Ambidextrous is the condition of having no directional bias: building a whole from parts and constraining a whole to cohere with all parts yield the same result. Neither bottom-up assembly nor top-down constraint has priority, because constitution is mutual.
Ambidextrous arises in Movement IV: Geometric Cohesion as a consequence of constructibility. When a relational configuration’s parts mutually determine each other — when no part floats free of the web — then the two fundamental ways of composing wholes from parts become interchangeable. You can assemble the whole by gluing parts together, or you can constrain the whole by requiring compatibility with all parts. The results are the same, under both the necessity (Must) and possibility (May) modalities.
This lack of directional bias is a hallmark of relational structure. In a framework where things are constituted through their relations, neither the parts nor the whole is ontologically prior. The key law: constructibility implies ambidexterity — mutual determination guarantees directional symmetry.
Mathematical correspondence
Ambidexterity corresponds to the coincidence of homotopy colimits and homotopy limits under both modalities. In the category-theoretic setting, this means the canonical comparison map between the homotopy colimit and homotopy limit is an equivalence.
Related
- Stratify — provides the directed structure needed to check ambidexterity
- Constructible — constructibility implies ambidexterity
- Must — necessity modality under which the coincidence holds
- May — possibility modality under which the coincidence holds