Every classification system you have built so far has a hidden assumption: one dimension is enough.
The previous lesson (L-0237) explored boundary cases — items that resist fitting neatly into any single category. Those boundary cases expose weaknesses in your classification system. But there is a different kind of classification failure that boundary cases do not reveal. It happens when every item fits its category perfectly and the system still cannot answer the questions you need answered. The problem is not that your categories are wrong. The problem is that you have only one set of them.
A single classification dimension is like a single axis on a graph. It organizes items along one line. But most real collections of items vary along multiple independent dimensions simultaneously. A book has a genre, a publication date, a reading difficulty, a language, and a subject matter. A person has a profession, a nationality, an age cohort, an expertise level, and a set of interests. A task has a priority, a status, an owner, a deadline, and a project affiliation. Classifying along any single dimension collapses the others into invisibility. Cross-cutting categories restore them.
This lesson is about the principle and practice of classifying the same items along multiple independent dimensions — and why this seemingly simple idea has transformed fields from library science to social psychology to database engineering to personal knowledge management.
Ranganathan's revolution: classification has facets
The modern understanding of cross-cutting categories begins with S. R. Ranganathan, an Indian mathematician and librarian who, between 1924 and 1933, developed the Colon Classification — the first faceted classification system. Before Ranganathan, library classification systems like Dewey Decimal and the Library of Congress treated each book as belonging to a single class. A book about the economics of rice farming in India would be shoved into one slot: economics, or agriculture, or India. The slot you chose determined which questions the catalog could answer and which it could not.
Ranganathan saw the fundamental flaw. A subject is not a single thing. It is a composite of independent facets that can be analyzed separately and recombined. He identified five fundamental facets using the acronym PMEST: Personality (the core entity or focal subject), Matter (the material, substance, or properties), Energy (the processes, operations, or activities), Space (the geographic location), and Time (the temporal period). These facets are arranged in decreasing order of concreteness — from the most specific aspect of a subject to the most general (Ranganathan, 1933).
In Ranganathan's system, a book about rice cultivation techniques in India during the 1950s is not filed under one heading. It is analyzed into its facets: Personality = rice, Matter = cultivation, Energy = techniques, Space = India, Time = 1950s. Each facet is independent. You can search for all books about rice (regardless of place or time), all books about India (regardless of subject), or all books about cultivation techniques (regardless of crop or location). The colons in Colon Classification literally separate the facets, allowing them to be recombined.
The significance is not the specific system — Colon Classification itself was complex and never achieved wide adoption. The significance is the principle: any single classification dimension is a projection that collapses other dimensions. To classify without loss, you need facets — multiple independent dimensions applied to the same items simultaneously.
This principle has become ubiquitous, even if Ranganathan's name has not. Every time you use a filter sidebar on an e-commerce website — narrowing by brand, price range, color, size, customer rating — you are using faceted classification. Amazon was one of the early pioneers of faceted search, and today it is a standard feature of virtually every e-commerce platform. The left sidebar of an Amazon search is Ranganathan's PMEST in commercial form: multiple independent dimensions, each with its own values, combinable in any configuration. A laptop can be simultaneously categorized as Dell (brand), $500-$1000 (price), 16GB (RAM), 15-inch (screen), and 4+ stars (rating). No single-dimension filing system could support this.
Cross-cutting cleavages: when overlapping categories reduce conflict
The power of cross-cutting categories extends far beyond organizing libraries and products. In political science, the concept of cross-cutting cleavages describes a phenomenon where overlapping group memberships reduce the intensity of conflict between groups.
A cleavage is a division that splits a society into opposing groups: rich versus poor, urban versus rural, religious versus secular, ethnic majority versus minority. When cleavages are reinforcing — when the same people are always on the same side of every divide — conflict intensifies. If every poor person is also rural, also a religious minority, and also from the same ethnic group, every political issue becomes a proxy war between two monolithic blocs. But when cleavages cross-cut — when your economic ally is your religious opponent, and your ethnic kinsman is your political adversary — the intensity of any single conflict is dampened, because attacking your opponent on one dimension means attacking your ally on another.
