Things and Nothing

 by Thomas Scarborough

As this year draws to a close, we soar beyond the turbulent things which have so exercised philosophical hearts and minds, to consider for a moment one of the very abstract and timeless questions of philosophy: ‘things’ and their opposites.

There are, in this world, ‘things’. Or so we suppose. These are also called objects, entities, items, existents, or beings—terms which, by and large, all mean the same thing. The philosopher William Rowe wrote that a ‘thing’ is any item whose existence is acknowledged by a system of ontology, whether that item be particular, universal, abstract, or concrete. The whole universe, even, may be called a ‘thing’. So far so good.

But what is the opposite of a thing? Or what is its contrast, or complement? Nothing, perhaps. But how could there be ‘nothing’? That would seem to be supreme philosophical nonsense. Or suppose that there is a thing which failed to exist? It never came into being. What should we say about that?

Somebody observed that all of our philosophical concepts may be grouped in pairs. Where we find ‘altruism’, we find ‘egoism’; where we find ‘theism’, ‘atheism’; where we find ‘realism’, ‘anti-realism’—and so on, from A to Z. Some do the same with ‘things’. Where there are things, we find nothing. The philosophers Bradley Rettler and Andrew Bailey comment,

‘It’s not clear whether anyone sincerely endorses the thesis that there is nothing, However, it has been defended several times over.’

One could contend that ‘things’ are things in space and time, while nothings are not—like numbers, for instance, or society, or force. Or one could say that things exist, but properties do not. Say, a house exists, but its karma does not. In that case, a great many things ‘do not exist’. Or one could say, as the existentialists do, that one may experience Nothing. But existentialists are afraid of Nothing, jokes the philosopher Simon Blackburn, where there is nothing to be afraid of.

There is one obvious way that we can try to solve the problem, and many have taken this course: namely, first define a ‘thing’. If what chiefly defines a ‘thing’ is that it is, then of course, its opposite must be a thing which is not—perhaps rather, nothing. But is that properly the way to define a thing?

I shall here accept the view, for the sake of argument, that all the things we call things are things: things which exist in space and time (objects), things which happen (events), and things which exist in the mind (concepts). Now suppose that, in order to create all of these things, we need to differentiate them from what the philosopher and psychologist William James called the ‘undifferentiated stream of experience’.

Things have contours. They have definition. But the opposite of things do not. When things lose their contours, they slip back into the undifferentiated stream. Another way of putting it is that, if nothing is not related to the rest of reality—not a word, not a motion, not an entity, not an event—then we artificially separate things when we call them ‘things’. Artificially, because we strip away from them their completeness.

To create a 'nut', we throw away the fruit, and the tree, and the soil, and the air, and the universe. If we included all these things which are essential to the nut's existence, we could never isolate a nut as a thing. Therefore it is simply 'an edible kernel', or something of the sort.  We strip away the interconnections or interdependencies, to create something which is self-contained.  

The philosopher of science Alan Chalmers describes our reality like this:

‘Many kinds of processes are at work in the world around us, and they are all superimposed on, and interact with, each other ...’

If this is true, then it stands to reason that any ‘thing’ which we cut out from this whole is not wholly itself. 'Nothing' is therefore that which gives birth to things. It is that which exists before we create the contours which create things. In his translation of Lao Tzu, Sam Hamill writes, ‘There was some undifferentiated something here, before heaven and earth.’

The opposite of things, therefore, is a world which is without them—because they have not emerged from it. Nothing was the plastic rattle, before the infant apprehended it. Nothing was the theory, before the scientist formulated it. Nothing was the environment, before it emerged in our minds and hearts. Nothing is all those things which could be, but are not, or are yet to come, because they have no contours.

And the Universe Shrugged

Posted by Keith Tidman

It’s not a question of whether humankind will become extinct, but when.

