The tip of a pendulum traces a boring arc as it swings back and forth, but magic happens when we add a single joint to the arm. Now the tip traces a wonderful pattern as the lower segment swings around the upper segment. Even more wondrous, unless the initial displacement of the pendulum is exactly the same, the pattern that is traced will be different. The addition of a single joint to the arm of the pendulum creates a near infinity of patterns.

This kind of infinity is everywhere once we know where to look for them.1 Every snowflake really is unique, given that each one contains about ten quintillion (a million times a million times a million) water molecules that crystalize in different ways. Sex creates an infinity of genetic combinations. Musical variety and the number of forms that can be created from a lump of clay will never be exhausted.

It's easy to become awestruck by these infinities, but I’m here to say that they lack something important. We need to go beyond infinity, to steal Buzz Lightyear’s signature line.2

Why are we attracted to infinities?  In part because they imply infinite potential, enabling us to pursue our dreams without limits. As the scientist and Jesuit priest Pierre Teilhard de Chardin put it, “Our duty, as men and women, is to proceed as if limits to our ability did not exist. We are collaborators in creation.”

But the pursuit of any particular dream—or any concrete objective, for that matter—is inherently a winnowing process, resulting in something that is quintessentially finite. Without the finite realizations of infinite potential, infinities aren’t worth wanting.

The very nature of life can be used to illustrate my point. Its infinite diversity so impressed Darwin that he described it as “endless forms most beautiful”. But any particular species is put together in just the right way to survive and reproduce in its environment.  A species occupies a tiny region of a nearly infinite parameter space and departures from that region result in death. When we reflect on infinity, we must include the infinite number of ways that things can go wrong.

Darwinian evolution combines three ingredients: Variation (organisms differ in just about everything that can be measured about them), selection (their differences make a difference in terms of survival and reproduction) and replication (offspring tend to resemble their parents). When these three ingredients are combined, organisms change over time in the direction of becoming better adapted to their environments.  Variation is where infinite possibilities play a positive role, while selection and replication play the winnowing roles. Going beyond infinity means the full Darwinian process, not just the variation part.

In my book This View of Life, I make this point by comparing a snowflake with the skeleton of an angelfish. Both are physical structures with intricate beauty. Snowflakes form by a purely physical process of water molecules crystalizing around particles in the air.

The uniqueness of each snowflake reflects the uniqueness of its temperature and moisture environment as it falls toward earth. The skeleton also forms by a purely physical process, but that process has been molded by natural selection to produce the same form, with only minor variations that stay within the envelope required to survive and reproduce, despite variation in the physical environment of the fish. That miracle of regulation should invoke awe and wonder in us, at least as much as our appreciation of infinities.

For me, the angelfish skeleton is beautiful in a different way than the beauty of a snowflake or the patterns traced by a jointed pendulum.  That’s because the skeleton is not just highly structured, but structured to do something. It is functionally organized. Human engineered objects such as a pocket watch, an aerodynamically efficient car, or a suspension bridge are beautiful in the same way. And the more dependent we are on their functionality, the more beautiful they become.

The same goes for works of art, which lack utility in some respects but are immensely useful—even essential—for providing meaning in our lives that ultimately result in action. And the creation a particular work of art is a winnowing process, with the artist as the agent of selection.

I experienced this while writing my novel Atlas Hugged.  Creating a world with over sixty characters was one of the most engaging experiences of my life and every word was scrutinized. Much of the winnowing took place beneath my conscious awareness. A new plot development would bubble up and I would declare “Of course! That’s how it must be!” And of course I wrote the novel to make a difference in the world, no less than my scientific research, nonfiction writing, and real-world change efforts. Any work of art that provides meaning is utilitarian in this sense.

Two more images will consolidate what I mean by going beyond infinity. The first is a lump of clay, which has infinite potential but will not be found in any art gallery. The second is a particular work of art titled “Hill of Indulgence”, by Dr. Gindi, who has organized this series of essays about infinity. Her essay on the piece describes the meaning it is intended to convey, “about what it means to be human and to embody the crests and falls of our lives.” Every detail of the sculpture has been shaped to convey this meaning: How he steps. His upturned chin. The delight on his face. Even the experience written into his skin. It is the shaping influence of the artist that makes the sculpture so much more meaningful than a mere lump of clay.

In our appreciation of life, our human constructed world, and art, let us celebrate not just infinite potential but the full evolutionary process.

References:

[1] I am defining infinity as a vast number of possibilities, realizing that this is different than the mathematical concept of infinity.

[2] Buzz Lightyear is the astronaut toy in the Walt Disney film series Toy Story.

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Originally published as part of a series of essays on infinity organized by the sculptor Dr. Gindi.