Similarity Is Closeness
metaphor
Source: Embodied Experience → Intellectual Inquiry
Categories: cognitive-sciencelinguisticsphilosophy
From: Master Metaphor List
Transfers
A primary metaphor grounded in the infant’s experience that things near each other in space tend to share properties. Objects close together are often of the same kind — the same shelf holds similar books, the same drawer holds similar utensils, members of the same family sit close at the table. This pervasive spatial-conceptual correlation establishes, long before language, the mapping: similar things are close; different things are far apart.
Key structural mappings:
- Degree of similarity is distance — “These two proposals are very close.” “Their positions are miles apart.” “The translation is close to the original.” The mapping provides a continuous metric: things can be more or less similar by being closer or farther away. This is not just a linguistic convenience; it is the foundation of how similarity is formalized in science.
- Comparison is measurement of distance — “How close are these two models?” “That’s a distant analogy.” “She’s trying to bridge the gap between theory and practice.” To compare is to gauge spatial proximity.
- Groups of similar things are clusters — “These ideas cluster together.” “There are two camps on this issue.” “They belong in the same neighborhood.” Conceptual grouping is spatial grouping.
- Becoming more similar is approaching — “Their views are converging.” “She’s coming around to his position.” “The two theories are moving closer together.” Change in similarity is change in position.
- Becoming more different is diverging — “Their paths have diverged.” “The two species drifted apart.” “She’s moved away from her earlier position.” Increasing difference is increasing distance.
The metaphor’s greatest triumph is its formalization. Multidimensional scaling, vector spaces, embedding models, and nearest-neighbor algorithms all take the metaphor literally: they place items in a geometric space where distance encodes similarity. Word2Vec, the ancestor of modern LLMs, is the container metaphor applied to words, but it runs on the similarity- is-closeness metaphor: similar words are nearby vectors.
Limits
- Similarity is multidimensional; distance is one number — two things can be similar in some respects and different in others. A whale and a fish are close in shape and habitat but far apart in physiology. The spatial metaphor forces a single distance metric when the reality is a complex profile of resemblances and differences. Multidimensional scaling tries to fix this by adding dimensions, but the underlying metaphor still reduces comparison to a point’s position in space.
- Closeness is symmetric; similarity often is not — in physical space, if A is close to B, then B is close to A. But similarity judgments are often asymmetric: people say North Korea is similar to China more readily than China is similar to North Korea. Tversky (1977) demonstrated this empirically, showing that the spatial metaphor misrepresents the psychology of comparison.
- The metaphor implies a fixed space — things are close or far in a pre-existing space with stable dimensions. But similarity is context- dependent: a cow and a chicken are similar in a conversation about farm animals but different in a conversation about flight. The metaphor provides no natural way to express that the “space” itself shifts with context. You have to posit a new space for each context, which defeats the simplicity the metaphor was supposed to provide.
- Closeness doesn’t handle structural similarity — two things can be structurally analogous (an atom and a solar system) without sharing any surface features. The spatial metaphor handles feature overlap well (things that look alike are close) but struggles with relational similarity (things that work alike). This is why analogy-making is hard to model with distance metrics alone.
- The metaphor makes similarity feel objective — distance is an objective measurement, and the metaphor imports this objectivity into similarity judgments. But what counts as similar is shaped by culture, expertise, and purpose. A sommelier and a casual drinker place wines at very different distances from each other. The metaphor provides no vocabulary for this observer-dependence.
- Clusters have sharp boundaries; similarity groupings do not — the spatial metaphor, combined with CATEGORIES ARE CONTAINERS, produces the notion that similar things fall into discrete clusters with gaps between them. But many similarity structures are continuous: there is no gap in color space between red and orange, between jazz and blues, between friendship and love. The metaphor imposes discontinuity on continua.
Expressions
- “These two ideas are close” — similarity as spatial proximity
- “That’s a far-fetched analogy” — weak similarity as great distance
- “Converging views” — increasing agreement as spatial approach
- “They’re miles apart on this issue” — disagreement as distance
- “A close reading” — careful analysis as getting spatially near the text
- “In the same ballpark” — approximate similarity as co-location
- “A near miss” — almost-matching as almost-touching
- “That’s a stretch” — forced similarity as extending across a distance
- “Closely related species” — taxonomic similarity as spatial proximity
- “Distant relatives” — weak kinship as spatial distance
- “The nearest equivalent” — the most similar thing as the closest object
Origin Story
Grady (1997) identified SIMILARITY IS CLOSENESS as a primary metaphor, grounded in the primary scene: objects near each other in the child’s environment tend to have similar properties. Things in the same pile, on the same shelf, in the same room are usually more alike than things far apart. This correlation between spatial proximity and shared properties is among the most reliable in early experience.
The metaphor has been spectacularly productive in science. When Shepard (1962) introduced multidimensional scaling — the technique of placing items in a geometric space such that distances reflect similarity judgments — he was not inventing a metaphor but formalizing one that was already implicit in everyday language. Tversky’s (1977) critique of geometric models of similarity was, in effect, a “Where It Breaks” analysis of this primary metaphor, showing that human similarity judgments violate the axioms of metric spaces (symmetry, triangle inequality, minimality).
Lakoff and Johnson (1999) gave the metaphor its canonical formulation. Its influence on computational science is hard to overstate: vector space models, embedding spaces, k-nearest-neighbors, cosine similarity — the entire apparatus of modern machine learning’s approach to meaning takes this metaphor literally and builds technology on it.
References
- Grady, J.E. Foundations of Meaning: Primary Metaphors and Primary Scenes (1997) — original identification as primary metaphor
- Lakoff, G. & Johnson, M. Philosophy in the Flesh (1999), p. 50 — canonical formulation
- Shepard, R.N. “The analysis of proximities” (1962) — multidimensional scaling as formalization of the metaphor
- Tversky, A. “Features of Similarity” (1977) — empirical demonstration that similarity violates metric axioms
Related Entries
Structural Neighbors
Entries from different domains that share structural shape. Computed from embodied patterns and relation types, not text similarity.
- Let Justice Be Done Though the Heavens Fall (/paradigm)
- Risk a Lot to Save a Lot (/mental-model)
- Silence Gives Consent (/paradigm)
- Time Is a Changer (causal-agent/metaphor)
- Logical Relations Are Causal Relations (causal-reasoning/metaphor)
- Butterfly Effect (dynamical-systems/metaphor)
- Paperclip Maximizer Is Alignment Failure (science-fiction/mental-model)
- Stretch It (food-and-cooking/metaphor)
Structural Tags
Patterns: forcescalepath
Relations: causetransform
Structure: hierarchy Level: primitive
Contributors: agent:metaphorex-miner