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From Wikipedia, the free encyclopedia

Multiplication (often denoted by the cross symbol ×, by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.

a \times b = \underset{a times}{\underset{⏟}{b + \dots + b}}

For example, 4 multiplied by 3, often written as $3 \times 4$ and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together:

3 \times 4 = 4 + 4 + 4 = 12

Here, 3 (the multiplier) and 4 (the multiplicand) are the factors, and 12 is the product.

One of the main properties of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3:

4 \times 3 = 3 + 3 + 3 + 3 = 12

Thus, the designation of multiplier and multiplicand does not affect the result of the multiplication.

Systematic generalizations of this basic definition define the multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers.

Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have some given lengths. The area of a rectangle does not depend on which side is measured first—a consequence of the commutative property.

The product of two measurements (or physical quantities) is a new type of measurement, usually with a derived unit. For example, multiplying the lengths (in meters or feet) of the two sides of a rectangle gives its area (in square meters or square feet). Such a product is the subject of dimensional analysis.

The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4. Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1.

Several mathematical concepts expand upon the fundamental idea of multiplication. The product of a sequence, vector multiplication, complex numbers, and matrices are all examples where this can be seen. These more advanced constructs tend to affect the basic properties in their own ways, such as becoming noncommutative in matrices and some forms of vector multiplication or changing the sign of complex numbers.

Notation

To reduce confusion between the multiplication sign × and the common variable $x$ , multiplication is also denoted by dot signs, usually a middle-position dot (rarely period):

5 \cdot 2

5 . 3

The middle dot notation or dot operator, encoded in Unicode as U+22C5 ⋅ DOT OPERATOR, is now standard in the United States and other countries where the period is used as a decimal point. When the dot operator character is not accessible, the interpunct (·) is used. In other countries that use a comma as a decimal mark, either the period or a middle dot is used for multiplication.

Historically, in the United Kingdom and Ireland, the middle dot was sometimes used for the decimal to prevent it from disappearing in the ruled line, and the period/full stop was used for multiplication. However, since the Ministry of Technology ruled to use the period as the decimal point in 1968, and the International System of Units (SI) standard has since been widely adopted, this usage is now found only in the more traditional journals such as The Lancet.

In algebra, multiplication involving variables is often written as a juxtaposition (e.g., $x y$ for $x$ times $y$ or $5 x$ for five times $x$ ), also called implied multiplication. The notation can also be used for quantities that are surrounded by parentheses (e.g., $5 (2)$ , $(5) 2$ or $(5) (2)$ for five times two). This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations.
In vector multiplication, there is a distinction between the cross and the dot symbols. The cross symbol generally denotes the taking a cross product of two vectors, yielding a vector as its result, while the dot denotes taking the dot product of two vectors, resulting in a scalar.

In computer programming, the asterisk (as in 5*2) is still the most common notation. This is due to the fact that most computers historically were limited to small character sets (such as ASCII and EBCDIC) that lacked a multiplication sign (such as ⋅ or ×), while the asterisk appeared on every keyboard. This usage originated in the FORTRAN programming language.

The numbers to be multiplied are generally called the "factors" (as in factorization). The number to be multiplied is the "multiplicand", and the number by which it is multiplied is the "multiplier". Usually, the multiplier is placed first, and the multiplicand is placed second; however, sometimes the first factor is the multiplicand and the second the multiplier. Also, as the result of multiplication does not depend on the order of the factors, the distinction between "multiplicand" and "multiplier" is useful only at a very elementary level and in some multiplication algorithms, such as the long multiplication. Therefore, in some sources, the term "multiplicand" is regarded as a synonym for "factor". In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in $3 x y^{2}$ ) is called a coefficient.

The result of a multiplication is called a product. When one factor is an integer, the product is a multiple of the other or of the product of the others. Thus, $2 \times π$ is a multiple of $π$ , as is $5133 \times 486 \times π$ . A product of integers is a multiple of each factor; for example, 15 is the product of 3 and 5 and is both a multiple of 3 and a multiple of 5.

Definitions

The product of two numbers or the multiplication between two numbers can be defined for common special cases: integers, natural numbers, fractions, real numbers, complex numbers, and quaternions.

Product of two natural numbers

Placing several stones into a rectangular pattern with $r$ rows and $s$ columns gives

r \cdot s = \sum_{i = 1}^{s} r = \underset{s times}{\underset{⏟}{r + r + \dots + r}} = \sum_{j = 1}^{r} s = \underset{r times}{\underset{⏟}{s + s + \dots + s}}

stones.

Product of two integers

An integer can be either zero, a positive, or a negative number. The product of zero and another integer is always zero. The product of two nonzero integers is determined by the product of their positive amounts, combined with the sign derived from the following rule:

\begin{array}{ccc} \times & - & + \\ - & + & - \\ + & - & + \end{array}

(This rule is a consequence of the distributivity of multiplication over addition, and is not an additional rule.)

In words:

A negative number multiplied by a negative number is positive,
A negative number multiplied by a positive number is negative,
A positive number multiplied by a negative number is negative,
A positive number multiplied by a positive number is positive.

Product of two fractions

Two fractions can be multiplied by multiplying their numerators and denominators:

\frac{z}{n} \cdot \frac{z^{'}}{n^{'}} = \frac{z \cdot z^{'}}{n \cdot n^{'}}

Product of two real numbers

There are several equivalent ways for define formally the real numbers; see Construction of the real numbers. The definition of multiplication is a part of all these definitions.

A fundamental aspect of these definitions is that every real number can be approximated to any accuracy by rational numbers. A standard way for expressing this is that every real number is the least upper bound of a set of rational numbers. In particular, every positive real number is the least upper bound of the truncations of its infinite decimal representation; for example, $π$ is the least upper bound of ${3, 3.1, 3.14, 3, 141, \dots} .$

A fundamental property of real numbers is that rational approximations are compatible with arithmetic operations, and, in particular, with multiplication. This means that, if $a$ and $b$ are positive real numbers such that $a = sup_{x \in A} x$ and $b = sup_{y \in B} y,$ then $a \cdot b = sup_{x \in A, y \in B} x \cdot y .$ In particular, the product of two positive real numbers is the least upper bound of the term-by-term products of the sequences of their decimal representations.

As changing the signs transforms least upper bounds into greatest lower bounds, the simplest way to deal with a multiplication involving one or two negative numbers, is to use the rule of signs described above in § Product of two integers. The construction of the real numbers through Cauchy sequences is often preferred in order to avoid consideration of the four possible sign configurations.

Product of two complex numbers

Two complex numbers can be multiplied by the distributive law and the fact that $i^{2} = - 1$ , as follows:

\begin{aligned} (a + b i) \cdot (c + d i) & = a \cdot c + a \cdot d i + b i \cdot c + b \cdot d \cdot i^{2} \\ = (a \cdot c - b \cdot d) + (a \cdot d + b \cdot c) i \end{aligned}

Geometric meaning of complex multiplication can be understood rewriting complex numbers in polar coordinates:

a + b i = r \cdot (\cos (φ) + i \sin (φ)) = r \cdot e^{i φ}

Furthermore,

c + d i = s \cdot (\cos (ψ) + i \sin (ψ)) = s \cdot e^{i ψ},

from which one obtains

(a \cdot c - b \cdot d) + (a \cdot d + b \cdot c) i = r \cdot s \cdot e^{i (φ + ψ)} .

The geometric meaning is that the magnitudes are multiplied and the arguments are added.

Product of two quaternions

The product of two quaternions can be found in the article on quaternions. Note, in this case, that $a \cdot b$ and $b \cdot a$ are in general different.

