Principle of Least Action
“I have struggled all my life to get the maximum meaning in the simplest possible form.”
—Anne Truitt, Daybook (1982)
The quote is by American sculptor Anne Truitt, but I often repeat it to myself as if it were an inherited mantra. I’ve come to think that, if there were such a thing as an ethics of form, it would look a lot like this: seeking the exact gesture, the perfect curvature, the radical economy that allows something to manifest with the least amount of matter possible. It’s not about saying little, but about not saying more than is necessary.
Ironically, that instinctive need to distill—not to reduce—finds its echo in a concept from physics that has served me as a theoretical framework: the principle of least action.
In physics, it’s postulated that every system—from a particle to a galaxy—evolves from an initial state to a final one by following the path that minimizes a quantity called action, which is the integral of kinetic energy minus potential energy over time (Lanczos, 1970).
In other words: nature doesn’t choose just any trajectory, but the one that, without shortcuts or detours, completes its transformation with the greatest efficiency and the least possible resistance.
Avoiding waste.
Minimizing noise.
The universe, if it can, avoids the unnecessary.
Light, for instance, knows this. When a beam passes from air into water, its trajectory bends. At first glance it may seem like a deviation, a detour. But in reality, it’s the fastest path possible. This was discovered by the Frenchman Pierre de Fermat in the 17th century: light doesn’t follow the shortest path in terms of distance, but the one that minimizes travel time (Fermat, 1662). It’s known as the principle of least time. A truth that remains valid centuries later, and which falls under an even broader and deeper principle: that of least action (Maupertuis, 1744).
In classical mechanics, when an apple falls from a tree, its path is not random. Among all the infinite curves it could trace from the branch to the ground, gravity chooses the only one that minimizes action—that quantity that combines energy and duration. This was formulated by Joseph-Louis Lagrange in the 18th century and later refined by William Rowan Hamilton (Goldstein et al., 2002): every physical system evolves following the path that makes its action extreme—and usually minimal. If there were another way to fall that used less energy in the same time, or required less time with the same energy, that would be the path. But there isn’t. What we observe is not chance—it is the natural consequence of a universal principle of economy.
Even the planets in our system understand it. The elliptical orbits they describe around the Sun are not the result of chance nor simply the effect of gravity pulling on them. There is something deeper: a natural law of economy. Isaac Newton explained how this force of attraction works. But later, thanks to Lagrange and Hamilton, we learned that the planets don’t spin just any way: among all the possible trajectories, they follow precisely the one that most efficiently balances energy expenditure and time. Not the shortest path, nor the fastest—but the most balanced. Each orbit is, deep down, an obedience to that equilibrium. A choreography not invented, but imposed. A silent prayer to the principle of least action.
What if that same logic could be applied to art? What if painting were also a matter of choosing the simplest path—not the easiest—between an intention and its appearance? Every time I face the creation of a new image, I ask myself the same questions: What is essential and what is accessory? When is a form enough? How many ideas can fit on this surface without getting in the way? How much weight can a painting bear before collapsing? How do you know when to stop? How do you identify the exact threshold where the minimal becomes activated and the maximal impoverishes?
The plastic solution doesn’t impose itself: it emerges. It’s not about expression, but about adjustment. About calibrating relationships, weights, intensities. About arriving—through trial and through listening—at that exact configuration that needs nothing more. Nor less. As if the image, in its silent balance, also obeyed a law of least action. A kind of clarity that cannot be explained, but is recognized.
Sometimes, that urgency for subtraction is not experienced as an aesthetic choice, but as a vital necessity. “I had to get rid of everything unnecessary… in order to save myself,” wrote Estonian composer Arvo Pärt (Hillier, 1997). It’s not a formal pruning, but an existential one. An inner force pushing toward reduction. Toward a bareness that is not emptiness, but core.
