the fictitious zeroth element. However, the address of that fictitious element could very well be the address of some other item in memory not related to the array. Superficially, the fictitious element doesn't scale well to multidimensional arrays. Indexing multidimensional arrays from zero makes a naive (contiguous) conversion to a linear address space (systematically varying one index after the other) look simpler than when indexing from one. For instance, when mapping the three-dimensional array to a linear array L[M⋅N⋅P], both with M⋅N⋅P elements, the index r in the linear array to access a specific element with in zero-based indexing, i.e. [0 ≤ x < P], [0 ≤ y < N], [0 ≤ z < M], and [0 ≤ r < M⋅N⋅P], is calculated by . Organizing all arrays with 1-based indices ([1 ≤ x′ ≤ P], [1 ≤ y′ ≤ N], [1 ≤ z′ ≤ M], [1 ≤ r′ ≤ M⋅N⋅P]), and assuming an analogous arrangement of the elements, gives to access the same element, which arguably looks more complicated. Of course, since and A simple and everyday-life example is positional notation, which the invention of the zero made possible. In positional notation, tens, hundreds, thousands and all other digits start with zero, only units start at one. This situation can lead to some confusion in terminology. In a zero-based indexing scheme, the first element is "element number zero"; likewise, the twelfth element is "element number eleven". Therefore, an analogy from the ordinal numbers to the quantity of objects numbered appears; the highest index of n objects will be , and it refers to the nth element. For this reason, the first element is sometimes referred to as the zeroth element, in an attempt to avoid confusion. Science In mathematics, many sequences of numbers or of polynomials are indexed by nonnegative integers, for example, the Bernoulli numbers and the Bell numbers. In both mechanics and statistics, the zeroth moment is defined, representing total mass in the case of physical density, or total probability, i.e. one, for a probability distribution. The zeroth law of thermodynamics was formulated after the first, second, and third laws, but considered more fundamental, thus its name. In biology, an organism is said to have zero-order intentionality if it shows "no intention of anything at all". This would include a situation where the organism's genetically predetermined phenotype results in a fitness benefit to itself, because it did