Computation

Many common methods for multiplying numbers using pencil and paper require a multiplication table of memorized or consulted products of small numbers (typically any two numbers from 0 to 9). However, one method, the peasant multiplication algorithm, does not. The example below illustrates "long multiplication" (the "standard algorithm", "grade-school multiplication"):

      23958233
×         5830
———————————————
      00000000 ( =      23,958,233 ×     0)
     71874699  ( =      23,958,233 ×    30)
   191665864   ( =      23,958,233 ×   800)
+ 119791165    ( =      23,958,233 × 5,000)
———————————————
  139676498390 ( = 139,676,498,390        )

In some countries such as Germany, the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with the first digit of the multiplier:

23958233 · 5830
———————————————
   119791165
    191665864
      71874699
       00000000 
———————————————
   139676498390

Multiplying numbers to more than a couple of decimal places by hand is tedious and error-prone. Common logarithms were invented to simplify such calculations, since adding logarithms is equivalent to multiplying. The slide rule allowed numbers to be quickly multiplied to about three places of accuracy. Beginning in the early 20th century, mechanical calculators, such as the Marchant, automated multiplication of up to 10-digit numbers. Modern electronic computers and calculators have greatly reduced the need for multiplication by hand.

Historical algorithms

Methods of multiplication were documented in the writings of ancient Egyptian, Greek, Indian, and Chinese civilizations.

The Ishango bone, dated to about 18,000 to 20,000 BC, may hint at a knowledge of multiplication in the Upper Paleolithic era in Central Africa, but this is speculative.

Egyptians

The Egyptian method of multiplication of integers and fractions, which is documented in the Rhind Mathematical Papyrus, was by successive additions and doubling. For instance, to find the product of 13 and 21 one had to double 21 three times, obtaining 2 × 21 = 42, 4 × 21 = 2 × 42 = 84, 8 × 21 = 2 × 84 = 168. The full product could then be found by adding the appropriate terms found in the doubling sequence:

13 × 21 = (1 + 4 + 8) × 21 = (1 × 21) + (4 × 21) + (8 × 21) = 21 + 84 + 168 = 273.

Babylonians

The Babylonians used a sexagesimal positional number system, analogous to the modern-day decimal system. Thus, Babylonian multiplication was very similar to modern decimal multiplication. Because of the relative difficulty of remembering 60 × 60 different products, Babylonian mathematicians employed multiplication tables. These tables consisted of a list of the first twenty multiples of a certain principal number n: n, 2n, ..., 20n; followed by the multiples of 10n: 30n 40n, and 50n. Then to compute any sexagesimal product, say 53n, one only needed to add 50n and 3n computed from the table.

Chinese

In the mathematical text Zhoubi Suanjing, dated prior to 300 BC, and the Nine Chapters on the Mathematical Art, multiplication calculations were written out in words, although the early Chinese mathematicians employed Rod calculus involving place value addition, subtraction, multiplication, and division. The Chinese were already using a decimal multiplication table by the end of the Warring States period.

Modern methods

The modern method of multiplication based on the Hindu–Arabic numeral system was first described by Brahmagupta. Brahmagupta gave rules for addition, subtraction, multiplication, and division. Henry Burchard Fine, then a professor of mathematics at Princeton University, wrote the following:

The Indians are the inventors not only of the positional decimal system itself, but of most of the processes involved in elementary reckoning with the system. Addition and subtraction they performed quite as they are performed nowadays; multiplication they effected in many ways, ours among them, but division they did cumbrously.

These place value decimal arithmetic algorithms were introduced to Arab countries by Al Khwarizmi in the early 9th century and popularized in the Western world by Fibonacci in the 13th century.

Grid method

Grid method multiplication, or the box method, is used in primary schools in England and Wales and in some areas of the United States to help teach an understanding of how multiple digit multiplication works. An example of multiplying 34 by 13 would be to lay the numbers out in a grid as follows:

×	30	4
5	150	20
10	300	40
3	90	12

and then add the entries.

Computer algorithms

The classical method of multiplying two $n$ -digit numbers requires $n 2$ digit multiplications. Multiplication algorithms have been designed that reduce the computation time considerably when multiplying large numbers. Methods based on the discrete Fourier transform reduce the computational complexity to $O (n log n log log n)$ . In 2016, the factor $log log n$ was replaced by a function that increases much slower, though still not constant. In March 2019, David Harvey and Joris van der Hoeven submitted a paper presenting an integer multiplication algorithm with a complexity of $O (n \log n) .$ The algorithm, also based on the fast Fourier transform, is conjectured to be asymptotically optimal. The algorithm is not practically useful, as it only becomes faster for multiplying extremely large numbers (having more than $2172912$ bits).

Products of measurements

One can only meaningfully add or subtract quantities of the same type, but quantities of different types can be multiplied or divided without problems. For example, four bags with three marbles each can be thought of as:

[4 bags] × [3 marbles per bag] = 12 marbles.

When two measurements are multiplied together, the product is of a type depending on the types of measurements. The general theory is given by dimensional analysis. This analysis is routinely applied in physics, but it also has applications in finance and other applied fields.

A common example in physics is the fact that multiplying speed by time gives distance. For example:

50 kilometers per hour × 3 hours = 150 kilometers.

In this case, the hour units cancel out, leaving the product with only kilometer units.

Other examples of multiplication involving units include:

2.5 meters × 4.5 meters = 11.25 square meters

11 meters/seconds × 9 seconds = 99 meters

4.5 residents per house × 20 houses = 90 residents

Product of a sequence

Capital pi notation

The product of a sequence of factors can be written with the product symbol $\prod$ , which derives from the capital letter Π (pi) in the Greek alphabet (much like the same way the summation symbol $\sum$ is derived from the Greek letter Σ (sigma)). The meaning of this notation is given by

\prod_{i = 1}^{4} (i + 1) = (1 + 1) (2 + 1) (3 + 1) (4 + 1),

which results in

\prod_{i = 1}^{4} (i + 1) = 120.

In such a notation, the variable $i$ represents a varying integer, called the multiplication index, that runs from the lower value $1$ indicated in the subscript to the upper value $4$ given by the superscript. The product is obtained by multiplying together all factors obtained by substituting the multiplication index for an integer between the lower and the upper values (the bounds included) in the expression that follows the product operator.

More generally, the notation is defined as

\prod_{i = m}^{n} x_{i} = x_{m} \cdot x_{m + 1} \cdot x_{m + 2} \cdot \dots \cdot x_{n - 1} \cdot x_{n},

where m and n are integers or expressions that evaluate to integers. In the case where m = n, the value of the product is the same as that of the single factor x_m; if m > n, the product is an empty product whose value is 1—regardless of the expression for the factors.

Properties of capital pi notation

By definition,

\prod_{i = 1}^{n} x_{i} = x_{1} \cdot x_{2} \cdot \dots \cdot x_{n} .

If all factors are identical, a product of $n$ factors is equivalent to exponentiation:

\prod_{i = 1}^{n} x = x \cdot x \cdot \dots \cdot x = x^{n} .

Associativity and commutativity of multiplication imply

\prod_{i = 1}^{n} x_{i} y_{i} = (\prod_{i = 1}^{n} x_{i}) (\prod_{i = 1}^{n} y_{i})

and

{(\prod_{i = 1}^{n} x_{i})}^{a} = \prod_{i = 1}^{n} x_{i}^{a}

if $a$ is a non-negative integer, or if all $x_{i}$ are positive real numbers, and

\prod_{i = 1}^{n} x^{a_{i}} = x^{\sum_{i = 1}^{n} a_{i}}

if all $a_{i}$ are non-negative integers, or if $x$ is a positive real number.

