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Income inequality metrics

Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. While different theories may try to explain how income inequality comes about, income inequality metrics simply provide a system of measurement used to determine the dispersion of incomes. The concept of inequality is distinct from poverty and fairness.

Income distribution has always been a central concern of economic theory and economic policy. Classical economists such as Adam Smith, Thomas Malthus and David Ricardo were mainly concerned with factor income distribution, that is, the distribution of income between the main factors of production, land, labour and capital. It is often related to wealth distribution, although separate factors influence wealth inequality.

Modern economists have also addressed this issue, but have been more concerned with the distribution of income across individuals and households. Important theoretical and policy concerns include the relationship between income inequality and economic growth. The article economic inequality discusses the social and policy aspects of income distribution questions.

Defining income
All of the metrics described below are applicable to evaluating the distributional inequality of various kinds of resources. Here the focus is on income as a resource. As there are various forms of "income", the investigated kind of income has to be clearly described.

One form of income is the total amount of goods and services that a person receives, and thus there is not necessarily money or cash involved. If a subsistence farmer in Uganda grows his own grain, it will count as income. Services like public health and education are also counted in. Often expenditure or consumption (which is the same in an economic sense) is used to measure income. The World Bank uses the so-called "living standard measurement surveys" to measure income. These consist of questionnaires with more than 200 questions. Surveys have been completed in most developing countries.

Applied to the analysis of income inequality within countries, "income" often stands for the taxed income per individual or per household. Here, income inequality measures also can be used to compare the income distributions before and after taxation in order to measure the effects of progressive tax rates.

Properties of inequality metrics
In the discrete case, an economic inequality index may be represented by a function I(x), where x is a set of n economic values (e.g. wealth or income) x={x1,x2,...,xn} with xi being the economic value associated with "economic agent" i.

In the economic literature on inequality four properties are generally postulated that any measure of inequality should satisfy:

I(P(x))=I(x) $$ I(\alpha x)=I(x) $$ I(x \cup x)=I(x) $$
 * Anonymity or symmetry
 * This assumption states that an inequality metric does not depend on the "labeling" of individuals in an economy and all that matters is the distribution of income. For example, in an economy composed of two people, Mr. Smith and Mrs. Jones, where one of them has 60% of the income and the other 40%, the inequality metric should be the same whether it is Mr. Smith or Mrs. Jones who has the 40% share. This property distinguishes the concept of inequality from that of fairness where who owns a particular level of income and how it has been acquired is of central importance. An inequality metric is a statement simply about how income is distributed, not about who the particular people in the economy are or what kind of income they "deserve".
 * This is generally expressed mathematically as:
 * where P(x) is any permutation of x;
 * Scale independence or homogeneity
 * This property says that richer economies should not be automatically considered more unequal by construction. In other words, if every person's income in an economy is doubled (or multiplied by any positive constant) then the overall metric of inequality should not change. Of course the same thing applies to poorer economies. The inequality income metric should be independent of the aggregate level of income. This may be stated as:
 * where α is a positive real number.
 * Population independence
 * Similarly, the income inequality metric should not depend on whether an economy has a large or small population. An economy with only a few people should not be automatically judged by the metric as being more equal than a large economy with many people. This means that the metric should be independent of the level of population. This is generally written:
 * where $$x \cup x$$ is the union of x with (a copy of) itself.
 * Transfer principle
 * The Pigou–Dalton, or transfer principle, is the assumption that makes an inequality metric actually a measure of inequality. In its weak form it says that if some income is transferred from a rich person to a poor person, while still preserving the order of income ranks, then the measured inequality should not increase. In its strong form, the measured level of inequality should decrease.

Other useful but not mandatory properties include:

I(y \cup z)=w_y(y,z) I(y)+w_z(y,z)I(z)+w_\mu(y,z) I({\mu_y,\mu_z}) $$ \mu_x=\frac{1}{n}\sum_1^n x_i $$
 * Non-negativity
 * The index I(x) is greater than or equal to zero.
 * Egalitarian zero
 * The index I(x) is zero in the egalitarian case, when all values xi are equal.
 * Bounded above by maximum inequality
 * The index I(x) attains its maximum value for maximum inequality. (all xi are zero except one) This value is usually unity as the number of agents n approaches infinity.
 * Subgroup decomposability
 * This property states that if a set of agents x is divided into two disjoint subsets (y and z) then the I(x) is expressible as:
 * where μ(x) and μ(y) are the mean incomes of x and y.
 * and the w functions are scalar weighting function of the sets y and z. In a stronger statement, wy = μy / μx and wz = μz / μx.

Common income inequality metrics
Among the most common metrics used to measure inequality are the Gini index (also known as Gini coefficient), the Theil index, and the Hoover index. They have all four properties described above.

An additional property of an inequality metric that may be desirable from an empirical point of view is that of 'decomposability'. This means that if a particular economy is broken down into sub-regions, and an inequality metric is computed for each sub region separately, then the measure of inequality for the economy as a whole should be a weighted average of the regional inequalities plus a term proportional to the inequality in the averages of the regions. (in a weaker form, it means that it should be an explicit function of sub-regional inequalities, though not necessarily linear). Of the above indexes, only the Theil index has this property.

Because these income inequality metrics are summary statistics that seek to aggregate an entire distribution of incomes into a single index, the information on the measured inequality is reduced. This information reduction of course is the goal of computing inequality measures, as it reduces complexity.

A weaker reduction of complexity is achieved if income distributions are described by shares of total income. Rather than to indicate a single measure, the society under investigation is split into segments, such as into quintiles (or any other percentage of population). Usually each segment contains the same share of income earners. In case of an unequal income distribution, the shares of income available in each segment are different.

In many cases the inequality indices mentioned above are computed from such segment data without evaluating the inequalities within the segments. The higher the number of segments (such as deciles instead of quintiles), the closer the measured inequality of distribution gets to the real inequality. (If the inequality within the segments is known, the total inequality can be determined by those inequality metrics which have the property of being "decomposable".)

Quintile measures of inequality satisfy the transfer principle only in its weak form because any changes in income distribution outside the relevant quintiles are not picked up by this measures; only the distribution of income between the very rich and the very poor matters while inequality in the middle plays no role.

Details of the three inequality measures are described in the respective Wikipedia articles. The following subsections cover them only briefly.

Gini index

The Gini index is a summary statistic that measures how equitably a resource is distributed in a population; income is a primary example. In addition to a self-contained presentation of the Gini index, we give two equivalent ways to interpret this summary statistic: first in terms of the percentile level of the person who earns the average dollar, and second in terms of how the lower of two randomly chosen incomes compare, on average, to mean income.

The Gini is the sum, over all income-ordered population percentiles, of the shortfall, from equal share, of the cumulative income up to each population percentile, with that summed shortfall divided by the greatest value that it could have, with complete inequality.

The range of the Gini index is between 0 and 1 (0% and 100%), where 0 indicates perfect equality and 1 (100%) indicates maximum inequality.

The Gini index is the most frequently used inequality index. The reason for its popularity is that it is easy to understand how to compute the Gini index as a ratio of two areas in Lorenz curve diagrams. This measure tries to capture the overall dispersion of income; however, it tends to place different levels of importance on the bottom, middle and top end of the distribution. As a disadvantage, the Gini index only maps a number to the properties of a diagram, but the diagram itself is not based on any model of a distribution process. The "meaning" of the Gini index only can be understood empirically. Additionally, the Gini does not capture where in the distribution the inequality occurs. As a result, two very different distributions of income can have the same Gini index.

20:20 ratio
The 20:20 or 20/20 ratio compares how much richer the top 20% of populations are to the bottom 20% of a given population. This can be more revealing of the actual impact of inequality in a population, as it reduces the effect on the statistics of outliers at the top and bottom and prevents the middle 60% from statistically obscuring inequality that is otherwise obvious in the field. The measure is used for the United Nations Development Programme Human Development Indicators. The 20:20 ratio for example shows that Japan and Sweden have a low equality gap, where the richest 20% only earn 4 times the poorest 20%, whereas in the UK the ratio is 7 times and in the US 8 times. Some believe the 20:20 ratio is a more useful measure as it correlates well with measures of human development and social stability including the index of child well-being, index of health and social problems, population in prison, physical health, mental health and many others.

Palma ratio
The Palma ratio is defined as the ratio of the richest 10% of the population's share of gross national income divided by the poorest 40%'s share. It is based on the work of Chilean economist Gabriel Palma who found that middle class incomes almost always represent about half of gross national income while the other half is split between the richest 10% and poorest 40%, but the share of those two groups varies considerably across countries.

The Palma ratio addresses the Gini index's over-sensitivity to changes in the middle of the distribution and insensitivity to changes at the top and bottom, and therefore more accurately reflects income inequality's economic impacts on society as a whole. Palma has suggested that distributional politics pertains mainly to the struggle between the rich and poor, and who the middle classes side with.

The carbon Palma ratio, which is derived from the income Palma ratio and described as the ratio of the total emissions of the top 10% of emitters to those of the bottom 40%, is proposed as a new indicator to inform the international community and the general public about the distribution inequality of carbon emissions among individuals. The ratio is calculated both within and between countries using an elastic relationship between individual emissions and income. The results show that the carbon Palma ratios in most developing countries are generally high, implying that they should concentrate more on coordinating regional and income inequalities and primarily encouraging high emitters to reduce in order to enhance emissions and income equity at the same time. The carbon Palma ratios in developed countries are comparatively lower; however, their greater historical obligations to warming indicate that they significantly reduce emissions of all people, in order to increase national mitigation contributions systematically. On a global scale, the current carbon Palma ratio is noticeably higher than within any country, indicating an exceedingly severe inequality when individual emissions are considered outside territorial boundaries.

