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Julia set

In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic".

The Julia set of a function  $f$  is commonly denoted $$\operatorname{J}(f),$$ and the Fatou set is denoted $$\operatorname{F}(f).$$ These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.

Formal definition
Let $$f(z)$$ be a non-constant holomorphic function from the Riemann sphere onto itself. Such functions $$f(z)$$ are precisely the non-constant complex rational functions, that is, $$f(z) = p(z)/q(z)$$ where $$p(z)$$ and $$q(z)$$ are complex polynomials. Assume that p and q have no common roots, and at least one has degree larger than 1. Then there is a finite number of open sets $$F_1, ..., F_r$$ that are left invariant by $$f(z)$$ and are such that:
 * 1) The union of the sets $$F_i$$ is dense in the plane and
 * 2) $$f(z)$$ behaves in a regular and equal way on each of the sets $$F_i$$.

The last statement means that the termini of the sequences of iterations generated by the points of $$F_i$$ are either precisely the same set, which is then a finite cycle, or they are finite cycles of circular or annular shaped sets that are lying concentrically. In the first case the cycle is attracting, in the second case it is neutral.

These sets $$F_i$$ are the Fatou domains of $$f(z)$$, and their union is the Fatou set $$\operatorname{F}(f)$$ of $$f(z)$$. Each of the Fatou domains contains at least one critical point of $$f(z)$$, that is, a (finite) point z satisfying $$f'(z) = 0$$, or $$f(z) = \infty$$ if the degree of the numerator $$p(z) $$ is at least two larger than the degree of the denominator $$q(z)$$, or if $$f(z) = 1/g(z) + c$$ for some c and a rational function $$g(z)$$ satisfying this condition.

The complement of $$\operatorname{F}(f)$$ is the Julia set $$\operatorname{J}(f)$$ of $$f(z)$$. If all the critical points are preperiodic, that is they are not periodic but eventually land on a periodic cycle, then $$\operatorname{J}(f)$$ is all the sphere. Otherwise, $$\operatorname{J}(f)$$ is a nowhere dense set (it is without interior points) and an uncountable set (of the same cardinality as the real numbers). Like $$\operatorname{F}(f)$$, $$\operatorname{J}(f)$$ is left invariant by $$f(z)$$, and on this set the iteration is repelling, meaning that $$|f(z) - f(w)| > |z - w| $$ for all w in a neighbourhood of z (within $$\operatorname{J}(f)$$). This means that $$f(z)$$ behaves chaotically on the Julia set. Although there are points in the Julia set whose sequence of iterations is finite, there are only a countable number of such points (and they make up an infinitesimal part of the Julia set). The sequences generated by points outside this set behave chaotically, a phenomenon called deterministic chaos.

There has been extensive research on the Fatou set and Julia set of iterated rational functions, known as rational maps. For example, it is known that the Fatou set of a rational map has either 0, 1, 2 or infinitely many components. Each component of the Fatou set of a rational map can be classified into one of four different classes.

Equivalent descriptions of the Julia set

 * $$\operatorname{J}(f)$$ is the smallest closed set containing at least three points which is completely invariant under f.
 * $$\operatorname{J}(f)$$ is the closure of the set of repelling periodic points.
 * For all but at most two points $$\;z \in X\;,$$ the Julia set is the set of limit points of the full backwards orbit $$\bigcup_n f^{-n}(z).$$ (This suggests a simple algorithm for plotting Julia sets, see below.)
 * If f is an entire function, then $$\operatorname{J}(f)$$ is the boundary of the set of points which converge to infinity under iteration.
 * If f is a polynomial, then $$\operatorname{J}(f)$$ is the boundary of the filled Julia set; that is, those points whose orbits under iterations of f remain bounded.

Properties of the Julia set and Fatou set
The Julia set and the Fatou set of f are both completely invariant under iterations of the holomorphic function f:
 * $$f^{-1}(\operatorname{J}(f)) = f(\operatorname{J}(f)) = \operatorname{J}(f),$$
 * $$f^{-1}(\operatorname{F}(f)) = f(\operatorname{F}(f)) = \operatorname{F}(f).$$

Examples
For $$f(z) = z^{2}$$ the Julia set is the unit circle and on this the iteration is given by doubling of angles (an operation that is chaotic on the points whose argument is not a rational fraction of $$2\pi$$). There are two Fatou domains: the interior and the exterior of the circle, with iteration towards 0 and ∞, respectively.

For $$g(z) = z^{2} - 2$$ the Julia set is the line segment between −2 and 2. There is one Fatou domain: the points not on the line segment iterate towards ∞. (Apart from a shift and scaling of the domain, this iteration is equivalent to $$x \to 4(x - \tfrac{1}{2})^{2}$$ on the unit interval, which is commonly used as an example of chaotic system.)