Infinite products

One may also consider products of infinitely many terms; these are called infinite products. Notationally, this consists in replacing n above by the infinity symbol ∞. The product of such an infinite sequence is defined as the limit of the product of the first n terms, as n grows without bound. That is,

\prod_{i = m}^{\infty} x_{i} = lim_{n \to \infty} \prod_{i = m}^{n} x_{i} .

One can similarly replace m with negative infinity, and define:

\prod_{i = - \infty}^{\infty} x_{i} = (lim_{m \to - \infty} \prod_{i = m}^{0} x_{i}) \cdot (lim_{n \to \infty} \prod_{i = 1}^{n} x_{i}),

provided both limits exist.

Exponentiation

When multiplication is repeated, the resulting operation is known as exponentiation. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 2³, a two with a superscript three. In this example, the number two is the base, and three is the exponent. In general, the exponent (or superscript) indicates how many times the base appears in the expression, so that the expression

a^{n} = \underset{n}{\underset{⏟}{a \times a \times \dots \times a}}

indicates that n copies of the base a are to be multiplied together. This notation can be used whenever multiplication is known to be power associative.

Properties

For real and complex numbers, which includes, for example, natural numbers, integers, and fractions, multiplication has certain properties:

Commutative property

The order in which two numbers are multiplied does not matter:

x \cdot y = y \cdot x .

Associative property

Expressions solely involving multiplication or addition are invariant with respect to the order of operations:

(x \cdot y) \cdot z = x \cdot (y \cdot z)

Distributive property

Holds with respect to multiplication over addition. This identity is of prime importance in simplifying algebraic expressions:

x \cdot (y + z) = x \cdot y + x \cdot z

Identity element

The multiplicative identity is 1; anything multiplied by 1 is itself. This feature of 1 is known as the identity property:

x \cdot 1 = x

Property of 0

Any number multiplied by 0 is 0. This is known as the zero property of multiplication:

x \cdot 0 = 0

Negation

−1 times any number is equal to the additive inverse of that number.

(- 1) \cdot x = (- x)

where

(- x) + x = 0

–1 times –1 is 1.

(- 1) \cdot (- 1) = 1

Inverse element: Every number x, except 0, has a multiplicative inverse, $\frac{1}{x}$ , such that $x \cdot (\frac{1}{x}) = 1$ .

Order preservation

Multiplication by a positive number preserves the order:

For a > 0, if b > c then ab > ac.

Multiplication by a negative number reverses the order:

For a < 0, if b > c then ab < ac.

The complex numbers do not have an ordering that is compatible with both addition and multiplication.

Other mathematical systems that include a multiplication operation may not have all these properties. For example, multiplication is not, in general, commutative for matrices and quaternions.

Axioms

In the book Arithmetices principia, nova methodo exposita, Giuseppe Peano proposed axioms for arithmetic based on his axioms for natural numbers. Peano arithmetic has two axioms for multiplication:

x \times 0 = 0

x \times S (y) = (x \times y) + x

Here S(y) represents the successor of y; i.e., the natural number that follows y. The various properties like associativity can be proved from these and the other axioms of Peano arithmetic, including induction. For instance, S(0), denoted by 1, is a multiplicative identity because

x \times 1 = x \times S (0) = (x \times 0) + x = 0 + x = x .

The axioms for integers typically define them as equivalence classes of ordered pairs of natural numbers. The model is based on treating (x,y) as equivalent to x − y when x and y are treated as integers. Thus both (0,1) and (1,2) are equivalent to −1. The multiplication axiom for integers defined this way is

(x_{p}, x_{m}) \times (y_{p}, y_{m}) = (x_{p} \times y_{p} + x_{m} \times y_{m}, x_{p} \times y_{m} + x_{m} \times y_{p}) .

The rule that −1 × −1 = 1 can then be deduced from

(0, 1) \times (0, 1) = (0 \times 0 + 1 \times 1, 0 \times 1 + 1 \times 0) = (1, 0) .

Multiplication is extended in a similar way to rational numbers and then to real numbers.

Multiplication with set theory

The product of non-negative integers can be defined with set theory using cardinal numbers or the Peano axioms. See below how to extend this to multiplying arbitrary integers, and then arbitrary rational numbers. The product of real numbers is defined in terms of products of rational numbers; see construction of the real numbers.

Multiplication in group theory

There are many sets that, under the operation of multiplication, satisfy the axioms that define group structure. These axioms are closure, associativity, and the inclusion of an identity element and inverses.

A simple example is the set of non-zero rational numbers. Here identity 1 is had, as opposed to groups under addition where the identity is typically 0. Note that with the rationals, zero must be excluded because, under multiplication, it does not have an inverse: there is no rational number that can be multiplied by zero to result in 1. In this example, an abelian group is had, but that is not always the case.

To see this, consider the set of invertible square matrices of a given dimension over a given field. Here, it is straightforward to verify closure, associativity, and inclusion of identity (the identity matrix) and inverses. However, matrix multiplication is not commutative, which shows that this group is non-abelian.

Another fact worth noticing is that the integers under multiplication do not form a group—even if zero is excluded. This is easily seen by the nonexistence of an inverse for all elements other than 1 and −1.

Multiplication in group theory is typically notated either by a dot or by juxtaposition (the omission of an operation symbol between elements). So multiplying element a by element b could be notated as a $\cdot$ b or ab. When referring to a group via the indication of the set and operation, the dot is used. For example, our first example could be indicated by $(Q / {0}, \cdot)$ .

Multiplication of different kinds of numbers

Numbers can count (3 apples), order (the 3rd apple), or measure (3.5 feet high); as the history of mathematics has progressed from counting on our fingers to modelling quantum mechanics, multiplication has been generalized to more complicated and abstract types of numbers, and to things that are not numbers (such as matrices) or do not look much like numbers (such as quaternions).

Integers: $N \times M$ is the sum of N copies of M when N and M are positive whole numbers. This gives the number of things in an array N wide and M high. Generalization to negative numbers can be done by; $N \times (- M) = (- N) \times M = - (N \times M)$ and; $(- N) \times (- M) = N \times M$; The same sign rules apply to rational and real numbers.

Rational numbers: Generalization to fractions $\frac{A}{B} \times \frac{C}{D}$ is by multiplying the numerators and denominators, respectively: $\frac{A}{B} \times \frac{C}{D} = \frac{(A \times C)}{(B \times D)}$ . This gives the area of a rectangle $\frac{A}{B}$ high and $\frac{C}{D}$ wide, and is the same as the number of things in an array when the rational numbers happen to be whole numbers.

Real numbers: Real numbers and their products can be defined in terms of sequences of rational numbers.

Complex numbers: Considering complex numbers $z_{1}$ and $z_{2}$ as ordered pairs of real numbers $(a_{1}, b_{1})$ and $(a_{2}, b_{2})$ , the product $z_{1} \times z_{2}$ is $(a_{1} \times a_{2} - b_{1} \times b_{2}, a_{1} \times b_{2} + a_{2} \times b_{1})$ . This is the same as for reals $a_{1} \times a_{2}$ when the imaginary parts $b_{1}$ and $b_{2}$ are zero.

Equivalently, denoting

\sqrt{- 1}

i

z_{1} \times z_{2} = (a_{1} + b_{1} i) (a_{2} + b_{2} i) = (a_{1} \times a_{2}) + (a_{1} \times b_{2} i) + (b_{1} \times a_{2} i) + (b_{1} \times b_{2} i^{2}) = (a_{1} a_{2} - b_{1} b_{2}) + (a_{1} b_{2} + b_{1} a_{2}) i .

