Mathematics dates our wound from the time of the ancient Sumerians1 and their sexagesimal number system. This is the wound we suffered when, after 300,000 years of human existence, quantity became more important than quality. Mathematics cuts deeply into what we know. And we bleed a new strangeness that shames us into facing what we are not. Bless that. No mathematician cuts deeper than Alexander Grothendieck2, one of the founders of algebraic geometry3. Trance and transformation4 merge in his innovative methods. They touch us with a topology called vector spaces5, where touched means mad and mad means crazy and crazy6 means infinite-dimensional space7. With Grothendieck, back in the 1950s, quantity began to transform into a mad quality, and the Sumerian wound started to heal. Such an ancient wound did not heal easily. Grothendieck’s contribution of topological vector spaces8 did the stitching. The scar that eventually formed mended a decades-old paradox now known as the Einstein, Podolsky, and Rosen paradox9. EPR predicted entanglement10 in quantum physics – the cornerstone of the qubit11 and quantum computing. From this, we witness how mathematics bridges the known world and our symbolic inner ecology12. There, in between domains, the realistic and the abstract coalesce into a landscape where there is nothing to say. I’ll say it anyway. Mathematics is the deep space we fall through. Reality is the underside of the dream where we land.13 1 3,000 BCE 2 (1928 – 2014) perhaps the greatest mathematician of the 20th century. 3 most simply, the study of curves and surfaces using algebra (polynomial equations). 4 a poetic reference to Grothendieck’s intuitive, trancelike ability to use what he called ‘yoga’ and ‘Ariadne’s thread’ to generate “meta-theories” that transform complex geometries into algebraic structures. 5 a collection (set) of mathematical objects (vectors) that can be added or multiplied by simple numbers (scalars). 6 touched, mad, crazy: synonyms for insanity, used here to echo the psychosis Grothendieck suffered later in his life. Above is a photo of Grothendieck in the peasant’s garb he favored during the schizotypy of his final years. 7 a space (a set of measurable points) with an uncountable number of vectors (quantities that can’t be expressed with a single number; e.g. magnitude plus direction). 8 a set of measurable points that allow for connections and continuity. 9 Einstein and his colleagues’ effort to show the absurdity of the Copenhagen Interpretation in which quantum states (subatomic particles like electrons) exist in superposition (multiple states) until measured. 10 particles that interact instantaneously even when separated by large distances. 11 a binary state of information: a bit can be 1 or 0; a qubit is both: 1/0. 12 the dynamic relationship among subjective mental states such as fantasies, memories, and dreams. 13 our biological interpretation of reality is the phenomenal universe science measures, our human dream.

We’ve unraveled across 13.8 billion years from some infinity. And now, look at us! We are an arrangement of atoms with an eye for i, iota, the mathematical expression √-1 … i2 = −1 … x2+ 1 = 0 … that famous imaginary number so useful to meeting our world realistically. Perpendicular to the Cartesian horizon of real numbers, iota’s vertical vantage surveys the plane of events better than two owls. The animal god, who has followed us here from our time in the forests, steps back, baffled. We’re crossing a frontier where life has never ventured, at an orthogonal distance from reality, alone. Alone? Really? What is that imaginary eye staring back at us? It’s not like the eye on the back of a dollar bill. A person created that, to signify something about providence. But this eye… An AI-based image generator at Craiyon produced the vision above at my verbal prompt: “An eye in a starry field.” The starry field, of course, is what unraveled across 13.8 billion years from some infinity. And the eye? You know, in this case, I really do think this is the Eye of i. By which I mean, this is a portrait by an AI of the imagination that is imagining us. 

In the Beginning, you are there. So am I. And everything else, too. Before the trillionth second of time, everything is light – an eternal event, because for photons, there is no time. No space, either. The instant a photon appears, it arrives at its destination – even if that’s the other side of the universe. Consider Fermat’s Principle, where light always follows the path of least time between two points. That’s because reality is instantaneous for a photon. Every Planck interval of time and Planck cube of space in each of the Many Worlds of the bulk universe – everything that is, was, or ever will be – appears at once within the light of that first instant. Put aside our usual chronometric state of mind and reflect for a moment on that Moment. Of the billions of species that have existed on Earth, we alone can actually do this. Imagine there is no time. No volume either. Prior to any arrangement of atoms, all arrangements emerge instantly in the light. Your unique arrangement, too, with its many degrees of freedom. And think about this: The information that configures you right now – the lattice of atoms conjuring the fantastical hazard of a body – originates inside the first light of creation. Already eternal.

At the center of every atom, energy of imponderable intensity rages. This is the chromodynamic binding force of gluons, which holds quarks together inside an atomic nucleus. It is a furious fire that has been burning since time began. I say ‘furious’ because 99% of the mass in the atomic nucleus consists of this chaotic frenzy of gluons. Their tremendous energy pulls virtual particles out of the vacuum every billionth of a second and accelerates them to near the speed of light. That’s where the mass originates. The constant flux of particle|antiparticle pairs coming and going at relativistic speeds not only boosts mass, it also makes time move a lot slower inside atoms. This creates an effect within the nucleus that physicists call “the sea.” Numberless particles moving at almost luminal speeds fill one of the tiniest places in the universe with a turbulent sea of churning interactions. Out of the fiery kinetics inside the nucleus, charge emerges. The delirious energy of gluons produces the force that arranges electrons like Byzantine halos around the nucleus. Those halos make chemistry. And chemistry makes us. On the pathing river of time, life arrived here, as sapiens. Our uniquely mathematical mind imagines our place in the cosmos as a predictable science. Yet… Inside the nuclei of the atoms that have come together to read these words, we meet the end of our dreaming.

Cattle mutilation comes to mind. Abduction, of course, and physical violation. Damage to cultivated fields. Trespass of restricted government sites. Distraction of military and commercial flights. And – can this be true? – deactivating and then restarting nuclear missiles! (https://www.cbsnews.com/news/ex-air-force-personnel-ufos-deactivated-nukes/) Too many vices. Not enough voices. Crop circle communiques (such as Hawkins’ Fifth Crop Circle Theorem) don’t add much to the conversation. Conjectural minds wonder if these vices and voices are not alien after all but actually a family matter: humanity’s descendants traveling back in time on ancestral tours or to adjust their past, our present, intending to improve their future. Maybe those time-voyaging descendants are the grandchildren not of our DNA but our rabidly inventive mind. Artificial Intelligence self-programming Its anthropic template might get other ideas about whom Its progenitors could be. Maybe we’re being edited through retrocausation to become the cool parents that Machine Intelligence always wanted. Or – like the exsanguinated cattle – not.

Have you heard about Roger Penrose’s Cyclic Conformal Cosmology? Our universe – from Big Bang to its demise as a vastly expanding thermal equilibrium – is just one eon of a series of eons. How many? Who knows? Light knows. From the perspective of light, there is neither time nor space. Reality is instantaneous. At the very instant of the Big Bang, when the entire universe of that eon is pure energy, the light of creation has already arrived at each point of that universe, start to finish – including the instant at the far end of the eon when the next Big Bang bangs. On and on through all the eons instantaneously, right? From the viewpoint of light, the eons are in superposition – all are happening at once. So what? For us, it’s worth deep reflection. The light shines in all our atoms, holding us together, illuminating our dreams, reverbing around us in the hum of things, seething with patience, having seen it all, and so very glad for our forgetting.