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Ministry of Internal Affairs (Russia)

The Ministry of Internal Affairs of the Russian Federation (MVD; Министерство внутренних дел [МВД], Ministerstvo vnutrennikh del) is the interior ministry of Russia.

The MVD is responsible for law enforcement in Russia through its agencies the Police of Russia, Migration Affairs, Drugs Control, Traffic Safety, the Centre for Combating Extremism, and the Investigative Department. The MVD is headquartered in Zhitnaya Street 16 in Yakimanka, Moscow. Vladimir Kolokoltsev has been the Minister of Internal Affairs since 2012.

Russian Empire (1802-1917)
The first interior ministry (MVD) in Russia was created by Tsar Alexander I on 28 March 1802. The MVD was one of the most powerful governmental bodies of the Empire, responsible for the police forces and Internal Guards, and the supervision of gubernial administrations. Its initial responsibilities also included prisons, firefighting, state enterprises, the state postal system, state property, construction, roads, medicine, clergy, natural resources, and nobility; most of them were transferred to other ministries and government bodies by the mid-19th century.

Police
As the central government began to further partition the countryside, the ispravniks (chiefs of police) were distributed among the sections. Serving under them in their principal localities were commissaries. and alike were armed with broad and obscurely-defined powers which, combined with the fact that they were for the most part illiterate and wholly ignorant of the law, formed crushing forces of oppression. Towards the end of the reign of Alexander II, the government, in order to preserve order in the country districts, also created a special class of mounted rural policemen (, from, order), who, in a time without habeas corpus, were armed with power to arrest all suspects on the spot. These rapidly became the terror of the countryside. Finally, in the towns of the rural countryside, every house was provided with a "guard dog" of sorts, in the form of a porter, who was charged with the duty of reporting the presence of any suspicious characters or anything of interest to the police.

Secret Police
In addition there was also the secret police, in direct subordination to the ministry of the interior, of which the principal function was the discovery, prevention, and extirpation of political sedition. Its most famous development was the so-called Third Section (of the imperial chancery) instituted by Emperor Nicholas I in 1826. This was entirely independent of the ordinary police, but was associated with the previously existing Special Corps of Gendarmes, whose chief was placed at its head. Its object had originally been to keep the emperor in close touch with all the branches of the administration and to bring to his notice any abuses and irregularities, and for this purpose its chief was in constant personal contact with the sovereign.

Following the growth of the revolutionary movement and the assassination of Emperior Alexander II, the Department of State Police inherited the secret police functions of the dismissed Third Section and transferred the most capable Gendarmes to the Okhrana. In 1896 the powers of the minister were extended at the expense of those of the under-secretary, who remained only at the head of the corps of gendarmes; but by a law of 24 September 1904 this was reversed, and the under-secretary was again placed at the head of all the police with the title of under-secretary for the administration of the police.

By World War I, the department had spawned a counter-intelligence section. After the February Revolution of 1917, the Gendarmes and the Okhrana were disbanded as anti-revolutionary.

Soviet era (1917-89)

Having won the October Revolution, the Bolsheviks disbanded the tsarist police forces and formed an all-proletarian Workers' and Peasants' Militsiya under the NKVD of the Russian SFSR. After the establishment of the USSR, there was no Soviet (federal) NKVD until 1934. In March 1946, all of the People's Commissariats (NK) were redesignated as Ministries (M). The NKVD was renamed the MVD of the USSR, along with its former subordinate, the NKGB which became the MGB of the USSR. The NKVDs of Union Republics also became Ministries of Internal Affairs subordinate to MVD of the USSR.

Secret police became a part of MVD after Lavrenty Beria merged the MGB into the MVD in March 1953. Within a year Beria's downfall caused the MVD to be split up again; after that, the MVD retained its "internal security" (police) functions, while the new KGB took on "state security" (secret police) functions.

In his efforts to fight bureaucracy and maintain 'Leninist principles', Nikita Khrushchev, as the Premier of the Soviet Union, called for the dismissal of the All-Union MVD. The Ministry ceased to exist in January 1960, and its functions were transferred to the respective Republican Ministries. The MVD of the Russian SFSR was renamed the Ministry for Securing the Public Order in 1962. Leonid Brezhnev again recreated the All-Union Ministry for Securing the Public Order in July 1966, and later assigned Nikolai Shchelokov as Minister; the RSFSR Ministry was disbanded for the second time, the first being at the creation of the NKVD of the Soviet Union. The MVD regained its original title in 1968. Another role of the reformed MVD was to combat economic crimes, that is, to suppress private business which was largely prohibited by socialist law. This fight was never successful, due to the pervasive nature of the black market.

By the mid-1980s, the image of the people's militsiya was largely compromised by the corruption and disorderly behaviour of both enlisted and officer staff (the most shocking case was the robbery and Murder of Vyacheslav Afanasyev by a group of militsiya officers stationed in the Moscow Metro in 1980).

Organizational changes
The Russian MVD re-formed as the MVD of the Russian SFSR in 1990, following the restoration of the republican Russian Council of Ministers and the Supreme Soviet of Russia. It continued in its functions when Russia gained independence from the Soviet Union in 1991. the Ministry controlled: the Politsiya (formerly Militsiya), the General Administration for Traffic Safety, and the Federal Drug Control Service.

Since the disbanding of the Russian Tax Police Service in 2003, the MVD also investigates economic crimes. Two long-time units of the Imperial MVD and NKVD, the Russian Firefighting Service and the Federal Prisons Service, transferred to the Russian Ministry of Emergency Situations in 2001 and to the Russian Ministry of Justice in 2006, respectively. The last reorganization abolished Main Directorates inherited from the NKVD in favour of Departments. In 2012, career police officer Vladimir Kolokoltsev became the Minister of Internal Affairs in Russia.

On 5 April 2016, Russian President Vladimir Putin ordered the Russian Internal Troops, OMON (the Special Purpose Mobility Unit), and SOBR (SWAT) forces to form the basis of the newly created National Guard of Russia, and these close to 200,000 public order, special police, and internal troop forces previously under the command of the MVD were reassigned to the Security Council of Russia. In turn and on the same day, the Federal Drug Control Service and the Federal Migration Service merged into the MVD, and are now known as the Main Directorate for Drugs Control and the Main Directorate for Migration Affairs, respectively.

2005-19
In 2006, investigative journalist Anna Politkovskaya was murdered. Six years later, the former head of surveillance at Moscow’s main Internal Affairs Directorate was found guilty of organizing her murder by tracking her movements and giving a gun to the killer.

In December 2019, Distributed Denial of Secrets listed a leak from Russia's Ministry of the Interior, portions of which detailed the deployment of Russian troops to Ukraine, at a time when the Kremlin was denying a military presence there. Some material from that leak was published in 2014, about half of it was not, and WikiLeaks reportedly rejected a request to host the files two years later, at a time when Julian Assange was focused on exposing Democratic Party documents passed to WikiLeaks by Kremlin hackers.

2020-present
The founder and editor of the independent news site Koza.Press, known professionally as Irina Slavina, was harassed by law enforcement for years. On October 2, 2020, she committed suicide by self-immolation outside a regional Ministry of Internal Affairs building, writing on Facebook, “For my death, please blame the Russian Federation.”

In September 2023, Russia's Ministry of Internal Affairs decided to have an appeal by imprisoned opposition leader Alexey Navalny challenging his 19-year prison sentence on extremism charges held by a court behind closed doors, and the appeal was dismissed. Supporters of Navalny said he was being silenced for criticizing President Vladimir Putin's government. In 2020 Navalny was poisoned in Russia with the Soviet-era nerve agent Novichok.

Telecommunications service providers are required to grant the Ministry of Internal Affairs 24-hour remote access to their client databases, including telephone and electronic communication and records, enabling the Ministry to track private communications and internet activity without the users' knowledge. The law permits authorities to monitor telephone calls in real time.

Sports

 * Former HC MVD of the KHL

Russian

 * Timeline of MVD, 1801–1997

title: Ministry of Internal Affairs (Russia)


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Pareto distribution

The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto, but the concepts are distinct, and only Pareto distributions with shape value ($α$) of log45 ≈ 1.16 precisely reflect it. Empirical observation has shown that this 80-20 distribution fits a wide range of cases, including natural phenomena and human activities.

Definitions
If X is a random variable with a Pareto (Type I) distribution, then the probability that X is greater than some number x, i.e., the survival function (also called tail function), is given by

 * $$\overline{F}(x) = \Pr(X>x) = \begin{cases}

\left(\frac{x_\mathrm{m}}{x}\right)^\alpha & x\ge x_\mathrm{m}, \\ 1 & x < x_\mathrm{m}, \end{cases} $$

where xm is the (necessarily positive) minimum possible value of X, and α is a positive parameter. The type I Pareto distribution is characterized by a scale parameter xm and a shape parameter α, which is known as the tail index. If this distribution is used to model the distribution of wealth, then the parameter α is called the Pareto index.

Cumulative distribution function
From the definition, the cumulative distribution function of a Pareto random variable with parameters α and xm is

 * $$F_X(x) = \begin{cases}

1-\left(\frac{x_\mathrm{m}}{x}\right)^\alpha & x \ge x_\mathrm{m}, \\ 0 & x < x_\mathrm{m}. \end{cases}$$

Probability density function
It follows (by differentiation) that the probability density function is

 * $$f_X(x)= \begin{cases} \frac{\alpha x_\mathrm{m}^\alpha}{x^{\alpha+1}} & x \ge x_\mathrm{m}, \\ 0 & x < x_\mathrm{m}. \end{cases} $$

When plotted on linear axes, the distribution assumes the familiar J-shaped curve which approaches each of the orthogonal axes asymptotically. All segments of the curve are self-similar (subject to appropriate scaling factors). When plotted in a log-log plot, the distribution is represented by a straight line.

Moments and characteristic function

 * The expected value of a random variable following a Pareto distribution is
 * $$\operatorname{E}(X)= \begin{cases} \infty & \alpha\le 1, \\
 * $$\operatorname{E}(X)= \begin{cases} \infty & \alpha\le 1, \\

\frac{\alpha x_{\mathrm{m}}}{\alpha-1} & \alpha>1. \end{cases}$$
 * The variance of a random variable following a Pareto distribution is

 * $$\operatorname{Var}(X)= \begin{cases}

\infty & \alpha\in(1,2], \\ \left(\frac{x_\mathrm{m}}{\alpha-1}\right)^2 \frac{\alpha}{\alpha-2} & \alpha>2. \end{cases}$$

 * (If α ≤ 1, the variance does not exist.)