To be clear, I’m not talking about a devastatingly runaway climate; the predations of human beings on ecosystems; an asteroid slamming into Earth; a super-volcano erupting; a thermonuclear conflagration; a global contagion; rogue artificial intelligence; an eventual red-giant sun engulfing us; the pending collision of the Milky Way and Andromeda galaxies. Nor am I talking about the record of short-lived survival of our forerunners, like the Neanderthals, Denisovans, and Homo erectus, all of whom slid into extinction after unimpressive spans.

Rather, I’m speaking of cosmic death!

Cosmic death will occur according to standard physics, including cosmology. Because of the accelerating expansion of the universe and the irrepressibility of entropy — the headlong plunge toward evermore disorder and chaos — eventually no new stars will form, and existing stars will burn out. The universe will become uninhabitable long before its actual demise. Eventually a near vacuum will result. Particles that remain will be so unimaginably distanced from one another that they’ll seldom, if ever, interact. This is the ultimate end of the universe, when entropy reaches its maximum or so-called thermodynamic equilibrium, more descriptively dubbed ‘heat death’. There’s no place to duck; spacefaring won’t make a difference. Nowhere in the universe is immune.

Assuredly, heat death will take trillions of years to happen. However, might anyone imagine that the timeframe veils the true metaphysical significance of universal extinction, including the extinction of humans and all other conscious, intelligent life? And does it really make a difference if it’s tens of years or tens of trillions of years? Don’t the same ontological questions about being still searingly pertain, irrespective of timescale? Furthermore, does it really make a difference if this would be the so-called ‘sixth extinction’, or the thousandth, or the millionth, or the billionth? Again, don’t the same questions still pertain? There remains, amidst all this, the reality of finality. The consequences — the upshot of why this actuality matters to us existentially — stay the same, immune to time.

So, to ask ‘what is the meaning of life?’ — that old chestnut from inquiring minds through the millennia — likely becomes moot and even unanswerable, in the face of surefire universal extinction. As we contemplate the wafer-thin slice of time that makes up our eighty-or-so-year lifespans, the question seems to make a bit of sense. That select, very manageable timeframe puts us into our comfort zone; we can assure ourselves of meaning, to a degree. But the cosmological context of cosmic heat death contemptuously renders the question about life’s purpose without an answer; all bets are off. And, in face of cosmic thermodynamic death, it’s easy to shift to another chestnut: why, in light of all this, is there something rather than nothing? All this while we may justifiably stay in awe of the universe’s size and majesty, yet know the timing and inevitability of our own extinction rests deterministically in its hands.

A more suitable question might be whether we were given, evolutionarily, consciousness and higher-order intelligence for a reason, making it possible for us to reflect on and try to make sense of the universe. And where that ‘reason’ for our being might originate: an ethereal source, something intrinsic to the cosmos itself, or other. It’s possible that the answer is simply that humankind is incidental, consigning issues like beginnings to unimportance or even nonsense. After all, if the universe dies, and is itself therefore arguably incidental, we may be incidental, too. Again, the fact that the timeframe is huge is immaterial to these inquiries. Also immaterial is whether there might, hypothetically, be another, follow-on Big Bang. Whereby the cosmological process restarts, to include a set of natural physical laws, the possible evolution of intelligent life, and, let’s not overlook it, entropy all over again.

We compartmentalise our lives, to make sense of the bits and pieces that competitively and sometimes contradictorily impact us daily. And in the case of cosmic death and the extinction of life — ours and everyone else’s possibly dotting the universe — that event’s speck-like remoteness in distant time and the vastness of space understandably mollifies. This, despite the event’s unavoidability and hard-to-fathom, hard-to-internalise conclusiveness, existential warts and all. To include, one might suppose, the end of history, the end of physics, and the end of metaphysics! This end of everything might challenge claims to any singular specialness of our and other species, all jointly riding our home planets to this peculiar end. 

