Category: Life

The surprising power of n=2

We are enmeshed in data every day. It shapes our decisions, informs our perspectives, and drives much of modern life. Often, we wish for more data; rarely do we wish for less.

Yet there are moments when all we have is a single datapoint. And what can we do with just one? One datapoint offers almost nothing. It is isolated, contextless, and inert—a fragment of information without relationship or meaning. One datapoint might as well be no datapoint.

But two datapoints? That’s transformative. Moving from one to two is not just an incremental improvement; it is a fundamental shift. Your dataset has doubled in size, a 100% increase. More importantly, with two datapoints, you can begin to make connections. You can compare and combine, correlate and coordinate.

From Isolation to Interaction

Consider the possibilities unlocked by having two datapoints rather than one. A single name—first or last—is practically useless; it cannot identify a person. But a full name—two datapoints—suddenly carries weight. It situates someone in a specific context, distinguishing them from others and enabling meaningful identification.

The same holds true for testimony. A single witness to a crime might not provide enough perspective to reconstruct what happened. Their account could be unreliable, incomplete, or subjective. But with two witnesses, we gain a second perspective. Their testimonies can corroborate or contradict each other, offering a deeper understanding of the event.

Or think about computation. A solitary binary digit—0 or 1—cannot do much. It is a static state. But introduce a second binary digit, and the world changes. With two bits, you unlock four possible combinations (00, 01, 10, 11), the foundation of all logical computation. Every computer, no matter how powerful, builds its intricate systems of thought from this basic doubling.

The Exponential Power of Pairing

Why is the shift from one to two so significant? It is not simply the doubling of data, but the transition from isolation to interaction. A single datapoint cannot create relationships, patterns, or meaning. It is static. Two datapoints, however, introduce dynamics. They allow for comparison and combination, for movement between states, for a framework within which meaning can emerge.

This leap—from one to two—is the smallest step toward creating systems of knowledge. Science relies on comparisons to establish causality. A single experimental result is meaningless without a control group to measure it against. Literature and language depend on dualities—protagonist and antagonist, question and answer, speaker and audience. Even human vision is based on the comparison of binocular inputs, it is our two eyes that allow us to see depth.

AI and the Power of Two

The transformative power of n=2 is most recently demonstrated in the operation of generative AI. At its core, generative AI depends on the interaction of two distinct but interdependent datasets: the training data and the user’s prompt. The training data serves as the foundation—a vast repository of language patterns, structures, and examples amassed from diverse sources. This data alone, however, is inert; it is an immense collection of information without activation or direction. Similarly, a prompt—a fragment of input text provided by a user—is meaningless without context. It is a solitary datapoint, incapable of producing anything on its own.

When these two datasets combine, however, the true power of AI is unlocked. The training data provides a rich, multidimensional context, while the prompt activates specific pathways within that context, directing the AI to generate meaningful output. This dynamic interaction transforms static data into a creative process. Much like the leap from one to two datapoints, the relationship between the training data and the prompt enables the emergence of patterns, coherence, and utility. Without the prompt, the AI remains silent; without the training data, the prompt is purposeless. Together, they form a system capable of producing complex and contextually relevant language.

This relationship between training data and prompts underscores the profound significance of pairing, the power of n=2. The interaction between these two elements mirrors a broader principle: meaning arises not from isolation, but from connection. Just as two witnesses can construct a fuller account of an event, and two binary digits can enable computation, the union of training data and prompts enables AI to simulate human-like language and reasoning, creating systems that are both dynamic and generative. The leap from one to two here is not just a quantitative doubling—it is a qualitative transformation that makes the impossible possible.

Building Toward Complexity

Two is not the end point; it is the beginning. Once we have two datapoints, we can imagine three, then four, and so on, building increasingly complex systems. But we should not overlook the profound importance of the leap from one to two. It is the first and most crucial step toward understanding—toward the ability to identify patterns, make connections, and draw conclusions.

N=2 is the minimum threshold for meaning, the simplest structure capable of supporting complexity. From two datapoints, entire worlds of logic, creativity, and understanding can unfold.

The sum of everything

Do you all ever think about infinity? It’s one of those things unique to human cognition and thus sort of unavoidable, like object permanence or episodic foresight. We are forced to confront the infinite as a matter of course. Yet to ponder the infinite is paradoxical, for thinking of it limits the limitless.

The concept of infinity comes out of mathematics of course, but I think it transcends the disciplinary borders typically ascribed to it. Infinity has more in common with faith and religion than math. The infinite and God both contain similar qualities of omnipotence, and like the ontological argument for the existence of God, if we can conceive of infinity in our minds–a watered down version–then it must exist in a purer form elsewhere. To imagine the infinite implies that an even more infinite infinity exists outside of us.

Outside of math class, infinity is historically contingent, repackaged by different cultures to reflect the specific historical conditions surrounding them. In Ancient Greece, when thinkers were just beginning to grapple with the concept, infinity was first inferred from the banal. The infinite presented itself in such mundane tasks as walking from point A to B, a distance with infinite halfway points between, or in the shapeless water of a river, infinitely turning in on itself so that one can “never step in the same river twice.”

For us today, the infinite reveals itself in myriad other ways, consumer choices chief among them. I often find myself mindlessly scrolling through Netflix’s seemingly infinite offerings, squandering two hours of my day. I am similarly paralyzed by the infinite consumer choices aggregated on Amazon or on display at grocery stores, so much so I often don’t purchase whatever it was I needed in the first place. I also experience a flavor of the infinite when I think about voting. While election votes are not technically infinite, there are enough of them relative to the one of mine that political outcomes feel infinitely distant and detached from my singular blue vote cast in a red state, a snowflake in an avalanche as a popular analogy goes.

While there are important mathematical operations involving infinity–I mean, it’s a crucial part of calculus, after all–I think infinity has more impact conceptually than arithmetically. The infinite is, in other words, more rhetorical than numerical. Like a drinking glass, it gives shape to the aqueous nature of existing in an infinitely expanding and timeless universe; it names a sensation commonly felt among individuals living infinitely singular lives in a godless world of billions. Many abstractions short circuit our cognitive console, but naming them cools us down. We can’t really experience the purely infinite, but we can name it. We can know it’s out there.

Knowing something exists is a prerequisite for ignoring it. And maybe it’s time to start ignoring the infinite. Calculus has taught us many things, but perhaps most importantly it resolves part of infinity’s paradoxical nature. We now know that the infinite is only one side of the equation. You can divide a number in half infinitely, but add all those divisions up and you get back to the whole number you started with. In our culture and our politics and our lives, we are too fixated on one side of the equation—the side with infinite divisions. The other side remains a self contained unit, a finite value that the infinitesimally small divisions must add up to, even if there are an infinite number of them. I think we all stand to benefit from a greater focus on the whole rather than the infinitely divided parts.