 * The raw moments are

 * $$\mu_n'= \begin{cases} \infty & \alpha\le n, \\ \frac{\alpha x_\mathrm{m}^n}{\alpha-n} & \alpha>n. \end{cases}$$

 * The moment generating function is only defined for non-positive values t ≤ 0 as

 * $$M\left(t;\alpha,x_\mathrm{m}\right) = \operatorname{E} \left [e^{tX} \right ] = \alpha(-x_\mathrm{m} t)^\alpha\Gamma(-\alpha,-x_\mathrm{m} t)$$
 * $$M\left(0,\alpha,x_\mathrm{m}\right)=1.$$

Thus, since the expectation does not converge on an open interval containing $$t=0$$ we say that the moment generating function does not exist.
 * The characteristic function is given by

 * $$\varphi(t;\alpha,x_\mathrm{m})=\alpha(-ix_\mathrm{m} t)^\alpha\Gamma(-\alpha,-ix_\mathrm{m} t),$$

 * where Γ(a, x) is the incomplete gamma function.

The parameters may be solved for using the method of moments.

Conditional distributions
The conditional probability distribution of a Pareto-distributed random variable, given the event that it is greater than or equal to a particular number $$x_1$$ exceeding $$x_\text{m}$$, is a Pareto distribution with the same Pareto index $$\alpha$$ but with minimum $$x_1$$ instead of $$x_\text{m}$$. This implies that the conditional expected value (if it is finite, i.e. $$\alpha>1$$) is proportional to $$x_1$$. In case of random variables that describe the lifetime of an object, this means that life expectancy is proportional to age, and is called the Lindy effect or Lindy's Law.

A characterization theorem
Suppose $$X_1, X_2, X_3, \dotsc$$ are independent identically distributed random variables whose probability distribution is supported on the interval $$[x_\text{m},\infty)$$ for some $$x_\text{m}>0$$. Suppose that for all $$n$$, the two random variables $$\min\{X_1,\dotsc,X_n\}$$ and $$(X_1+\dotsb+X_n)/\min\{X_1,\dotsc,X_n\}$$ are independent. Then the common distribution is a Pareto distribution.

Geometric mean
The geometric mean (G) is

 * $$ G = x_\text{m} \exp \left( \frac{1}{\alpha} \right).$$

Harmonic mean
The harmonic mean (H) is

 * $$ H = x_\text{m} \left( 1 + \frac{ 1 }{ \alpha } \right).$$

Graphical representation
The characteristic curved 'long tail' distribution, when plotted on a linear scale, masks the underlying simplicity of the function when plotted on a log-log graph, which then takes the form of a straight line with negative gradient: It follows from the formula for the probability density function that for x ≥ xm,

 * $$\log f_X(x)= \log \left(\alpha\frac{x_\mathrm{m}^\alpha}{x^{\alpha+1}}\right) = \log (\alpha x_\mathrm{m}^\alpha) - (\alpha+1) \log x.$$

Since α is positive, the gradient −(α + 1) is negative.

Generalized Pareto distributions
There is a hierarchy of Pareto distributions known as Pareto Type I, II, III, IV, and Feller–Pareto distributions. Pareto Type IV contains Pareto Type I–III as special cases. The Feller–Pareto distribution generalizes Pareto Type IV.

Pareto types I–IV
The Pareto distribution hierarchy is summarized in the next table comparing the survival functions (complementary CDF).

When μ = 0, the Pareto distribution Type II is also known as the Lomax distribution.

In this section, the symbol xm, used before to indicate the minimum value of x, is replaced by σ.

The shape parameter α is the tail index, μ is location, σ is scale, γ is an inequality parameter. Some special cases of Pareto Type (IV) are

 * $$ P(IV)(\sigma, \sigma, 1, \alpha) = P(I)(\sigma, \alpha),$$
 * $$ P(IV)(\mu, \sigma, 1, \alpha) = P(II)(\mu, \sigma, \alpha),$$
 * $$ P(IV)(\mu, \sigma, \gamma, 1) = P(III)(\mu, \sigma, \gamma).$$

The finiteness of the mean, and the existence and the finiteness of the variance depend on the tail index α (inequality index γ). In particular, fractional δ-moments are finite for some δ > 0, as shown in the table below, where δ is not necessarily an integer.

Feller–Pareto distribution
Feller defines a Pareto variable by transformation U = Y−1 − 1 of a beta random variable ,Y, whose probability density function is

 * $$ f(y) = \frac{y^{\gamma_1-1} (1-y)^{\gamma_2-1}}{B(\gamma_1, \gamma_2)}, \qquad 00,$$

where B is the beta function. If

 * $$ W = \mu + \sigma(Y^{-1}-1)^\gamma, \qquad \sigma>0, \gamma>0,$$

then W has a Feller–Pareto distribution FP(μ, σ, γ, γ1, γ2).

If $$U_1 \sim \Gamma(\delta_1, 1)$$ and $$U_2 \sim \Gamma(\delta_2, 1)$$ are independent Gamma variables, another construction of a Feller–Pareto (FP) variable is

 * $$W = \mu + \sigma \left(\frac{U_1}{U_2}\right)^\gamma$$

and we write W ~ FP(μ, σ, γ, δ1, δ2). Special cases of the Feller–Pareto distribution are

 * $$FP(\sigma, \sigma, 1, 1, \alpha) = P(I)(\sigma, \alpha)$$
 * $$FP(\mu, \sigma, 1, 1, \alpha) = P(II)(\mu, \sigma, \alpha)$$
 * $$FP(\mu, \sigma, \gamma, 1, 1) = P(III)(\mu, \sigma, \gamma)$$
 * $$FP(\mu, \sigma, \gamma, 1, \alpha) = P(IV)(\mu, \sigma, \gamma, \alpha).$$

Inverse-Pareto Distribution / Power Distribution
When a random variable $$Y$$ follows a pareto distribution, then its inverse $$X=1/Y$$ follows an Inverse Pareto distribution. Inverse Pareto distribution is equivalent to a Power distribution

 * $$Y\sim \mathrm{Pa}(\alpha, x_m) = \frac{\alpha x_m^\alpha}{y^{\alpha+1}} \quad (y \ge x_m) \quad \Leftrightarrow \quad X\sim \mathrm{iPa}(\alpha, x_m) = \mathrm{Power}(x_m^{-1}, \alpha) = \frac{\alpha x^{\alpha-1}}{(x_m^{-1})^\alpha} \quad (0< x \le x_m^{-1})$$

Relation to the exponential distribution
The Pareto distribution is related to the exponential distribution as follows. If X is Pareto-distributed with minimum xm and index α, then

 * $$ Y = \log\left(\frac{X}{x_\mathrm{m}}\right) $$

is exponentially distributed with rate parameter α. Equivalently, if Y is exponentially distributed with rate α, then

 * $$ x_\mathrm{m} e^Y$$

is Pareto-distributed with minimum xm and index α.

This can be shown using the standard change-of-variable techniques:

\begin{align} \Pr(Y<y) & = \Pr\left(\log\left(\frac{X}{x_\mathrm{m}}\right)<y\right) \\ & = \Pr(X<x_\mathrm{m} e^y) = 1-\left(\frac{x_\mathrm{m}}{x_\mathrm{m}e^y}\right)^\alpha=1-e^{-\alpha y}. \end{align} $$

The last expression is the cumulative distribution function of an exponential distribution with rate α.

Pareto distribution can be constructed by hierarchical exponential distributions. Let $$\phi | a \sim \text{Exp}(a)$$ and $$\eta | \phi \sim \text{Exp}(\phi) $$. Then we have $$p(\eta | a) = \frac{a}{(a+\eta)^2}$$ and, as a result, $$a+\eta \sim \text{Pareto}(a, 1)$$.

More in general, if $$\lambda \sim \text{Gamma}(\alpha, \beta)$$ (shape-rate parametrization) and $$\eta | \lambda \sim \text{Exp}(\lambda) $$, then $$\beta + \eta \sim \text{Pareto}(\beta, \alpha)$$.

Equivalently, if $$Y \sim \text{Gamma}(\alpha,1) $$ and $$X \sim \text{Exp}(1)$$, then $$x_{\text{m}} \! \left(1 + \frac{X}{Y}\right) \sim \text{Pareto}(x_{\text{m}}, \alpha)$$.

Relation to the log-normal distribution
The Pareto distribution and log-normal distribution are alternative distributions for describing the same types of quantities. One of the connections between the two is that they are both the distributions of the exponential of random variables distributed according to other common distributions, respectively the exponential distribution and normal distribution. (See the previous section.)

Relation to the generalized Pareto distribution
The Pareto distribution is a special case of the generalized Pareto distribution, which is a family of distributions of similar form, but containing an extra parameter in such a way that the support of the distribution is either bounded below (at a variable point), or bounded both above and below (where both are variable), with the Lomax distribution as a special case. This family also contains both the unshifted and shifted exponential distributions.

The Pareto distribution with scale $$x_m$$ and shape $$\alpha$$ is equivalent to the generalized Pareto distribution with location $$\mu=x_m$$, scale $$\sigma=x_m/\alpha$$ and shape $$\xi=1/\alpha$$ and, conversely, one can get the Pareto distribution from the GPD by taking $$x_m = \sigma/\xi$$ and $$\alpha=1/\xi$$ if $$\xi > 0$$.

Bounded Pareto distribution
The bounded (or truncated) Pareto distribution has three parameters: α, L and H. As in the standard Pareto distribution α determines the shape. L denotes the minimal value, and H denotes the maximal value.

The probability density function is

 * $$\frac{\alpha L^\alpha x^{-\alpha - 1}}{1-\left(\frac{L}{H}\right)^\alpha}$$,

where L ≤ x ≤ H, and α > 0.

Generating bounded Pareto random variables
If U is uniformly distributed on (0, 1), then applying inverse-transform method

 * $$U = \frac{1 - L^\alpha x^{-\alpha}}{1 - (\frac{L}{H})^\alpha}$$
 * $$x = \left(-\frac{U H^\alpha - U L^\alpha - H^\alpha}{H^\alpha L^\alpha}\right)^{-\frac{1}{\alpha}}$$

is a bounded Pareto-distributed.

Symmetric Pareto distribution
The purpose of the Symmetric and Zero Symmetric Pareto distributions is to capture some special statistical distribution with a sharp probability peak and symmetric long probability tails. These two distributions are derived from the Pareto distribution. Long probability tails normally means that probability decays slowly, and can be used to fit a variety of datasets. But if the distribution has symmetric structure with two slow decaying tails, Pareto could not do it. Then Symmetric Pareto or Zero Symmetric Pareto distribution is applied instead.