Seymour Martin Lipset, in his 1960 book Political Man, provided an in-depth analysis of this mechanism. Lipset and Stein Rokkan's subsequent 1967 analysis in Party Systems and Voter Alignments demonstrated that societal cleavages arising from historical turning points crystallized into stable party systems, with cross-cutting variants serving to stabilize democracies. The mechanism is straightforward: cross-cutting cleavages create sympathies for differing arguments and improve communication across divisions, increasing the likelihood of conciliation rather than escalation (Lipset & Rokkan, 1967).
The epistemological lesson is precise: how you categorize people determines whether you see them as allies or enemies. If you classify colleagues only by department, then every resource allocation decision is Engineering versus Marketing versus Sales. But if you add cross-cutting categories — project team membership, expertise area, seniority level, office location — the same people who are rivals in one dimension become collaborators in another. Cross-cutting categories do not just organize more accurately. They structurally reduce the polarization that single-dimension classification creates.
Intersectionality: where cross-cutting categories create unique positions
In 1989, legal scholar Kimberle Crenshaw introduced the concept of intersectionality in her paper "Demarginalizing the Intersection of Race and Sex." Her argument was that existing legal and theoretical frameworks treated race and gender as separate, independent categories — and that this separation made the specific experiences of Black women invisible. A discrimination claim based on race was calibrated to the experiences of Black men. A discrimination claim based on gender was calibrated to the experiences of white women. Black women, positioned at the intersection of both categories, found that neither framework captured their reality (Crenshaw, 1989).
Intersectionality is, at its core, a claim about cross-cutting categories. The categories of race and gender are not parallel tracks that can be analyzed independently and then summed. They interact. The experience of being classified simultaneously as Black and as a woman is not "the Black experience" plus "the woman experience." It is a distinct position created by the intersection — a position that single-dimension analysis cannot detect.
For classification practice, the lesson is subtle but crucial: cross-cutting categories do not merely multiply the number of views you can take. They create emergent positions at the intersections that have properties not predictable from any single dimension. When you classify your notes by both topic and project, the notes that sit at the intersection of "machine learning" and "hiring process" form a category — AI-assisted hiring — that might never have appeared in either single-dimension view. The intersection is not just a filter. It is a site of discovery.
Database design: the architecture of cross-cutting classification
Software engineers encounter cross-cutting categories as one of the first structural problems in database design. The problem has a precise technical form: the many-to-many relationship.
Consider a database tracking books and authors. A book can have multiple authors, and an author can write multiple books. This is a many-to-many relationship — it cannot be represented by putting an "author" field in the books table or a "book" field in the authors table. The solution, fundamental to relational database design, is a junction table (also called a bridge table or associative table) that contains pairs of foreign keys: one pointing to a book, one pointing to an author. Each row in the junction table represents one instance of the relationship "this author contributed to this book."
This is cross-cutting classification implemented in data structures. The books table classifies books by their intrinsic properties (title, ISBN, publication date). The authors table classifies authors by theirs (name, birth year, nationality). The junction table classifies the relationship between them — and it allows each entity to participate in arbitrarily many relationships without being forced into a single category.
Database normalization — the systematic process of eliminating redundancy and ensuring data integrity — is, in this light, a discipline for properly separating cross-cutting dimensions. First Normal Form requires that each column contain atomic values (no lists hiding multiple category memberships in a single field). Third Normal Form requires that every non-key attribute depends on the key, the whole key, and nothing but the key — which means each dimension is stored independently, not tangled with others. When you normalize a database, you are doing what Ranganathan did for library classification: separating independent dimensions so they can be queried independently and recombined as needed.
The anti-pattern — denormalization, or collapsing multiple dimensions into a single flat structure for performance or convenience — trades classification power for speed. A denormalized table that stores "author_name" directly in the books table is faster to read but cannot cleanly answer "which authors have written books in both physics and poetry?" That question requires the cross-cutting structure that denormalization destroyed.
Tags versus folders: the everyday cross-cutting dilemma
For most people, the most visceral encounter with cross-cutting categories happens in personal knowledge management. It is the tags-versus-folders debate, and it is a direct instantiation of the tension between single-dimension and multi-dimensional classification.
A folder hierarchy is a tree. Each item lives in exactly one location. You file a note about "hiring best practices" under either "Management" or "HR Processes" or "Recruiting." The moment you file it, every other organizational dimension collapses. You can find it by navigating to the folder you chose. You cannot find it by navigating to any of the folders you did not choose.
