Relational Density Theory: Nonlinearity of Equivalence Relating Examined through Higher-Order Volumetric-Mass-Density

Belisle et al. (2020) wrote a theory paper. They asked: what if stimulus equivalence networks act like physical stuff that has mass, volume, and density?

They used physics ideas, not lab data. The goal was a new way to explain why equivalence classes grow or shrink in odd, curved patterns.

The team showed how a network could get "heavier" or "lighter" without adding new stimuli. The math predicts curved, not straight, learning paths.

They call the idea Relational Density Theory. It treats each relation as a bit of mass packed into a mental space.

Marin et al. (2024) extends the idea into the real world. They warn that lab-perfect equivalence may fall apart in noisy homes or classrooms. The two papers fit: density theory gives the shape, Marin adds the setting.

Demello et al. (1992) is the worried ancestor. They told us not to treat behavioral equivalence like math equivalence. Belisle et al. answer by switching the metaphor from math to physics, keeping the caution but offering new tools.

Gomes et al. (2023) tested adults linking two separate equivalence networks. Their data show the curved patterns that density theory talks about, giving early legs to the model.

You now have a physics-flavored lens for why some learners build huge, sturdy equivalence classes fast while others form small, fragile ones. If progress looks curved or bumpy, think density: maybe the network is "over-packed" and needs spacing, or maybe it needs more "mass" in the form of shared cues. Try spacing your stimuli or adding common reinforcer pictures the way Vaidya et al. (2021) did, then watch if the curve smooths out.