The Cumulative distribution function (CDF) of Symmetric Pareto distribution is defined as following:

$$F(X) = P(x < X ) = \begin{cases} \tfrac{1}{2}({b \over 2b-X}) ^a & X<b \\ 1- \tfrac{1}{2}(\tfrac{b}{X})^a& X\geq b \end{cases}$$

The corresponding probability density function (PDF) is:

$$p(x) = {ab^a \over 2(b+\left\vert x-b \right\vert)^{a+1}},X\in R$$

This distribution has two parameters: a and b. It is symmetric by b. Then the mathematic expectation is b. When, it has variance as following:

$$E((x-b)^2)=\int_{-\infty}^{\infty} (x-b)^2p(x)dx={2b^2 \over (a-2)(a-1) }

$$

The CDF of Zero Symmetric Pareto (ZSP) distribution is defined as following:

$$F(X) = P(x < X ) = \begin{cases} \tfrac{1}{2}({b \over b-X}) ^a & X<0 \\ 1- \tfrac{1}{2}(\tfrac{b}{b+X})^a& X\geq 0 \end{cases}$$

The corresponding PDF is:

$$p(x) = {ab^a \over 2(b+\left\vert x \right\vert)^{a+1}},X\in R$$

This distribution is symmetric by zero. Parameter a is related to the decay rate of probability and (a/2b) represents peak magnitude of probability.

Multivariate Pareto distribution
The univariate Pareto distribution has been extended to a multivariate Pareto distribution.

Estimation of parameters
The likelihood function for the Pareto distribution parameters α and xm, given an independent sample x = (x1, x2, ..., xn), is

 * $$L(\alpha, x_\mathrm{m}) = \prod_{i=1}^n \alpha \frac {x_\mathrm{m}^\alpha} {x_i^{\alpha+1}} = \alpha^n x_\mathrm{m}^{n\alpha} \prod_{i=1}^n \frac {1}{x_i^{\alpha+1}}.$$

Therefore, the logarithmic likelihood function is

 * $$\ell(\alpha, x_\mathrm{m}) = n \ln \alpha + n\alpha \ln x_\mathrm{m} - (\alpha + 1) \sum_{i=1} ^n \ln x_i.$$

It can be seen that $$\ell(\alpha, x_\mathrm{m})$$ is monotonically increasing with xm, that is, the greater the value of xm, the greater the value of the likelihood function. Hence, since x ≥ xm, we conclude that

 * $$\widehat x_\mathrm{m} = \min_i {x_i}.$$

To find the estimator for α, we compute the corresponding partial derivative and determine where it is zero:

 * $$\frac{\partial \ell}{\partial \alpha} = \frac{n}{\alpha} + n \ln x_\mathrm{m} - \sum _{i=1}^n \ln x_i = 0.$$

Thus the maximum likelihood estimator for α is:

 * $$\widehat \alpha = \frac{n}{\sum _i \ln (x_i/\widehat x_\mathrm{m}) }.$$

The expected statistical error is:

 * $$\sigma = \frac {\widehat \alpha} {\sqrt n}. $$

Malik (1970) gives the exact joint distribution of $$(\hat{x}_\mathrm{m},\hat\alpha)$$. In particular, $$\hat{x}_\mathrm{m}$$ and $$\hat\alpha$$ are independent and $$\hat{x}_\mathrm{m}$$ is Pareto with scale parameter xm and shape parameter nα, whereas $$\hat\alpha$$ has an inverse-gamma distribution with shape and scale parameters n − 1 and nα, respectively.

General
Vilfredo Pareto originally used this distribution to describe the allocation of wealth among individuals since it seemed to show rather well the way that a larger portion of the wealth of any society is owned by a smaller percentage of the people in that society. He also used it to describe distribution of income. This idea is sometimes expressed more simply as the Pareto principle or the "80-20 rule" which says that 20% of the population controls 80% of the wealth. As Michael Hudson points out (The Collapse of Antiquity [2023] p. 85 & n.7) "a mathematical corollary [is] that 10% would have 65% of the wealth, and 5% would have half the national wealth.” However, the 80-20 rule corresponds to a particular value of α, and in fact, Pareto's data on British income taxes in his Cours d'économie politique indicates that about 30% of the population had about 70% of the income. The probability density function (PDF) graph at the beginning of this article shows that the "probability" or fraction of the population that owns a small amount of wealth per person is rather high, and then decreases steadily as wealth increases. (The Pareto distribution is not realistic for wealth for the lower end, however. In fact, net worth may even be negative.) This distribution is not limited to describing wealth or income, but to many situations in which an equilibrium is found in the distribution of the "small" to the "large". The following examples are sometimes seen as approximately Pareto-distributed:

 * All four variables of the household's budget constraint: consumption, labor income, capital income, and wealth.
 * The sizes of human settlements (few cities, many hamlets/villages)
 * File size distribution of Internet traffic which uses the TCP protocol (many smaller files, few larger ones)
 * Hard disk drive error rates
 * Clusters of Bose–Einstein condensate near absolute zero
 * The values of oil reserves in oil fields (a few large fields, many small fields)
 * The length distribution in jobs assigned to supercomputers (a few large ones, many small ones)
 * The standardized price returns on individual stocks
 * Sizes of sand particles
 * The size of meteorites
 * Severity of large casualty losses for certain lines of business such as general liability, commercial auto, and workers compensation.
 * Amount of time a user on Steam will spend playing different games. (Some games get played a lot, but most get played almost never.)
 * In hydrology the Pareto distribution is applied to extreme events such as annually maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Pareto distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.
 * In Electric Utility Distribution Reliability (80% of the Customer Minutes Interrupted occur on approximately 20% of the days in a given year).

Relation to Zipf's law
The Pareto distribution is a continuous probability distribution. Zipf's law, also sometimes called the zeta distribution, is a discrete distribution, separating the values into a simple ranking. Both are a simple power law with a negative exponent, scaled so that their cumulative distributions equal 1. Zipf's can be derived from the Pareto distribution if the $$x$$ values (incomes) are binned into $$N$$ ranks so that the number of people in each bin follows a 1/rank pattern. The distribution is normalized by defining $$x_m$$ so that $$\alpha x_\mathrm{m}^\alpha = \frac{1}{H(N,\alpha-1)}$$ where $$H(N,\alpha-1)$$ is the generalized harmonic number. This makes Zipf's probability density function derivable from Pareto's.

 * $$f(x) = \frac{\alpha x_\mathrm{m}^\alpha}{x^{\alpha+1}} = \frac{1}{x^s H(N,s)}$$

where $$s = \alpha-1$$ and $$x$$ is an integer representing rank from 1 to N where N is the highest income bracket. So a randomly selected person (or word, website link, or city) from a population (or language, internet, or country) has $$f(x)$$ probability of ranking $$x$$.

Relation to the "Pareto principle"
The "80–20 law", according to which 20% of all people receive 80% of all income, and 20% of the most affluent 20% receive 80% of that 80%, and so on, holds precisely when the Pareto index is $$\alpha = \log_4 5 = \cfrac{\log_{10} 5}{\log_{10} 4} \approx 1.161$$. This result can be derived from the Lorenz curve formula given below. Moreover, the following have been shown to be mathematically equivalent:
 * Income is distributed according to a Pareto distribution with index α > 1.
 * There is some number 0 ≤ p ≤ 1/2 such that 100p % of all people receive 100(1 − p)% of all income, and similarly for every real (not necessarily integer) n > 0, 100pn % of all people receive 100(1 − p)n percentage of all income. α and p are related by
 * $$1-\frac{1}{\alpha}=\frac{\ln(1-p)}{\ln(p)}=\frac{\ln((1-p)^n)}{\ln(p^n)}$$

This does not apply only to income, but also to wealth, or to anything else that can be modeled by this distribution.

This excludes Pareto distributions in which 0 < α ≤ 1, which, as noted above, have an infinite expected value, and so cannot reasonably model income distribution.

Relation to Price's law
Price's square root law is sometimes offered as a property of or as similar to the Pareto distribution. However, the law only holds in the case that $$\alpha=1$$. Note that in this case, the total and expected amount of wealth are not defined, and the rule only applies asymptotically to random samples. The extended Pareto Principle mentioned above is a far more general rule.

Lorenz curve and Gini coefficient

The Lorenz curve is often used to characterize income and wealth distributions. For any distribution, the Lorenz curve L(F) is written in terms of the PDF f or the CDF F as

 * $$L(F)=\frac{\int_{x_\mathrm{m}}^{x(F)}xf(x)\,dx}{\int_{x_\mathrm{m}}^\infty xf(x)\,dx} =\frac{\int_0^F x(F')\,dF'}{\int_0^1 x(F')\,dF'}$$

where x(F) is the inverse of the CDF. For the Pareto distribution,

 * $$x(F)=\frac{x_\mathrm{m}}{(1-F)^{\frac{1}{\alpha}}}$$

and the Lorenz curve is calculated to be

 * $$L(F) = 1-(1-F)^{1-\frac{1}{\alpha}},$$

For $$0<\alpha\le 1$$ the denominator is infinite, yielding L=0. Examples of the Lorenz curve for a number of Pareto distributions are shown in the graph on the right.

According to Oxfam (2016) the richest 62 people have as much wealth as the poorest half of the world's population. We can estimate the Pareto index that would apply to this situation. Letting ε equal $$62/(7\times 10^9)$$ we have:
 * $$L(1/2)=1-L(1-\varepsilon)$$

or
 * $$1-(1/2)^{1-\frac{1}{\alpha}}=\varepsilon^{1-\frac{1}{\alpha}}$$

The solution is that α equals about 1.15, and about 9% of the wealth is owned by each of the two groups. But actually the poorest 69% of the world adult population owns only about 3% of the wealth.

The Gini coefficient is a measure of the deviation of the Lorenz curve from the equidistribution line which is a line connecting [0, 0] and [1, 1], which is shown in black (α = ∞) in the Lorenz plot on the right. Specifically, the Gini coefficient is twice the area between the Lorenz curve and the equidistribution line. The Gini coefficient for the Pareto distribution is then calculated (for $$\alpha\ge 1$$) to be

 * $$G = 1-2 \left (\int_0^1L(F) \, dF \right ) = \frac{1}{2\alpha-1}$$

(see Aaberge 2005).

Random variate generation
Random samples can be generated using inverse transform sampling. Given a random variate U drawn from the uniform distribution on the unit interval (0, 1], the variate T given by

 * $$T=\frac{x_\mathrm{m}}{U^{1/\alpha}}$$

is Pareto-distributed. If U is uniformly distributed on [0, 1), it can be exchanged with (1 − U).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Pareto distribution


text:
Regular space

In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms.