Other times, as in the case of British painter John McLean, it can be experienced almost as a mystical revelation, an epiphany. “I think with my own work that the simpler I can make it, in a strange way, the more profound I feel it is,” he wrote (Gooding, 2009). The stripped-down form is no longer a strategy or a stylistic gesture—it’s a pathway to the essential. A truth that doesn’t impose itself, but appears. Like a murmur that, by not raising its voice, becomes clearer.
In physics, as in painting, the path that minimizes action is often also the most beautiful, the most stable, the one that contains the deepest logic. Formal economy is not scarcity, but concentration of meaning. Like in haikus, or in a well-written theorem, beauty manifests when form is exact, inevitable, almost natural.
That is what painting is for me: a way to resist noise, acceleration, the superfluous.
To choose the minimal as an ethical—not aesthetic—gesture. Like someone learning to be quiet so that the essential may be heard.
When the work no longer says “this is,” but “this is enough.”
Path Integral Formulation
While in classical physics, if you throw a ball, there is only one trajectory that connects the starting point with the endpoint—the parabolic curve dictated by gravity—in quantum mechanics, the world works differently.
In the 1940s, Richard Feynman proposed a radical formulation: that a subatomic particle—like electrons or photons—when moving from one point to another, does not choose a single path, but explores all possible paths simultaneously (Feynman & Hibbs, 1965).
Every imaginable curve—straight, jagged, impossible—is simultaneously considered by the particle.
This idea, known as the path integral formulation, is not just a metaphor: it is a precise mathematical description of how nature operates at the subatomic scale. Each possible trajectory is assigned a “phase,” a complex value linked to its corresponding action. Some phases cancel each other out (destructive interference), others reinforce one another (constructive interference). The observable result—the trajectory we perceive as real—is the sum of all possible itineraries, but filtered through this network of interferences (Schulman, 2005). The one that minimizes action does prevail, yes, but that choice doesn’t happen in a vacuum: it is the product of a range of options that collapse into a precise form.
That image—the one of infinite paths explored simultaneously—is not unfamiliar to me.
In my expanded painting, behind every formal idea ready to be executed, there follows a constellation of variations, of derivatives. Explorations of the same pictorial proposal with different iterations that I call chromatic poems.
Each panel then becomes one of these phases, possible trajectories, that formulate the path integral. Each painting is an essay.
Essay in all its meanings. In the philosophical sense—a presentation of subjective reflections. In the scientific sense—a controlled trial conducted to test something. And in the artistic sense—practice or rehearsal of a work, song, or choreography before public presentation.
Curiously, those essays tend not to work alone. Or at least not in the same way they become activated by juxtaposition, when shown in context, as a whole.
Those pieces need to accumulate, to touch, to vibrate together in order to fully activate. In diptychs, triptychs, polyptychs, series. Not as repetitions, but as simultaneous explorations of the same intention. And it is only in that addition, previously referred to as constructive interference, where the greatest meaning appears, revealing, in the viewer’s mind, the perfect trajectory.
As in quantum mechanics, it is the unfolding of chromatic poems that, when they collapse, generates a clarity that no isolated image could sustain.
I don’t paint the final image. I paint the field of possibilities that contains it. And in that gathering—when nothing cancels out, when nothing gets in the way—sometimes something happens.
Something that doesn’t explain. That doesn’t decide. But that, for an instant, seems inevitable.
References
- Feynman, R.P. & Hibbs, A.R. (1965) Quantum Mechanics and Path Integrals. New York: McGraw-Hill.
- Fermat, P. de (1662) Oeuvres. Paris.
- Goldstein, H., Poole, C. & Safko, J. (2002) Classical Mechanics. 3rd ed. San Francisco: Addison-Wesley.
- Gooding, M. (2009) John McLean: Paintings 1959–2009. London: Flowers.
- Hillier, P. (1997) Arvo Pärt. Oxford: Oxford University Press.
- Lanczos, C. (1970) The Variational Principles of Mechanics. 4th ed. Toronto: University of Toronto Press.
- Maupertuis, P.L.M. de (1744) Mémoires de l’Académie des Sciences de Paris.
- Schulman, L.S. (2005) Techniques and Applications of Path Integration. New York: Dover Publications.