Hoover index
The Hoover index is the simplest of all inequality measures to calculate: It is the proportion of all income which would have to be redistributed to achieve a state of perfect equality.

In a perfectly equal world, no resources would need to be redistributed to achieve equal distribution: a Hoover index of 0. In a world in which all income was received by just one family, almost 100% of that income would need to be redistributed (i.e., taken and given to other families) in order to achieve equality. The Hoover index then ranges between 0 and 1 (0% and 100%), where 0 indicates perfect equality and 1 (100%) indicates maximum inequality.

Galt score
The Galt score is a simple ratio of a company's CEO pay to the pay of that company's median worker. A company which pays its CEO many times more than its median employee will have a high Galt score.

It is named for the fictional character John Galt in Ayn Rand's novel Atlas Shrugged (1957).

The score is calculated using the total compensation of the CEO, including salary, bonuses, the value of stock awards and employee stock options, as well as non-equity incentive plan compensation, and nonqualified deferred compensation.

Coefficient of variation
Coefficient of variation (CV) used as a measure of income inequality is conducted by dividing the standard deviation of the income (square root of the variance of the incomes) by the mean of income. Coefficient variation will be therefore lower in countries with smaller standard deviations implying more equal income distribution.

It has the advantages of being mathematically tractable and its square is subgroup decomposable, but it is not bounded from above. This simple form of measurement is not being commonly used mostly for its two considerable limitations. The first one could be attributed to CV not having and upper limit, unlike the Gini coefficient, therefore causing difficulties with interpretation and comparison. Secondly, as the mean and standard deviation may be heavily affected by anomalous borderline values, the coefficient would not be an appropriate choice of income inequality measure for a case of abnormal data distribution.

Compared to the Gini coefficient in practice, CV puts higher weight on the right tail of the scale, making it sensitive to the rich. Coefficient of variation may be a suitable choice of measure iIf the goal of a study is to analyze the wealth concentration at the top of the distribution.

Variance of the Natural Logarithm of Income
The variance of log Income is described as variance applied to the distribution of log incomes. This scale invariant measure of relative inequality is sensitive to the left tail, making it ideal to use when studying the levels of poverty of the lower income half (the poor).

Wage share
Wage share is the ratio between Compensation of employees and GDP. In other words, it is the total of employees' income divided by the national income.

Sen poverty measure
Sen poverty measure combines the Gini coefficient for people living below the poverty line with headcount ration of poverty and the average income of these below the poverty line. This measure has been developed by Nobel Prize winner Amartya Sen but has not yet been used in the field of income inequality hypothesis. Although it has been greeted with enthusiasm, the Sen poverty index does not fulfill number of ideal conditions, e.g. it fails to satisfy the transfer axiom, it is not decomposable or subgroup consistent.

Theil index
As described in a section below, Theil-L is an income-distribution's dis-entropy per person, measured with respect to maximum entropy (which is achieved with complete equality). (In an alternative interpretation of it, Theil-L is the natural-logarithm of the geometric-mean of the ratio: (mean income)/(income i), over all the incomes. The related Atkinson(1) is just 1 minus the geometric-mean of (income i)/(mean income), over the income distribution.) Because a transfer between a larger income & a smaller one will change the smaller income's ratio more than it changes the larger income's ratio, the transfer-principle is satisfied by this index.

A Theil index of 0 indicates perfect equality. A Theil index of 1 indicates that the distributional entropy of the system under investigation is almost similar to a system with an 82:18 distribution. This is slightly more unequal than the inequality in a system to which the "80:20 Pareto principle" applies. The Theil index can be transformed into an Atkinson index, which has a range between 0 and 1 (0% and 100%), where 0 indicates perfect equality and 1 (100%) indicates maximum inequality. (See Generalized entropy index for the transformation.)

The Theil index is an entropy measure. As for any resource distribution and with reference to information theory, "maximum entropy" occurs once income earners cannot be distinguished by their resources, i.e. when there is perfect equality. In real societies people can be distinguished by their different resources, with the resources being incomes. The more "distinguishable" they are, the lower is the "actual entropy" of a system consisting of income and income earners. Also based on information theory, the gap between these two entropies can be called "redundancy". It behaves like a negative entropy.

For the Theil index also the term "Theil entropy" had been used. This caused confusion. As an example, Amartya Sen commented on the Theil index, "given the association of doom with entropy in the context of thermodynamics, it may take a little time to get used to entropy as a good thing." It is important to understand that an increasing Theil index does not indicate an increasing entropy, instead it indicates an increasing redundancy (decreasing entropy).

High inequality yields high Theil redundancies. High redundancy means low entropy. But this does not necessarily imply that a very high inequality is "good", because very low entropies also can lead to explosive compensation processes. Neither does using the Theil index necessarily imply that a very low inequality (low redundancy, high entropy) is "good", because high entropy is associated with slow, weak and inefficient resource allocation processes.

There are three variants of the Theil index. When applied to income distributions, the first Theil index (Theil-L) relates to how income is distributed to income earners, whereas the second Theil index (Theil-T) relates to how income-earners are distributed to incomes.

A third "symmetrized" Theil index (Theil-S) is the arithmetic average of the two previous indices. The formula of the third Theil index has some similarity with the Hoover index (as explained in the related articles). As in case of the Hoover index, the symmetrized Theil index does not change when swapping the incomes with the income earners. How to generate that third Theil index by means of a spreadsheet computation directly from distribution data is shown below.

An important property of the Theil index which makes its application popular is its decomposability into the between-group and within-group component. For example, the Theil index of overall income inequality can be decomposed in the between-region and within region components of inequality, while the relative share attributable to the between-region component suggests the relative importance of spatial dimension of income inequality.

Comparison of the Theil index and the Hoover index
The Theil index indicates the distributional redundancy of a system, within which incomes are assigned to income earners in a stochastic process. In comparison, the Hoover index indicates the minimum size of the income share of a society, which would have to be redistributed in order to reach maximum entropy. Not to exceed that minimum size would require a perfectly planned redistribution. Therefore, the Hoover index is the "non-stochastic" counterpart to the "stochastic" Theil index.

Applying the Theil index to allocation processes in the real world does not imply that these processes are stochastic: the Theil yields the distance between an ordered resource distribution in an observed system to the final stage of stochastic resource distribution in a closed system. Similarly, applying the Hoover index does not imply that allocation processes occur in a perfectly planned economy: the Hoover index yields the distance between the resource distribution in an observed system to the final stage of a planned "equalization" of resource distribution. For both indices, such an equalization only serves as a reference, not as a goal.

For a given distribution the Theil index can be larger than the Hoover index or smaller than the Hoover index:
 * For high inequalities the Theil index is larger than the Hoover index. This means for achieving equilibrium (maximum entropy) in a closed system, more resources would have to be reallocated than in case of a planned and optimized reallocation process, where only the necessary minimum share of resources would have to be reallocated. For an open system the export of entropy (import of redundancy) would allow to maintain the distribution dynamics driven by high inequality.
 * For low inequalities the Theil index is smaller than the Hoover index. Here, on the path to reaching equilibrium, a planned and optimized reallocation of resources would contribute more to the dynamics of redistribution than stochastic redistribution. This also is intuitively understandable, as low inequalities also weaken the urge to redistribute resources. People in such a system may tolerate or even foster an increase the inequality. As this is would be an increase of redundancy (an decrease of entropy), redundancy would have to be imported into (entropy would have to be exported from) the society. In that case the society needs to be an open system. In order to increase the redundancy in the distribution category of a society as a closed system, entropy needs to be exported from the subsystem operating in that economic category to other subsystems with other entropy categories in the society. For example, social entropy may increase. However, in the real world, societies are open systems, but the openness is restricted by the entropy exchange capabilities of the interfaces between the society and the environment of that society. For societies with a resource distribution which entropywise is similar to the resource distribution of a reference society with a 73:27 split (73% of the resources belong to 27% of the population and vice versa), the point where the Hoover index and the Theil index are equal, is at a value of around 46% (0.46) for the Hoover index and the Theil index.

Atkinson index
Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure useful in determining which end of the distribution contributed most to the observed inequality.

The Atkinson ε parameter is often called the "inequality aversion parameter", since it regulates the sensitivity of the implied social welfare losses from inequality to income inequality as measured by some corresponding generalised entropy index. The Atkinson index is defined in reference to a corresponding social welfare function, where mean income multiplied by one minus the Atkinson index gives the welfare equivalent equally distributed income.

The index can be turned into a normative measure by imposing a coefficient ε to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing ε, the level of "inequality aversion", appropriately. The Atkinson index becomes more sensitive to changes at the lower end of the income distribution as ε increases. Conversely, as the level of inequality aversion falls (that is, as ε approaches 0) the Atkinson becomes less sensitive to changes in the lower end of the distribution. The Atkinson index is for no value of ε highly sensitive to top incomes because of the common restriction that ε is nonnegative.

Ratios
Another common class of metrics is to take the ratio of the income of two different groups, generally "higher over lower". This compares two parts of the income distribution, rather than the distribution as a whole; equality between these parts corresponds to 1:1, while the more unequal the parts, the greater the ratio. These statistics are easy to interpret and communicate, because they are relative (this population earns twice as much as this population), but, since they do not fall on an absolute scale, do not provide an absolute measure of inequality.