The functions f and g are of the form $$z^2 + c$$, where c is a complex number. For such an iteration the Julia set is not in general a simple curve, but is a fractal, and for some values of c it can take surprising shapes. See the pictures below.

For some functions f(z) we can say beforehand that the Julia set is a fractal and not a simple curve. This is because of the following result on the iterations of a rational function:

$f$

This means that each point of the Julia set is a point of accumulation for each of the Fatou domains. Therefore, if there are more than two Fatou domains, each point of the Julia set must have points of more than two different open sets infinitely close, and this means that the Julia set cannot be a simple curve. This phenomenon happens, for instance, when f(z) is the Newton iteration for solving the equation $$\;P(z) := z^n - 1 =  0 ~ : ~ n > 2\;$$:

 * $$f(z) = z - \frac{P(z)}{P'(z)} = \frac{\;1 + (n-1)z^n\;}{nz^{n-1}} ~ .$$

The image on the right shows the case n = 3.

Quadratic polynomials
A very popular complex dynamical system is given by the family of complex quadratic polynomials, a special case of rational maps. Such quadratic polynomials can be expressed as
 * $$f_c(z) = z^2 + c ~,$$

where c is a complex parameter. Fix some $$R > 0$$ large enough that $$R^2 - R \ge |c|.$$ (For example, if $$ is in the Mandelbrot set, then $$|c| \le 2,$$ so we may simply let $$R = 2~.$$) Then the filled Julia set for this system is the subset of the complex plane given by
 * $$K(f_c) = \left\{z \in \mathbb C : \forall n \in \mathbb N, |f_c^n(z)| \le R \right\}~,$$

where $$f_c^n(z)$$ is the nth iterate of $$f_c(z).$$ The Julia set $$J(f_c)$$ of this function is the boundary of $$K(f_c)$$.

The parameter plane of quadratic polynomials – that is, the plane of possible c values – gives rise to the famous Mandelbrot set. Indeed, the Mandelbrot set is defined as the set of all c such that $$J(f_c)$$ is connected. For parameters outside the Mandelbrot set, the Julia set is a Cantor space: in this case it is sometimes referred to as Fatou dust.

In many cases, the Julia set of c looks like the Mandelbrot set in sufficiently small neighborhoods of c. This is true, in particular, for so-called Misiurewicz parameters, i.e. parameters c for which the critical point is pre-periodic. For instance:
 * At c = i, the shorter, front toe of the forefoot, the Julia set looks like a branched lightning bolt.
 * At c = −2, the tip of the long spiky tail, the Julia set is a straight line segment.

In other words, the Julia sets $$J(f_c)$$ are locally similar around Misiurewicz points.

Generalizations
The definition of Julia and Fatou sets easily carries over to the case of certain maps whose image contains their domain; most notably transcendental meromorphic functions and Adam Epstein's finite-type maps.

Julia sets are also commonly defined in the study of dynamics in several complex variables.

Pseudocode
The below pseudocode implementations hard code the functions for each fractal. Consider implementing complex number operations to allow for more dynamic and reusable code.

Pseudocode for normal Julia sets

 * $$f(z) = z^2 + c$$

Pseudocode for multi-Julia sets

 * $$f(z) = z^n + c$$

Another recommended option is to reduce color banding between iterations by using a renormalization formula for the iteration.

Such formula is given to be,
 * $$mu = k + 1 - \frac{\log{\log{|z_{k}|}}}{\log{n}}$$
 * $$\forall f_{c,n}(z) = z^{n} + \text{lower power terms} + c$$

where $$k$$ is the escaping iteration, bounded by some $$K$$ such that $$0 \leq k < K$$ and $$ K \in \mathbb{N}$$, and $$|z_{k}|$$ is the magnitude of the last iterate before escaping.

This can be implemented, very simply, like so:

The difference is shown below with a Julia set defined as $$f_{c, 2}(z)$$ where $$ c = -0.835 - 0.321i $$.

The potential function and the real iteration number
The Julia set for $$f(z) = z^{2}$$ is the unit circle, and on the outer Fatou domain, the potential function φ(z) is defined by φ(z) = log|z|. The equipotential lines for this function are concentric circles. As $$|f(z)| = |z|^{2}$$ we have

 * $$\varphi(z) = \lim_{k\to\infty} \frac{\log|z_k|}{2^k},$$

where $$z_k$$ is the sequence of iteration generated by z. For the more general iteration $$f(z) = z^2 + c$$, it has been proved that if the Julia set is connected (that is, if c belongs to the (usual) Mandelbrot set), then there exist a biholomorphic map ψ between the outer Fatou domain and the outer of the unit circle such that $$|\psi(f(z))| = |\psi(z)|^{2}$$. This means that the potential function on the outer Fatou domain defined by this correspondence is given by:

 * $$\varphi(z) = \lim_{k\to\infty} \frac{\log|z_k|}{2^k}. $$

This formula has meaning also if the Julia set is not connected, so that we for all c can define the potential function on the Fatou domain containing ∞ by this formula. For a general rational function f(z) such that ∞ is a critical point and a fixed point, that is, such that the degree m of the numerator is at least two larger than the degree n of the denominator, we define the potential function on the Fatou domain containing ∞ by:

 * $$\varphi(z) = \lim_{k\to\infty} \frac{\log|z_k|}{d^k},$$

where d = m − n is the degree of the rational function.

