Infinite in All Directions

From superstrings to vibrant wings

What do superstrings, blackholes, meteor showers, and butterflies have in common? To the physicist Freeman Dyson, each of them are examples of immense beauty and diversity on different levels of abstraction.

Superstrings, for one, is an attempt to explain every elementary particle and fundamental force in a unified theory. It reflects our capacity for controlled imagination and unending desire for understanding. Black holes, on the other hand, are more than theoretical abstractions. They tell of real regions in spacetime where gravity is so overwhelming that even light cannot escape.

Meteor showers are even closer to home. They invigorate the night sky and remind us of the cosmic interventions that shaped the arc of evolutionary history. It was, after all, an asteroid that triggered the Cretaceous extinction—making room for us furtive mammals.

This brings us to the butterfly. “A symbol of evanescent beauty and a living proof that nature’s imagination is richer than our own,” writes Dyson. Somehow, in its humble, larval life as a caterpillar—with “a speck of neural tissue” for a brain that is “about a million times smaller than a human brain”—the insect makes its way. The little critter feeds on more than a hundred leaves before undergoing one of life’s most creative transformations. The vibrant winged creature that emerges from this metamorphosis, unaware of its own achievement, takes off, sometimes over vast distances, to begin the cycle anew. It is an ancient succession that is at least 200 million years old, long before our human ancestors walked the Earth.

Of conscious minds

Perhaps most surprising of all is that people exist to appreciate the systems that they are a part of—that tiny structures and interconnections inside our skull have coalesced into something we call the mind. Do you not find it strange and curious that the universe gave rise to something that could think, listen, and dream about itself?

But “there is no reason whatsoever for believing that our brain is the ne plus ultra of an organ of thought”, writes Erwin Schrödinger in What is Life. “It is more likely than not that a species could acquire a similar contraption whose corresponding imagery compares with ours as ours does with that of the dog.”

Life, after all, is “a biological blind alley.” While our mammalian regime provided the preconditions for nature to endow us with intelligence; insects stumbled onto another plan by way of exoskeletons, wings, and other biologic architectures. “Circumstance”, Schrodinger writes, “is bound to render gradual adaptive changes in the life-history of the individual very difficult.”

Still, the conceptual ‘mind’ can manifest itself in many ways. Who’s to say what another hundred million years of evolution might do for the swarm intelligence of ants, bees, or termites. Nature, you must remember, is most imaginative.

Dyson agrees but goes further. He suggests “that the tendency of mind to infiltrate and control matter is a law of nature.” Sure, individual brains, species, or planets may die out. But intelligence, he suspects, will spring about in one way or another. “If our species is extinguished, others will be wiser or luckier”, he says. The “mind is patient.”

Maximum diversity

Equally surprising, I think, is the stability of it all. Storms rage and land quakes, but you and I can go to bed tonight and wake up tomorrow with some recollection of this conversation. All the while, our humble Earth orbits around the Sun, as the Sun voyages around the center of the Milky Way, while our galaxy is busy too, dancing with Andromeda.

The Anthropic Principle tells us that the Universe must be of the type that gives rise to intelligent observers, or we would not otherwise be here to speculate about it. As the polymath Michael Polanyi says, “this universe is still dead, but it already has the capacity of coming to life.” It is a humble reminder that we are ultimately a small part of a grand play.

Dyson hypothesizes further, suggesting “that the universe is constructed according to a principle of maximum diversity.” Perhaps this is already seen in ecology, culture, and technology—from coral reefs to songbirds to nuclear missiles. “To this process of growth and diversification”, Dyson “sees no end”, at least until our star gives up.

“Life is like a little glow, scarcely kindled yet, in these void immensities.”
H.G. Wells. (1920). The Outline of History.

Symmetry breakings

Scientists are also beginning to understand the “symmetry breakings” and “increasing complications” that characterize the hierarchies of nature and science. While we won’t get into technicalities here, it is the idea that “more is different” as we move from particle-physics to many-body physics to chemistry and so on. As the physicist Philip Anderson reminds, “psychology is not applied biology, nor is biology applied chemistry.” New emergent laws and concepts are needed to make sense of the rich structures that confront us at each level.

As Dyson explains:

“The development of the universe from its earliest beginnings is regarded as a succession of symmetry-breakings. As it emerges from the moment of creation in the Big Bang, the universe is completely symmetrical and featureless. As it cools to lower and lower temperatures, it breaks one symmetry after another, allowing more and more diversity of structure to come into existence… Life too is symmetry-breaking. In the beginning a homogeneous ocean somehow differentiated itself into cells and animalcules, predators and prey. Later on, a homogeneous population of apes differentiated itself into languages and cultures, arts and sciences and religions. Every time a symmetry is broken, new levels of diversity and creativity become possible.”
Freeman Dyson. (1988). Infinite in All Directions.

Unifiers and diversifiers

Dyson observes that scientists tend to fall into one of two groups: the unifiers like Albert Einstein that seek to reduce the Universe into a set of manageable laws and equations; and the diversifiers like the geologist Emil Wiechert who suspect that nature itself is an endless tunnel of discovery. Both views, of course, “are complementary”, says Dyson. They help us to see “inward and backward into the past… [and] outward and forward into the future.”

Nearly a century ago, however, Kurt Godel upended the dream for unification in pure mathematics. As mathematician Javier Fresan explains in The Folly of Reason, Godel’s incompleteness theorem tells us that “no recursive and consistent axiomatization of arithmetic can be complete. Put another way, there will always be some true properties of the numbers that we cannot prove with axioms.” A diversifier himself, Dyson wonders whether “the notion of a final statement of the laws of physics will prove as illusory” as mathematics.

Of course, relative to the length of human history, science is just getting underway. Perhaps it is not at all dissimilar to the caterpillars that catch our eyes. Science too is feeding and growing. And it is not obvious as to the transformations it will take. Does the caterpillar know what it will become? For now, we can only speculate at the future complications that may or may not await us.

Indeed, from superstrings to butterflies, what we have, Dyson says, are rainforests of possibilities at every level of organization and emergence. “Instead of a few succinct equations to summarize the universe of physics, we have a luxuriant growth of mathematical structures, as diverse as the phenomena that they attempt to describe.” So we ought to look at the universe and our problems, as Dyson does, as “a lover of diversity.”

As Emil Wiechert writes:

“We have to abandon completely the idea that by going into the realm of the small we shall reach the ultimate foundations of the universe… The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us.”
Emil Wiechert. (1896). Lecture to the Physics and Economics Society of Konigsberg. In Freeman Dyson. (1988). Infinite in All Directions.

Sources and further reading

Dyson, Freeman. (1988). Infinite in All Directions.
Fresan, Javier. (2010). The Folly of Reason.
Schrödinger, Erwin. (1944). What is Life?
Weichert, Emil. (1896). Lecture to the Physics and Economics Society of Konigsberg.
Ferris, Timothy. (1992). The Mind’s Sky.