Ratio of percentiles
Particularly common to compare a given percentile to the median, as in the first chart here; compare seven-number summary, which summarizes a distribution by certain percentiles. While such ratios do not represent the overall level of inequality in the population as a whole, they provide measures of the shape of income distribution. For example, the attached graph shows that in the period 1967–2003, US income ratio between median and 10th and 20th percentile did not change significantly, while the ratio between the median and 80th, 90th, and 95th percentile increased. This reflects that the increase in the Gini coefficient of the US in this time period is due to gains by upper income earners (relative to the median), rather than by losses by lower income earners (relative to the median).

Share of income

A related class of ratios is "income share", the percentage of the national income received by some specified richest or poorest percentage-segment of the population.

The population, but the Lorenz Curve (discussed in the Gini section) graphs the cumulative income of the bottom-income x% of the population, for all x from 0 to 100. However, when commenting on the data, it can be expressed as the inverse, showing the percentage of income of the wealthiest x%.

An important and obvious property of the Lorenz curve is that, if country A has a higher cumulative national-income share for (say) the poorest 1%, in comparison to country B, then:
 * 1) If the two countries' Lorenz curves don't cross, then country A's Lorenz curve is everywhere higher than that of country B, meaning that, for any X from 0 to 100, the poorest X% of the population have a greater national-income-share in country A than in country B.
 * 2) If the two countries' Lorenz curves cross, then it's a near-certainty that, on the poor side of the crossing-point, country A has a higher Lorenz curve, meaning that, for any poorest X% of the population up to the crossing-point, country A's population has a greater national-income-share.

When inequality does harm, it does most of it at the poorer end of the population. At an any given income-ordered percentile, a greater national-income-share means a greater received percentage of the equal-share (the national mean income).

So the country with a greater cumulative national-income-share for the poorest 1% will have a greater cumulative received percentage of equal-share for the poorest X%, either for every percentile X, or (if the Lorenz curves cross), for the percentiles on the poorer side of the crossing-point.

Some sources report several Lorenz-curve data-points (cumulative national income-shares up to several percentiles).

As mentioned above, taking the ratio of income share to subpopulation size corresponds to a ratio of mean subpopulation income relative to mean income.

Because income distribution is generally positively skewed, mean is higher than median, so ratios to mean are lower than ratios to median. This is particularly used to measure that fraction of income accruing to top earners – top 10%, 1%, 0.1%, 0.01%, and also "top 100" earners or the like; in the US top 400 earners is 0.0002% of earners (2 in 1,000,000) – to study concentration of income – wealth condensation, or rather income condensation. For example, in the chart at right, US income share of top earners was approximately constant from the mid-1950s to the mid-1980s, then increased from the mid-1980s through 2000s; this increased inequality was reflected in the Gini coefficient.

For example, in 2007 the top decile (10%) of US earners accounted for 49.7% of total wages ($$4.97 \approx 5$$ times fraction under equality), and the top 0.01% of US earners accounted for 6% of total wages (600 times fraction under equality).

Normative approach
Normative interpretation of inequality through inequality indexes means that there is a relationship between an inequality index and a social-evaluation ordering defined on the incomes — incomes (nominal or real) of the members of society. Incomes are typically assigned to individuals rather than households by using an adult equivalence scale.

Normative approach has been discussed by Charles Blackorby, Walter Bossert and David Donaldson in the work "Income Inequality Measurement: The Normative Approach".

Statistical approach
Statistical interpretation of inequality is based on fiscal data and the parameter α from the model of Pareto (1895) as an income inequality measure. This approach is further discussed in work "Income Inequality Measurement: The Statistical Approach" by Giovanni M. Giorgi.

Spreadsheet computations
The Gini coefficient, the Hoover index and the Theil index as well as the related welfare functions can be computed together in a spreadsheet. The welfare functions serve as alternatives to the median income.

In the table, fields with a yellow background are used for data input. From these data inequality measures as well as the related welfare functions are computed and displayed in fields with green background.

In the example given here, "Theil index" stands for the arithmetic mean of a Theil index computed for the distribution of income within a society to the individuals (or households) in that society and a Theil index computed for the distribution of the individuals (or households) in the society to the income of that society. The difference between the Theil index and the Hoover index is the weighting of the relative deviation D. For the Hoover index the relative deviation D per group is weighted with its own sign. For the Theil index the relative deviation D per group is weighted with the information size provided by the income per individual in that group.

For the computation the society usually is divided into income groups. Often there are four or five groups consisting of a similar number of individuals in each group. In other cases the groups are created based on income ranges which leads to having different numbers of individuals in the different groups. The table above shows a computation of inequality indices for four groups. For each group the number of individuals (or households) per group A and the total income in that group E is specified.

The parameter pairs A and E need to be sorted for the computation of the Gini coefficient. (For the Theil index and the Hoover index no sorting is required.) A and E have to be sorted so that the values in the column "Income per individual" are lined up in ascending order.

Proper use

 * 1) When using income metrics, it has to be made clear how income should be defined. Should it include capital gains, imputed house rents from home ownership, and gifts? If these income sources or alleged income sources (in the case of "imputed rent") are ignored (as they often are), how might this bias the analysis? How should non-paid work (such as parental childcare or doing one's own cooking instead of hiring a chef for every meal) be handled? Wealth or consumption may be more appropriate measures in some situations. Broader quality of life metrics might be useful.
 * 2) The comparison of inequality measures requires that the segmentation of compared groups (societies etc.) into quintiles should be similar.
 * 3) Distinguish properly, whether the basic unit of measurement is households or individuals. The Gini value for households is always lower than for individuals because of income pooling and intra-family transfers. And households have a varying number of members. The metrics will be influenced either upward or downward depending on which unit of measurement is used.
 * 4) Consider life cycle effects. In most Western societies, an individual tends to start life with little or no income, gradually increase income till about age 50, after which incomes will decline, eventually becoming negative. This affects the conclusions which can be drawn from a measured inequality. It has been estimated (by A.S. Blinder in The Decomposition of Inequality, MIT press) that 30% of measured income inequality is due to the inequality an individual experiences as they go through the various stages of life.
 * 5) Clarify whether real or nominal income distributions should be used. What effect will inflation have on absolute measures? Do some groups (e.g., pensioners) feel the effect of inflation more than others?
 * 6) When drawing conclusion from inequality measurements, consider how we should allocate the benefits of government spending? How does the existence of a social security safety net influence the definition of absolute measures of poverty? Do government programs support some income groups more than others?
 * 7) Inequality metrics measure inequality. They do not measure possible causes of income inequality. Some alleged causes include: life cycle effects (age), inherited characteristics (IQ, talent), willingness to take chances (risk aversion), the leisure/industriousness choice, inherited wealth, economic circumstances, education and training, discrimination, and market imperfections.
 * 8) Inequality metrics are anonymous. They ignore certain effects of income mobility, in which the identity of "who is rich" and "who is poor" is considered. For example, at a particular time, Alice may have $10 and Bob may have $2. At some time later, Bob may have $10 and Alice may have $2. The inequality index will be the same in both cases and rather high. However, the inequality of the average will be zero, since Alice's and Bob's average holdings are equal ($6). The $8 which has changed hands is a measure of wealth mobility and the average inequality is generally higher than the inequality of the average.

Keeping these points in mind helps to understand the problems caused by the improper use of inequality measures. However, they do not render inequality coefficients invalid. If inequality measures are computed in a well explained and consistent way, they can provide a good tool for quantitative comparisons of inequalities.

Inequality, growth, and progress
Evidence from a broad panel of recent academic studies shows that there is a nonlinear relation between income inequality and the rate of growth and investment. Very high inequality slows growth; moderate inequality encourages growth. Studies differ on the effect of very low inequality.

Robert J. Barro, Harvard University found in his study "Inequality and Growth in a Panel of Countries" that higher inequality tends to retard growth in poor countries and encourage growth in well-developed regions. Underscoring the need for initiatives like the United Nations Sustainable Development Goal 10, aim at reducing inequality. According to Pak Hung Mo, income inequality has significant negative effect on the rate of GDP growth. In their work "Income Inequality and Economic Growth", they found out that the most important is the transfer channel while the least important is the human capital channel. However, the direct impact of income inequality on the rate of productivity growth accounts for more than 55 percent of its overall total effect. This indicates that the effects of income inequality on economic growth are much more complicated than what we have perceived or modeled.

In their study for the World Institute for Development Economics Research, Giovanni Andrea Cornia and Julius Court (2001) reach slightly different conclusions. The authors therefore recommend to pursue moderation also as to the distribution of wealth and particularly to avoid the extremes. Both very high egalitarianism and very high inequality cause slow growth. Considering the inequalities in economically well developed countries, public policy should target an 'efficient inequality range'. The authors claim that such efficiency range roughly lies between the values of the Gini coefficients of 0.25 (inequality close to the least unequal European counties) and 0.40 (close to the level of inequality of US.

According to the work "Inequality of Opportunity, Income Inequality, and Economic Growth," the relationship between income inequality and economic growth is mediated by the level of equality of opportunity, as identified by intergenerational mobility. After a number of recently developed internationally comparable measures of intergenerational mobility they confirmed that the negative impact of income inequality on growth increases as intergenerational mobility decreases. The findings imply that excluding intergenerational mobility leads to misspecification, which explains why the empirical literature on income inequality and growth has been so inconclusive.

Another researcher has shown that in perfect markets inequality does not influence growth.

The precise shape of the inequality-growth curve obviously varies across countries depending upon their resource endowment, history, remaining levels of absolute poverty and available stock of social programs, as well as on the distribution of physical and human capital.

