Variation, Constraint and Selection (VCS) Pattern
A fundamental pattern driving natural phenomena and human endeavors
"Variety is the very spice of life, that gives it all its flavor." - William Cowper.
The power of variation isn't just a philosophical idea, it's everywhere we look. From the way nature tinkers with life through evolution, to the sparks of creativity in art, music, and problem-solving, variation plays a central role. In Mathematics, Calculus of Variations is an optimization technique widely applicable in practical fields. Even computer algorithms, like those used in machine learning, rely on variation to explore possibilities (think Evolutionary Algorithms, Markov Chain Monte Carlo or Variational Autoencoders). And it's even a concept explored in philosophy, like Husserl's idea of Eidetic Variation.
In the world of music, variation has long been a cornerstone of composition and improvisation. Johann Sebastian Bach's iconic Goldberg Variations stand as a testament to the power of this concept. In this masterpiece, Bach explores a staggering 30 variations on a simple sarabande bass line, each one unveiling new dimensions of the original theme. But Bach wasn't the only one who loved variations. Composers throughout history have used them as a playground to explore ideas, sharpen their skills, and unleash creativity within a set framework.
Variation is a universal operator to generate possibilities from the present state. This idea goes hand-in-hand with the concept of the "adjacent possible," coined by scientist Stuart Kauffman. This idea suggests that at any given moment, there exists a set of possibilities that are one step away from being realized. By exploring variations on what currently exists, we can access these adjacent possibilities, leading to innovations and discoveries.
For the search space for possibilities, we need to define dynamically what the set or the space of all possibilities is. This space is bounded by the use of constraints and rules. Constraints provide a scaffolding of variations.
For musical variations on a theme, the theme is the initial constraint. In Stable Diffusion, the prompt and/or initial image are the initial conditions. Additional constraints can be added to express the instrument and media use, the style, techniques and emotional context. In chess, the set of all possible moves is constrained by the rules of the game.
The surprising idea that limitations can actually boost creativity is captured perfectly in:
Igor Stravinsky's famous quote: "The more constraints one imposes, the more one frees one's self."
It's a paradoxical notion that resonates beyond music, suggesting that limitations can actually spur innovation by forcing us to think more creatively within defined parameters. See the earlier discussions in “Why Deep Inside the Box Thinking is a Prerequisite for Creativity”
But here's the catch: sometimes the biggest obstacles we face are the ones we create for ourselves (self-imposed constraints) . Our assumptions, our biases, even our past experiences and cultural background can box us in without us even realizing it. So before we try to "think outside the box," we need to make sure we're not trapped in the wrong box to begin with!
In the visual arts, we see artists exploring variations on themes to profound effect. Katsushika Hokusai's series "Thirty-six Views of Mount Fuji," which includes the famous "The Great Wave off Kanagawa," demonstrates how a single subject can yield numerous interpretations. Each print in the series offers a different perspective on Mount Fuji, varying elements such as foreground, weather conditions, and human activity.
Similarly, in Zen Buddhism, the practice of drawing Enso circles—simple, hand-drawn circles that represent enlightenment, strength, and the universe—embraces the concept of variation.
Each Enso is unique, a product of the moment in which it was created, embodying the idea that each attempt at perfection yields a different, equally valid result.
The world of mathematics and computer science has also harnessed the power of variation to solve complex problems and generate new insights. Techniques such as Evolutionary Algorithms mimicking natural Evolution, Markov Chain Monte Carlo (MCMC), Variational Autoencoders (VAE), and Diffusion Models all rely on the principle of generating variations to explore possibility spaces and optimize solutions. In some of these algorithms, the constraints could be probability distributions, either known explicitly or approximated through sampling.
These approaches have applications ranging from Bayesian statistics to image generation, demonstrating the versatility of variation as a problem-solving tool.
In philosophy, Edmund Husserl's method of Eidetic Variation provides yet another example of how variation can be used as a tool for understanding. This phenomenological technique involves mentally varying the properties of an object or concept to discern its essential nature. By imagining different variations of a phenomenon, philosophers aim to identify its invariant features, thus gaining insight into its fundamental essence.
For example, to understand the essence of the concept “car”, we can imagine cars with zebra stripes, two wheels, cars that fly, and so on, to establish which is a car or not a car. Is a car without seats still a car? This is equivalent to probing the boundaries of the constraints of the object. The invariant features are those that stay within the boundaries, shared by all variations.
However it is wrong to think of Eidetic Variation as a logical exercise. Husserl believed that the underlying whole of the essence can only be grasped intuitively.
Shifting our focus to the natural world, we find that variation is the engine driving evolutionary processes. As
Richard Dawkins eloquently puts it, "The universe is a grand book...continuously studied, and continuously re-written and re-edited, by reproductive variations on its own pages."
This metaphor beautifully captures the essence of how genetic variations, accumulating over time, lead to the diversity of life we see around us. Variations occur through mutations and combinations by sexual reproduction.
Imagine the natural world. Charles Darwin, peering into the heart of evolution, famously wrote,
"It is not the strongest of the species that survives, nor the most intelligent, but the one most adaptable to change." - Charles Darwin
This adaptability, this capacity for change, hinges on the VCS triad. Genetic variations, arising spontaneously, provide the raw material. Environmental constraints, the struggle for survival, act as a sieve. And natural selection, the ultimate arbiter, favors those variations best suited to the challenges at hand.
Selection can sometimes be idealized as finding a maximal value of a score, such as fitness measure or finding a minimal loss value. The whole VCS pattern becomes just a mathematical optimization problem.
But in general, in Decision Making and Problem Solving, the VCS pattern can be more complicated. We may have the existence of multiple objectives, qualitative objectives, and circularity of rational decisions such as in Ecological Rationality. Here an organism's cognitive processes and decision-making strategies are shaped by the specific demands and constraints of its environment. It suggests that what is considered rational or optimal behavior may vary depending on the ecological context in which an organism exists.
In conclusion, the VCS triad of Variation, Constraint and selection provides a powerful lens for understanding a wide range of phenomena, from mathematical optimization to philosophical inquiry and creative problem-solving. Recognizing this pattern allows us to better appreciate the interplay of possibility, limitation, and choice in shaping the world around us and the solutions we create.