Quand le changement ne suffit pas : Réduction, absorbabilité et identification de la plasticité
Abstract
How can we distinguish a structural transformation from a mere variation in representation? Drawing on the critical program of Book I of the *Treatise on Adaptive Systems*, this article develops a constructive procedure that allows us to subject a claimed plasticity to three complementary tests: reduction, absorbability, and identification under an explicitly specified observational framework. The approach is illustrated using a decision-making system for granting microcredit, in which a time-varying decision rule, a variable contributive domain, and a parameter θ interpolating between two aggregation regimes are considered in succession. For a variable distribution, the introduction of an augmented state space shows—under an explicit hypothesis regarding the closure and representability of its evolution—how variability can be absorbed into the state of a system with a fixed distribution. For a variable contributive domain, a compatible extension to a universal domain allows us to test, in a similar manner, whether the observed variation constitutes a structural difference. Finally, for the family Hθ(f, µ) = θC(f, µ) + (1 − θ)S(f, µ), a conditional parametric injectivity proposition establishes that, for a fixed capacity, θ is distinguishable within the family of operators if and only if the two aggregation regimes C and S do not coincide over the entire admissible class. These results lead to a rigorous distinction between existence, representability, operability, contribution, observability, and identifiability. Above all, they show that an observable variation—even one that is parametrically identifiable—is not sufficient to establish irreducible plasticity: the difference must still resist competing transformations that could absorb it and remain distinguishable relative to the chosen observation framework. The article thus arrives at a precise set of specifications for any future construction: before proposing an adaptation operator, one must determine which variations cannot be reduced, absorbed, or rendered equivalent by a competing representation.
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BibTeX
@misc{andriamanantena2026quand,
title = {{Quand le changement ne suffit pas : Réduction, absorbabilité et identification de la plasticité}},
author = {Philibert Andriamanantena},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05801231v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Quand le changement ne suffit pas : Réduction, absorbabilité et identification de la plasticité
AU - Philibert Andriamanantena
PY - 2026
DA - 2026/10/15
PB - HAL
UR - https://hal.science/hal-05801231v1
AB - How can we distinguish a structural transformation from a mere variation in representation? Drawing on the critical program of Book I of the *Treatise on Adaptive Systems*, this article develops a constructive procedure that allows us to subject a claimed plasticity to three complementary tests: reduction, absorbability, and identification under an explicitly specified observational framework. The approach is illustrated using a decision-making system for granting microcredit, in which a time-varying decision rule, a variable contributive domain, and a parameter θ interpolating between two aggregation regimes are considered in succession. For a variable distribution, the introduction of an augmented state space shows—under an explicit hypothesis regarding the closure and representability of its evolution—how variability can be absorbed into the state of a system with a fixed distribution. For a variable contributive domain, a compatible extension to a universal domain allows us to test, in a similar manner, whether the observed variation constitutes a structural difference. Finally, for the family Hθ(f, µ) = θC(f, µ) + (1 − θ)S(f, µ), a conditional parametric injectivity proposition establishes that, for a fixed capacity, θ is distinguishable within the family of operators if and only if the two aggregation regimes C and S do not coincide over the entire admissible class. These results lead to a rigorous distinction between existence, representability, operability, contribution, observability, and identifiability. Above all, they show that an observable variation—even one that is parametrically identifiable—is not sufficient to establish irreducible plasticity: the difference must still resist competing transformations that could absorb it and remain distinguishable relative to the chosen observation framework. The article thus arrives at a precise set of specifications for any future construction: before proposing an adaptation operator, one must determine which variations cannot be reduced, absorbed, or rendered equivalent by a competing representation.
ER -