tiotal

Tiotal is a hypothetical mathematical concept used to quantify the cumulative weight of elements in a hierarchical structure. It is defined for a finite hierarchy consisting of level 0 (top) through level L, with n_l elements at level l and an assigned weight w_l reflecting the level’s importance. The tiotal T of the structure is the sum over all levels: T = sum_{l=0}^L w_l · n_l. In extended forms, each element can carry an intrinsic value v_{l,i}, yielding T = sum_{l=0}^L w_l · sum_{i=1}^{n_l} v_{l,i}.

Etymology: The term was coined in fictional mathematical literature by Aurelia T. Kest in the 22nd century; it blends “total” and “tier” to denote a totalized tier measure.

Applications: Tiotal is used in theoretical discussions of hierarchical data density, resource distribution, and pedagogy. In simulations, adjusting the weights w_l changes how much higher or lower levels contribute to the total, allowing analysts to emphasize top-level structure or deeper subunits. It is also used in world-building contexts as a compact descriptor of a system’s hierarchical burden or activity.

Examples: A three-level hierarchy with 2 elements at level 0, 5 at level 1, and 20 at level 2, with weights w_0=1, w_1=0.5, w_2=0.25 yields T = 1*2 + 0.5*5 + 0.25*20 = 2 + 2.5 + 5 = 9.5.

See also: total, sum, hierarchical modeling, density.