Definitions

A topological space X is a regular space if, given any closed set F and any point x that does not belong to F, there exists a neighbourhood U of x and a neighbourhood V of F that are disjoint. Concisely put, it must be possible to separate x and F with disjoint neighborhoods.

A ' or ' is a topological space that is both regular and a Hausdorff space. (A Hausdorff space or T2 space is a topological space in which any two distinct points are separated by neighbourhoods.) It turns out that a space is T3 if and only if it is both regular and T0. (A T0 or Kolmogorov space is a topological space in which any two distinct points are topologically distinguishable, i.e., for every pair of distinct points, at least one of them has an open neighborhood not containing the other.) Indeed, if a space is Hausdorff then it is T0, and each T0 regular space is Hausdorff: given two distinct points, at least one of them misses the closure of the other one, so (by regularity) there exist disjoint neighborhoods separating one point from (the closure of) the other.

Although the definitions presented here for "regular" and "T3" are not uncommon, there is significant variation in the literature: some authors switch the definitions of "regular" and "T3" as they are used here, or use both terms interchangeably. This article uses the term "regular" freely, but will usually say "regular Hausdorff", which is unambiguous, instead of the less precise "T3". For more on this issue, see History of the separation axioms.

A is a topological space where every point has an open neighbourhood that is regular. Every regular space is locally regular, but the converse is not true. A classical example of a locally regular space that is not regular is the bug-eyed line.

Relationships to other separation axioms
A regular space is necessarily also preregular, i.e., any two topologically distinguishable points can be separated by neighbourhoods. Since a Hausdorff space is the same as a preregular T0 space, a regular space which is also T0 must be Hausdorff (and thus T3). In fact, a regular Hausdorff space satisfies the slightly stronger condition T2½. (However, such a space need not be completely Hausdorff.) Thus, the definition of T3 may cite T0, T1, or T2½ instead of T2 (Hausdorffness); all are equivalent in the context of regular spaces.

Speaking more theoretically, the conditions of regularity and T3-ness are related by Kolmogorov quotients. A space is regular if and only if its Kolmogorov quotient is T3; and, as mentioned, a space is T3 if and only if it's both regular and T0. Thus a regular space encountered in practice can usually be assumed to be T3, by replacing the space with its Kolmogorov quotient.

There are many results for topological spaces that hold for both regular and Hausdorff spaces. Most of the time, these results hold for all preregular spaces; they were listed for regular and Hausdorff spaces separately because the idea of preregular spaces came later. On the other hand, those results that are truly about regularity generally don't also apply to nonregular Hausdorff spaces.

There are many situations where another condition of topological spaces (such as normality, pseudonormality, paracompactness, or local compactness) will imply regularity if some weaker separation axiom, such as preregularity, is satisfied. Such conditions often come in two versions: a regular version and a Hausdorff version. Although Hausdorff spaces aren't generally regular, a Hausdorff space that is also (say) locally compact will be regular, because any Hausdorff space is preregular. Thus from a certain point of view, regularity is not really the issue here, and we could impose a weaker condition instead to get the same result. However, definitions are usually still phrased in terms of regularity, since this condition is more well known than any weaker one.

Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition. Regular spaces should also be contrasted with normal spaces.

Examples and nonexamples
A zero-dimensional space with respect to the small inductive dimension has a base consisting of clopen sets. Every such space is regular.

As described above, any completely regular space is regular, and any T0 space that is not Hausdorff (and hence not preregular) cannot be regular. Most examples of regular and nonregular spaces studied in mathematics may be found in those two articles. On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems. Of course, one can easily find regular spaces that are not T0, and thus not Hausdorff, such as an indiscrete space, but these examples provide more insight on the T0 axiom than on regularity. An example of a regular space that is not completely regular is the Tychonoff corkscrew.

Most interesting spaces in mathematics that are regular also satisfy some stronger condition. Thus, regular spaces are usually studied to find properties and theorems, such as the ones below, that are actually applied to completely regular spaces, typically in analysis.

There exist Hausdorff spaces that are not regular. An example is the set R with the topology generated by sets of the form U — C, where U is an open set in the usual sense, and C is a fixed nonclosed subset of R with empty interior.

Elementary properties
Suppose that X is a regular space. Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G. In fancier terms, the closed neighbourhoods of x form a local base at x. In fact, this property characterises regular spaces; if the closed neighbourhoods of each point in a topological space form a local base at that point, then the space must be regular.

Taking the interiors of these closed neighbourhoods, we see that the regular open sets form a base for the open sets of the regular space X. This property is actually weaker than regularity; a topological space whose regular open sets form a base is semiregular.

title: Regular space


text:
Scalar

Scalar may refer to:

 * Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers
 * Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number
 * Lorentz scalar, a quantity in the theory of relativity which is invariant under a Lorentz transformation
 * Pseudoscalar, a quantity that behaves like a scalar, except that it changes sign under a parity inversion
 * Scalar (computing), any non-composite value
 * Scalar boson, in physics, a boson subatomic particle whose spin equals zero

title: Scalar


text:
Talk:Kazimierz Kuratowski

Untitled
Did Kuratowski's original description of topological spaces with closure operators really apply only to separated spaces? The modern version certainly applies to any topological space. -- Toby Bartels, Thursday, May 23, 2002

 * That is my understanding. The fact that Kuratowski's closure applied only to Hausdorff spaces is mentioned in
 * Hocking and Young, Topology, ISBN 0486656764
 * -- Miguel

The statement of Kuratowski's theorem about planar graphs that was given here was incorrect. See Talk:planar graph. AxelBoldt 00:52 13 Jun 2003 (UTC)

Biography
This whole section needs to be rewritten. For one, it is barely chronological. Angry bee (talk) 06:01, 7 February 2011 (UTC) Forget not being chornolgoglogyical, it's really hard to read. PARAGRAPHS AND BULLET POINTS. They help. 81.131.112.223 (talk) 23:51, 30 March 2011 (UTC)

 * Ay, you're right, it's a complete mess.  Volunteer Marek   20:41, 18 November 2011 (UTC)

The sentence "This was the subject of a French doctoral thesis written by Zygmunt Janiszewski." is not clear. French?? And did Janiszewski write Kuratowski's thesis or just supervised it, until he died? HarDan (talk) 09:24, 24 January 2024 (UTC)

contibutions section
From the article, "...His contributions to mathematics include:... identification of the ordered pair (x,y) with the set {{x},{x,y}};"

That may be true, but I've heard Norbert Weiner did something with that as well.24.7.28.186 (talk) 20:29, 18 November 2011 (UTC)
 * Never mind, in fact that's what Wiener article explains, and that Kuratowski put it into its present form.24.7.28.186 (talk) 20:41, 18 November 2011 (UTC)

1920 article is not about topology
I found the title and volume/date/journal for Kuratowski's 1920 article about finite sets in parentheses just after the sentence about "an axiomatic construction of topology via the closure axioms". However, this article has nothing at all on this subject. This 1920 article only introduces the Kuratowski finiteness definition and shows that it is equivalent to the standard numerical definition of finiteness. It's only 2 pages and 7 lines long, and it's about set theory only.

I have added a bibliographic reference for this significant article. However, it is not connected with the topology at all. So maybe someone who knows about Kuratowski's topology contributions could fix that up. I think the 1920 paper should remain in the bibliography on this page, but not at that location in the article. --Alan U. Kennington (talk) 10:23, 8 August 2014 (UTC)

title: Talk:Kazimierz Kuratowski


text:
66 BC

Year 66 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Lepidus and Tullus (or, less frequently, year 688 Ab urbe condita). The denomination 66 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Republic

 * Consuls: Manius Aemilius Lepidus and Lucius Volcatius Tullus.
 * Catiline accused of conspiring against the Roman Republic with Autronius and the younger Sulla (also in 63 BC during the consulship of Cicero).
 * The alliance between Mithridates VI of Pontus and Tigranes II of Armenia is broken.
 * Tigranes II is forced to surrender, by a payment of 6,000 talents, and is reinstated by Pompey as a "friend of the Roman people" to hold Armenia as a buffer zone.
 * Battle of the Lycus: Pompey the Great decisively defeats Mithridates VI, effectively ending the Third Mithridatic War.
 * Gaius Antonius elected Roman praetor.
 * The lex Manilia, supported by Cicero gives Pompey command over all of Asia.
 * Cicero becomes praetor in Rome.

Judea

 * Aristobulus II becomes king and high priest of Judea, until 63 BC.

Births

 * Octavia (the Younger), grandniece of Julius Caesar (d. 11 BC)

Deaths

 * Licinius Macer, Roman annalist

title: 66 BC


text:
67 BC

Year 67 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Piso and Glabrio (or, less frequently, year 687 Ab urbe condita). The denomination 67 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Republic

 * Consuls: Manius Acilius Glabrio and Gaius Calpurnius Piso.
 * During Pompey's war against the pirates, he raises a fleet of 500 warships and fights with great success.
 * The lex Gabinia gives Pompey command of the Mediterranean and its coasts for 50 miles inland for three years. He defeats the pirates in three months and pacifies Cilicia.
 * Pompey divides the Mediterranean into 13 zones – six in the West and seven in the East – to each of which he assigns a fleet under an admiral.
 * Pompey offers the ex-pirates and their families clemency, he settles them in agricultural colonies in eastern Mediterranean lands.
 * Pompey takes over the command of Lucius Lucullus in the war against Mithridates VI, and reaps the fruit of the latter's victories.
 * Lex Acilia Calpurnia: permanent exclusion from office in cases of electoral corruption.
 * Lex Roscia theatralis.
 * Julius Caesar reconciles with Pompey and Crassus
 * Julius Caesar marries Pompeia, a granddaughter of Sulla

Judea

 * Hyrcanus II becomes king of Judea, for first time (until 66 BC), upon the death of his mother, Salome Alexandra.

Pontus

 * Mithridates VI invades Pontus and defeats a Roman army at the Battle of Zela.
 * After his victory at Zela Mithridates started consolidating his power in Pontus; restoring his rule over his old kingdom.
 * Lucullus returned to Pontus, but his troops refused to campaign for him any longer and he withdrew to Galatia.

China

 * December – The army of the Han dynasty Chinese commander Zheng Ji is victorious over the Xiongnu in the Battle of Jushi.

Births

 * Arsinoe IV of Egypt, daughter of Ptolemy XII (and probably Cleopatra V) (d. 41 BC)
 * Sextus Pompey, Roman general and governor (d. 35 BC)

Deaths

 * Lucius Cornelius Sisenna, Roman general and historian (b. c. 120 BC)
 * Salome Alexandra, queen of Judea (b. 139 BC)

title: 67 BC


text:
Kerckhoffs's principle

Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be secure, even if everything about the system, except the key, is public knowledge. This concept is widely embraced by cryptographers, in contrast to security through obscurity, which is not.