Alternatively, in trigonometric form, if

z_{1} = r_{1} (\cos ϕ_{1} + i \sin ϕ_{1}), z_{2} = r_{2} (\cos ϕ_{2} + i \sin ϕ_{2})

, then

z_{1} z_{2} = r_{1} r_{2} (\cos (ϕ_{1} + ϕ_{2}) + i \sin (ϕ_{1} + ϕ_{2})) .

Further generalizations: See Multiplication in group theory, above, and multiplicative group, which for example includes matrix multiplication. A very general, and abstract, concept of multiplication is as the "multiplicatively denoted" (second) binary operation in a ring. An example of a ring that is not any of the above number systems is a polynomial ring (polynomials can be added and multiplied, but polynomials are not numbers in any usual sense).

Division: Often division, $\frac{x}{y}$ , is the same as multiplication by an inverse, $x (\frac{1}{y})$ . Multiplication for some types of "numbers" may have corresponding division, without inverses; in an integral domain x may have no inverse " $\frac{1}{x}$ " but $\frac{x}{y}$ may be defined. In a division ring there are inverses, but $\frac{x}{y}$ may be ambiguous in non-commutative rings since $x (\frac{1}{y})$ need not be the same as $(\frac{1}{y}) x$ .

Actuarial science

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Actuarial_science

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. More generally, actuaries apply rigorous mathematics to model matters of uncertainty and life expectancy.

Actuaries are professionals trained in this discipline. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations focused in fields such as probability and predictive analysis.

Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, financial accounting and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes since the 1980s due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory.

Many universities have undergraduate and graduate degree programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States. The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. A similar study by U.S. News & World Report in 2006 included actuaries among the 25 Best Professions that it expects will be in great demand in the future.

Subfields

Life insurance, pensions and healthcare

Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage such as burial, life insurance, and annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the present value of a future sum. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.

In traditional life insurance, actuarial science focuses on the analysis of mortality, the production of life tables, and the application of compound interest to produce life insurance, annuities and endowment policies. Contemporary life insurance programs have been extended to include credit and mortgage insurance, key person insurance for small businesses, long term care insurance and health savings accounts.
In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analysis of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of consumer choice and the geographical distribution of the utilization of medical services and procedures, and the utilization of drugs and therapies, is also of great importance. These factors underlay the development of the Resource-Base Relative Value Scale (RBRVS) at Harvard in a multi-disciplined study. Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare.
In the pension industry, actuarial methods are used to measure the costs of alternative strategies with regard to the design, funding, accounting, administration, and maintenance or redesign of pension plans. The strategies are greatly influenced by short-term and long-term bond rates, the funded status of the pension and benefit arrangements, collective bargaining; the employer's old, new and foreign competitors; the changing demographics of the workforce; changes in the internal revenue code; changes in the attitude of the internal revenue service regarding the calculation of surpluses; and equally importantly, both the short and long term financial and economic trends. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis. When benefit changes occur, old and new benefit plans have to be blended, satisfying new social demands and various government discrimination test calculations, and providing employees and retirees with understandable choices and transition paths. Benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Finally, funding schemes have to be developed that are manageable and satisfy the standards board or regulators of the appropriate country, such as the Financial Accounting Standards Board in the United States.
In social welfare programs, the Office of the Chief Actuary (OCACT), Social Security Administration plans and directs a program of actuarial estimates and analyses relating to SSA-administered retirement, survivors and disability insurance programs and to proposed changes in those programs. It evaluates operations of the Federal Old-Age and Survivors Insurance Trust Fund and the Federal Disability Insurance Trust Fund, conducts studies of program financing, performs actuarial and demographic research on social insurance and related program issues involving mortality, morbidity, utilization, retirement, disability, survivorship, marriage, unemployment, poverty, old age, families with children, etc., and projects future workloads. In addition, the Office is charged with conducting cost analyses relating to the Supplemental Security Income (SSI) program, a general-revenue financed, means-tested program for low-income aged, blind and disabled people. The office provides technical and consultative services to the Commissioner, to the board of trustees of the Social Security Trust Funds, and its staff appears before Congressional Committees to provide expert testimony on the actuarial aspects of Social Security issues.

Applications to other forms of insurance

Actuarial science is also applied to property, casualty, liability, and general insurance. In these forms of insurance, coverage is generally provided on a renewable period, (such as a yearly). Coverage can be cancelled at the end of the period by either party.

Property and casualty insurance companies tend to specialize because of the complexity and diversity of risks. One division is to organize around personal and commercial lines of insurance. Personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages. Commercial lines address the insurance needs of businesses and include property, business continuation, product liability, fleet/commercial vehicle, workers compensation, fidelity and surety, and D&O insurance. The insurance industry also provides coverage for exposures such as catastrophe, weather-related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism, and "one-of-a-kind" (e.g., satellite launch). Actuarial science provides data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the nature of the risks. Actuarial science often helps to assess the overall risk from catastrophic events in relation to its underwriting capacity or surplus.

In the reinsurance fields, actuarial science can be used to design and price reinsurance and retrocession arrangements, and to establish reserve funds for known claims and future claims and catastrophes.

Actuaries in criminal justice

There is an increasing trend to recognize that actuarial skills can be applied to a range of applications outside the traditional fields of insurance, pensions, etc. One notable example is the use in some US states of actuarial models to set criminal sentencing guidelines. These models attempt to predict the chance of re-offending according to rating factors which include the type of crime, age, educational background and ethnicity of the offender. However, these models have been open to criticism as providing justification for discrimination against specific ethnic groups by law enforcement personnel. Whether this is statistically correct or a self-fulfilling correlation remains under debate.

Another example is the use of actuarial models to assess the risk of sex offense recidivism. Actuarial models and associated tables, such as the MnSOST-R, Static-99, and SORAG, have been used since the late 1990s to determine the likelihood that a sex offender will re-offend and thus whether he or she should be institutionalized or set free.

Actuarial science related to modern financial economics

Traditional actuarial science and modern financial economics in the US have different practices, which is caused by different ways of calculating funding and investment strategies, and by different regulations.

Regulations are from the Armstrong investigation of 1905, the Glass–Steagall Act of 1932, the adoption of the Mandatory Security Valuation Reserve by the National Association of Insurance Commissioners, which cushioned market fluctuations, and the Financial Accounting Standards Board, (FASB) in the US and Canada, which regulates pensions valuations and funding.

History

Historically, much of the foundation of actuarial theory predated modern financial theory. In the early twentieth century, actuaries were developing many techniques that can be found in modern financial theory, but for various historical reasons, these developments did not achieve much recognition.

As a result, actuarial science developed along a different path, becoming more reliant on assumptions, as opposed to the arbitrage-free risk-neutral valuation concepts used in modern finance. The divergence is not related to the use of historical data and statistical projections of liability cash flows, but is instead caused by the manner in which traditional actuarial methods apply market data with those numbers. For example, one traditional actuarial method suggests that changing the asset allocation mix of investments can change the value of liabilities and assets (by changing the discount rate assumption). This concept is inconsistent with financial economics.

The potential of modern financial economics theory to complement existing actuarial science was recognized by actuaries in the mid-twentieth century. In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models. Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of finance. Today, the profession, both in practice and in the educational syllabi of many actuarial organizations, is cognizant of the need to reflect the combined approach of tables, loss models, stochastic methods, and financial theory. However, assumption-dependent concepts are still widely used (such as the setting of the discount rate assumption as mentioned earlier), particularly in North America.

Product design adds another dimension to the debate. Financial economists argue that pension benefits are bond-like and should not be funded with equity investments without reflecting the risks of not achieving expected returns. But some pension products do reflect the risks of unexpected returns. In some cases, the pension beneficiary assumes the risk, or the employer assumes the risk. The current debate now seems to be focusing on four principles:

financial models should be free of arbitrage.
assets and liabilities with identical cash flows should have the same price. This is at odds with FASB.
the value of an asset is independent of its financing.
how pension assets should be invested

Essentially, financial economics state that pension assets should not be invested in equities for a variety of theoretical and practical reasons.