Literature

 * A.B. Atkinson and F. Bourguignon, ed. (2000). Handbook of Income Distribution, v. 1. Elsevier.table of contents
 * _____," International Encyclopedia of the Social & Behavioral Sciences (2001), pp. 7265–7271. Abstract.
 * Yoram Amiel (Author), Frank A. Cowell: Thinking about Inequality: Personal Judgment and Income Distributions, 2000
 * Philip B. Coulter: Measuring Inequality, 1989

title: Income inequality metrics


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Sibylline Books

The Sibylline Books (Libri Sibyllini) were a collection of oracular utterances, set out in Greek hexameter verses, that, according to tradition, were purchased from a sibyl by the last king of Rome, Lucius Tarquinius Superbus, and consulted at momentous crises through the history of the Roman Republic and the Empire.

Only fragments have survived, the rest being lost or deliberately destroyed. The Sibylline Books are not the same as the Sibylline Oracles, twelve books of prophecies thought to be of Judaeo-Christian origin.

History

According to the Roman tradition, the oldest collection of Sibylline books appears to have been made about the time of Solon and Cyrus at Gergis on Mount Ida in the Troad; it was attributed to the Hellespontine Sibyl and was preserved in the temple of Apollo at Gergis. From Gergis the collection passed to Erythrae, where it became famous as the oracles of the Erythraean Sibyl. It would appear to have been this very collection that found its way to Cumae (see the Cumaean Sibyl) and from Cumae to Rome.

The story of the acquisition of the Sibylline Books by the seventh and last king of Rome, Lucius Tarquinius Superbus ("Tarquinius", ruled 534 to 509 B.C., d. 495 B.C.), is one of the famous legendary elements of Roman history. An old woman, possibly a Cumaean Sibyl, offered to Tarquinius nine books of these prophecies at an exorbitant price; when the king declined to purchase them, she burned three and offered the remaining six to Tarquinius at the same price, which he again refused. Thereupon, she burned three more and repeated her offer, maintaining the same price. Tarquinius then consulted the Augurs whose importance in Roman history is averred by Livy. The Augurs deplored the loss of the six books and urged purchase of the remaining three. Tarquinius then purchased the last three at the full original price, and had them preserved in a sacred vault beneath the Capitoline temple of Jupiter. The story is alluded to in Varro's lost books quoted in Lactantius Institutiones Divinae (I: 6) and by Origen, and told by Aulus Gellius (Noctes Atticae 1, 19).

The Roman Senate kept tight control over the Sibylline Books, and entrusted them to the care of two patricians. In 367 BC, the number of custodians was increased to ten, five patricians and five plebeians, who were called the decemviri sacris faciundis. Subsequently, probably in the time of Sulla, their number was increased to fifteen, the quindecimviri sacris faciundis. They were usually ex-consuls or ex-praetors. They held office for life, and were exempt from all other public duties. They had the responsibility of keeping the books in safety and secrecy. The 15 individuals were custodians of the Sibylline Books that were kept on the Palatine. These officials, at the command of the Senate, consulted the Sibylline Books in order to discover not exact predictions of definite future events in the form of prophecy, but the religious observances necessary to avert extraordinary calamities and to expiate ominous prodigies (comets and earthquakes, showers of stones, plague, and the like). It was only the rites of expiation prescribed by the Sibylline Books, according to the interpretation of the oracle that were communicated to the public, and not the oracles themselves, which left ample opportunity for abuses.

In particular, the keepers of the Sibylline Books had the superintendence of the worship of Apollo, of the "Great Mother" Cybele or Magna Mater, and of Ceres, which had been introduced upon recommendations as interpreted from the Sibylline Books. The Sibylline Books motivated the construction of eight temples in ancient Rome, aside from those cults that have been interpreted as mediated by the Sibylline Books simply by the Greek nature of the deity. Thus, one important effect of the Sibylline Books was their influence on applying Greek cult practice and Greek conceptions of deities to indigenous Roman religion, which was already indirectly influenced through Etruscan religion. As the Sibylline Books had been collected in Anatolia, in the neighborhood of Troy, they recognized the gods and goddesses and the rites observed there and helped introduce them into Roman state worship, a syncretic amalgamation of national deities with the corresponding deities of Greece, and a general modification of the Roman religion.

Since they were written in hexameter verse and in Greek, the college of curators was always assisted by two Greek interpreters. The books were kept in the Temple of Jupiter on the Capitol, and, when the temple burned in 83 BC, they were lost. The Roman Senate sent envoys in 76 BC to replace them with a collection of similar oracular sayings, in particular collected from Ilium, Erythrae, Samos, Sicily, and Africa. This new Sibylline collection was deposited in the restored temple, together with similar sayings of native origin, e.g. those of the Sibyl at Tibur (the 'Tiburtine Sibyl') of the brothers Marcius, and others, which had been circulating in private hands but which were called in, to be delivered to the Urban Praetor, private ownership of such works being declared illicit, and to be evaluated by the Quindecimviri, who then sorted them, retaining only those that appeared true to them.

From the Capitol they were transferred by Augustus as pontifex maximus in 12 BC, to the Temple of Apollo Palatinus, after they had been examined and copied; there they remained until about AD 405. According to the poet Rutilius Claudius Namatianus, the general Flavius Stilicho (died AD 408) burned them, as they were being used to attack his government. The last known consultation was in 363 CE.

Some supposedly genuine Sibylline verses are preserved in the Book of Marvels or Memorabilia of Phlegon of Tralles (2nd century AD). These represent an oracle, or a combination of two oracles, of seventy hexameters in all. They report the birth of an androgyne, and prescribe a long list of rituals and offerings to the gods. Their authenticity has been questioned.

Relationship with the "Sibylline Oracles"
The Sibylline Oracles were quoted by the Roman-Jewish historian Josephus (late 1st century) as well as by numerous Christian writers of the second century, including Athenagoras of Athens who, in a letter addressed to Marcus Aurelius in ca. AD 176, quoted verbatim a section of the extant Oracles, in the midst of a lengthy series of other classical and pagan references such as Homer and Hesiod, stating several times that all these works should already be familiar to the Roman Emperor. Copies of the actual Sibylline Books (as reconstituted in 76 BC) were still in the Roman Temple at this time. The Oracles are nevertheless thought by modern scholars to be anonymous compilations that assumed their final form in the fifth century, after the Sibylline Books perished. They are a miscellaneous collection of Jewish and Christian portents of future disasters, that may illustrate the confusions about sibyls that were accumulating among Christians of Late Antiquity.

Consultations of the Books cited in history
An incomplete list of consultations of the Sibylline Books recorded by historians:
 * 399 BC: The books were consulted following a pestilence, resulting in the institution of the lectisternium ceremony. (Livy 5, 13)
 * 348 BC: A plague struck Rome after a brief skirmish with the Gauls and Greeks. Another lectisternium was ordered. (Livy 7, 27)
 * 345 BC: The books were consulted when a "shower of stones rained down and darkness filled the sky during daylight". Publius Valerius Publicola was appointed dictator to arrange a public holiday for religious observances. (Livy 7, 28)
 * 295 BC: They were consulted again following a pestilence, and reports that large numbers of Appius Claudius' army had been struck by lightning. A Temple was built to Venus near the Circus Maximus. (Livy 10, 31)
 * 293 BC: After yet another plague, the books were consulted, with the prescription being 'that Aesculapius must be brought to Rome from Epidaurus'; however, the Senate, being preoccupied with the Samnite wars, took no steps beyond performing one day of public prayers to Aesculapius. (Livy 10, 47)
 * 240/238 BC: The Ludi Florales, or "Flower Games", were instituted after consulting the books.

 * 216 BC: When Hannibal annihilated the Roman Legions at Cannae, the books were consulted, and on their recommendation, two Gauls and two Greeks were buried alive in the city's marketplace.
 * 205–204 BC: During the Second Punic War, upon consultation of the Sibylline Books, an image of Cybele was transferred from Pessinos (Pessinous or Pergamon) to Rome. An embassy was sent to Attalus I of Pergamon to negotiate the transfer. Publius Cornelius Scipio Nasica and Claudia Quinta were said to have received the image of Cybele at Ostia on her arrival in 204 BC. Cybele's image was placed within the Temple of Victory on the Palatine. In honour of Cybele a lectisternium was performed and her games, the Megalesia, were held. The image of Cybele was moved to the Temple of the Magna Mater in 191 BC when the temple was dedicated by Marcus Junius Brutus in the consulship of Publius Cornelius Scipio Nasica. A fragment of Valerius Antias from Livy's Ab Urbe Condita 36.36.4 records that Megalesia were again held in 191 BC and that "[they] were the first to be held with dramatic performances".
 * 143 BC: Frontinus relates a story in which the Decemvirs consulted the books on another matter and found that a proposed project for the Aqua Marcia was improper, along with the Anio. After a debate in the Senate the project was resumed, presumably the necessity for water outweighed the oracle. Sextus Julius Frontinus, Aqueducts of Rome, Book I, Ch 7.
 * 63 BC: Believing in a prediction of the books that 'three Cornelii' would dominate Rome, Publius Cornelius Lentulus Sura took part in the conspiracy of Catiline (Plutarch, Life of Cicero, XVII)
 * 55 BC: As Romans deliberated sending a force to restore Ptolemy XII to the throne of Egypt, lightning struck the statue of Jupiter on the Alban Mount; the oracles were consulted, and one was found to read "If the King of Egypt comes to you asking for assistance, refuse him not your friendship, yet do not grant him any army, or else you will have toil and danger". This considerably delayed Ptolemy's return. (Dio Cassius History of Rome 39:15)
 * 44 BC: According to Suetonius, a sibylline prediction that only a king could triumph over Parthia fueled rumors that Caesar, leader of the then republic, was aspiring to kingship. (Caesar, 79)
 * 15 AD: When the Tiber river flooded the lower parts of Rome, one of the priests suggested consulting the books, but Emperor Tiberius refused, preferring to keep the divine things secret. (Tacitus, Annales I, 76)
 * 64 AD: The Emperor Nero consulted them following the Great Fire of Rome. (Tacitus, Annales XV, 44)
 * 271 AD: The books were consulted following the Roman defeat at Placentia by the Alamanni.
 * 312 AD: Maxentius consulted the Sibylline Books in preparation for combat with Constantine, who had just taken all of Maxentius' northern Italian cities and was marching on Rome.
 * 363 AD: Julian the Apostate consulted the books in preparation for marching against the Sassanids. The response mailed from Rome "in plain terms warned him not to quit his own territories that year". (Ammianus Marcellinus, History of Rome, XXIII 1, 7)
 * 405 AD: Stilicho ordered the destruction of the Sibylline Books, possibly because Sibylline prophecies were being used to attack his government in the face of the attack of Alaric I.