Tags are cross-cutting categories. The same note can be tagged #management, #hiring, #best-practices, and #interview-process. Each tag is an independent dimension. You can retrieve the note from any of those dimensions, and you can combine them: "show me everything tagged both #hiring and #best-practices." Tags implement Ranganathan's facets for personal notes.
Tiago Forte, who developed the PARA system (Projects, Areas, Resources, Archives), originally criticized tags as too taxing and low-value relative to their maintenance cost. His system uses a folder hierarchy with four categories organized by actionability rather than topic. But Forte's more recent work acknowledges the value of tags when used strategically — specifically as cross-cutting connections within a folder-based structure. The insight is not that tags replace folders. It is that tags add dimensions that folders cannot provide (Forte, 2022).
Nick Milo's approach, using Maps of Content (MOCs) within the Linking Your Thinking framework, offers a different solution to the same problem. Rather than tags or folders, Milo uses curated index notes that pull together links to related content — creating navigational layers that function like cross-cutting categories without requiring formal tagging infrastructure. A Map of Content for "Decision Making" might link to notes that live in completely different folder locations, creating a cross-cutting view through manual curation rather than automated filtering.
The mature position in the tags-versus-folders debate is not either/or. It is recognizing that folders provide one classification dimension and tags provide additional cross-cutting dimensions, and that the right architecture depends on how many dimensions you actually need. If you only ever retrieve notes by topic, a folder hierarchy is sufficient and simpler. If you regularly need to answer questions that cut across topics — "what did I write about decision-making in the context of hiring?" — you need cross-cutting categories, whether implemented as tags, links, metadata fields, or Maps of Content.
How many dimensions do you actually need?
The principle of cross-cutting categories is powerful, but it carries a cost. Every additional dimension requires maintenance. Every item must be classified not once but N times, where N is the number of active dimensions. The combinatorial explosion is real: 5 values on each of 4 dimensions produces 625 possible intersections. If most of those intersections are empty, the classification system is generating complexity without generating insight.
The pragmatic question is: how many dimensions does a given collection actually require?
The answer depends on how many fundamentally different questions you need to ask of the collection. If you only ever need to ask "what topic is this about?", one dimension suffices. If you also need "when did I create this?" and "what project is this for?" and "how confident am I in this?", you need four dimensions. The test for each candidate dimension is simple: does this dimension enable a question I actually ask and cannot currently answer? If yes, add it. If no, it is noise.
In practice, most collections benefit from two to four cross-cutting dimensions. Beyond four, the maintenance cost typically exceeds the retrieval benefit. This is not a universal law — a well-designed database can support dozens of dimensions because the maintenance is automated. But for human-maintained systems like personal note collections, task managers, and classification frameworks, the sweet spot is usually:
- A primary organizational dimension (topic, project, or type — the thing that determines where the item "lives")
- A status or lifecycle dimension (draft, active, archived, completed — the thing that tracks where the item is in its journey)
- One to two context dimensions (source, audience, urgency, confidence level — the things that answer cross-cutting questions you frequently ask)
Ranganathan needed five facets because he was classifying all human knowledge. You probably do not need five. But you almost certainly need more than one.
AI and the Third Brain: multi-label classification
The AI parallel to cross-cutting categories is multi-label classification — one of the fundamental problem types in machine learning.
In standard (multiclass) classification, an AI model assigns each input to exactly one category. An email is spam or not-spam. An image contains a cat, a dog, or a bird. Each input gets one label. This is the folder model: mutually exclusive, single-dimension.
In multi-label classification, each input can receive multiple labels simultaneously. A movie is tagged as both "science fiction" and "romance." A medical image is flagged for both "fracture" and "soft tissue damage." A news article is classified as "politics," "economics," and "international." The labels are not mutually exclusive. This is the tag model: cross-cutting, multi-dimensional.
Multi-label classification is technically harder than single-label. The model must learn not just which labels apply but which combinations of labels co-occur — because the presence of one label may change the probability of another. A movie tagged "animation" is more likely to also be tagged "family" than "horror." These label dependencies are the machine-learning equivalent of intersectionality: the labels interact, and the interactions carry information that the individual labels do not.