Kerckhoffs's principle was phrased by American mathematician Claude Shannon as "the enemy knows the system", i.e., "one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them". In that form, it is called Shannon's maxim.

Another formulation by American researcher and professor Steven M. Bellovin is: "In other words — design your system assuming that your opponents know it in detail. (A former official at NSA's National Computer Security Center told me that the standard assumption there was that serial number 1 of any new device was delivered to the Kremlin.)"

Origins
The invention of telegraphy radically changed military communications and increased the number of messages that needed to be protected from the enemy dramatically, leading to the development of field ciphers which had to be easy to use without large confidential codebooks prone to capture on the battlefield. It was this environment which led to the development of Kerckhoffs' requirements.

Auguste Kerckhoffs was a professor of German language at Ecole des Hautes Etudes Commerciales (HEC) in Paris. In early 1883, Kerckhoffs' article, La Cryptographie Militaire, was published in two parts in the Journal of Military Science, in which he stated six design rules for military ciphers. Translated from French, they are:

 * 1) The system must be practically, if not mathematically, indecipherable;
 * 2) It should not require secrecy, and it should not be a problem if it falls into enemy hands;
 * 3) It must be possible to communicate and remember the key without using written notes, and correspondents must be able to change or modify it at will;
 * 4) It must be applicable to telegraph communications;
 * 5) It must be portable, and should not require several persons to handle or operate;
 * 6) Lastly, given the circumstances in which it is to be used, the system must be easy to use and should not be stressful to use or require its users to know and comply with a long list of rules.

Some are no longer relevant given the ability of computers to perform complex encryption. The second rule, now known as Kerckhoffs's principle, is still critically important.

Explanation of the principle
Kerckhoffs viewed cryptography as a rival to, and a better alternative than, steganographic encoding, which was common in the nineteenth century for hiding the meaning of military messages. One problem with encoding schemes is that they rely on humanly-held secrets such as "dictionaries" which disclose for example, the secret meaning of words. Steganographic-like dictionaries, once revealed, permanently compromise a corresponding encoding system. Another problem is that the risk of exposure increases as the number of users holding the secrets increases.

Nineteenth century cryptography, in contrast, used simple tables which provided for the transposition of alphanumeric characters, generally given row-column intersections which could be modified by keys which were generally short, numeric, and could be committed to human memory. The system was considered "indecipherable" because tables and keys do not convey meaning by themselves. Secret messages can be compromised only if a matching set of table, key, and message falls into enemy hands in a relevant time frame. Kerckhoffs viewed tactical messages as only having a few hours of relevance. Systems are not necessarily compromised, because their components (i.e. alphanumeric character tables and keys) can be easily changed.

Advantage of secret keys
Using secure cryptography is supposed to replace the difficult problem of keeping messages secure with a much more manageable one, keeping relatively small keys secure. A system that requires long-term secrecy for something as large and complex as the whole design of a cryptographic system obviously cannot achieve that goal. It only replaces one hard problem with another. However, if a system is secure even when the enemy knows everything except the key, then all that is needed is to manage keeping the keys secret.

There are a large number of ways the internal details of a widely used system could be discovered. The most obvious is that someone could bribe, blackmail, or otherwise threaten staff or customers into explaining the system. In war, for example, one side will probably capture some equipment and people from the other side. Each side will also use spies to gather information.

If a method involves software, someone could do memory dumps or run the software under the control of a debugger in order to understand the method. If hardware is being used, someone could buy or steal some of the hardware and build whatever programs or gadgets needed to test it. Hardware can also be dismantled so that the chip details can be examined under the microscope.

Maintaining security
A generalization some make from Kerckhoffs's principle is: "The fewer and simpler the secrets that one must keep to ensure system security, the easier it is to maintain system security." Bruce Schneier ties it in with a belief that all security systems must be designed to fail as gracefully as possible:

Any security system depends crucially on keeping some things secret. However, Kerckhoffs's principle points out that the things kept secret ought to be those least costly to change if inadvertently disclosed.

For example, a cryptographic algorithm may be implemented by hardware and software that is widely distributed among users. If security depends on keeping that secret, then disclosure leads to major logistic difficulties in developing, testing, and distributing implementations of a new algorithm – it is "brittle". On the other hand, if keeping the algorithm secret is not important, but only the keys used with the algorithm must be secret, then disclosure of the keys simply requires the simpler, less costly process of generating and distributing new keys.

Applications
In accordance with Kerckhoffs's principle, the majority of civilian cryptography makes use of publicly known algorithms. By contrast, ciphers used to protect classified government or military information are often kept secret (see Type 1 encryption). However, it should not be assumed that government/military ciphers must be kept secret to maintain security. It is possible that they are intended to be as cryptographically sound as public algorithms, and the decision to keep them secret is in keeping with a layered security posture.

Security through obscurity
It is moderately common for companies, and sometimes even standards bodies as in the case of the CSS encryption on DVDs, to keep the inner workings of a system secret. Some argue this "security by obscurity" makes the product safer and less vulnerable to attack. A counter-argument is that keeping the innards secret may improve security in the short term, but in the long run, only systems that have been published and analyzed should be trusted.

Steven Bellovin and Randy Bush commented:

title: Kerckhoffs's principle


text:
68 BC

Year 68 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Metellus/Vatia and Rex (or, less frequently, year 686 Ab urbe condita). The denomination 68 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Republic

 * Consuls: Lucius Caecilius Metellus and Quintus Marcius Rex.
 * October 6 – Lucius Lucullus defeats Tigranes II of Armenia in the Battle of Artaxata.
 * Gaius Antonius Hybrida elected praetor.
 * Tribune of the plebs Gaius Antius Restio passes the Lex Antia sumptuaria law forbidding Roman magistrates from attending banquets.
 * Ostia, the harbour city of Ancient Rome, is sacked by pirates. The port is set on fire and the consular war fleet is destroyed.

Osroene

 * Abgar II becomes ruler of Osroene.

Births

 * Arsinoe IV of Egypt, daughter of Ptolemy XII (and probably Cleopatra V) (d. 41 BC)

Deaths

 * Antiochus of Ascalon, Greek philosopher (b. c. 130 BC)
 * Cornelia, wife of Julius Caesar (b. 94 BC)
 * Huo Guang, official of the western Han Dynasty
 * Lucius Caecillius Metellus, Roman consul

title: 68 BC


text:
69 BC

Year 69 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Hortensius and Metellus (or, less frequently, year 685 Ab urbe condita). The denomination 69 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

Roman Republic

 * October 6 – Roman Republic troops under Lucius Lucullus defeat the army of Tigranes II of Armenia in the Battle of Tigranocerta, and capture Tigranocerta, capital of Armenia.
 * Consuls: Quintus Caecilius Metellus Creticus and Quintus Hortensius.
 * Antiochus XIII Asiaticus is installed as king of Syria.
 * Parthians and Romans re-establish Euphrates as a frontier.
 * Gaius Julius Caesar is a quaestor in Spain.

Egypt

 * Ptolemy XII deposes Cleopatra V, and becomes sole ruler.

Greece

 * Kydonia, an ancient city on the island of Crete falls to Roman military forces.
 * Rhodes becomes a bulwark against pirates, the Rhodians are unable to suppress piracy in the Aegean Sea. Delos gets the status of a free port.

Births

 * Cleopatra VII Philopator, queen of Egypt (d. 30 BC)
 * Hyeokgeose, Korean king and founder of Silla (d. AD 4)
 * Wang Zhengjun, empress of the Western Han dynasty (d. AD 13)

Deaths

 * Cleopatra II Selene, queen of Egypt
 * Julia, wife of Gaius Marius (b. c. 130 BC)

title: 69 BC


text:
The Magician's Nephew

The Magician's Nephew is a portal fantasy children's novel by C. S. Lewis, published in 1955 by The Bodley Head. It is the sixth published of seven novels in The Chronicles of Narnia (1950–1956). In recent editions, which sequence the books according to Narnia history, it is volume one of the series. Like the others, it was illustrated by Pauline Baynes whose work has been retained in many later editions. The Bodley Head was a new publisher for The Chronicles, a change from Geoffrey Bles who had published the previous five novels.

The Magician's Nephew is a prequel to the series. The middle third of the novel features the creation of the Narnia world by Aslan the lion, centred on a section of a lamp-post brought by accidental observers from London in 1900. The visitors then participate in the beginning of Narnia's history, 1000 years before The Lion, the Witch and the Wardrobe (which inaugurated the series in 1950).

The frame story, set in England, features two children ensnared in experimental travel via "the wood between the worlds". Thus, the novel shows Narnia and our middle-aged world to be only two of many in a multiverse, which changes as some worlds begin and others end. It also explains the origin of foreign elements in Narnia, not only the lamp-post but also the White Witch and a human king and queen.

Lewis began The Magician's Nephew soon after completing The Lion, the Witch and the Wardrobe, spurred by a friend's question about the lamp-post in the middle of nowhere, but he needed more than five years to complete it. The story includes several autobiographical elements and explores a number of themes with general moral and Christian implications, including atonement, original sin, temptation, and the order of nature.

Plot summary
The story begins in London during the summer of 1900. Two children, Digory and Polly, meet while playing in the adjacent gardens of a row of terraced houses. They decide to explore the abandoned attic beyond Digory's house, but do not walk far enough, and find themselves in Uncle Andrew's study. Uncle Andrew tricks Polly into touching a yellow magic ring, causing her to vanish. Then he explains to Digory that he has been dabbling in magic, and that the rings allow travel between one world and another. He blackmails Digory into taking another yellow ring to follow wherever Polly has gone, and two green rings so that they both can return.

Digory finds himself transported to a sleepy woodland with an almost narcotic effect; he finds Polly nearby. The woodland is filled with pools. Digory and Polly surmise that the wood is not really a proper world at all but a "Wood between the Worlds", similar to the attic that links their houses back in England, and that each pool leads to a separate universe. They decide to explore a different world before returning to England, and jump into one of the nearby pools. They then find themselves in a desolate abandoned city of the ancient world of Charn. Inside the ruined palace, they discover statues of Charn's former kings and queens, which degenerate from the fair and wise to the unhappy and cruel. They find a bell with a hammer and an inscription inviting the finder to strike the bell.

Despite protests from Polly, Digory rings the bell. This awakens the last of the statues, a witch queen named Jadis, who—to avoid defeat in battle—had deliberately killed every living thing in Charn by speaking the "Deplorable Word". As the only survivor left in her world, she placed herself in an enchanted sleep that would only be broken by someone ringing the bell.