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

title: Sibylline Books


text:
Quiripi language

Quiripi (pronounced, also known as Mattabesic, Quiripi-Unquachog, Quiripi-Naugatuck, and Wampano) was an Algonquian language formerly spoken by the indigenous people of southwestern Connecticut and central Long Island,  including the Quinnipiac, Unquachog, Mattabessett (Wangunk), Podunk, Tunxis, and Paugussett (subgroups Naugatuck, Potatuck, Weantinock). It has been effectively extinct since the end of the 19th century, although Frank T. Siebert, Jr., was able to record a few Unquachog words from an elderly woman in 1932.

Affiliation and dialects
Quiripi is considered to have been a member of the Eastern Algonquian branch of the Algonquian language family. It shared a number of linguistic features with the other Algonquian languages of southern New England, such as Massachusett and Mohegan-Pequot, including the shifting of Proto-Eastern Algonquian * and * to and, respectively, and the palatalization of earlier * before certain front vowels. There appear to have been two major dialects of Quiripi: an "insular" dialect spoken on Long Island by the Unquachog and a "mainland" dialect spoken by the other groups in Connecticut, principally the Quinnipiac.

Attestation
Quiripi is very poorly attested, though some sources do exist. One of the earliest Quiripi vocabularies was a 67-page bilingual catechism compiled in 1658 by Abraham Pierson, the elder, during his ministry at Branford, Connecticut, which remains the chief source of modern conclusions about Quiripi. Unfortunately, the catechism was "poorly translated" by Pierson, containing an "unidiomatic, non-Algonquian sentence structure." It also displays signs of dialect mixture. Other sources of information on the language include a vocabulary collected by the Rev. Ezra Stiles in the late 1700s and a 202-word Unquachog vocabulary recorded by Thomas Jefferson in 1791, though the Jefferson vocabulary also shows clear signs of dialect mixture and "external influences." Additionally, three early hymns written circa 1740 at the Moravian Shekomeko mission near Kent, Connecticut, have been translated by Carl Masthay.

Phonology
Linguist Blair Rudes attempted to reconstitute the phonology of Quiripi, using the extant documentation, comparison with related Algonquian languages, as "reconstructing forward" from Proto-Algonquian. In Rudes' analysis, Quiripi contained the following consonant phonemes:

Quiripi's vowel system as reconstituted by Rudes was similar to that of the other Southern New England Algonquian languages. It consisted of two short vowels and, and four long vowels , , , and.

Orthography

 * a –
 * â –
 * ch –
 * h –
 * i –
 * k –
 * m –
 * n –
 * o –
 * ô –
 * p –
 * r –
 * s –
 * sh –
 * t –
 * u –
 * w –
 * y –

title: Quiripi language


text:
Palacio de Bellas Artes

The Palacio de Bellas Artes (Palace of Fine Arts) is a prominent cultural center in Mexico City. This hosts performing arts events, literature events and plastic arts galleries and exhibitions (including important permanent Mexican murals). "Bellas Artes" for short, has been called the "art cathedral of Mexico", and is located on the western side of the historic center of Mexico City which is close to the Alameda Central park.

Bellas Artes replaced the original National Theater, built in the late 19th century. The latter was demolished as part of urban redesign in Mexico City, and a more opulent building was planned to celebrate the centennial of the Mexican War of Independence in 1910. The initial design and construction was undertaken by Italian architect Adamo Boari in 1904, but complications arising from the soft subsoil and the political problem both before and during the Mexican Revolution, hindered then stopped construction completely by 1913. Construction resumed in 1932 under Mexican architect Federico Ernesto Mariscal Piña and was completed in 1934. It was then inaugurated on November 29, 1934.

The exterior of the building is primarily Art Nouveau and Neoclassical and the interior is primarily Art Deco. The building is best known for its murals by González Camarena, Diego Rivera, Siqueiros and others, as well as the many exhibitions and theatrical performances it hosts, including the Ballet Folklórico de México.

History

The oldest known structure on the site was the Convent of Santa Isabel, whose church was built in 1680. However, significant Mexica finds, such as a sacrificial altar in the shape of a plumed snake have been found here. The convent area suffered frequent drought during the early canal period and development here grew quickly.

In spite of this, the convent remained until it was forcibly closed in the 1860s by the Reform Laws. It was replaced by a textile mill and lower-class housing.

A section of this housing, on Santa Isabel Alley, was torn down and replaced by the National Theater in the latter 19th century. During the late 19th century and very early 20th, this theatre was the site of most of Mexico City's high culture, presenting events such as theatre, operettas, Viennese dance and more.

It was then decided to replace this building with a more opulent one for the upcoming Centennial of Mexican Independence celebrations in 1910. The old theatre was demolished in 1901, and the new theatre would be called the Gran Teatro de Ópera. The work was awarded to Italian architect Adamo Boari, who favored neoclassical and art nouveau styles and who is responsible for the Palacio del Correo which is across the street. Adamo Boari promised in October 1904 to build a grand metallic structure, which at that time only existed in the United States, but not to this size. The first stone of the building was placed by Porfirio Díaz in 1904. Despite the 1910 deadline, by 1913, the building was hardly begun with only a basic shell. One reason for this is that the project became more complicated than anticipated as the heavy building sank into the soft spongy subsoil. The other reason was the political and economic instability that would lead to the Mexican Revolution. Full hostilities suspended construction of the palace completely and Adamo Boari returned to Italy.

The project would sit unfinished for about twenty years. In 1932, construction resumed under Mexican architect Federico Ernesto Mariscal Piña. Mariscal completed the interior but updated it from Boari's plans to the more modern Art Deco style. The building was completely finished in 1934, and was inaugurated on 29 November of that year. The inaugural work presented in the theatre was "La Verdad Sospechosa" by Juan Ruiz de Alarcón in 1934. In 1946, the Instituto Nacional de Bellas Artes (National Institute of the Fine Arts) was created as a government agency to promote the arts and was initially housed at the Museo Nacional de Artes Plásticas, the Museo del Libro and other places. It is now at the Palacio.

In this theatre, Maria Callas debuted in the opera Norma in 1950.

In 2002, the palace was the scene of the funeral of María Félix.

Since its initial construction, very little has been updated or modified. However, intensive renovation efforts were begun in 2009 for the upcoming 2010 celebrations. Much of the equipment and machinery is original from the early 20th century. Much of the technological equipment is being updated, especially in the theatre which needs computerized lights, sound systems and other improvements. Other work will improve the acoustics. Upgrades to the theatre will allow for multimedia shows which were not available before. The main hall has had no renovation or upgrade work since it opened in 1934. Renovations here will lessen the number of people the hall can accommodate but should make the area more comfortable.

The building

The palace has a mixture of a number of architectural styles; however, it is principally Art Nouveau and Art Deco. Art Nouveau dominates the exterior, which was done by Adamo Boari, and the inside is dominated by Art Deco, which was completed by Federico Mariscal. Since construction began in 1904, the theater (which opened in 1934) has sunk some four meters into the soft soil of Mexico City. The main facade, which faces Avenida Juárez, is made of white Italian Carrara marble. In the interior of the portal are sculptures by Italian Leonardo Bistolfi. It consists of "Harmony", surrounded by "Pain", "Rage", "Happiness", "Peace" and "Love". Another portion of the facade contains cherubs and sculptures representing music and inspiration. On the plaza front of the building, designed by Boari, there are four Pegasus sculptures which were made by Spanish Agustí Querol Subirats. These had been in the Zocalo before being brought here. The roof covering the center of the building is made of crystal designed by Hungarian Géza Maróti and depicts the muses with Apollo. One aspect of the Palace which has since disappeared is the "Pergola", which was located in the Alameda. It was constructed to house pictorial exhibitions for the 1910 celebrations, but it was demolished in 1973.

The interior is also surfaced in Carrara marble. It divides into three sections: the main hall with adjoining smaller exhibition halls, the theatre and the offices of the Insituto Nacional de Bellas Artes. The main hall is covered by the Marotti glass and iron roof. It and the balconies of all three upper floors can be seen from the ground floor below. In areas of the main hall, pre-Hispanic motifs done in Art Deco style, such as serpents’ heads on window arches and Maya Chaac masks on the vertical light panels distinguish this interior from its contemporaries. The smaller exhibition halls are located on the first and second floors. The first floor is decorated with crystal lamps, created by Edgar Brandt and hold murals by Rufino Tamayo. The Adamo Boari and Manuel M. Ponce halls hold music and literature events. And the National and International halls are for exhibitions. The second floor has smaller exhibition halls as well as murals by José Clemente Orozco, David Alfaro Siqueiros, Diego Rivera, Jorge González Camarena, Roberto Montenegro and Manuel Rodríguez Lozano. The third floor is occupied by the Museum of Architecture. The ironwork was designed in Italy by Alessandro Mazzucotelli and in Mexico by Luis Romero Soto.