For your Third Brain practice, the multi-label pattern matters because it mirrors how AI tools process and retrieve your externalized knowledge. When you ask an AI assistant to "find my notes about hiring that relate to decision-making frameworks," you are issuing a multi-label query. The AI's ability to answer depends on whether your notes have been classified along the dimensions the query invokes. If your notes have only a topic tag, the AI can find "hiring" notes but cannot filter for the "decision-making" subset. Cross-cutting categories in your personal system give AI better retrieval surfaces — more ways to match a query to the right items.
This extends to how large language models themselves organize knowledge internally. Transformer architectures represent concepts as high-dimensional vectors — positions in a space with hundreds or thousands of dimensions. A word like "bank" occupies a position that encodes its financial meaning, its river meaning, and dozens of other contextual facets simultaneously. The model does not file "bank" into one folder. It positions "bank" in a multi-dimensional space where different dimensions encode different facets of meaning. This is cross-cutting classification at the level of representation itself.
The practical implication: when you build your externalized knowledge system, structure it the way both human cognition and AI retrieval actually work — not as a single hierarchy, but as a multi-dimensional space where items can be found from any relevant angle.
The protocol: adding cross-cutting dimensions to an existing system
Here is a practical method for introducing cross-cutting categories to a classification system you already use:
Step 1: Identify the question you cannot answer. You have a system. It works for certain queries. What query does it fail on? "Show me all the notes I wrote about Topic X in the context of Project Y." "Which of my tasks are both urgent and related to client Z?" The unanswerable question reveals the missing dimension.
Step 2: Name the missing dimension. The question "which tasks relate to client Z?" implies a dimension: client association. The question "which notes were written in the context of Project Y?" implies a dimension: project context. Name it explicitly.
Step 3: Define the values. What are the possible values along this new dimension? Keep the value set small — ideally 3-7 values to start. You can always add values later. You cannot easily remove them once items have been classified.
Step 4: Classify existing items. This is the expensive step. Go through your existing collection and assign each item a value on the new dimension. If this feels too burdensome, classify only new items going forward — the historical collection will gradually become the minority as new items accumulate.
Step 5: Test cross-cutting queries. Combine the new dimension with the existing one. Do the results answer the question from Step 1? Do they reveal unexpected patterns? If the cross-cutting view generates no insight, the dimension may not be worth maintaining.
Step 6: Evaluate maintenance cost. After two weeks of maintaining the new dimension, assess: is the ongoing classification effort sustainable? Does the retrieval benefit justify it? A dimension that is useful but unsustainable is worse than no dimension at all, because inconsistent classification generates false confidence in query results.
The bridge to compression
Cross-cutting categories add richness to classification. The next lesson (L-0239) introduces a counterbalancing force: every classification system is a compression technique, and compression means deliberately discarding information. Cross-cutting dimensions add information. Compression removes it. The tension between these two forces — between multi-dimensional richness and the cognitive cost of maintaining it — is the central design challenge of every classification system you will ever build.
The question is never "how many dimensions can I add?" It is "which dimensions earn their maintenance cost?"
Sources:
- Ranganathan, S. R. (1933). Colon Classification. Madras: Madras Library Association.
- Lipset, S. M. (1960). Political Man: The Social Bases of Politics. Garden City, NY: Doubleday.
- Lipset, S. M., & Rokkan, S. (1967). "Cleavage Structures, Party Systems, and Voter Alignments." In Party Systems and Voter Alignments: Cross-National Perspectives. New York: Free Press.
- Crenshaw, K. (1989). "Demarginalizing the Intersection of Race and Sex: A Black Feminist Critique of Antidiscrimination Doctrine, Feminist Theory, and Antiracist Politics." University of Chicago Legal Forum, 1989(1), Article 8.
- Allport, G. W. (1954). The Nature of Prejudice. Reading, MA: Addison-Wesley.
- Forte, T. (2022). Building a Second Brain: A Proven Method to Organize Your Digital Life and Unlock Your Creative Potential. New York: Atria Books.
- Tsoumakas, G., & Katakis, I. (2007). "Multi-label Classification: An Overview." International Journal of Data Warehousing and Mining, 3(3), 1-13.