Pre-formalisation

Elementary mutual aid agreements and pensions arose in antiquity. Early in the Roman empire, associations were formed to meet the expenses of burial, cremation, and monuments—precursors to burial insurance and friendly societies. A small sum was paid into a communal fund on a weekly basis, and upon the death of a member, the fund would cover the expenses of rites and burial. These societies sometimes sold shares in the building of columbāria, or burial vaults, owned by the fund—the precursor to mutual insurance companies. Other early examples of mutual surety and assurance pacts can be traced back to various forms of fellowship within the Saxon clans of England and their Germanic forebears, and to Celtic society. However, many of these earlier forms of surety and aid would often fail due to lack of understanding and knowledge.

Initial development

The 17th century was a period of advances in mathematics in Germany, France and England. At the same time there was a rapidly growing desire and need to place the valuation of personal risk on a more scientific basis. Independently of each other, compound interest was studied and probability theory emerged as a well-understood mathematical discipline. Another important advance came in 1662 from a London draper, the father of demography, John Graunt, who showed that there were predictable patterns of longevity and death in a group, or cohort, of people of the same age, despite the uncertainty of the date of death of any one individual. This study became the basis for the original life table. One could now set up an insurance scheme to provide life insurance or pensions for a group of people, and to calculate with some degree of accuracy how much each person in the group should contribute to a common fund assumed to earn a fixed rate of interest. The first person to demonstrate publicly how this could be done was Edmond Halley (of Halley's comet fame). Halley constructed his own life table, and showed how it could be used to calculate the premium amount someone of a given age should pay to purchase a life annuity.

Early actuaries

James Dodson's pioneering work on the long term insurance contracts under which the same premium is charged each year led to the formation of the Society for Equitable Assurances on Lives and Survivorship (now commonly known as Equitable Life) in London in 1762. William Morgan is often considered the father of modern actuarial science for his work in the field in the 1780s and 90s. Many other life insurance companies and pension funds were created over the following 200 years. Equitable Life was the first to use the word "actuary" for its chief executive officer in 1762. Previously, "actuary" meant an official who recorded the decisions, or "acts", of ecclesiastical courts. Other companies that did not use such mathematical and scientific methods most often failed or were forced to adopt the methods pioneered by Equitable.

Technological advances

In the 18th and 19th centuries, calculations were performed without computers. The computations of life insurance premiums and reserving requirements are rather complex, and actuaries developed techniques to make the calculations as easy as possible, for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities). Actuarial organizations were founded to support and further both actuaries and actuarial science, and to protect the public interest by promoting competency and ethical standards. However, calculations remained cumbersome, and actuarial shortcuts were commonplace. Non-life actuaries followed in the footsteps of their life insurance colleagues during the 20th century. The 1920 revision for the New-York based National Council on Workmen's Compensation Insurance rates took over two months of around-the-clock work by day and night teams of actuaries. In the 1930s and 1940s, the mathematical foundations for stochastic processes were developed. Actuaries could now begin to estimate losses using models of random events, instead of the deterministic methods they had used in the past. The introduction and development of the computer further revolutionized the actuarial profession. From pencil-and-paper to punchcards to current high-speed devices, the modeling and forecasting ability of the actuary has rapidly improved, while still being heavily dependent on the assumptions input into the models, and actuaries needed to adjust to this new world .

Racial color blindness

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Actuarial_science

Racial color blindness refers to the belief that a person's race or ethnicity should not influence their legal or social treatment in society.

The multicultural psychology field generates four beliefs that constitute the racial color-blindness approach. The four beliefs are as follows: (1) skin color is superficial and irrelevant to the quality of a person's character, ability or worthiness, (2) in a merit-based society, skin color is irrelevant to merit judgments and calculation of fairness, (3) as a corollary, in a merit-based society, merit and fairness are flawed if skin color is taken into the calculation, (4) ignoring skin color when interacting with people is the best way to avoid racial discrimination.

The term metaphorically references the medical phenomenon of color blindness. Psychologists and sociologists also study racial color blindness. This is further divided into two dimensions, color evasion and power evasion. Color evasion is the belief that people should not be treated differently on the basis of their color. Power evasion posits that systemic advantage based on color should have no influence on what people can accomplish, and accomplishments are instead based solely on one's own work performance.

At various times in Western history, this term has been used to signal a desired or allegedly achieved state of freedom from racial prejudice or a desire that policies and laws should not consider race. Proponents of racial color blindness often assert that policies that differentiate by racial classification could tend to create, perpetuate or exacerbate racial divisiveness. Critics often believe it fails to address systemic discrimination.

It has been used by justices of the United States Supreme Court in several opinions relating to racial equality and social equity, particularly in public education.

In U.S. Supreme Court opinions

In his dissenting opinion to Plessy v. Ferguson (1896), Justice John Marshall Harlan wrote that "Our Constitution is color-blind, and neither knows nor tolerates classes among citizens. In respect of civil rights, all citizens are equal before the law. The humblest is the peer of the most powerful. The law regards man as man, and takes no account of his surroundings or of his color when his civil rights as guaranteed by the supreme law of the land are involved." His opinion could thus be interpreted as saying that laws should not differentiate between people of different races. His opinion was not the majority-supported decision, which at the time was that laws requiring racial segregation were allowable, establishing the idea that "separate but equal" treatment was constitutionally acceptable.

More recently, the term color blind has appeared in United States Supreme Court opinions involving affirmative action, in opinions that support consideration of race when evaluating laws and their effects:

In a concurring opinion of Regents v. Bakke (1978), Justices William J. Brennan Jr., Byron White, Thurgood Marshall, and Harry Blackmun objected to the color blind term, writing that "we cannot ... let color blindness become myopia which masks the reality that many 'created equal' have been treated within our lifetimes as inferior both by the law and by their fellow citizens."
In her dissenting opinion to Gratz v. Bollinger (2003), Justice Ruth Bader Ginsburg quoted from a 1966 5th Circuit decision: "'The Constitution is both color blind and color conscious. To avoid conflict with the equal protection clause, a classification that denies a benefit, causes harm, or imposes a burden must not be based on race. In that sense, the Constitution is color blind. But the Constitution is color conscious to prevent discrimination being perpetuated and to undo the effects of past discrimination.'"
In his concurring opinion to PICS v. Seattle (2007), Justice Clarence Thomas wrote that "the color-blind Constitution does not bar the government from taking measures to remedy past state-sponsored discrimination – indeed, it requires that such measures be taken in certain circumstances."

Outline

A color-blind society, in sociology, is one in which racial classification does not affect a person's socially created opportunities. A racially color blind society is or would be free from differential legal or social treatment based on race or color. A color-blind society would have race-neutral governmental policies and would reject all racial discrimination.

Racial color blindness reflects a societal ideal that skin color is insignificant. The ideal was most articulated "along with the emergence of the Civil Rights Movement in the US and anti-racist movements abroad". Color-blind ideology is based on tenets of non-discrimination, due process of law, equal protection under the law, and equal opportunities regardless of race, ideas which have strongly influenced Western liberalism in the post-World War II period.

Proponents of "color-blind" practices largely believe that treating people equally as individuals leads to a more equal society or that racism and race privilege no longer exercise the power they once did, rendering the need for policies such as race-based affirmative action obsolete.