At the entrance of the theatre, there are mascarons in bronze with depictions of Tlaloc, and Chaac, the Aztec and Maya deities of water, which along with the rest were designed by Gianette Fiorenzo. On the arch over the stage there are representations of various mythological personas such as the Muses with Apollo. This was constructed in Hungary in the workshops of Géza Maróti. However, the most impacting aspect is the stage "curtain" which is a stained glass foldable panel created out of nearly a million pieces of iridescent colored glass by Tiffany's in New York. This stage curtain is the only one of its type in any opera house in the world and weighs 24 tons. The design of the curtain has the volcanos Popocatépetl and Iztaccíhuatl in the center. Around them is a Mexican landscape surrounded by images of sculptures from Yautepec and Oaxaca. This design was inspired by work done by artist Gerardo Murillo (Dr. Atl). The theatre has a capacity of 1,590.

Events

The Palace has been the scene of some of the most notable events in music, dance, theatre, opera and literature and has hosted important exhibitions of painting, sculpture and photography. It has hosted some of the biggest names from both Mexico and abroad. It has hosted poetry events as well as those related to popular culture. Artists and companies are from all parts of Mexico and abroad. It has been called the "Cathedral of Art in Mexico". It was declared an artistic monument in 1987 by UNESCO. The building is administered by the Instituto Nacional de Bellas Artes of the federal government. The palace receive on average 10,000 visitors each week.

Two of the best-known groups which regularly perform here are the Ballet Folklórico de México Compania Nacional de Opera de Bellas Artes and the National Symphonic Orchestra. The first performs in the theatre twice a week and is a spectacle of pre and post Hispanic dance of Mexico. A typical program includes Aztec ritual dances, agricultural dances from Jalisco, a fiesta in Veracruz, a wedding celebration — all accompanies by mariachis, marimba players and singers. Regular annual events include the Premio Quorum for Mexican designers in graphic and industrial materials and the Premios Ariel for Mexican films.

Numerous individual events have been held here. These include several exhibitions of Frida Kahlo's work, and a number of appearances by Luciano Pavarotti. In 1987, Bellas Artes hosted a legendary performance of Jesusa Rodríguez's Donna Giovanni, an adaptation of Mozart's opera with a female cast. Other appearances have been made by Mexican baritone Jorge Lagunes (2002) and Catalan guitarist Joan Manuel Serrat (2003). Events that have been held here include "ABCDF Palabras de Ciudad" (2002) showing life in popular housing in photographs and video, "Bordados del Mexico Antiguo" (Embroidery of Old Mexico) showing processes, history and design, Rem Koolhaas Premio Pritzker 2000" conference and "Exchanging Views: Visions of Latin America" which was an exhibit from the collection of Patricia Phelps de Cisneros comprising 148 works by 72 artists from across Latin America in 2006.

Occasionally, the plaza in front of the Palace is the scene of protests such as those against the Iraq War in 2003 and against bullfighting in 2010.

Murals
The floors between the ground floor and the uppermost floor are dominated by a number of murals painted by most of the famous names of Mexican muralism.

On the 2nd floor are two early-1950s works by Rufino Tamayo: México de Hoy (Mexico Today) and Nacimiento de la Nacionalidad (Birth of Nationality), a symbolic depiction of the creation of the mestizo (person of mixed indigenous and Spanish ancestry) identity.

At the west end of the 3rd floor is El hombre controlador del universo (Man, controller of the universe- known as Man at the Crossroads), originally commissioned for New York's Rockefeller Center in 1933. The mural depicts a variety of technological and societal themes (such as the discoveries made possible by microscopes and telescopes) and was controversial for its inclusion of Lenin and a Soviet May Day parade. The Rockefellers were not happy with the painting and the incomplete work was eventually destroyed and painted over. Rivera recreated it here in 1934. On the north side of the third floor are David Alfaro Siqueiros' three-part La Nueva Democracia (New Democracy) and Rivera's four-part Carnaval de la Vida Mexicana (Carnival of Mexican Life); to the east is José Clemente Orozco's La Katharsis (Catharsis), depicting the conflict between humankind's 'social' and 'natural' aspects.

Museo del Palacio de Bellas Artes

The Museo del Palacio de Bellas Artes (Museum of the Palace of Fine Arts) is the organization that takes care of the permanent murals and other artwork in the building as well as arrange temporary exhibits. These exhibits cover a wide range of media and feature Mexican and international artists, focusing on classic and contemporary artists.

Museo Nacional de Arquitectura
The Museo Nacional de Arquitectura (Museum of Architecture) occupies the top floor of the building, covered by the glass and iron roof. It contains exhibitions from renowned Mexican architects including models, designs and photographs of major works. The museum also arranges temporary exhibitions of its collections in other facilities to expose the Mexican public to the country's rich architectural heritage. Some of the major architects featured at the museum include Jaime Ortiz Monasterio, Carlos Mijares Bracho, Adamo Boari and Luis Barragán. The museum is divided into four sections called "Arquitectura-contrastes: Jaime Ortiz Monasterio y Carlos Mijares Bracho", "Corpus Urbanístico de la Ciudad de México", "Teatro Nacional de México (Plano original)" and "Teatro Nacional de México." There are also temporary exhibits on contemporary architecture.

title: Palacio de Bellas Artes


text:
TV Azteca

Televisión Azteca, S.A.B. de C.V., commonly known as TV Azteca, is a Mexican multimedia conglomerate owned by Grupo Salinas. It is the second-largest mass media company in Mexico after Televisa. It primarily competes with Televisa as well as some local operators. It owns two national television networks, Azteca Uno and Azteca 7, and operates two other nationally distributed services, adn40 and A Más+. All three of these networks have transmitters in most major and minor cities.

TV Azteca also operates Azteca Trece Internacional, reaching 13 countries in Central and South America, and formerly part of the Azteca América network in the United States. Its flagship program is the newscast Hechos.

Formation
In the early 1990s, the presidency of Carlos Salinas de Gortari privatized many government assets. Among them was the Instituto Mexicano de la Televisión, known as Imevisión, which owned two national television networks (Red Nacional 7 and Red Nacional 13) and three local TV stations. In preparation for the privatization, the Imevisión stations were parceled into a variety of newly created companies, the largest of which was named Televisión Azteca, S.A. de C.V.

With the exception of Canal 22, which was spun off to Conaculta, one bidder won all of the stations. On July 18, 1993, Mexico's Finance Ministry, the Secretaría de Hacienda y Crédito Público (SHCP), announced that Radio Televisora del Centro, a group controlled by Ricardo Salinas Pliego, was the winner of the auction to acquire the "state-owned media package", which also included Imevisión's studios in the Ajusco area of Mexico City. The winning bid amounted to US$645 million. The new group soon took on the Televisión Azteca name for the entire operation and soon challenged Televisa, turning what had been a television monopoly into a television duopoly. The two conglomerates held 97 percent of the commercial television concessions in the country.

Expansion
In 1998, TV Azteca announced an investment of US$25 million in XHTVM-TV, which was owned by Javier Moreno Valle through concessionaire Televisora del Valle de México, S.A. de C.V. Under the deal, Azteca restructured TVM and took control of ad sales and most programming duties, while Moreno Valle's CNI news service retained some primetime space. However, in 2000, Moreno Valle broke the contract with Azteca, alleging Azteca of filling up time allotted to CNI and not fulfilling the obligations in the contract. In December 2002, Azteca used private security guards to retake control of the XHTVM facilities on Cerro del Chiquihuite in Mexico City. However, the Mexican government stepped into the dispute and forced Azteca to relinquish control of XHTVM. In 2005, an employee strike that crippled CNI, Moreno Valle's mounting legal troubles, and a deal with the 5% owner of the concessionaire allowed Azteca to buy the remainder of the station and retake control of XHTVM, under the name Proyecto 40, in 2006.

On March 7, 2011, TV Azteca changed its name to Azteca, reflecting its growth into a multimedia company. However, in May 2016, the TV Azteca name was restored.

TV Azteca is the second largest mass media company in México after Televisa. These two big organizations control the 97% of mass media in Mexico. TV Azteca was funded in 1993 by Ricardo Salinas Pliego. TV Azteca has 31% of the 465 television concessions in México. The auction of the state channels and the granting of further concessions to TV Azteca further strengthen their connection. It also owns Azteca banks, Azteca insurance, Iusacell, programing pay television, cinemas, live theater, news channels, newspapers, Azteca music, an acting school, Azteca consumer products, Azteca internet, Azteca series, Azteca sports, stadiums, etc. TV Azteca is another company which also serves the government however to a much lesser extent than Televisa. TV Azteca also receives lucrative contracts from the Mexican government, and therefore the information that emits is also controlled by the actual government. The news that is normally emitted by TV Azteca is 25% news bulletins that come from advertising, and infotainment relying on celebrities and biased editorials.

On March 21, 2023, creditors for the company pushed the company into an involuntary Chapter 11 bankruptcy petition in the U.S. However, on April 26, TV Azteca asked the New York bankruptcy judge to dismiss its Chapter 11 case due to it being pointless to start reorganization proceedings for the company anywhere but Mexico. On June 1, 2023, TV Azteca was suspended from the Mexico Stock Exchange.