The children recognise Jadis as evil and attempt to flee, but she follows them back to England by clinging to them as they clutch their rings. In England, she discovers that her magical powers do not work, although she retains her superhuman strength. Dismissing Uncle Andrew as a poor magician, she enslaves him and orders him to fetch her a "chariot"—a hansom cab—so she can set about conquering Earth. They leave, and she attracts attention by robbing a jeweller's shop in London. The police chase after her cab, until she crashes at the foot of the Kirke house. Jadis breaks off and tears an iron rod from a nearby lamp-post, using it to fight off police and onlookers when they mock her.

When Jadis threatens the crowd, Polly and Digory grab her and put on their rings to take her out of their world –along with Uncle Andrew, Frank the cab-driver, and Frank's horse, Strawberry, who were all touching each other when the children grabbed their rings. In the Wood between the Worlds, Strawberry, when attempting to drink from one of the ponds, accidentally brings everyone into another world: a dark, empty void. At first, Digory believes it to be Charn, but Jadis recognises it as a world not yet created. They then all witness the creation of a new world by the lion Aslan, who brings stars, plants, and animals into existence as he sings. Jadis, as terrified by his singing as the others are attracted to it, tries to kill Aslan with the iron rod; but it rebounds harmlessly off him, and in the creative soil of the new world it sprouts into a growing lamp-post. Jadis flees in terror.

Aslan gives some animals the power of speech, commanding them to use it for justice and merriment or else risk becoming regular animals once again. Frank the cabby and his wife Helen are then crowned King and Queen of Narnia. Aslan confronts Digory with his responsibility for bringing Jadis into his young world, and tells Digory he must atone by helping to protect the new land of Narnia from her evil. Aslan transforms Strawberry, Frank's horse, into a winged horse called Fledge, and Digory and Polly fly on him to a distant garden high in the mountains. Digory's task is to take an apple from a tree in this garden and plant it in Narnia. At the garden Digory finds a sign warning not to steal from the garden.

Digory picks one of the apples for his mission, but their overpowering smell tempts him. Jadis appears, having herself eaten an apple to become immortal, leaving her with pale white skin. She tempts Digory either to eat an apple himself and join her in immortality, or steal one to take back to Earth to heal his dying mother. Digory resists, knowing his mother would never condone theft, but hesitates. He sees through the Witch's ploy when she suggests he leave Polly behind –not knowing Polly can get away by her own ring. Foiled, the Witch departs for the North, and taunts Digory for his refusal to eat the apple and gain immortality. Digory returns to Narnia and plants the apple, which grows into a mature tree behind them while the coronation proceeds. Aslan tells Digory how the tree works – anyone who steals the apples gets their heart's desire, but in a form that renders it extremely disagreeable. In the Witch's case, she has achieved immortality, but it only means eternal misery because of her evil heart. Moreover, the magic apples are now a horror to her, so much so that the apple tree will repel her for centuries to come, but not forever. With Aslan's permission, Digory takes an apple from the new tree to heal his mother. Aslan returns Digory, Polly, and Uncle Andrew to England. Frank and his wife Helen (transported from England by Aslan) stay to rule Narnia as its first King and Queen. The Narnian creatures live in peace and joy, and neither the Witch nor any other enemy will come to trouble Narnia for many hundreds of years.

Digory's apple restores his mother's health as his father returns for good after being away on business in India, and he and Polly remain lifelong friends. Uncle Andrew reforms and gives up magic, but still enjoys bragging about his adventures with the Witch. Digory plants the apple's core with Uncle Andrew's rings in the back yard of his aunt's home in London, and it grows into a large tree. Soon afterwards, Digory's family inherits a mansion in the country, and many years later the apple tree blows down in a storm. Digory, now a middle-aged professor, has its wood made into a wardrobe, setting up the events in The Lion, the Witch and the Wardrobe.

Principal characters

 * Digory Kirke: The boy who becomes the Professor in The Lion, the Witch and the Wardrobe
 * Polly Plummer: Digory's friend, who lives next door
 * Mabel Kirke: Digory's mother
 * Andrew Ketterley: Digory's uncle, a minor magician
 * Letitia Ketterley: Uncle Andrew's sister
 * Jadis: Empress of Charn, who becomes the White Witch appearing in The Lion, the Witch and the Wardrobe
 * Aslan: The Lion who creates Narnia and kills Jadis in The Lion, the Witch and the Wardrobe
 * King Frank: A cabby who becomes the first king of Narnia and ancestor of the kings of Archenland
 * Queen Helen: The wife of King Frank, the first queen of Narnia, and the ancestress of the Archenlanders
 * Fledge: The winged horse, formerly the cab-horse Strawberry, who carries Polly and Digory to the mountain garden

Writing
Lewis had originally intended only to write the one Narnia novel, The Lion, the Witch and the Wardrobe. However, when Roger Lancelyn Green asked him how a lamp-post came to be standing in the midst of Narnian woodland, Lewis was intrigued enough by the question to attempt to find an answer by writing The Magician's Nephew, which features a younger version of Professor Kirke from the first novel.

The Magician's Nephew seems to have been the most challenging Narnia novel for Lewis to write. The other six Chronicles of Narnia books were written between 1948 and 1953, The Magician's Nephew was written over a five-year period between 1949 and 1954. He started in the summer of 1949 after finishing The Lion, the Witch and the Wardrobe, but came to a halt after producing 26 pages of manuscript and did not resume work until two years later. This may be as a result of the autobiographical aspects of the novel, as it reflects a number of incidents and parallels very close to his own experiences.

He returned to The Magician's Nephew late in 1950, after completing The Silver Chair. He managed to finish close to three-quarters of the novel, and then stopped work once again after Roger Green, to whom Lewis showed all his writing at the time, suggested there was a structural problem in the story. Finally he returned to the novel in 1953, after finishing The Last Battle in the spring of that year and completed early in 1954.

Lewis originally titled the novel "Polly and Digory"; his publisher changed it to The Magician's Nephew. This book is dedicated to "the Kilmer family".

The Lefay Fragment
The original opening of the novel differs greatly from the published version, and was abandoned by Lewis. It is now known as 'The Lefay Fragment', and is named after Mrs Lefay, Digory's fairy godmother, who is mentioned in the final version as Uncle Andrew's godmother, a less benevolent user of magic, who bequeathed him the box of dust used to create the magic rings.

In the Lefay Fragment, Digory is born with the ability to speak to (and understand) trees and animals; the distinction between Talking and non-Talking Beasts which was to become such a characteristic feature of the Narnian world is absent. Digory lives with an Aunt Gertrude, a former school mistress with an officious, bullying nature, who has ended up as a Government minister after a lifetime of belligerent brow-beating of others. Whenever his aunt is absent, Digory finds solace with the animals and trees, including a squirrel named Pattertwig. Polly enters the story as a girl next door who is unable to understand the speech of non-human creatures. She wants to build a raft to explore a stream which leads to an underground world. Digory helps construct the raft, but saws a branch from a tree necessary to complete it, in order not to lose face with Polly. This causes him to lose his supernatural powers of understanding the speech of trees and animals. The following day he is visited by his godmother Mrs Lefay who knows that Digory has lost his abilities and gives him a card with the address of a furniture shop which she instructs him to visit. At this point the fragment ends.

Pattertwig and Aunt Gertrude do not appear in the final version of the novel. Pattertwig does, however, appear as a Narnian creature in Prince Caspian, and Aunt Gertrude's career path is retraced by the Head of Experiment House in The Silver Chair.

Authenticity
Some doubt has been cast on the authenticity of the Lefay Fragment, as the handwriting in the manuscript differs in some ways from Lewis's usual style, and the writing is not of a similar calibre to his other work. Also in August 1963 Lewis had given instructions to Douglas Gresham to destroy all his unfinished or incomplete fragments of manuscript when his rooms at Magdalene College, Cambridge were being cleaned out, following his resignation from the college early in the month.

Autobiographical elements
A number of aspects of The Magician's Nephew are parallels with Lewis's own life. Both Digory and Lewis were children in the early 1900s, both wanted a pony, and both were faced with the death of their mothers in childhood. Digory is separated from his father, who is in India, and misses him. Lewis was educated in England after his mother's death, while his father remained in Ireland. He also had a brother in India. Both Lewis and Digory were voracious readers as children, and both are better with books than with numbers. Digory (and Polly) struggle with sums when trying to work out how far they must travel along the attic space to explore an abandoned house, Lewis failed the maths entrance exam for Oxford University. Lewis remembered rainy summer days from his youth and Digory is faced with the same woe in the novel. Additionally Digory becomes a professor when he grows up, who takes in evacuated children during World War II.

The character of Andrew Ketterley also closely resembles Robert Capron, a schoolmaster at Wynyard School, which Lewis attended with his brother, whom Lewis suggested during his teens would make a good model for a villain in a future story. Ketterley resembles Capron in his age, appearance, and behaviour.

Style
The Magician's Nephew is written in a lighter tone than other Chronicles of Narnia books, in particular The Last Battle, which was published after. It frequently makes use of humour; this perhaps reflects the sense of looking back at an earlier part of the century with affection, and Lewis as a middle-aged man recalling his childhood during those years. There are a number of humorous references to life in the old days, in particular school life. Humorous exchanges also take place between Narnian animals. Jadis's attempt to conquer London is portrayed as more comical than threatening, and further humour derives from the contrast between the evil empress and Edwardian London and its social mores, and her humiliation of bumbling Andrew Ketterley after discovering he is not as powerful a sorcerer as she is (or was). This recalls the style of Edith Nesbit's children's books. Lewis was fond of these books, which he read in childhood, a number were set in the same period and The Magician's Nephew has some apparent references or homages to them.

Reading order
The Magician's Nephew was originally published as the sixth book in the Narnia Chronicles. Most reprintings of the novels until the 1980s also reflected the order of original publication. In 1980 HarperCollins published the series ordered by the chronology of the events in the novels. This meant The Magician's Nephew was numbered as the first in the series. HarperCollins, which had previously published editions of the novels outside the United States, also acquired the rights to publish the novels in that country in 1994 and used this sequence in the uniform worldwide edition published in that year.

Laurence Krieg, a young fan, wrote to Lewis, asking him to adjudicate between his views of the correct sequence of reading the novels – according to the sequence of events, with The Magician's Nephew being placed first – and that of his mother, who thought the order of publication was more appropriate. Lewis wrote back, appearing to support the younger Krieg's views, although he did point out that perhaps it would not matter what order they were read in.