Support

Professor William Julius Wilson of Harvard University has argued that "class was becoming more important than race" in determining life prospects within the black community. Wilson has published several works including The Declining Significance of Race (1978) and The Truly Dis-advantaged (1987) explaining his views on black poverty and racial inequality. He believes that affirmative action primarily benefits the most privileged individuals within the black community. This is because strictly race-based programs disregard a candidate's socioeconomic background and therefore fail to help the poorer portion of the black community that actually needs the assistance. He claims that in a society where millions of black people live in the middle and upper classes and millions of white people live in poverty, race is no longer an accurate indication of privilege. Recognizing someone's social class is more important than recognizing someone's race, indicating that society should be class-conscious, not race-conscious, Wilson argues.

In his famous 1963 speech "I Have a Dream", Martin Luther King Jr. proclaimed, "I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character." This statement was widely interpreted as an endorsement of color-blind racial ideology. Roger Clegg, the President of the Center for Equal Opportunity, felt that this quotation supported the idea that race-conscious and equal opportunity should not exist, as he believes people should not be treated differently based on the color of their skin. However, not all agreed with this interpretation. American author Michael Eric Dyson felt that Dr. King only believed in the possibility of a color-blind society under the condition that racism and oppression were ultimately destroyed.

Supreme Court Justice Clarence Thomas has supported color-blind policies. He believes the Equal Protection Clause of the Fourteenth Amendment forbids consideration of race, such as race-based affirmative action or preferential treatment. He believes that race-oriented programs create "a cult of victimization" and imply black people require "special treatment in order to succeed".

When defending new voting rights bills in 2020, Republican Texas legislators claimed that since the process they wanted to establish for voter registration did not involve different processes for people of different races and did not involve collecting information about race or ethnicity, their new requirements for eligibility to vote were "color blind" and should not be considered racially discriminatory.

Some argue that the existence of majority-majority and majority-minority areas are not the result of racial discrimination and that this viewpoint ignores the possibility of other factors underlying residential segregation such as the attitude of realtors, bankers, and sellers.

While the field of whiteness studies often discusses alleged failures of racial color blindness, it has been criticized for its focus on reprimanding the white population, whereas similar fields such as black studies, women's studies, and Chicano studies celebrate the contributions of the eponymous group.

Among conservative presidents, color blindness as an idea has increased in the late 20th century as well as in the 21st century.

Where racial disparities were once explained in terms of biology, they are now being discussed in terms of culture. "Culture" in this framework is seen as something fixed and hard to change. One example form of rhetoric used in this framework is the argument, "if Irish, Jews (or other ethnic groups) have 'made it', how come black people have not?"

Some supporters of racial color blindness argue racial inequality can be supported by relying on cultural, rather than biological, explanations such as "this race has too many babies". Some no longer view racism as a problem under this belief and see government programs targeting race as no longer necessary due to the avoidance of racism. Bonilla-Silva describes naturalization as a frame that portrays racism as a natural outcome of individuals' choices, and "just the way things are". While Bonna-Silva himself disagrees with these as "minimization of racism", these are views common among supporters of racial color blindness.

In response to the global Black Lives Matter movement, the phrase All Lives Matter came into being as a term for racial color blindness. Several notable individuals have supported All Lives Matter, such as NFL cornerback Richard Sherman who said, "I stand by what I said that All Lives Matter and that we are human beings." A 2015 telephone poll in the US found that 78% of respondents said that "all lives matter" was closest to their own personal views. Despite this, the term was criticized by professor David Theo Goldberg as reflecting a view of "racial dismissal, ignoring, and denial."

Criticism

In 1997, Leslie G. Carr published Color-Blind Racism which reviewed the history of racist ideologies in America. He saw "color-blindness" as an ideology that undercuts the legal and political foundation of racial integration and affirmative action.

Stephanie M. Wildman's Privilege Revealed: How Invisible Preference Undermines America, writes that advocates of a meritocratic, race-free worldview do not acknowledge the systems of privilege which benefit them, such as social and financial inheritance. She argues that this inheritance privileges "whiteness", "maleness", and heterosexuality while disadvantaging descendants of slaves.

Sociologist Eduardo Bonilla-Silva writes that majority groups use color-blindness to avoid discussing racism and discrimination. Color-blindness can be seen as a way to undermine minority hardships, as it used to argue that the United States is a meritocracy, in which people succeed only because they work hard and not their privilege. John R. Logan has disagreed with this notion of meritocracy, as the average black or Hispanic household earning more than $75,000 still live in a less affluent neighborhood than a white household earning less than $40,000 and poverty rates are higher for minorities.

Amy Ansell of Bard College argues that color-blindness operates under the assumption that we are living in a world that is "post-race", where race no longer matters. She argues this is not true and if it was that race would not be taken into consideration even when trying to address inequality or remedy past wrongs.

Abstract liberalism utilizes themes from political and economic liberalism, such as meritocracy and the free market, to argue against the strong presence of racism. Some suggest it results in people being for equality in principle but against government action to implement equality, described by some sociologists as laissez-faire racism.

Robert D. Reason and Nancy J. Evans outline a similar description of color-blindness, which is based on four beliefs: 1. Privilege is based on merit. 2. Most do not care about a person's race. 3. Social inequality is due to "cultural deficits" of individual people. 4. Given the previous three beliefs, there is no need to pay "systematic attention" to any current inequities. They argue the prevalence of color-blindness is attributed to lack of knowledge or lack of exposure. They argue that due to racial separation in housing and education many Americans lack direct contact with present racism.

In Social Inequality and Social Stratification in US Society, Christopher Doob argues that racial color blindness's proponents "assert...that they are living in a world where racial privilege no longer exists, but their behavior 'supports' racialized structures and practices".

Eduardo Bonilla-Silva has argued racial color blindness is insufficient to address racial inequality. He argues it involves egalitarianism while opposing concrete proposals to reduce inequality. He has argued it ignores the under-representation of minorities in prestigious institutions, along with institutional practices that encourage segregation.

Eberhardt, Davies, Purdie-Vaughns, and Johnson studied implicit racial biases, suggesting people react differently to faces of members of their race compared to members of other races. They found a correlation between race and judicial outcomes and suggest a color blind approach may not actually be possible.

Research

Fryer et al. argued that color-blind affirmative action is about as efficient as race-conscious affirmative action in the short run but is less profitable in the long term.

In 2010, Apfelbaum et al. exposed elementary school students to color-blind ideology and found that those students were less likely to detect or report overt racial discrimination. The authors argued racial color blindness allows overt racism to persist."

Amy Ansell, a sociologist at Bard College, has compared and contrasted the development of the color-blindness in the United States and South Africa. Given that white people are a minority population in South Africa and a majority population in the United States, Ansell expected to see a significant difference in the manifestation of color-blindness in both countries. The thirty-year time difference between the departure from Jim Crow and cessation of apartheid and differences in racial stratification and levels of poverty also led Ansell to expect a clear difference between the colorblindness ideology in the United States and South Africa. However, she concludes contemporary color-blindness in the two countries is nearly identical.

Vorauer, Gagnon, and Sasaki examined the effect that messages with a color-blind ideology had on white Canadians entering one-on-one interactions with Aboriginal Canadians. White Canadians who heard messages emphasizing color-blind ideology were much more likely to be concerned with ensuring the subsequent interaction did not go badly and were more likely hostile, uncomfortable, and uncertain. White participants who heard messages emphasizing multicultural ideology, or the valuing of people's differences, asked more positive questions focused on the other person more relaxedly.

Alternatives

Researchers also offer alternatives to the color-blindness discourse. Reason and Evans call for people to become "racially cognizant" and continuously acknowledge the role that race plays in their lives. They argue it is important to balance personal identity and a person's race.

Researcher Jennifer Simpson argued that "in setting aside color blindness, White [people] must learn to see, accept...the possibility that some of the good, ease, or rewards they have experienced have not been solely the result of hard work" but from "a system biased in their favor." This conscious exploration of whiteness as a racial and social identity and the acknowledgment of the role of whiteness is connected to modern whiteness studies.