Perhaps we have no choice, in the meantime, to conduct ourselves in ways that reflect our belief systems and acknowledge the institutional tools (sociological, political, spiritual) used to referee those beliefs. As an everyday priority, we’ll surely continue to convert those beliefs into norms, to improve society and the quality of life in concrete, actionable ways. Those norms and institutions enable us to live an orderly existence — one that our minds can plumb and make rational sense of. Even though that may largely be a salve, it may be our best (realistically, only) default behaviour in contending with daily realities, ranging from the humdrum to the spectacular. We tend to practice what’s called ‘manic defence’, whereby people distract themselves by focusing on things other than what causes their anxiety and discomfort.

The alternative — to capitulate, falling back upon self-indulgent nihilism — is untenable, insupportable, and unsustainable. We are, after all, quite a resilient species. And we live every day with comparatively attainable horizons. There remains, moreover, a richness to our existence, when our existence is considered outside of extraordinary universal timeframes. Accordingly, we go on with our lives with optimism, not dwelling on the fact that something existential will eventually happen — our collective whistling past the graveyard, one might say. We seldom, if ever, factor this universal expiry date into our thinking — understandably so. There would be little to gain, on any practical level, in doing otherwise. Cosmic thermodynamic death, after all, doesn’t concern considerations of morality. Cosmic death is an amoral event, devoid of concerns about its rightness or wrongness. It will happen matter of factly.

Meanwhile, might the only response to cosmic extinction — and with it, our extinction — be for the universe and humanity to shrug?

Picture Post #48: Philosophic Reflections on a Lunar View of Earth

Image Credit: NASA/JSC  This view taken  July 20, 1969,  from the Apollo 11 spacecraft shows the Earth rising above the moon's horizon. 

Posted by Keith Tidman

Half a century after the Apollo 11 astronauts stepped onto the heavily pockmarked moon, a quarter of a million miles away, much of the world has recently been savoring again the grandeur of the achievement. 

The feat symbolized humankind’s intrepid instincts. To venture into space as explorers once riskily did across Earth’s threatening oceans and landmasses. To satisfy a gnawing curiosity, placing footprints, as those astronauts did, onto unknown and little-known shores.

From this comparatively short distance, Earth still looks startlingly small and lonely — even humble, given its cloaking by the atmosphere. How might the image of our planet change, then, as cameras peel back even farther: from elsewhere in the Milky Way and well beyond? After all, distances in space eventually become light-years.

As Earth shrinks with distance, does the meaningfulness of our planet and its inhabitants shrink in parallel, in the vast cosmic backdrop? Or do, say, the ‘volume and mass’ of what fundamentally matters about us rebelliously remain the same, no matter Earth’s size in the surrounding expanse? 

A rebelliousness that, one might submit, emerges from a web of human ‘consciousness’ that stretches around the planet — the collective synapses of seven billion people ceaselessly firing: the churn of dreams, imaginings, creations.

The seeming peacefulness here is just that: ‘seeming’. The pacific panorama masks the authentic nature of Earth: roiling with both natural and human activity. The phantom tranquility conceals one particular instinctual human behaviour: successive wars filling millennia of history. One has to wonder what in the human genome leads mankind to war to remedy differences and quench hegemonic cravings.

As we gaze, from moon’s vantage point, upon the orb of Earth, with its thin coating of air and water, we are starkly reminded of how vulnerably brittle the Earth’s environment is. And the responsibility humanity has as active guardians, to nurture the planet as the planet symbiotically nurtures us. Critical to the survival of our species.

What happens if we poison or exhaust the planet? Or will nature itself, being perhaps indifferent to humanity and coolly subjecting us to its whim, thereby render the planet uninhabitable, leading to another major extinction event? Are we only renters, not owners? Has the lunar walk deceived us into thinking we can leave Earth behind and inhabit somewhere else? Is that humanity’s imperative?