Some literary scholars have argued that the publication order is more effective in drawing the readers into the world of Narnia. In the book Lewis wrote first, Lucy Pevensie's discovery of the wardrobe that opens onto a forest and a mysterious lamp-post creates a sense of suspense about an unknown land she is discovering for the first time. This would be anticlimactic if the reader has already been introduced to Narnia in The Magician's Nephew and already knows the origins of Narnia, the wardrobe, and the lamp-post. Lewis scholar Peter Schakel points out that the narrative of The Magician's Nephew assumes that the reader has already read The Lion, the Witch and the Wardrobe and is now being shown its beginnings.

Paul Ford cites several scholars who have weighed in against the decision of HarperCollins to present the books in the order of their internal chronology, and continues, "most scholars disagree with this decision and find it the least faithful to Lewis's deepest intentions". These scholars argue that the narrative of The Magician's Nephew appears to assume that the reader has already read The Lion, the Witch and the Wardrobe and is now being shown its beginnings.

Parallels with the Book of Genesis
Lewis suggested that he did not directly intend to write his Narnia stories as Christian tales, but that these aspects appeared subconsciously as he wrote, although the books did become Christian as they progressed. He thought that the tales were not direct representations or allegory, but that they might evoke or remind readers of Biblical stories. In The Lion, the Witch and the Wardrobe, Aslan is a Christ-like figure who suffers a death of atonement and returns to life in a similar way to Christ's crucifixion and resurrection. The Magician's Nephew has similar biblical allusions, reflecting aspects of the Book of Genesis such as the creation, original sin and temptation.

Parallels with events in the Book of Genesis include the forbidden fruit represented by an Apple of Life. Jadis tempts Digory to eat one of the forbidden apples in the garden, as the serpent tempts Eve into eating a forbidden fruit in the Garden of Eden; unlike Eve however, Digory rejects the offer. (Lewis's Perelandra also features a re-enactment of the same Biblical story, which in that book also ends with the tempter foiled and the fall avoided.)

While the creation of Narnia closely echoes the creation of the Earth in the Book of Genesis, there are a number of important differences. Human beings are not created in Narnia by Aslan, they are brought into Narnia from our own world. Unlike Genesis, where souls are given only to human beings, animals and half-human half-animal creatures such as Fauns and Satyrs and even trees and watercourses are given souls and the power of rational thought and speech. This appears to suggest Lewis combined his Christian outlook with his fondness for nature, myths and fairy tales.

Parallels may also be found in Lewis's other writings. Jadis's references to "reasons of State", and her claim to own the people of Charn and to be beyond morality, represent the eclipse of the medieval Christian belief in natural law by the political concept of sovereignty, as embodied first in royal absolutism and then in modern dictatorships. Uncle Andrew represents the Faustian element in the origins of modern science.

The Holy Spirit and the breath of life
On a number of occasions in the Chronicles of Narnia, Aslan uses his breath to give strength to characters, demonstrating his benevolent power of bringing life. He specifically does so in The Magician's Nephew when a "long warm breath" gives life to Narnia. Lewis used the symbol of breath to represent the Holy Spirit, also known as the Holy Ghost. Both spirit and ghost are translations of the word for breath in Hebrew and Greek. The flash from the stars when the Narnian animals are given the ability to talk also most probably represents the Holy Spirit or "breath of life" of Genesis chapter 2, as well as (possibly) the scholastic concept of the divine active intellect that inspires human beings with rationality.

Nature and a natural order
The Magician's Nephew suggests two opposing approaches to nature, a good approach associated with Aslan as creator and an evil approach associated with human deviation from divine intentions and the harmony of a natural order. On the one hand there is the beauty of Aslan's creation of Narnia, which is suggested as having a natural order by the use of musical harmony to bring landscapes and living things into being. There is also a distinct order to the process of creation, from earth to plants to animal, which evokes the concept of The Great Chain of Being. Lewis himself was a strong believer in the intrinsic value of nature for itself, rather than as a resource to be exploited. This is perhaps reflected in how Aslan also gives speech to spiritual aspects of nature, such as naiads in the water and dryads in the trees. Andrew Ketterley and Jadis represent an opposite, evil approach of bending the forces of nature to human will for their own gain. They see nature solely as a resource to use for their plans and thus disturb and destroy the natural order.

John Milton's Paradise Lost
The sacred Garden in the west of the Narnian world is surrounded by a "high wall of green turf" with branches of trees overhanging it, and "high gates of gold, fast shut, facing due east", which must be the only entrance because the travellers "walked nearly all the way round it" before they found them. In all these points Lewis echoes John Milton's description of Eden in Paradise Lost:

 * The verdurous wall of Paradise up sprung...

 * And higher than that Wall a circling row
 * Of goodliest trees loaden with fairest fruit,
 * Blossoms and fruits at once of golden hue,
 * Appeerd, with gay enameld colours mixt...

 * One gate there only was, and that look'd east
 * On th' other side...

Jadis takes on echoes of Satan from the same work: she climbs over the wall of the Garden in contempt of the command to enter only by the gate, and proceeds to tempt Digory as Satan tempted Eve, with lies and half-truths.

Some details of the creation of Narnia, such as the emergence of animals from the ground, and the way they shake earth from their bodies are also similar to passages in Paradise Lost, and may also have been inspired by descriptions of the processes of nature in the seventh book of Edmund Spenser's The Faerie Queene.

The Garden of the Hesperides
Four years before the publication of the first Narnia book, Lewis had written as follows on the experience of reading really good poetry for the first time: ...I did not in the least feel that I was getting in more quantity or better quality a pleasure I had already known. It was more as if a cupboard which one had hitherto valued as a place for hanging coats proved one day, when you opened the door, to lead to the garden of the Hesperides...

The element of the cupboard leading to a new world Lewis proceeded to use in The Lion, the Witch and the Wardrobe, but the snowy Narnia of that book is quite unlike the balmy Garden of the Hesperides, most of whose major mythological features appear as attributes of the sacred Garden in The Magician's Nephew where it differs from the Biblical or Miltonian Eden. It is set in the far West of the world; it has a watchful guardian; a hero (Digory) is sent, like Hercules, to fetch an apple from it; a female villain (Jadis) steals another of the apples, like Eris. Since the eponymous Hesperides were daughters of Hesperus, the god of the planet Venus in the evening, advocates of the planetary theory adduce this as evidence for a special association between The Magician's Nephew and Venus.

Edith Nesbit
Lewis read Edith Nesbit's children's books as a child and was extremely fond of them. The Magician's Nephew refers to these books in the opening of the novel as though their events were true, mentioning the setting of the piece as being when "Mr. Sherlock Holmes was still living in Baker Street and the Bastables were looking for treasure in the Lewisham Road". The Bastables were children who appeared in a number of Edith Nesbit's stories. In addition to being set in the same period and location as several of Nesbit's stories, The Magician's Nephew also has some similarities with Nesbit's The Story of the Amulet (1906). This novel focuses on four children living in London who discover a magic amulet. Their father is away and their mother is ill, as is the case with Digory. They also manage to transport the queen of ancient Babylon to London and she is the cause of a riot; a very similar event takes place in The Magician's Nephew when Polly and Digory transport Queen Jadis to London and she also causes a similar disturbance.

J. R. R. Tolkien
The creation of Narnia may also have been influenced by his close friend J. R. R. Tolkien's The Silmarillion, which also contains a creation scene driven by the effect of music.

Morgan Le Fay and Pandora's Box
Lewis greatly enjoyed stories of Arthurian legend and wrote poetry about this world. Mrs Lefay visits Digory in The Lefay Fragment, and becomes Andrew Ketterley's nefarious godmother in the finished novel. She gives Ketterley a box from Atlantis containing the dust from which he constructs the rings Digory and Polly use to travel between worlds. Both Lefays are allusions to Morgan Le Fay, a powerful sorceress in a number of versions of King Arthur's tales, who is often portrayed as evil. The box itself is also evocative of Pandora's box from Greek myth, which also contained dangerous secrets.

The Atlantis legend
The box of dust enabling travel between worlds originated in Atlantis. Both Lewis and Tolkien were fascinated by the Atlantis legend. The degeneration of Charn's rulers, Jadis's ancestors, from the early kind and wise to the later cruel and arrogant is reminiscent of the similar degeneration in Tolkien's Númenor, the fabled island kingdom that finally sank under the waves due to the sinfulness of its latter inhabitants. The world of Charn was destroyed when Jadis spoke The Deplorable Word, a form of knowledge ancient Charnian scholars feared for its destructive potential. A number of commentators believed Lewis was referring to the use of the atomic bomb, used less than a decade earlier. It is perhaps more likely that Lewis was echoing the mythical destruction of Atlantis by the forces of evil and arrogance. As noted by Alice Ward, the comparison with nuclear arms is made explicit in Aslan's last warning: "You [Earth] are growing more like it [Charn]. It is not certain that some wicked one of your race will not find out a secret as evil as The Deplorable Word and use it to destroy all living things".

Theatrical
Aurand Harris was a well-known American playwright for children, whose works are among the most performed in that medium. He wrote 36 plays for children including an adaption of The Magician's Nephew. The play was first performed on 26 May 1984 by the Department of Drama, University of Texas, Austin and staged at the B. Iden Payne Theatre. A musical score by William Penn was written for use with productions of the play.

Erina Caradus wrote a playscript for The Magician's Nephew that was performed in Dunedin, New Zealand in 2005.

Film
An agreement among representatives of 20th Century Fox, Walden, and the C. S. Lewis estate determined that The Magician's Nephew would be the basis for the next film following the release of the 2010 film The Voyage of the Dawn Treader. However, in October 2011, Douglas Gresham confirmed that Walden Media's contract with the C. S. Lewis estate had expired.

On 1 October 2013, the C.S. Lewis Company announced that they had entered into an agreement with producer Mark Gordon to jointly develop and produce The Chronicles of Narnia: The Silver Chair, ultimately deciding to continue releasing the films to mirror the novel series' publication order.

In October 2018, Netflix announced an agreement with the C.S. Lewis Company. Netflix will develop and produce new series and movies based on The Chronicles of Narnia. Mark Gordon of Entertainment One, Douglas Gresham and Vincent Sieber will serve as producers for films and executive producers for series.

TV
In 2003, the BBC produced a 10-part version read by Jane Lapotaire and signed by Jean St Clair wearing different Narnia-like clothes in British Sign Language, for the TV series Hands Up! which was first broadcast on the 16 January 2003. Jean signed in front of various high quality illustrations representing parts of the novel. It was later repeated on CBBC on the 3 December 2007, and BBC Two on the 16 September 2008.

Radio
A BBC Radio 4 adaptation exists. Focus on the Family also made an adaptation of this book with a full cast, sound editing, and music. Both productions adapted all seven books.

