The ideas you need are already connected. You just can't see the path.
You know things that, combined, would produce insights you've never had. The connection between behavioral economics and evolutionary biology exists in your knowledge — loss aversion maps to threat detection maps to survival heuristics. But you've never traced that chain, so the relationship stays invisible. Two clusters of hard-won understanding sit three hops apart, and you treat them as unrelated fields.
This is not a storage problem. You have the nodes. You have the edges. What you lack is traversal — the act of finding the shortest route between two ideas and examining what that route reveals.
The shortest path between two seemingly unrelated concepts is one of the most powerful operations you can perform on your own knowledge. It doesn't add new information. It reveals structure that was already there.
The algorithm that changed how we think about connection
In 1956, Edsger Dijkstra sat at a cafe terrace in Amsterdam with his fiancee and, in roughly twenty minutes, designed an algorithm for finding the shortest path between two nodes in a graph. Published in 1959 as "A Note on Two Problems in Connexion with Graphs," the algorithm became foundational to computer science — used today in GPS navigation, network routing protocols, and social network analysis.
Dijkstra's insight was deceptively simple: start at one node, explore all immediate neighbors, then explore their neighbors, always tracking the cheapest cumulative cost. The algorithm guarantees you find the shortest path, not by searching every possible route, but by expanding outward intelligently — always extending the shortest known partial path first.
This matters for personal knowledge because your graph has the same structure. Every concept you understand is a node. Every relationship you've recognized is an edge. And between any two nodes, there exists a shortest path — the minimal chain of relationships that connects them. You don't need to discover new knowledge to find it. You need to traverse what you already have.
Six degrees of separation is a shortest-path finding
In 1967, psychologist Stanley Milgram at Harvard ran an experiment that became one of the most cited studies in social science. He asked people in Nebraska and Kansas to get a letter to a target person in Boston by forwarding it to someone they knew on a first-name basis, who would forward it to someone they knew, and so on.
Among the chains that reached the target, the average path length was about five and a half intermediaries. Milgram never actually used the phrase "six degrees of separation" — playwright John Guare later popularized it — but the finding was remarkable: in a country of 200 million people, any two individuals were connected by roughly six handshakes.
In 2011, Facebook and the University of Milan formalized this with data. Analyzing the entire Facebook network — 721 million active users and 69 billion friendship links — Lars Backstrom, Johan Ugander, and colleagues found that the average distance between any two users was 4.74 hops. By 2016, with 1.6 billion users, it had dropped to 4.57. They titled the paper "Four Degrees of Separation."
The shrinking number illustrates something important: as networks grow denser, shortest paths get shorter. The same principle applies to your knowledge graph. Every new concept you add, every new relationship you notice, potentially shortens the path between previously distant ideas. The graph gets more connected, and hidden connections get easier to find.
Small worlds: why short paths exist everywhere
In 1998, Duncan Watts and Steven Strogatz published a landmark paper in Nature that explained why shortest paths tend to be short in real networks. Their finding: most networks are "small worlds" — highly clustered locally (your friends tend to know each other) yet connected globally by a few long-range links.
Take a regular network — imagine people standing in a circle, each connected only to their nearest neighbors. Path lengths are long because you have to traverse the entire circumference. Now randomly rewire just a small fraction of those connections — maybe 1% — to connect to distant nodes. Path lengths collapse dramatically. A handful of shortcuts transform a large, locally-clustered network into one where everything is close to everything.
Your knowledge graph has this structure. You have dense local clusters — the concepts within a single domain are tightly interconnected. And you have a few bridge concepts that span domains. Those bridges are your long-range links. They're the reason a seemingly impossible connection between, say, music theory and protein folding might be only three hops away.
The implication: short paths between distant ideas are not lucky accidents. They're a structural property of how knowledge organizes itself. If your graph has any cross-domain connections at all, short paths probably exist between far more pairs of ideas than you suspect.
Undiscovered public knowledge: paths nobody has walked
The most striking demonstration of shortest-path discovery in knowledge comes from Don Swanson, an information scientist at the University of Chicago. In 1986, Swanson published "Fish Oil, Raynaud's Syndrome, and Undiscovered Public Knowledge" — a paper that connected two completely separate bodies of medical literature.
One body of research established that patients with Raynaud's disease had abnormally high blood viscosity. A separate body of research established that dietary fish oil reduces blood viscosity. Neither literature cited the other. No paper in the fish-oil corpus mentioned Raynaud's. No paper in the Raynaud's corpus mentioned fish oil. The two fields were, in graph terms, disconnected components as far as their citation networks were concerned.
But Swanson found the path: Raynaud's disease maps to high blood viscosity maps to fish oil's blood-thinning properties. Two hops. The connection was latent in the published literature — public, available to anyone — yet nobody had traversed it. Subsequent clinical studies confirmed the hypothesis: fish oil does help with Raynaud's syndrome.
Swanson called this undiscovered public knowledge: information that is publicly available yet functionally invisible because the intermediate connections have never been made explicit. His work became the foundation of an entire field — literature-based discovery — and it is fundamentally a shortest-path problem. The knowledge existed. The edges existed. Nobody had walked the path.
Your personal knowledge graph contains your own undiscovered public knowledge. Ideas you've learned, connections that are latent, insights waiting for someone to trace the route from A to B through C.