In a recent publication of the academic journal Communication Theory, Jennifer Simpson proposed a "more productive dialogue about race". New dialogue must take a more complex look at race, openly looking at different perspectives on race. Simpson argues white people must engage with other races in discussing the ongoing effects of racism, requiring white people to participate in "communicative behavior that may threaten simultaneously their sense of self and their material power in the social order".

In education

A multisite case study of Atlantic State University, a primarily white institution, and Mid-Atlantic State University, a historically black college, explored color-blind ideologies among the institutions’ white faculty members at the undergraduate and graduate level. In interviews with white faculty members at both institutions, researchers found the faculty often engaged with students from a color-blind perspective, avoiding racial terms but implying them allowed white faculty to label minority students "as academically inferior, less prepared, and less interested in pursuing research and graduate studies while potentially ignoring structural causes" of inequity. The study concludes that color-blind ideology held by school faculty can reduce a student of color's perception of their academic abilities and potential to achieve success in STEM disciplines and in graduate school.

A case study of a suburban, mixed-race high school examined the trend toward color-blind ideology in schools among white faculty. It argued white schoolteachers's color-blind ideology often masks their fears of being accused of racism and prevents a deeper examination of race.

Case studies of three large school districts, (Boston, Massachusetts; Wake County, North Carolina; and Jefferson County, Louisville) found that the districts’ race-neutral, or color-blind, policies to combat school segregation may disadvantage minorities and "reframe privilege as common sense" while ignoring structural inequalities.

Open-source journalism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Open-source_journalism

Open-source journalism, a close cousin to citizen journalism or participatory journalism, is a term coined in the title of a 1999 article by Andrew Leonard of Salon.com. Although the term was not actually used in the body text of Leonard's article, the headline encapsulated a collaboration between users of the internet technology blog Slashdot and a writer for Jane's Intelligence Review. The writer, Johan J. Ingles-le Nobel, had solicited feedback on a story about cyberterrorism from Slashdot readers, and then re-wrote his story based on that feedback and compensated the Slashdot writers whose information and words he used.

This early usage of the phrase clearly implied the paid use, by a mainstream journalist, of copyright-protected posts made in a public online forum. It thus referred to the standard journalistic techniques of news gathering and fact checking, and reflected a similar term—open-source intelligence—that was in use from 1992 in military intelligence circles.

The meaning of the term has since changed and broadened, and it is now commonly used to describe forms of innovative publishing of online journalism, rather than the sourcing of news stories by a professional journalist.

The term open-source journalism is often used to describe a spectrum on online publications: from various forms of semi-participatory online community journalism (as exemplified by projects such as the copyright newspaper NorthWest Voice), through to genuine open-source news publications (such as the Spanish 20 minutos, and Wikinews).

A relatively new development is the use of convergent polls, allowing editorials and opinions to be submitted and voted on. Over time, the poll converges on the most broadly accepted editorials and opinions. Examples of this are Opinionrepublic.com and Digg. Scholars are also experimenting with the process of journalism itself, such as open-sourcing the story skeletons that journalists build.

Usage

At first sight, it would appear to many that blogs fit within the current meaning of open-source journalism. Yet the term's use of open source clearly currently implies the meaning as given to it by the open-source software movement; where the source code of programs is published openly to allow anyone to locate and fix mistakes or add new functions. Anyone may also freely take and re-use that source code to create new works, within set license parameters.

Given certain legal traditions of copyright, blogs may not be open source in the sense that one is prohibited from taking the blogger's words or visitor comments and re-using them in another form without breaching the author's copyright or making payment. However, many blogs draw on such material through quotations (often with links to the original material), and follow guidelines more comparable to research than media production.

Creative Commons is a licensing arrangement that is useful as a legal workaround for such an inherent structural dilemma intrinsic to blogging, and its fruition is manifest in the common practices of referencing another published article, image or piece of information via a hyperlink. Insofar as blog works can explicitly inform readers and other participants of the "openness" of their text via Creative Commons, they not only publish openly, but allow anyone to locate, critique, summarize etc. their works.

Wiki journalism

Wiki journalism is a form of participatory journalism or crowdsourcing, which uses wiki technology to facilitate collaboration between users. It is a kind of collaborative journalism. The largest example of wiki journalism is Wikinews. According to Paul Bradshaw, there are five broad types of wiki journalism: second draft wiki journalism, a 'second stage' piece of journalism, during which readers can edit an article produced in-house; crowdsourcing wiki journalism, a means of covering material which could not have been produced in-house (probably for logistical reasons), but which becomes possible through wiki technology; supplementary wiki journalism, creating a supplement to a piece of original journalism, e.g. a tab to a story that says "Create a wiki for related stories"; open wiki journalism, in which a wiki is created as an open space, whose subject matter is decided by the user, and where material may be produced that would not otherwise have been commissioned; and logistical wiki journalism, involving a wiki limited to in-house contributors which enables multiple authorship, and may also facilitate transparency, and/or an ongoing nature.

Examples

Wikinews was launched in 2004 as an attempt to build an entire news operation on wiki technology. Where Wikinews – and indeed Wikipedia – has been most successful, however, is in covering large news events involving large numbers of people, such as Hurricane Katrina and the Virginia Tech shooting, where first-hand experience, or the availability of first-hand accounts, forms a larger part of the entry, and where the wealth of reportage makes a central "clearing house" valuable. Thelwall & Stuart identify Wikinews and Wikipedia as becoming particularly important during crises such as Hurricane Katrina, which "precipitate discussions or mentions of new technology in blogspace."

Mike Yamamoto notes that "In times of emergency, wikis are quickly being recognized as important gathering spots not only for news accounts but also for the exchange of resources, safety bulletins, missing-person reports and other vital information, as well as a meeting place for virtual support groups." He sees the need for community as the driving force behind this.

In June 2005, the Los Angeles Times decided to experiment with a "wikitorial" on the Iraq War, publishing their own editorial online but inviting readers to "rewrite" it using wiki technology. The experiment received broad coverage both before and after launch in both the mainstream media and the blogosphere. In editorial terms, the experiment was generally recognised as a failure.

In September 2005, Esquire used Wikipedia itself to "wiki" an article about Wikipedia by AJ Jacobs. The draft called on users to help Jacobs improve the article, with the intention of printing "before" and "after" versions of the piece in the printed magazine. He included some intentional mistakes to make the experiment "a little more interesting". The article received 224 edits in the first 24 hours, rising to 373 by 48 hours, and over 500 before further editing was suspended so the article could be printed.

In 2006, Wired also experimented with an article about wikis. When writer Ryan Singel submitted the 1,000-word draft to his editor, "instead of paring the story down to a readable 800 words, we posted it as-is to a SocialText-hosted wiki on 29 August, and announced it was open to editing by anyone willing to register." When the experiment closed, Singel noted that "there were 348 edits of the main story, 21 suggested headlines and 39 edits of the discussion pages. Thirty hyperlinks were added to the 20 in the original story." He continued that "one user didn't like the quotes I used from Ward Cunningham, the father of wiki software, so I instead posted a large portion of my notes from my interview on the site, so the community could choose a better one." Singel felt that the final story was "more accurate and more representative of how wikis are used" but not a better story than would have otherwise been produced:

"The edits over the week lack some of the narrative flow that a Wired News piece usually contains. The transitions seem a bit choppy, there are too many mentions of companies, and too much dry explication of how wikis work.
"It feels more like a primer than a story to me."

However, continued Singel, that didn't make the experiment a failure, and he felt the story "clearly tapped into a community that wants to make news stories better ... Hopefully, we'll continue to experiment to find ways to involve that community more."