Is there a solemnity about the rearward-looking scene of a distanced Earth — an evocation of awe, prompting reflection? Is there ‘an aloneness’, too? The silence of space contrasts with the known cacophony of Earth, the latter a buzzing hive of devices that magnify our voices and boisterously shout our presence. Will that cacophony continue or ultimately end?

Anyone whose culture might have included the pre-digital-age children’s game of marbles might nostalgically recognise, from this lunar distance, the surface appearance of Earth, with the gauzy, seemingly chaotic swirling patterns on Earth’s surface. Our mind’s eye might give recognisable form to those patterns.

Future generations will grasp, better than us, how this one step on another cosmic body, however craggy and nearby it is, served to spur far more ambitious tours through space, whether by human beings or sophisticated thinking apparatuses — to face down the harsh environment of space as we  scratch our exploratory itch.

PP #48: Philosophic Reflections on a Lunar View of Earth

This view taken  July 20, 1969,  from the Apollo 11 spacecraft shows the Earth rising
above the moon's horizon. (Image credit: NASA/JSC)

Posted by Keith Tidman

Half a century after the Apollo 11 astronauts stepped onto the heavily pockmarked moon, a quarter of a million miles away, much of the world has recently been savoring again the grandeur of the achievement. Reaffirmation of the ‘giant leap for mankind’ legendarily beamed back to Earth, and the ambitious revisualisation of our space-based destiny and vistas.

The feat symbolised humankind’s intrepid instincts. To venture into space, as Earth-bound explorers once riskily did across threatening oceans and landmasses. To satisfy a gnawing curiosity, placing footprints, as these resilient astronauts did, onto unknown and little-known shores. And in the doing, be in awe of the oneness and most-fundamental architecture of humanity — the very nature of our being.

From this comparatively short distance, Earth still looks startlingly small and lonely — even humble, given its cloaking by the atmosphere. Yet, humankind might discover it isn’t alone; the cosmos brims with habitable planets. In that endeavour, how might the image of our planet change, then, as cameras peel back even farther: from elsewhere in the Milky Way and well beyond? As distances in space turn into light-years.

As Earth shrinks with distance, does the meaningfulness of our planet and its inhabitants shrink in parallel, in the vast cosmic backdrop, contesting humankind’s immodestly self-styled honorific of ‘exceptional’? Does our reality change? Or do, say, the ‘volume and mass’ of what fundamentally matters about us — our purpose — rebelliously remain unaffected, defining our place in the larger scheme, no matter Earth’s size in the surrounding cold expanse? 

A rebelliousness that, one might submit, emerges from a web of human ‘consciousness’ that stretches around the planet — the neurons and synapses (connectomes) of seven-and-a-half billion people ceaselessly firing: the stuff of dreams, imaginings, creations. Integral, perhaps, to a larger cosmic consciousness: and again, the stuff of dreams, imaginings, creations.

The seeming peacefulness in the image at top is just that: ‘seeming’. The pacific panorama masks the true nature of Earth: roiling with both natural and human activity. The phantom tranquility conceals one of our instinctual human behaviours: successive wars filling millennia of history. One wonders what idiosyncratically in the human genome leads mankind to war to remedy differences and trifling grievances, as well as quench hegemonic cravings. All the while paradoxically juxtaposed with the astounding complexities of humankind’s diverse civilisations and cultures.

As we gaze, from moon’s vantage point, upon the orb of Earth, with its thin coating of air and water, we are reminded of how vulnerably brittle the Earth’s environment is. Especially at the environment’s intersections with not-uncommonly remorseless technology. Existential risks abound. We’re reminded of the responsibility humanity has as active (proactive) guardians, to nurture the planet as the planet symbiotically nurtures us. Critical, we might agree, to the survival and continued evolution of our species.

What happens if we misguidedly, even disinterestedly, poison or exhaust the planet, as it hangs precariously in space? Or might nature, perhaps indifferent to humanity and coolly subjecting us to its whim, itself render the planet uninhabitable — leading to another major extinction event? Are we only renters, not owners? Did the lunar visit introduce a new imperative: to leave Earth behind and inhabit somewhere else?