Terrestrial networks

 * In Mexico:

 * Outside Mexico:

Formerly owned

 * Azteca América: American broadcast network with programming from TV Azteca's three television national networks in Mexico and local news. The owner, HC2 Holdings, continued to use the Azteca branding under license. Ceased operations on December 31, 2022.
 * KAZA-TV used to be the flagship of Azteca América from 2001 to 2018 but was sold to Chicago-based Weigel Broadcasting, which stripped KAZA of its flagship status, and was replaced by MeTV as an O&O.

Cable

 * Az Noticias
 * Az Clic! (also broadcast as Azteca Clic)
 * Az Mundo
 * Az Corazón (also broadcast)
 * Az Cinema
 * Azteca Trece -1 hora
 * Azteca Trece -2 horas
 *  Azteca Deportes
 * Romanza+ África - African channel (co-owned with Venevisión)

Disputes and controversies
On 5 January 2005, the U.S. Securities and Exchange Commission (SEC) accused TV Azteca executives (including chairman Ricardo Salinas Pliego) of having personally profited from a multimillion-dollar debt fraud committed by TV Azteca and another company in which they held stock. The charges were among the first brought under the provisions of the Sarbanes-Oxley Act of 2002, introduced in the wake of the corporate financial scandals of that year.

The Federal Radio and Television Law (known as the Ley Televisa) was a bill concerning the licensing and regulation of the electromagnetic spectrum. The LFRT was favorable to both TV Azteca and Televisa (who together control 95 percent of all television frequencies) because it allowed them to renew their licenses without paying for them. According to The Economist, the Ley Federal de Radio y Televisión "raced through Congress confirming the country's longstanding television duopoly" and constituted a "giveaway of radio spectrum and a provision that allows broadcasting licenses to be renewed more or less automatically".

In February 2012, TV Azteca networks (Azteca 7, Azteca 13, and Proyecto 40) were dropped by Mexican cable-TV carriers representing more than 4 million subscribers in a carriage dispute over terms. Cable operators claimed that Azteca wanted to charge a fee by packaging its over-the-air stations with cable networks, such as news and soap opera channels, which potentially represented a higher cost to subscribers. After a nine-month absence, TV Azteca returned gradually to cable operators.

In August 2018, American Tower's Mexican Unit, MATC Infraestructura sued TV Azteca for $97 Million in a New York court for defaulting on a loan from the company.

Holdings
TV Azteca is part of the conglomerate Grupo Salinas, which includes the Grupo Elektra franchise of department stores, the Banco Azteca bank, and Seguros Azteca life insurance. TV Azteca also owns Liga MX soccer club, Monarcas Morelia.

Acting school
The network has set up an acting school, Centro de Estudios y Formación Actoral (CEFAT). Alumni include Iliana Fox, Luis Ernesto Franco, Adriana Louvier, Fran Meric, Bárbara Mori, Laura Palma and Adrián Rubio.

Record label
The network also owns a record label, Azteca Music, which was founded in 1996.

title: TV Azteca


text:
John Morgan

John Morgan may refer to:

Academics

 * John Morgan (economist) (born 1967), American economist
 * John Morgan (etiquette expert) (1959–2000), British expert on etiquette
 * John Morgan (mathematician) (born 1946), mathematician at Stony Brook University
 * John Minter Morgan (1782–1855), author and philanthropist
 * John Henry Morgan (born 1945), American professor of the history and philosophy of social science
 * J. R. Morgan (born 1950), classicist and author, Swansea University

Entertainment

 * John Morgan (poet) (1688–c. 1733), Welsh clergyman, scholar and poet
 * John Morgan (artist) (1822–1885), British painter
 * John Morgan (comedian) (1930–2004), Welsh-born Canadian comedian
 * John Morgan (sportscaster) (born 1950), American broadcaster and television producer
 * John Morgan (The Wurzels) (1941–2021), drummer for The Wurzels

Military

 * John Morgan (admiral) (born 1950), United States Navy admiral
 * John Hunt Morgan (1825–1864), Confederate general during the American Civil War
 * J. H. Morgan (1876–1955), British general and lawyer
 * John C. Morgan (1914–1991), United States Army Air Forces pilot and Medal of Honor recipient

Canada

 * John W. Morgan (born 1964), mayor (2000-2012) of Cape Breton Regional Municipality, Nova Scotia

UK

 * John Morgan (by 1524 – will proved 1559) (died 1550s), MP for Monmouth Boroughs
 * John Morgan (fl. 1563), MP for Carmarthen Boroughs
 * John Morgan (died by 1572), MP for Leominster
 * John Morgan (merchant) (died 1715), Member of Parliament for Monmouth, 1701–1705
 * Sir John Morgan, 2nd Baronet (c. 1650–1693), Member of Parliament for Radnor, 1681, and Herefordshire, 1685–1693
 * John Morgan (of Rhiwpera) (1671–1720), Member of Parliament for Monmouthshire, 1701–1720
 * Sir John Morgan, 4th Baronet (1710–1767), Member of Parliament for Hereford, 1734–1741, and Herefordshire, 1765–1767
 * John Morgan (of Dderw) (1742–1792), Member of Parliament for Brecon, 1769–1771, and Monmouthshire, 1771–1792
 * John Morgan (British politician) (1892–1940), Labour MP for Doncaster, 1938–1941
 * John Lloyd Morgan (1861–1944), Welsh MP for West Carmarthenshire, 1889–1910

U.S.

 * John Morgan (Wisconsin politician) (1846–1926), member of the Wisconsin State Assembly in 1917
 * John G. Morgan (Tennessee politician)
 * John Hill Morgan (1870–1945), American lawyer, politician, and art expert
 * John J. Morgan (1770–1849), U.S. Representative from New York
 * John S. Morgan (born 1963), member of the Maryland House of Delegates
 * John T. Morgan (1824–1907), U.S. Senator
 * John T. Morgan (judge) (c. 1830–1910), Chief Justice of the Idaho Supreme Court

Religion

 * John Morgan (archdeacon of Bangor) (1840–1924)
 * John Morgan (archbishop of Wales) (1886–1957), Archbishop of Wales, 1949–1957
 * John Morgan (bishop of St David's) (died 1504)
 * John Morgan (missionary) (1806–1865), New Zealand missionary
 * John Morgan (dean of Waterford), Dean of Waterford, 1877–1903
 * John Hamilton Morgan (1842–1894), leader and missionary in the LDS Church
 * John Aloysius Morgan (1909–2008), Australian prelate of the Roman Catholic Church

Association football (soccer)

 * John Morgan (footballer, born 1855) (1855–1937), Welsh international footballer
 * John Morgan (footballer, born 1876) (1876–?), Welsh international footballer
 * Jock Morgan (John Morgan, 1889–1983), Scottish footballer

Other sports

 * Pepper Morgan (John L. Morgan, fl. 1930s), American baseball player
 * John Adams Morgan (born 1930), American Olympic sailor
 * John Morgan (golfer) (1943–2006), English golfer
 * John Morgan (Australian footballer) (born 1953), Australian rules footballer for Melbourne
 * John Morgan (wrestler) (born 1963), American Olympic wrestler
 * John Morgan (rugby league) (fl. 1960s–1970s), Australian rugby league footballer
 * John Morgan (cricketer) (born 1977), English cricketer
 * John E. Morgan (born 1977), English golfer
 * John Morgan (mixed martial arts journalist) (born 1978), American mixed martial arts journalist
 * John Morgan (swimmer) (fl. 1984–1992), American Paralympic gold medal-winning swimmer

Others

 * John Morgan (physician) (1735–1789), founder of first medical school in colonial America at University of Pennsylvania
 * John Morgan (British journalist) (1929–1988), Welsh journalist and broadcaster
 * John Morgan (lawyer) (born 1956), lawyer, founder of the Morgan & Morgan law firm
 * John Morgan (of Tredegar), Welsh nobleman
 * J. P. Morgan Jr. (1867–1943), American banker
 * J. P. Morgan (1837–1913), American banker

Other uses

 * SS John Morgan, 1943 World War II liberty ship

title: John Morgan


text:
Confusion and diffusion

In cryptography, confusion and diffusion are two properties of a secure cipher identified by Claude Shannon in his 1945 classified report A Mathematical Theory of Cryptography. These properties, when present, work together to thwart the application of statistics, and other methods of cryptanalysis.

Confusion in a symmetric cipher is obscuring the local correlation between the input (plaintext), and output (ciphertext) by varying the application of the key to the data, while diffusion is hiding the plaintext statistics by spreading it over a larger area of ciphertext. Although ciphers can be confusion-only (substitution cipher, one-time pad) or diffusion-only (transposition cipher), any "reasonable" block cipher uses both confusion and diffusion. These concepts are also important in the design of cryptographic hash functions, and pseudorandom number generators, where decorrelation of the generated values is the main feature. Diffusion (and its avalanche effect) is also applicable to non-cryptographic hash functions.

Confusion
Confusion means that each binary digit (bit) of the ciphertext should depend on several parts of the key, obscuring the connections between the two.

The property of confusion hides the relationship between the ciphertext and the key.

This property makes it difficult to find the key from the ciphertext and if a single bit in a key is changed, the calculation of most or all of the bits in the ciphertext will be affected.

Confusion increases the ambiguity of ciphertext and it is used by both block and stream ciphers.

In substitution–permutation networks, confusion is provided by substitution boxes.

