Gradient
Description
The structural property that a dimension has direction — moving one way is cheap, the other expensive; one state attracts, another repels; one outcome is more likely than the symmetric alternative. The gradient concept is the anti-symmetry schema: when you see a situation where the symmetric framing feels off, gradient is often the correct framing. Often used as a corrective to “binary” or “symmetric” framings that lose information.
Triggers
User-initiated: Gradient is overwhelmingly a re-framing reach on the agent’s side rather than a lexically marked prompt cue. The concept fires when the user describes a binary or symmetric framing and the agent recognizes the actual structure is directional, or vice versa. Three recurring sub-shapes:
- Cost-asymmetric direction — cheap forward, expensive backward (this is the asymmetric-gate higher-order concept’s home base). Example: a manual review step that is redundant for a change altering only what a system contains but load-bearing for one altering how it behaves — the same check, asymmetric in value by the class of change it faces.
- Inflection / threshold — a parameter on a gradient hits a step-function (“the math inverts at X%,” “tips the balance”).
- Asymmetric-stability — a choice between options with no clearly correct answer, where one option is more stable than the other; the agent elevates it to a doctrine: for genuinely fuzzy questions with no right answer, prefer whichever option a process yields consistently. This sub-shape generalizes across decision domains — naming conventions, classification boundaries, even visual grammar, where symmetric vs. asymmetric marks carry predictable semantic loadings (“a boat heading somewhere” vs. “a stamp on a document”).
Agent-initiated: Agent notices the user is reaching for a binary/symmetric framing of a directional situation; surfaces gradient as the corrective. Often arises in orchestrator-evaluating-worker contexts (an orchestrator evaluating a worker’s directional cost/risk analysis).
Vocabulary cues: “asymmetric,” “asymmetry,” “gradient,” “directional,” “one direction cheap,” “expensive in the other direction,” “tips the balance,” “math inverts,” “asymmetric stability,” “stability beats correctness,” “ratchet,” “threshold,” “inflection,” “tipping point.”
Situation-shape signals: A decision being framed in binary terms when the underlying structure has a cost or stability differential along a continuous axis; a doctrine being proposed as universal when it should be artifact-class-conditional (cheap-and-overkill for class X, load-bearing for class Y).
Exclusions
- Genuine symmetry — mirror-image systems, undirected graphs; forcing a gradient frame loses information.
- Constant landscape — if there’s no actual variation along the dimension, gradient is degenerate.
Relationships
- asymmetric-gate — the specific higher-order concept where gradient meets a gating mechanism (one direction cheap, the other expensive).
- local-minimum — gradient + attractor; every local direction looks worse, but the global landscape has better attractors.
Examples
Thermal gradient (heat flow)
Domain: physics
A temperature gradient is a dimension with a built-in direction. Heat flows spontaneously down it — from hot to cold — for free, but moving heat the other way, cold to hot, takes work: a heat pump, a refrigerator, an energy bill. The axis is not symmetric; one direction is cheap and the reverse is expensive, which is exactly the anti-symmetry the gradient schema names. Wherever a quantity varies across space or time and travelling each way along it costs differently, the same shape recurs.
”The math inverts at 76%+”
Domain: computer-science
threshold observation: gradient becomes a step-function at a specific point.