Is there a solemnity about the rearward-looking scene of a distanced Earth — an awe that prompts reflection? A scene made all the more evocative by our believing that Earth is immersed in a sort of cosmic sea — of dark matter, dark energy, quantum fluctuations, and more. Is there the perception of ‘aloneness’, too, our seemingly distanced from everyone and everything else in that cosmic sea? The silence of the gaping, inky space contrasts with the cacophony of Earth, the latter a hive of devices that magnify our voices and echo our presence. Will that cacophony continue, or ultimately go silent?

In that presence, we marvel that humankind, dwelling on the comparatively tiny planet seen from the lunar perspective, nevertheless has the cognitive wherewithal to ponder and increasingly understand the cosmology of the whole universe: its beginning, its evolution, its current circumstances, its future. A study in the making, propelled by an irresistible impulse to know.

Anyone whose culture might have included the pre-digital-age children’s game of marbles may nostalgically recognise, from this lunar distance, the surface appearance of Earth, with its gauzy, chaotically swirling patterns. We admire its familiarly abstract beauty. All the while suspecting that there’s order interweaving the deception of chaos. Surrounding this marble-like Earth is a bewildering stillness and blackness — a blackness majestically interrupted, however, by galaxies and stunning phenomena like the Pillars of Creation.

Future generations will grasp, better than us, how this one step on another cosmic body, however craggy and nearby the moon is, served to spur far more ambitious tours through space, whether by human beings or sophisticated thinking apparatuses — to face down the harsh environment of space as we inexorably scratch our exploratory itch.

Is Mathematics Invented or Discovered?

Posted by Keith Tidman

I’m a Platonist. Well, at least insofar as how mathematics is presumed ‘discovered’ and, in its being so, serves as the basis of reality. Mathematics, as the mother tongue of the sciences, is about how, on one important epistemological level, humankind seeks to understand the universe. To put this into context, the American physicist Eugene Wigner published a paper in 1960 whose title even referred to the ‘unreasonable effectiveness’ of mathematics, before trying to explain why it might be so. His English contemporary, Paul Dirac, dared to go a step farther, declaring, in a phrase with a theological and celestial ring, that ‘God used beautiful mathematics in creating the world’. All of which leads us to this consequential question: Is mathematics invented or discovered, and does mathematics underpin universal reality?

‘In every department of physical science, there is only so much science … as there is mathematics’ — Immanuel Kant

If mathematics is simply a tool of humanity that happens to align with and helps to describe the natural laws and organisation of the universe, then one might say that mathematics is invented. As such, math is an abstraction that reduces to mental constructs, expressed through globally agreed-upon symbols, serving (in the complex realm of human cognition and imagination) as an expression of our reasoning and logic, in order to better grasp the natural world. According to this ‘anti-realist’ school of thought, it is through our probing that we observe the universe and that we then build mathematical formulae in order to describe what we see. Isaac Newton, for example, developed calculus to explain such things as the acceleration of objects and planetary orbits. Mathematicians sometimes refine their formulae later, to increasingly conform to what scientists learn about the universe over time. Another way to put it is that anti-realist theory is saying that without humankind around, mathematics would not exist, either. Yet, the flaw in this scientific paradigm is that it leaves the foundation of reality unstated. It doesn’t meet Galileo’s incisive and ponderable observation that:

‘The book of nature is written in the language of mathematics.’