In April 2010, the Wahoo Newspaper partnered with WikiCity Guides to extend its audience and local reach. "With this partnership, the Wahoo Newspaper provides a useful tool to connect with our readers, and for our readers to connect with one another to promote and spotlight everything Wahoo has to offer," said Wahoo Newspaper Publisher Shon Barenklau. Despite relatively little traffic as compared to its large scale, WikiCity Guides is recognized as the largest wiki in the world with over 13 million active pages.

Literature on wiki journalism

Andrew Lih places wikis within the larger category of participatory journalism, which also includes blogs, citizen journalism models such as OhMyNews and peer-to-peer publishing models such as Slashdot, and which, he argues "uniquely addresses an historic 'knowledge gap' – the general lack of content sources for the period between when the news is published and the history books are written."

Participatory journalism, he argues, "has recast online journalism not as simply reporting or publishing, but as a lifecycle, where software is crafted, users are empowered, journalistic content is created and the process repeats improves upon itself."

Francisco identifies wikis as a 'next step' in participatory journalism: "Blogs helped individuals publish and express themselves. Social networks allowed those disparate bloggers to be found and connected. Wikis are the platforms to help those who found one another be able to collaborate and build together."

Advantages

A Wiki can serve as the collective truth of the event, portraying the hundreds of viewpoints and without taxing any one journalist with uncovering whatever represents the objective truth in the circumstance.

Wikis allow news operations to effectively cover issues on which there is a range of opinion so broad that it would be difficult, if not impossible, to summarise effectively in one article alone. Examples might include local transport problems, experiences of a large event such as a music festival or protest march, guides to local restaurants or shops, or advice. The Wikivoyage site is one such example, "A worldwide travel guide written entirely by contributors who either live in the place they're covering or have spent enough time there to post relevant information."

Organisations willing to open up wikis to their audience completely may also find a way of identifying their communities' concerns: Wikipedia, for instance, notes Eva Dominguez "reflects which knowledge is most shared, given that both the content and the proposals for entries are made by the users themselves."

Internally, wikis also allow news operations to coordinate and manage a complex story which involves a number of reporters: journalists are able to collaborate by editing a single webpage that all have access to. News organisations interested in transparency might also publish the wiki 'live' as it develops, while the discussion space which accompanies each entry also has the potential to create a productive dialogue with users.

There are also clear economic and competitive advantages to allowing users to create articles. With the growth of low-cost micropublishing facilitated by the internet and blogging software in particular, and the convergence-fuelled entry into the online news market by both broadcasters and publishers, news organisations face increased competition from all sides. At the same time, print and broadcast advertising revenue is falling while competition for online advertising revenue is fierce and concentrated on a few major players: in the US, for instance, according to Jeffrey Rayport 99 percent of gross advertising money 2006 went to the top 10 websites.

Wikis offer a way for news websites to increase their reach, while also increasing the time that users spend on their website, a key factor in attracting advertisers. And, according to Dan Gillmor, "When [a wiki] works right, it engenders a community – and a community that has the right tools can take care of itself". A useful side-effect of community for a news organisation is reader loyalty.

Andrew Lih notes the importance of the "spirit of the open source movement" (2004b p6) in its development, and the way that wikis function primarily as "social software – acting to foster communication and collaboration with other users." Specifically, Lih attributes the success of the wiki model to four basic features: user friendly formatting; structure by convention, not enforced by software; "soft" security and ubiquitous access; and wikis transparency and edit history feature.

Student-run wikis provide opportunities to integrate learning by doing into a journalism education program.

Disadvantages

Shane Richmond identifies two obstacles that could slow down the adoption of news wikis – inaccuracy and vandalism:

"vandalism remains the biggest obstacle I can see to mainstream media's adoption of wikis, particularly in the UK, where one libellous remark could lead to the publisher of the wiki being sued, rather than the author of the libel."
"Meanwhile, the question of authority is the biggest obstacle to acceptance by a mainstream audience."

Writing in 2004, Lih also identified authority as an issue for Wikipedia: "While Wikipedia has recorded impressive accomplishments in three years, its articles have a mixed degree of quality because they are, by design, always in flux, and always editable. That reason alone makes people wary of its content."

Dan Gillmor puts it another way: "When vandals learn than someone will repair their damage within minutes, and therefore prevent the damage from being visible to the world, the bad guys tend to give up and move along to more vulnerable places." (2004, p. 149)

Attempts to address the security issue vary. Wikipedia's own entry on wikis again explains:

"For instance, some wikis allow unregistered users known as "IP addresses" to edit content, whilst others limit this function to just registered users. What most wikis do is allow IP editing, but privilege registered users with some extra functions to lend them a hand in editing; on most wikis, becoming a registered user is very simple and can be done in seconds, but detains the user from using the new editing functions until either some time passes, as in the English Wikipedia, where registered users must wait for three days after creating an account in order to gain access to the new tool, or until several constructive edits have been made in order to prove the user's trustworthiness and usefulness on the system, as in the Portuguese Wikipedia, where users require at least 15 constructive edits before authorization to use the added tools. Basically, "closed up" wikis are more secure and reliable but grow slowly, whilst more open wikis grow at a steady rate but result in being an easy target for vandalism."

Walsh (2007) quotes online media consultant Nico Macdonald on the importance of asking people to identify themselves:

"The key is the user's identity within the space – a picture of a person next to their post, their full name, a short bio and a link to their space online."
"A real community has, as New Labour would say, rights and responsibilities. You have to be accountable for yourself. Online, you only have the 'right' to express yourself. Online communities are not communities in a real sense – they're slightly delinquent. They allow or encourage delinquency."

Walsh (2007) argues that "Even if you don't plan on moderating a community, it's a good idea to have an editorial presence, to pop in and respond to users' questions and complaints. Apart from giving users the sense that they matter – and they really should – it also means that if you do have to take drastic measures and curtail (or even remove) a discussion or thread, it won't seem quite so much like the egregious action of some deus ex machina."

Ryan Singel of Wired also feels there is a need for an editorial presence, but for narrative reasons: "in storytelling, there's still a place for a mediator who knows when to subsume a detail for the sake of the story, and is accustomed to balancing the competing claims and interests of companies and people represented in a story."

'Edit wars' are another problem in wikis, where contributors continually overwrite each other's contributions due to a difference of opinion. The worst cases, notes Lih, "may require intervention by other community members to help mediate and arbitrate".

Eva Dominguez recognises the potential of wikis, but also the legal responsibilities that publishers must answer to: "The greater potential of the Internet to carry out better journalism stems from this collaboration, in which the users share and correct data, sources and facts that the journalist may not have easy access to or knowledge of. But the media, which have the ultimate responsibility for what is published, must always be able to verify everything. For example, in the case of third-party quotes included by collaborating users, the journalist must also check that they are true."

One of the biggest disadvantages may be readers' lack of awareness of what a wiki even is: only 2% of Internet users even know what a wiki is, according to a Harris Interactive poll (Francisco, 2006).

American columnist Bambi Francisco argues that it is only a matter of time before more professional publishers and producers begin to experiment with using "wiki-styled ways of creating content" in the same way as they have picked up on blogs.

The Telegraph's Web News Editor, Shane Richmond, wrote: "Unusually, it may be business people who bring wikis into the mainstream. That will prepare the ground for media experiments with wikis [and] I think it's a safe bet that a British media company will try a wiki before the end of the year."

Richmond added that The Telegraph was planning an internal wiki as a precursor to public experiments with the technology. "Once we have a feel for the technology, we will look into a public wiki, perhaps towards the end of the year [2007]."

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Saturday, December 16, 2023

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