The Erdos number: measuring intellectual distance
Mathematicians have a concrete and playful version of shortest-path thinking: the Erdos number. Paul Erdos, the prolific Hungarian mathematician who authored papers with over 500 collaborators, sits at the center of a collaboration graph. If you co-authored a paper with Erdos, your Erdos number is 1. If you co-authored with someone who co-authored with Erdos, your number is 2. And so on.
The median Erdos number of Fields Medalists — the highest honor in mathematics — is 3. This means that the greatest mathematical minds of the past century are typically only three collaboration-hops from a single individual.
The Erdos number is a shortest-path metric applied to intellectual collaboration, and it reveals something about how knowledge propagates. Ideas don't spread uniformly. They travel along paths of collaboration, mentorship, and shared interest. The structure of those paths determines what insights are available to whom — and how quickly breakthroughs in one subfield reach another.
In your own knowledge graph, some ideas have a low "Erdos number" relative to your core expertise — they're closely connected through multiple paths. Others sit at the periphery, connected by a single fragile chain. Knowing the distance between concepts tells you something about where your understanding is robust and where it's tenuous.
How your brain already does this (and why it fails)
Cognitive scientists have studied the mechanism by which humans connect distant concepts, and it maps closely to shortest-path traversal. Dedre Gentner's structure mapping theory (1983) describes how analogical reasoning works: when you notice that two situations share relational structure — not surface features, but the pattern of relationships between elements — you're effectively discovering a path between distant nodes.
The crucial finding from Gentner's research: the most creative analogies come from distant domains. Surface-similar comparisons (this startup is like that startup) produce obvious conclusions. Structurally similar but surface-distant comparisons (this startup's growth pattern resembles how epidemics spread) produce genuine insight. The shortest path between distant nodes traverses through abstract structural relationships, and that traversal is where creative thinking lives.
But the brain has limits. Without externalization, you can only traverse paths that fit within working memory's 3-to-5 item constraint (as established in earlier lessons). You start at node A, hold a few intermediate nodes, and lose track of the chain before reaching node B. This is why people feel that two ideas are "somehow connected" but can't articulate the connection — they've sensed a short path without being able to walk it.
A written knowledge graph solves this. Each intermediate node is externalized. The path is visible. You can trace it, examine it, and ask whether each hop is valid. The graph holds the traversal state that your working memory cannot.
AI path-finding: scaling what Swanson did by hand
What Swanson did manually with medical literature in 1986, AI systems now do at scale with knowledge graphs. In 2024, researchers at MIT developed SciAgents — a framework that uses large language models combined with ontological knowledge graphs to find hidden connections across scientific literature. The system works by sampling paths through a graph built from research papers, identifying structural parallels between concepts from different domains.
One of the most striking results came from Markus Buehler's work: an AI system analyzed 1,000 scientific papers on biological materials and used graph-based reasoning to discover deep parallels between biological structures and musical compositions. The connection — that certain protein folding patterns share structural properties with musical harmonic progressions — was found through path traversal across a knowledge graph. No single paper contained this insight. It emerged from the graph's structure.
This is Swanson's undiscovered public knowledge at machine scale. And it works the same way in your personal system. When you build a knowledge graph with typed, explicit connections, you create a substrate that supports path-finding — whether done by your own traversal, a graph visualization tool, or an AI system that can explore paths you'd never think to walk.
The practice: finding paths in your own graph
Shortest-path thinking becomes a concrete practice when you apply it deliberately:
When two ideas feel disconnected, search for intermediate nodes. Don't accept "these are different fields" as a conclusion. Ask: what concept belongs to both domains? What mechanism, principle, or pattern could serve as a bridge? The intermediate node is where the insight lives.
When you find a path, examine each edge. A shortest path of three hops contains two intermediate connections. Each connection is a claim — "A relates to B because of X." Make those claims explicit. Some will be strong (well-established relationships). Some will be weak (speculative associations). The weak links are where further learning or investigation is needed.
When a path surprises you, explore alternate routes. The shortest path is the most direct connection, but alternate paths through different intermediaries can reveal different facets of the relationship. If behavioral economics connects to evolutionary biology through threat detection, does it also connect through signaling theory? Through game theory? Each alternate path is a different lens on the same relationship.
When you add a new node, check what paths it creates. Every new concept in your graph potentially connects previously distant clusters. After adding a new idea, ask: what does this now connect that wasn't connected before? The answer often reveals the idea's deepest value — not its content in isolation, but the bridges it builds.
What this makes possible
When you develop the habit of finding shortest paths through your knowledge, something shifts in how you think about learning itself. New information stops being isolated facts to file and starts being potential connectors — bridge nodes that might dramatically shorten the distance between clusters in your graph.
You begin to notice that the most valuable concepts are often not the most detailed or the most novel, but the ones that connect the most distant parts of your existing knowledge. A single well-placed bridge node can transform your graph's topology, turning two isolated domains into a connected network where insights flow freely.
This is also why interdisciplinary thinkers tend to produce disproportionately creative work. They have more long-range connections in their knowledge graphs, which means shorter paths between a wider variety of ideas. The shortest path between "unrelated" fields, for them, is often only one or two hops — because they've already placed the bridge nodes.
As you trace these paths, you'll start to notice something else: clusters. The nodes that appear on many shortest paths — the ones that serve as waypoints between different regions of your graph — tend to group together in revealing ways. Those clusters tell you something about the structure of your knowledge that individual nodes never could. That's where we go next.