Computer programming[edit]
Origin[edit]
Martin Richards, creator of the BCPL language (a precursor of C), designed arrays initiating at 0 as the natural position to start accessing the array contents in the language, since the value of a pointer p used as an address accesses the position p + 0 in memory.[5][6] BCPL was first compiled for the IBM 7094; the language introduced no run-time indirection lookups, so the indirection optimization provided by these arrays was done at compile time.[6] The optimization was nevertheless important.[6][7]
In 1982 Edsger W. Dijkstra in his pertinent note Why numbering should start at zero[8] argued that arrays subscripts should start at zero as the latter being the most natural number. Discussing possible designs of array ranges by enclosing them in a chained inequality, combining sharp and standard inequalities to four possibilities, demonstrating that to his conviction zero-based arrays are best represented by non-overlapping index ranges, which start at zero, alluding to open, half-open and closed intervals as with the real numbers. Dijkstra's criteria for preferring this convention are in detail that it represents empty sequences in a more natural way (a ≤ i < a ?) than closed "intervals" (a ≤ i ≤ (a − 1) ?), and that with half-open "intervals" of naturals, the length of a sub-sequence equals the upper minus the lower bound (a ≤ i < b gives (b − a) possible values for i, with a, b, i all integers).
Science[edit]
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 not "intend" to express its genes.[13] In the similar sense, a computer may be considered from this perspective a zero-order intentional entity, as it does not "intend" to express the code of the programs it runs.[14]
In biological or medical experiments, initial measurements made before any experimental time has passed are said to be on the 0 day of the experiment.
In genomics, both 0-based and 1-based systems are used for genome coordinates.
Patient zero (or index case) is the initial patient in the population sample of an epidemiological investigation.
Other fields[edit]
The year zero does not exist in the widely used Gregorian calendar or in its predecessor, the Julian calendar. Under those systems, the year 1 BC is followed by AD 1. However, there is a year zero in astronomical year numbering (where it coincides with the Julian year 1 BC) and in ISO 8601:2004 (where it coincides with the Gregorian year 1 BC), as well as in all Buddhist and Hindu calendars.
In many countries, the ground floor in buildings is considered as floor number 0 rather than as the "1st floor", the naming convention usually found in the United States of America. This makes a consistent set with underground floors marked with negative numbers.
While the ordinal of 0 mostly finds use in communities directly connected to mathematics, physics, and computer science, there are also instances in classical music. The composer Anton Bruckner regarded his early Symphony in D minor to be unworthy of including in the canon of his works, and he wrote gilt nicht ("doesn't count") on the score and a circle with a crossbar, intending it to mean "invalid". But posthumously, this work came to be known as Symphony No. 0 in D minor, even though it was actually written after Symphony No. 1 in C minor. There is an even earlier Symphony in F minor of Bruckner's, which is sometimes called No. 00. The Russian composer Alfred Schnittke also wrote a Symphony No. 0.
In some universities, including Oxford and Cambridge, "week 0" or occasionally "noughth week" refers to the week before the first week of lectures in a term. In Australia, some universities refer to this as "O week", which serves as a pun on "orientation week". As a parallel, the introductory weeks at university educations in Sweden are generally called nollning (zeroing).
The United States Air Force starts basic training each Wednesday, and the first week (of eight) is considered to begin with the following Sunday. The four days before that Sunday are often referred to as "zero week".
24-hour clocks and the international standard ISO 8601 use 0 to denote the first (zeroth) hour of the day, consistent with using the 0 to denote the first (zeroth) minute of the hour and the first (zeroth) second of the minute. Also, the 12-hour clocks used in Japan use 0 to denote the hour immediately after midnight and noon in contrast to 12 used elsewhere, in order to avoid confusion whether 12 a.m. and 12 p.m. represent noon or midnight.
Robert Crumb's drawings for the first issue of Zap Comix were stolen, so he drew a whole new issue, which was published as issue 1. Later he re-inked his photocopies of the stolen artwork and published it as issue 0.
The Brussels ring road in Belgium is numbered R0. It was built after the ring road around Antwerp, but Brussels (being the capital city) was deemed deserving of a more basic number. Similarly the (unfinished) orbital motorway around Budapest in Hungary is called M0.
Zero is sometimes used in street addresses, especially in schemes where even numbers are one side of the street and odd numbers on the other. A case in point is Christ Church on Harvard Square, whose address is 0 Garden Street.
Formerly in Formula One, when a defending world champion did not compete in the following season, the number 1 was not assigned to any driver, but one driver of the world champion team would carry the number 0, and the other, number 2. This did happen both in 1993 and 1994 with Damon Hill carrying the number 0 in both seasons, as defending champion Nigel Mansell quit after 1992, and defending champion Alain Prost quit after 1993. However, in 2014 the series moved to drivers carrying career-long personalised numbers, instead of team-allocated numbers, other than the defending champion still having the option to carry number 1. Therefore 0 is no longer used in this scenario. It is not clear if it is available as a driver's chosen number, or whether they must be between 2 and 99, but it has not been used to date under this system.
Some team sports allow 0 to be chosen as a player's uniform number (in addition to the typical range of 1-99). The NFL voted to allow this from 2023 onwards.
A chronological prequel of a series may be numbered as 0, such as Ring 0: Birthday or Zork Zero.
The Swiss Federal Railways number certain classes of rolling stock from zero, for example, Re 460 000 to 118.
In the realm of fiction, Isaac Asimov eventually added a Zeroth Law to his Three Laws of Robotics, essentially making them four laws.
A standard roulette wheel contains the number 0 as well as 1-36. It appears in green, so is classed as neither a “red” nor “black” number for betting purposes. The card game Uno has number cards running from 0 to 9 along with special cards, within each coloured suit.
The Four Essential Freedoms of Free Software are numbered starting from zero. This is for historical reasons: the list originally had only three freedoms, and when the fourth was added it was placed in the zeroth position as it was considered more basic.