Core thesis
Morphological similarity, statistical correlation, functional equivalence, and causal linkage are often conflated in everyday language—but scientific reasoning demands they be strictly distinguished. Carcinization is nature's most vivid textbook on this trap.
Key points
- Carcinization: The term was coined in 1916 by zoologist Lancelot Alexander Borradaile. Research confirms that crab-like body plans evolved independently at least 5 times in decapod crustaceans:
- True crabs (Brachyura) — naturally crab-shaped
- Anomura (hermit crab relatives) — tails folded and flattened into crab form
- Porcelain crabs (Porcellanidae) — flattened from squat lobster morphology
- King crabs (Lithodidae) — widened and flattened from lobster-like bodies
- Coconut crabs (Birgus latro) — terrestrial hermit crabs that abandoned shells
- Their last common ancestor lived ~250 million years ago and did not look like a crab. Similar form arose from completely different evolutionary paths.
- The crab shape is an engineering optimum for benthic niches: flat wide body for defense and hiding in crevices, folded abdomen reducing vulnerable surface area, versatile strong claws, and fast bidirectional sideways escape. This is convergent evolution, not shared design or kinship.
- True crabs show 4 pairs of visible walking legs; Anomuran "fake crabs" show only 3 (the fourth pair is hidden), and their genomes place them closer to hermit crabs.
- Computer vision: adversarial examples—near-identical images (human perceptual similarity) with completely different model outputs.
- Economics: spurious correlations (pirates vs. global warming; Nicolas Cage films vs. pool drownings)—shared time trends without causal mechanisms.
- Neuroscience: humans and octopuses both evolved camera eyes, but with inverted vs. everted retinal layouts—similar function, different developmental paths.
- AI: whether emergence in large models reflects a genuine phase transition or an artifact of discrete evaluation metrics; similar capability curves don't imply the same underlying mechanism.
- Morphological similarity ≠ close kinship (carcinization)
- Matrix similarity ≠ functional equivalence (QKV)
- Statistical correlation ≠ causal mechanism (everywhere)
- Borradaile, L.A. (1916). "Notes on Carcinization." *Proceedings of the General Meetings for Scientific Business of the Zoological Society of London*.
- McLaughlin & Lemaitre (1997). "Carcinization in the Anomura – fact or fiction?"
- Wolfe et al. (2021). "How to Become a Crab: Phenotypic Constraints on a Recurring Body Plan."
- Pearl, J. (2009). *Causality: Models, Reasoning, and Inference*.
- Yule, G.U. (1903). "Notes on the Theory of Association of Attributes in Statistics."
The methodological triad
1. Similarity — "looks alike": descriptive, no mechanism (crab vs. porcelain crab; K/V projection matrices with cosine similarity 0.73; ice cream sales and drowning both rise with temperature). 2. Correlation — "vary together": statistical, no direction or mechanism. 3. Causation — "one produces the other": mechanistic, requires interventional verification.
The classic pitfall is the Yule-Simpson paradox: a drug works for men and for women separately but not overall, because sex is a confounder. Analogously, observing that claws correlate with benthic life doesn't mean either causes the other—both were jointly selected by environmental pressure.
Application to a QKV paper
Referenced paper: Do Transformers Need Three Projections? Systematic Study of QKV Variants
| Level | Carcinization | QKV paper | |---|---|---| | Observed similarity | Different species share crab form | K and V matrices similarity 0.73 | | Implicit assumption | Similar form = close kinship | Similar matrices = interchangeable function | | Actual relation | Similar form, different origins | Similar matrices, different roles (addressing vs. payload) | | Correct conclusion | Convergent evolution toward an optimum | Possibly low-rank constraints + network compensation enable sharing | | Wrong conclusion | "They're all crabs, so they're related" | "K ≈ V, so V is redundant" |
The paper's inferential chain—similarity observed → shared representation assumed → K=V experiments show small loss → independent V projection unnecessary—has a gap between steps 2 and 3. The small loss could instead reflect: 1. FFN compensation for information loss 2. Low-rank structure of self-attention allowing information overflow 3. Tasks insensitive to K/V separation
These support only "K=V is tolerable in this specific architecture/task," not "K and V are functionally equivalent."
Similarity traps elsewhere
How to avoid "carcinization thinking"
1. Ask for mechanisms, not just descriptions: Why are K and V similar—low-rank information or task properties? Under what conditions would sharing fail? 2. Distinguish "can" from "should": Small experimental loss shows compensation was found under specific constraints, not that independent projections were unnecessary in principle. 3. Seek counterexamples and boundary conditions: Convergent evolution only occurs in specific niches—crab form is not optimal in hydrothermal vents or open water. Similarly: does K=V work in cross-attention where K and V come from different inputs? In precision-retrieval tasks? 4. Accept "I don't know": The honest statement is that K=V sharing with small loss is an empirical finding, not theoretical insight, absent formal proof of functional equivalence.
Conclusion
Similarity is the most observable feature in both natural and artificial systems—and the most misleading:
Real scientific inference must move past the surface of similarity to ask: Why similar? Under what conditions? Does similarity imply interchangeability? Does dissimilarity imply infeasibility?
> Nature's warning to scientists: don't assume everything you see that looks like a crab belongs to the same family.