If, however, mathematics is regarded as the unshakably fundamental basis of the universe — whereby it acts, so to speak, as the native language of everything (embodying universal truths) — then humainity’s role becomes to discover the underlying numbers, equations, and axioms. According to this view, mathematics is intrinsic to nature and provides the building blocks — both proximate and ultimate — of the entire universe. An example consists of that part of the mathematics of Einstein’s theory of general relativity predicting the existence of ‘gravitational waves’, the presence of which would not be proven empirically until this century, through advanced technology and techniques. Per this kind of ‘Platonic’ school of thought, the numbers and relationships associated with mathematics would nonetheless still exist, describing phenomena and governing how they interrelate and in so doing bring a semblance of order to the universe — a universe that would exist even absent humankind. After all, this underlying mathematics existed before humans arrived upon the scene — merely awaiting our discovery — and this mathematics will persist long after us.

If this Platonic theory is the correct way to look at reality, as I believe it is, then it’s worth taking the issue to the next level, which is the unique role of mathematics in formulating truth and serving as the underlying reality of the universe — both quantitative and qualitative. As Aristotle summed it up,  the ‘principles of mathematics are the principles of all things’ — thus foreshadowing the possibility of what later became known in the mathematical and science world as a ‘theory of everything’, unifying all forces, including the still-defiant unification of quantum mechanics and relativity. 

As the Swedish-American cosmologist Max Tegmark provocatively put it, ‘There is only mathematics; that is all that exists’ — an unmistakably monist perspective. He colorfully goes on:

‘We all live in a gigantic mathematical object — one that’s more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced physics theories. Everything in our world is purely mathematical— including you.’

The point is that mathematics doesn’t just provide ‘models’ of physical, qualitative, and relational reality; as Descartes suspected centuries ago, mathematics is reality.

Mathematics thus doesn’t care, if you will, what one might ‘believe’; it dispassionately performs its substratum role, regardless. The more we discover the universe’s mathematical basis, the more we build on an increasingly robust, accurate understanding of universal truths and, even, get ever nearer to an uncannily precise, clear window onto all reality — foundational to the universe. 

In this role, mathematics has enormous predictive capabilities that pave the way to its inexhaustibly revealing reality. An example is the mathematical hypothesis stating that a particular fundamental particle exists whose field is responsible for the existence of mass. The particle was theoretically predicted, in mathematical form, in the 1960s by British physicist Peter Higgs. Existence of the particle — named the Higgs boson — was confirmed by tests some fifty-plus years later. Likewise, Fermat’s famous last theorem, conjectured in 1637, was not proven mathematically until some 360 years later, in 1994 — yet the ‘truth value’ of the theorem nonetheless existed all along.

Underlying this discussion is the unsurprising observation by the early-20th-century philosopher Edmund Husserl, who noted, in understated fashion, that ‘Experience by itself is not science’ — while elsewhere referring to ‘the profusion of insights’ that could be obtained from mathematical research. That process is one of discovery. Discovery, that is, of things that are true, even if we had not hitherto known them to be so. The ‘profusion of insights’ obtained in that mathematical manner renders a method that is complete and consistent enough to direct us to a category of understanding whereby all reality is mathematical reality.

Is Mathematics Invented or Discovered?

Posted by Keith Tidman

I’m a Platonist. Well, at least insofar as how mathematics is presumed ‘discovered’ and, in its being so, serves as the basis of reality. Mathematics, as the mother tongue of the sciences, is about how, on one important epistemological level, humankind seeks to understand the universe. To put this into context, the American physicist Eugene Wigner published a paper in 1960 whose title even referred to the ‘unreasonable effectiveness’ of mathematics, before trying to explain why it might be so. His English contemporary, Paul Dirac, dared to go a step farther, declaring, in a phrase with a theological and celestial ring, that ‘God used beautiful mathematics in creating the world’. All of which leads us to this consequential question: Is mathematics invented or discovered, and does mathematics underpin universal reality?

