would be a temporary illusion, which in the fullness of the unspooling of illusory time shall eventually disappear and return to full nothingness. This however looks like an impossibility, because as we saw above, reaching the status of a true vacuum is a necessary condition for reality to be an illusion, which can never be achieved.
The only solution we are left with is that something must give: there has to be a mistake somewhere. The mistake would be either in the assertion that mathematics cannot be the ultimate reality, or that free will does not exist. So which is it?
We have now come to a three-way fork in the road:
- If there was no Big Bang, or no single Big Bang in the case of a multiverse, math does not break down through twist because there cannot exist a unique wave function of the universe in the first place, and we have no free will (so that any mindstuff cannot be as fundamental as the mathematics it is subjected to), and neither the universe nor a possible multiverse are finite (so that math does not break down through Cantor’s antinomy), a form of mindless mathematics could well be the ultimate reality. In this latter case, everything would reduce to relationships between elements, objects, things, wave functions and reducible mind items. In such a universe, any existing mental aims and intentions must ultimately relate back to math, since math is all there is. To make this picture of reality stick, the picture of the birth of the universe through a single foundational Big Bang must be abandoned, so that no leftover entanglements exist between all of the different constituents of the universe, and there is no such thing as the wave function of the whole universe, or, as the case may be, the (necessarily finite) multiverse. In such a universe, any mindstuff’s scope and ability would also be limited by something called the Bekenstein bound, which limits the amount of information or knowledge that can be held within a finite volume. That need not bother us, because mindstuff in such a universe can only play second fiddle to ineluctable mathematics.
- If there is a wider and infinite multiverse, mathematics is unable to properly map its full reality (because of Cantor’s antinomy) and ultimately breaks down, and mindstuff becomes the primary contender for what ultimate reality is. Now unfettered from the Bekenstein bound, mindstuff may be infinitely capable.
- If all there is is our known universe, born through a Big Bang, then mathematics is seen to break down as well, but for a different reason: a perfectly valid equation (the ‘twisted’ wave function) loses its meaning for no discernible reason. However, well-nigh always in the history of mathematics, equations deemed at first to be meaningless, or thought to be mere artefacts devoid of real-world meaning, left over from some long calculation chain, turned out to have very real meaning (with e=mc² being a famous case in point), and it is hard to believe that in this one case the mathematics would indeed be meaningless. What the mathematics seems to be shouting loudly here is that this scenario is impossible: our known universe, the one that arose from a Big Bang a bit under 14 billion years ago, cannot be the whole shebang.
Beside cosmologists, many others, such as information theorists and modern philosophers have tried to tease out ultimate origins (discounting here the charming ‘little old lady’ quoted by Stephen Hawking, for whom the universe rests on a turtle’s back, with that turtle resting atop another turtle, with ‘turtles all the way down’.)
For information theorician Vlatko Vedral, information is the only concept capable to explain its own origin—and thereby everything else’s. He begins by analyzing in-depth reality and reaches the largely defensible conclusion that all reality is not only context-dependent, but context-generated. By ‘context’ is meant the dynamic web and weft of information exchange. The core of this approach to reality is that nothing ultimately exists save for interactions—aka information exchanges, which give rise to existence emerging as both the apparent items and artefacts of reality (such as particles and observers, such as the lab physicists in white coats which interact in some way with the particles), and, crucially, the laws of physics themselves which govern those interactions.
For instance, some particle causing a particle detector to click in reality does not exist: as Vlatko Vedral puts it, “Whether the detector clicks or not is a genuinely random event that cannot be predicted by any means. Ultimately, the click has no cause at all and therefore we have no underlying particles’1. He goes on to say “We can construct the whole of reality from nothingness by looking at it in terms of two distinct and interrelated arrows of pure knowledge, which kicks off the interplay between the two arrows.” According to this view, through a self-unfolding structuring of knowledge, emerging information creating itself out of pure nothingness first jells into a set of recognizable laws (which coalesce into becoming the laws of physics of the a-borning reality.) These laws in turn generate an emerging ever-narrowing structure of reality – such as recognizable particles and then their various embodiments and associations and built-up structures, all of which are in fact ultimately non-existent as independent entities.
Cutting a long story short, in this view the whole universe emerges randomly from non existence, much like an apparent particle detected by a particle detector ultimately does not exist but jells into its apparent existence by the co-emergence of physical laws out of, ultimately, total randomness. Information creates itself spontaneously without the need for a prior cause. Information then begets the illusion of reality from its evolving web of interactions – of information exchanges. Thus, reality has created itself from nothing – in effect, from information creating itself from non-information for no cause at all: presto! the universe creates itself out from information randomly emerging out of pure nothingness without cause, and the conundrum of ultimate origins is thereby solved.
In this author’s view at least, even if we accept the whole chain of reasoning that leads to statements such as ‘ the particle detector’s click has no cause at all and therefore there are no underlying particles ‘, there is still a flaw in the reasoning: the confusing of the laws of physics with those of mathematics. This entire line of reasoning can only work if the laws of mathematics existed prior, thereby enabling the emergence of the laws of physics: we have, by a roundabout way, rediscovered Vilenkin’s conclusion: mathematics must exist prior, and a condition of the existence of anything in any universe is that the disembodied laws of mathematics exist within pure nothingness – which hence cannot be said to be whole, pure nothingness.
From another angle, philosophers such as Phillip Goff have also weighed in, and offered interesting arguments, which fully jibe with the above.
It’s time to look at the evidence for the Big Bang, the furthest back appearance when reality ‘intruded upon the void’.