Bonding With Infinity: A journey with Giordano Bruno

“When we try to pick out anything by itself, we find it hitched to everything else in the universe. One fancies a heart like our own must be beating in every crystal and cell, and we feel like stopping to speak to the plants and animals as friendly fellow mountaineers.” John Muir (My First Summer in the Sierra, 1869)

Giordano Bruno’s Visionary Revolution

Giordano Bruno was a Renaissance thinker who argued for radical ideas in theology, mathematics and astronomy (and alchemy).

Bruno’s philosophical studies challenged not just the scientific views of his time, but also the limits of imagination itself, boldly redefining the kind of questions that one was allowed to pursue. While the Copernican transition from geocentrism to heliocentrism marked a significant step forward, Bruno took the revolution two times further. Once to propose that there is not only one sun in this heliocentric universe, but rather there are many, many worlds of planetary systems orbiting around their stellar body. And twice, by philosophically pushing against the very limits of the universe, suggesting that this universe of many-worlds is itself boundless, and in fact, infinite in expansion and variety. 

“Burchio: So then the other worlds are inhabited as ours is? Fracastorio: If not as ours is, then more nobly. In any case, those worlds are no less inhabited nor less worthy. For it is impossible that a sufficiently discerning rational mind could imagine that these innumerable worlds—each as magnificent as ours, or even more so—should be devoid of inhabitants like ourselves, or even superior.” (L’Infini, l’Univers et les Mondes)

In Bruno's rigor, a theory needs to be “possible, reasonable, true, and necessary”. Twice Bruno freed astronomers from too static perspectives—from the false immobility of Earth at the universe’s supposed center, and from our solar system's special, centered place in the cosmos. Deprived of our familiar central position and confronted infinite vastness, how easy it is to slip into an existential vertigo. While some are met with the unsettling awareness of humanity's fragility, Bruno was exhilarated by this infinite expansiveness, dissolving the medieval church's rigid separation between the perfect celestial realm and the imperfect earthly world.

Plurality in One Cosmos

“It is profound magic to draw contraries from the point of union” (Giordano Bruno)

In Bruno’s new cosmology, there is no central point, no privileged origin, no scale more important or fundamental over the others. No church, no dogma can contain the vastness of the cosmos. The smallest ladybug and the largest galaxy stand with equal dignity, equal weight and intrinsic value in the whole. Look up at the night sky. Even a single patch of darkness contains more galaxies than one can comprehend, each made up with billions of stars. Telescopes have yet to find an edge, a celestial dome, a final frontier. Space presents itself with a sort of uniform expansiveness and diversity in all directions, perhaps infinitely.

“Our senses admit their weakness by producing the appearance of a finite horizon—an appearance that is always shifting. For there is no horizon in itself, only a horizon relative to an observer.” (De immensio et innumerabilibus)

So, where is the center? It is everywhere and nowhere at once. More specifically, the center of the infinite universe is the one who observes this infinite—a center among infinite other observers, interconnected through cosmic bonds. It is precisely those bonds that a scientist must strive to study in order to comprehend the interconnected whole. One is unavoidably part of this whole, unable to ignore its own bonds to the object of observation.

"He is bound who holds the reason of the universe, or at least the nature of the particular thing he must bind—its disposition, its inclination, its manner, its use, its end." (De vinculis in genere)

How To Deal With Infinity

It is at the edge of infinities that physics offers some of its boldest ideas and encounters its most valiant challenges. It is in the singularities of General Relativity, the infinite density within black holes, the initial moment of the universe’s birth. Yet in my school years I was most awestruck by the mathematical dealings with infinities, ingeniously handling what we cannot grasp. While modern astronomy explores the immensity of the sky—that is still its tiniest fraction, and physics seeks to reconcile our knowledge of the smallest and largest scales of the universe, mathematics offers tools to smoothly slide between scales. The renormalization group is a powerful method used to determine how things change moving from different scales, leaving us with an impression of the cosmos where there is no inherently privileged plane. Neither the smallest particles nor the largest structures are of superior importance to understand the whole. One can slide from the small scales to the largest, and inversely, with no tells on which one must explain the other. Instead of providing a fundamental or preferential ground, it is about perspectives, gaining new points of understanding on new phenomena. Of course the tool should not be confused with the workings of reality, but it provides indications that different efficient conceptions of that reality are possible.

Alexandre Grothendieck—mathematician whose departure from academia was as abrupt as his contribution was momentous—called for a similar aspiration for a science more courageous, more dignified, more poetic, in reflection of the human adventure that it truly is. It takes bravery to ask real questions, and even more to appreciate the beauty of their possibilities where so many get paralyzed by the unknown.

How To Contemplate Infinity

Just as Bruno decentered humanity's cosmological outlook, theories and models show us that choosing scales or origins is a matter of perspective, of relationships between the components of the whole, of functional convenience. The rest remains entrusted to us—the observers—to inquire about meaning, to choose at which scale to put our attention, to select the lenses through which we comprehend our cosmos, to remember we are wearing lenses.