‘In every department of physical science, there is only so much science … as there is mathematics’ — Immanuel Kant

If mathematics is simply a tool of humanity that happens to align with and helps to describe the natural laws and organisation of the universe, then one might say that mathematics is invented. As such, math is an abstraction that reduces to mental constructs, expressed through globally agreed-upon symbols. In this capacity, these constructs serve — in the complex realm of human cognition and imagination — as a convenient expression of our reasoning and logic, to better grasp the natural world. According to this ‘anti-realist’ school of thought, it is through our probing that we observe the universe and that we then build mathematical formulae in order to describe what we see. Isaac Newton, for example, developed calculus to explain such things as the acceleration of objects and planetary orbits. Mathematicians sometimes refine their formulae later, to increasingly conform to what scientists learn about the universe over time. Another way to put it is that anti-realist theory is saying that without humankind around, mathematics would not exist, either. Yet, the flaw in this paradigm is that it leaves the foundation of reality unstated. It doesn’t meet Galileo’s incisive and ponderable observation that:

‘The book of nature is written in the language of mathematics.’

If, however, mathematics is regarded as the unshakably fundamental basis of the universe — whereby it acts as the native language of everything (embodying universal truths) — then humanity’s role becomes to discover the underlying numbers, equations, and axioms. According to this view, mathematics is intrinsic to nature and provides the building blocks — both proximate and ultimate — of the entire universe. An example consists of that part of the mathematics of Einstein’s theory of general relativity predicting the existence of ‘gravitational waves’; the presence of these waves would not be proven empirically until this century, through advanced technology and techniques. Per this ‘Platonic’ school of thought, the numbers and relationships associated with mathematics would nonetheless still exist, describing phenomena and governing how they interrelate, bringing a semblance of order to the universe — a math-based universe that would exist even absent humankind. After all, this underlying mathematics existed before humans arrived upon the scene — awaiting our discovery — and this mathematics will persist long after us.

If this Platonic theory is the correct way to look at reality, as I believe it is, then it’s worth taking the issue to the next level: the unique role of mathematics in formulating truth and serving as the underlying reality of the universe — both quantitative and qualitative. As Aristotle summed it up, the ‘principles of mathematics are the principles of all things’. Aristotle’s broad stroke foreshadowed the possibility of what millennia later became known in the mathematical and science world as a ‘theory of everything’, unifying all forces, including the still-defiant unification of quantum mechanics and relativity. 

As the Swedish-American cosmologist Max Tegmark provocatively put it, ‘There is only mathematics; that is all that exists’ — an unmistakably monist perspective. He colorfully goes on:

‘We all live in a gigantic mathematical object — one that’s more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced physics theories. Everything in our world is purely mathematical— including you.’

The point is that mathematics doesn’t just provide ‘models’ of physical, qualitative, and relational reality; as Descartes suspected centuries ago, mathematics is reality.

Mathematics thus doesn’t care, if you will, what one might ‘believe’; it dispassionately performs its substratum role, regardless. The more we discover the universe’s mathematical basis, the more we build on an increasingly robust, accurate understanding of universal truths, and get ever nearer to an uncannily precise, clear window onto all reality — foundational to the universe. 

In this role, mathematics has enormous predictive capabilities that pave the way to its inexhaustibly revealing reality. An example is the mathematical hypothesis stating that a particular fundamental particle exists whose field is responsible for the existence of mass. The particle was theoretically predicted, in mathematical form, in the 1960s by British physicist Peter Higgs. Existence of the particle — named the Higgs boson — was confirmed by tests some fifty-plus years later. Likewise, Fermat’s famous last theorem, conjectured in 1637, was not proven mathematically until some 360 years later, in 1994 — yet the ‘truth value’ of the theorem nonetheless existed all along.

Underlying this discussion is the unsurprising observation by the early-20th-century philosopher Edmund Husserl, who noted, in understated fashion, that ‘Experience by itself is not science’ — while elsewhere his referring to ‘the profusion of insights’ that could be obtained from mathematical research. That process is one of discovery. Discovery, that is, of things that are true, even if we had not hitherto known them to be so. The ‘profusion of insights’ obtained in that mathematical manner renders a method that is complete and consistent enough to direct us to a category of understanding whereby all reality is mathematical reality.