Diffusion
Diffusion means that if we change a single bit of the plaintext, then about half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then about half of the plaintext bits should change. This is equivalent to the expectation that encryption schemes exhibit an avalanche effect.

The purpose of diffusion is to hide the statistical relationship between the ciphertext and the plain text. For example, diffusion ensures that any patterns in the plaintext, such as redundant bits, are not apparent in the ciphertext. Block ciphers achieve this by "diffusing" the information about the plaintext's structure across the rows and columns of the cipher.

In substitution–permutation networks, diffusion is provided by permutation boxes (a.k.a. permutation layer). In the beginning of the 21st century a consensus had appeared where the designers preferred the permutation layer to consist of linear Boolean functions, although nonlinear functions can be used, too.

Theory
In Shannon's original definitions, confusion refers to making the relationship between the ciphertext and the symmetric key as complex and involved as possible; diffusion refers to dissipating the statistical structure of plaintext over the bulk of ciphertext. This complexity is generally implemented through a well-defined and repeatable series of substitutions and permutations. Substitution refers to the replacement of certain components (usually bits) with other components, following certain rules. Permutation refers to manipulation of the order of bits according to some algorithm. To be effective, any non-uniformity of plaintext bits needs to be redistributed across much larger structures in the ciphertext, making that non-uniformity much harder to detect.

In particular, for a randomly chosen input, if one flips the i-th bit, then the probability that the j-th output bit will change should be one half, for any i and j—this is termed the strict avalanche criterion. More generally, one may require that flipping a fixed set of bits should change each output bit with probability one half.

One aim of confusion is to make it very hard to find the key even if one has a large number of plaintext-ciphertext pairs produced with the same key. Therefore, each bit of the ciphertext should depend on the entire key, and in different ways on different bits of the key. In particular, changing one bit of the key should change the ciphertext completely.

Practical applications
Design of a modern block cipher uses both confusion and diffusion, with confusion changing data between the input and the output by applying a key-dependent non-linear transformation (linear calculations are easier to reverse and thus are easier to break).

Confusion inevitably involves some diffusion, so a design with a very wide-input S-box can provide the necessary diffusion properties, but will be very costly in implementation. Therefore, the practical ciphers utilize relatively small S-boxes, operating on small groups of bits ("bundles"). For example, the design of AES has 8-bit S-boxes, Serpent − 4-bit, BaseKing and 3-way − 3-bit. Small S-boxes provide almost no diffusion, so the resources are spent on simpler diffusion transformations. For example, the wide trail strategy popularized by the Rijndael design, involves a linear mixing transformation that provides high diffusion, although the security proofs do not depend on the diffusion layer being linear.

One of the most researched cipher structures uses the substitution-permutation network (SPN) where each round includes a layer of local nonlinear permutations (S-boxes) for confusion and a linear diffusion transformation (usually a multiplication by a matrix over a finite field). Modern block ciphers mostly follow the confusion layer/diffusion layer model, with the efficiency of the diffusion layer estimated using the so-called branch number, a numerical parameter that can reach the value $$s+1$$ for $s$ input bundles for the perfect diffusion transformation. Since the transformations that have high branch numbers (and thus require a lot of bundles as inputs) are costly in implementation, the diffusion layer is sometimes (for example, in the AES) composed from two sublayers, "local diffusion" that processes subsets of the bundles in a bricklayer fashion (each subset is transformed independently) and "dispersion" that makes the bits that were "close" (within one subset of bundles) to become "distant" (spread to different subsets and thus be locally diffused within these new subsets on the next round).

Analysis of AES
The Advanced Encryption Standard (AES) has both excellent confusion and diffusion. Its confusion look-up tables are very non-linear and good at destroying patterns. Its diffusion stage spreads every part of the input to every part of the output: changing one bit of input changes half the output bits on average. Both confusion and diffusion are repeated multiple times for each input to increase the amount of scrambling. The secret key is mixed in at every stage so that an attacker cannot precalculate what the cipher does. None of this happens when a simple one-stage scramble is based on a key. Input patterns would flow straight through to the output. It might look random to the eye but analysis would find obvious patterns and the cipher could be broken.

title: Confusion and diffusion


text:
User:Tsca

Editor since January 2004. See meta:user:tsca.

da:Bruger:Tsca de:Benutzer:Tsca csb:Brëkòwnik:Tsca pl:Wikipedysta:Tsca

title: User:Tsca


text:
NAIA men's basketball championship

The NAIA men's basketball national championship has been held annually by the National Association of Intercollegiate Athletics since 1937 to determine the national champion of men's college basketball among its members in the United States and Canada.

The tournament was established by James Naismith to crown a national champion for smaller colleges and universities and has been held every year since, with the exceptions of 1944 (due to World War II) and 2020 (due to the COVID-19 pandemic).

Since 2022, the tournament has featured 64 teams, with teams beginning play at one of sixteen regional sites with the winners of those regionals playing at the final venue.

From 1992 to 2020, the NAIA sponsored two championships, one for its Division I members and another for those in its Division II. The Division I tournament was played in Kansas City, Missouri while the Division II tournament moved locations several times (it finished, in 2020, at the Sanford Pentagon in Sioux Falls, South Dakota). During this time, the NAIA tournaments featured 32 teams with the entire events contested at one location in one week (rather than multiple locations over a series of weekends).

After the 2020 tournaments were cancelled, however, they were merged back into a single tournament, which initially featured 48 teams in 2021 before expanding to 64 teams in 2022.

All tournament games can be watched online through the official NAIA provider StretchInternet.

History
The Men's Basketball Championship is mostly played at the Municipal Auditorium in Kansas City, Missouri. It has been held in Kansas City every year since the tournament began except from 1994 to 2001, when it was played in Tulsa, Oklahoma, and in 2020, when no tournament was held. Kansas City will continue to host until at least 2024.

In 2018, the NAIA announced a new format for the 2021 tournament after the merger of D-I and D-II. Under the new format, the men's and women's tournaments each involve 64 teams (the first post-COVID tournaments in 2021 had 48 teams). The first two rounds are played at 16 separate sites, with only the 16 winners at these sites advancing to Kansas City.

The tournament MVP has been presented with the Chuck Taylor Most Valuable Player award since 1939. In 1948, the NAIA became the first national organization to open their intercollegiate postseason to black student-athletes due primarily to the media attention surrounding the Manhatten Jaspers. Manhattan, who had an all-white team, learned of the NAIA rule that prohibited blacks from participating in the tournament, and after asking the NAIA to rescind the rule, the NAIA refused and Manhattan withdrew from the tournament. "The battle might have ended there but for a man named Harry Henshel, who was a member of the U.S. Olympic basketball committee. One of the reasons that the NAIA tournament was so prestigious was that the champion was invited to compete at the Olympic trials in New York City in late March. (The other teams invited were the two NCAA finalists, three teams from the Amateur Athletic Union, the winner of the National Invitation Tournament, and a YMCA team.)" After reading in the New York papers that blacks could not participate in the tournament, Henshel suggested to the media that the NAIA national champion be eliminated from Olympic consideration. NAIA officials read Hershel’s statement in the papers and quickly took a telegraphic poll amongst its members the following day that rescinded the racial ban. In 1947, Coach John Wooden of Indiana State refused the invitation to the NAIA National Tournament primarily because Clarence J. Walker, the only black player on his team could not participate. Because of the stance taken by Manhattan and Harry Hansel, in 1948, Coach Wooden was able to take Walker to the tournament who became the first African-American student-athlete to play in the NAIA tournament. Walker, a vital role player, helped the Sycamores finish as the NAIA's national finalist. In 1957, Tennessee State became the first historically black college to win a national championship, and the first team to win three consecutive tournaments. As of 2017, Kentucky State is the only other school to do so (1970, 1971, 1972). Oklahoma City holds the record for the most tournament championships with six. OCU also holds the record for most national championship titles in NAIA women's basketball.

Results

 * Notes

Champions

 * Division II titles are not included in this list. Schools in italics are no longer in the NAIA.

 * Schools highlighted in pink are closed or no longer sponsor athletics.
 * Schools highlight in yellow have reclassified athletics from the NAIA.

title: NAIA men's basketball championship


text:
Sidney Smith

Sidney Smith may refer to:

People

 * Sydney Smith (1771–1845), English writer and clergyman
 * Sidney Smith (Royal Navy officer) (1764–1840) British naval officer
 * Syd Smith (baseball) (1883–1961), American baseball player and college football coach
 * Sidney Smith (Assyriologist) (1889–1979), institute director and academic
 * Sidney Smith (cartoonist) (1877–1935), American cartoonist
 * Sidney Smith (cricketer) (1929–1985), English cricketer
 * Sidney Smith (lawyer) (1823–1889), lawyer and politician in Upper Canada
 * Sidney Smith (rugby league), rugby league footballer of 1920s and 1930s
 * Sidney Smith (snooker player) (1908–1990), English billiards and snooker player
 * Sidney Earle Smith (1897–1959), Canadian university president and Secretary of State for External Affairs
 * Sidney Irving Smith (1843–1926), American zoologist
 * Sidney Lawton Smith (1845–1929), American designer, illustrator and bookplate artist
 * Sidney Maynard Smith (1875–1928), British surgeon and freemason
 * Sidney Oslin Smith Jr. (1923–2012), United States federal judge
 * Sidney R. J. Smith (1858–1913), English architect
 * Sidney Walter Smith (1893–1981), New Zealand politician
 * Sid Smith (actor) (1894–1928), American actor in silent films

Ships

 * Sir Sidney Smith, a list of ships by that name

title: Sidney Smith