Manga
A HarperCollins Japan manga adaptation, Chronicles Of Narnia: The Magician's Nephew: I Opened the Wrong Door! (ナルニア国物語: 魔術師のおい: 間違ったドアを開けた!), began publication in 2018, before concluding in 2020 after two volumes.

Critical reception
T.M. Wagner of SF Reviews said "The Magician's Nephew may not be the best of the Narnia novels, but it's a brisk and funny tale certain to delight its intended young audience", saying that it may not satisfy readers in their teenage years and older.

Jandy's Reading Room reviewed the book, saying that although they feel it is the weakest of the series, they would still recommend it. They say it "gives a wonderful picture of the beginning of a new world, in the manner of the Creation."

title: The Magician's Nephew


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Jehuda Cresques

Jehudà Cresques (, 1360-1410), also known as Jafudà Cresques, Jaume Riba, and Cresques lo Juheu ("Cresques the Jew"), was a converso cartographer from Majorca in the early 15th century.

Biography
The son of Abraham Cresques, a famous Jewish cartographer, he was born in a Jewish family in Majorca, in the Majorcan-Catalan speaking part of Crown of Aragon, in present-day Spain. Together he and his father were the probable authors of the famous Catalan Atlas of 1375.

Cresques' work was highly sought after. In 1390 John I of Aragon paid 60 livres and 8 sous for one of his maps. After the Aragonese persecutions of 1391 he was forcibly converted to Christianity, at which time he took the name Jaume Riba, Jacobus Ribus, in Latin. He appears to have remained in Majorca for a considerable time and to have become known to the people there as "lo jueu buscoler", the map Jew, or "el jueu de les bruixoles", the compass Jew.

'Mestre Jacome'
It has long been believed that Jehuda Cresques is the same person as 'Mestre Jacome', a Majorcan cartographer induced by the Portuguese prince Henry the Navigator to move to Portugal in the 1420s to train Portuguese map-makers in Majorcan-style cartography. 'Jacome of Majorca' was described as the head of Henry's legendary observatory and "school" at Sagres by Samuel Purchas, though the existence of the alleged school has long been discounted.

The identification of "Mestre Jacome" with Jehuda Cresques" is principally due to the Catalan historian Gonzalo de Reparaz (1930). More recent research argues that Jehuda Cresques was dead by 1410, and "Mestre Jacome" must have been someone else, identity still indeterminate - Majorca had many skilled Jewish cartographers.

title: Jehuda Cresques


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Darwin (operating system)

Darwin is the core Unix-like operating system of macOS (previously OS X and Mac OS X), iOS, watchOS, tvOS, iPadOS, audioOS, visionOS, and bridgeOS. It previously existed as an independent open-source operating system, first released by Apple Inc. in 2000. It is composed of code derived from NeXTSTEP, FreeBSD, other BSD operating systems, Mach, and other free software projects' code, as well as code developed by Apple.

Darwin is mostly POSIX-compatible, but has never, by itself, been certified as compatible with any version of POSIX. Starting with Leopard, macOS has been certified as compatible with the Single UNIX Specification version 3 (SUSv3).

History
The heritage of Darwin began with Unix derivatives supplemented by aspects of NeXT's NeXTSTEP operating system (later, since version 4.0, known as OPENSTEP), first released in 1989. After Apple bought NeXT in 1996, it announced it would base its next operating system on OPENSTEP. This was developed into Rhapsody in 1997, Mac OS X Server 1.0 in 1999, Mac OS X Public Beta in 2000, and Mac OS X 10.0 in 2001.

In 1999, Apple announced it would release the source code for the Mach 2.5 microkernel, BSD Unix 4.4 OS, and the Apache Web server components of Mac OS X Server. At the time, interim CEO Steve Jobs alluded to British naturalist Charles Darwin by announcing "because it's about evolution". In 2000, the core operating system components of Mac OS X were released as open-source software under the Apple Public Source License (APSL) as Darwin; the higher-level components, such as the Cocoa and Carbon frameworks, remained closed-source.

Up to Darwin 8.0.1, released in April 2005, Apple released a binary installer (as an ISO image) after each major Mac OS X release that allowed one to install Darwin on PowerPC and Intel x86 systems as a standalone operating system. Minor updates were released as packages that were installed separately. Darwin is now only available as source code. As of January 2023, Apple no longer mentions Darwin by name on its Open Source website and only publishes an incomplete collection of open-source projects relating to macOS and iOS.

Kernel
The kernel of Darwin is XNU, a hybrid kernel which uses OSFMK 7.3 (Open Software Foundation Mach Kernel) from the OSF, various elements of FreeBSD (including the process model, network stack, and virtual file system), and an object-oriented device driver API called I/O Kit. The hybrid kernel design provides the flexibility of a microkernel and the performance of a monolithic kernel.

Hardware and software support
The last bootable full release of Darwin supported 32-bit and 64-bit Apple PowerPC systems and 32-bit Intel PCs.

Darwin currently includes support for the 64-bit x86-64 variant of the Intel x86 processors used in Intel-based Macs and the 64-bit ARM processors used in the iPhone 5S and later, the 6th generation iPod Touch, the 5th generation iPad and later, the iPad Air family, the iPad Mini 2 and later, the iPad Pro family, the fourth generation and later Apple TVs, the HomePod family, and Macs with Apple silicon such as the 2020 Apple M1 Macs, as well as the Raspberry Pi 3B. An open-source port of the XNU kernel exists that supports Darwin on Intel and AMD x86 platforms not officially supported by Apple, though it does not appear to have been updated since 2009. An open-source port of the XNU kernel also exists for ARM platforms, though it has not been updated since 2016. Older versions supported some or all of 32-bit PowerPC, 64-bit PowerPC, 32-bit x86, and 32-bit ARM.

It supports the POSIX API by way of its BSD lineage (largely FreeBSD userland), so a large number of programs written for various other UNIX-like systems can be compiled on Darwin with no changes to the source code.

Darwin does not include many of the defining elements of macOS, such as the Carbon and Cocoa APIs or the Quartz Compositor and Aqua user interface, and thus cannot run Mac applications. It does, however, support a number of lesser-known features of macOS, such as mDNSResponder, which is the multicast DNS responder and a core component of the Bonjour networking technology, and launchd, an advanced service management framework.

License
In July 2003, Apple released Darwin under version 2.0 of the Apple Public Source License (APSL), which the Free Software Foundation (FSF) classifies as a free software license incompatible with the GNU General Public License. Previous versions were released under an earlier version of the APSL license, which did not meet the FSF definition of free software, although it did meet the requirements of the Open Source Definition.

Release history
The following is a table of major Darwin releases with their dates of release and their derivative operating system releases. Note that the corresponding releases may have been released on a different date.

Darwin 0–8 and corresponding Mac OS X releases
The jump in version numbers from Darwin 1.4.1 to 5.1 with the release of Mac OS X v10.1.1 was designed to tie Darwin to the Mac OS X version and build numbering system, which in turn is inherited from NeXTSTEP. In the build numbering system of macOS, every version has a unique beginning build number, which identifies what whole version of macOS it is part of. Mac OS X v10.0 had build numbers starting with 4, 10.1 had build numbers starting with 5, and so forth (earlier build numbers represented developer releases).

Darwin 20 onwards
''Note: the tables above contain the release dates of the corresponding OS releases. Build dates for Darwin versions are not publicly available; the commands below only give the build date for the XNU kernel.''

The command uname -r in Terminal will show the Darwin version number ("20.3.0"), and the command uname -v will show the XNU build version string, which includes the Darwin version number. The command sw_vers will show the corresponding ProductName ("macOS"), the ProductVersion number ("11.2.3") and the BuildVersion string ("20D91").

Derived projects
Due to the free software nature of Darwin, there have been projects that aim to modify or enhance the operating system.

OpenDarwin

OpenDarwin was a community-led operating system based on the Darwin system. It was founded in April 2002 by Apple Inc. and Internet Systems Consortium. Its goal was to increase collaboration between Apple developers and the free software community. Apple benefited from the project because improvements to OpenDarwin would be incorporated into Darwin releases; and the free/"open"-source community benefited from being given complete control over its own operating system, which could then be used in free software distributions such as GNU-Darwin.

On July 25, 2006, the OpenDarwin team announced that the project was shutting down, as they felt OpenDarwin had "become a mere hosting facility for Mac OS X related projects", and that the efforts to create a standalone Darwin operating system had failed. They also state: "Availability of sources, interaction with Apple representatives, difficulty building and tracking sources, and a lack of interest from the community have all contributed to this." The last stable release was version 7.2.1, released on July 16, 2004.

PureDarwin
PureDarwin is a project to create a bootable operating system image from Apple's released source code for Darwin. Since the halt of OpenDarwin and the release of bootable images since Darwin 8.x, it has been increasingly difficult to create a full operating system as many components became closed source. In 2015 the project created a preview release based on Darwin 9 with an X11 GUI, followed by a command-line only 17.4 Beta based on Darwin 17.

Other derived projects

 * XQuartz is a component of the X Window System that runs on macOS (Darwin). XDarwin, before the introduction of Apple's X11.app.
 * GNUstep is a free software implementation of the Cocoa (formerly OpenStep) Objective-C frameworks, widget toolkit, and application development tools for Unix-like operating systems.
 * Window Maker, a window manager designed to emulate the NeXT GUI as part of the wider GNUstep project.
 * WebKit is a browser engine primarily used in Apple's Safari web browser, as well as all web browsers on iOS and iPadOS.
 * MacPorts (formerly DarwinPorts), Fink, and Homebrew are projects to port UNIX programs to the Darwin operating system and provide package management. In addition, several standard UNIX package managers—such as RPM, pkgsrc, and Portage—have Darwin ports. Some of these operate in their own namespace so as not to interfere with the base system.
 * GNU-Darwin was a project that ports packages of free software to Darwin. They package OS images in a way similar to a Linux distribution.
 * The Darwine project was a port of Wine that allows one to run Microsoft Windows software on Darwin.
 * SEDarwin was a port of TrustedBSD mandatory access control framework and portions of the SELinux framework to Darwin. It was incorporated into Mac OS X 10.5.
 * The Darbat project was an experimental port of Darwin to the L4 microkernel family. It aims to be binary compatible with existing Darwin binaries.
 * The Darling project is a compatibility layer for running macOS binaries on Linux systems. It uses some Darwin source code.
 * There are various projects that focus on driver support: e.g., wireless drivers, wired NIC drivers   modem drivers, card readers, and the ext2 and ext3 file systems.
 * DarwinBSD Project is a Darwin project using pkgsrc for packages. It is an open source project.

title: Darwin (operating system)