If N is a very large number (e.g. 10100), and if k is the first iteration number such that $$|z_k| > N$$, we have that

 * $$\frac{\log|z_k|}{d^k} = \frac{\log(N)}{d^{\nu(z)}},$$

for some real number $$\nu(z)$$, which should be regarded as the real iteration number, and we have that:

 * $$\nu(z) = k - \frac{\log(\log|z_k|/\log(N))}{\log(d)},$$

where the last number is in the interval [0, 1).

For iteration towards a finite attracting cycle of order r, we have that if $$z^*$$ is a point of the cycle, then $$f(f(...f(z^*))) = z^*$$ (the r-fold composition), and the number

 * $$\alpha = \frac{1}{\left |(d(f(f(\cdots f(z))))/dz)_{z=z^*} \right |} \qquad ( > 1)$$

is the attraction of the cycle. If w is a point very near $$z^*$$ and w′ is w iterated r times, we have that

 * $$\alpha = \lim_{k\to\infty} \frac{|w - z^*|}{|w' - z^*|}.$$

Therefore, the number $$|z_{kr} - z^*|\alpha^{k}$$ is almost independent of k. We define the potential function on the Fatou domain by:

 * $$\varphi(z) = \lim_{k\to\infty} \frac{1}{(|z_{kr} - z^*|\alpha^{k})}.$$

If ε is a very small number and k is the first iteration number such that $$|z_k - z^*| < \epsilon$$, we have that

 * $$\varphi(z) = \frac{1}{(\varepsilon \alpha^{\nu(z)})}$$

for some real number $$\nu(z)$$, which should be regarded as the real iteration number, and we have that:

 * $$\nu(z) = k - \frac{\log(\varepsilon/|z_k - z^*|)}{\log(\alpha)}.$$

If the attraction is ∞, meaning that the cycle is super-attracting, meaning again that one of the points of the cycle is a critical point, we must replace α by

 * $$\alpha = \lim_{k\to\infty} \frac{\log|w' - z^*|}{\log|w - z^*|},$$

where w′ is w iterated r times and the formula for φ(z) by:

 * $$\varphi(z) = \lim_{k\to\infty} \frac{\log(1/|z_{kr} - z^*|)}{\alpha^k}. $$

And now the real iteration number is given by:

 * $$\nu(z) = k - \frac{\log(\log|z_k - z^*|/\log(\varepsilon))}{\log(\alpha)}.$$

For the colouring we must have a cyclic scale of colours (constructed mathematically, for instance) and containing H colours numbered from 0 to H−1 (H = 500, for instance). We multiply the real number $$\nu(z)$$ by a fixed real number determining the density of the colours in the picture, and take the integral part of this number modulo H.

The definition of the potential function and our way of colouring presuppose that the cycle is attracting, that is, not neutral. If the cycle is neutral, we cannot colour the Fatou domain in a natural way. As the terminus of the iteration is a revolving movement, we can, for instance, colour by the minimum distance from the cycle left fixed by the iteration.

Field lines
In each Fatou domain (that is not neutral) there are two systems of lines orthogonal to each other: the equipotential lines (for the potential function or the real iteration number) and the field lines.

If we colour the Fatou domain according to the iteration number (and not the real iteration number $$\nu(z)$$, as defined in the previous section), the bands of iteration show the course of the equipotential lines. If the iteration is towards ∞ (as is the case with the outer Fatou domain for the usual iteration $$z^{2} + c$$), we can easily show the course of the field lines, namely by altering the colour according as the last point in the sequence of iteration is above or below the x-axis (first picture), but in this case (more precisely: when the Fatou domain is super-attracting) we cannot draw the field lines coherently - at least not by the method we describe here. In this case a field line is also called an external ray.

Let z be a point in the attracting Fatou domain. If we iterate z a large number of times, the terminus of the sequence of iteration is a finite cycle C, and the Fatou domain is (by definition) the set of points whose sequence of iteration converges towards C. The field lines issue from the points of C and from the (infinite number of) points that iterate into a point of C. And they end on the Julia set in points that are non-chaotic (that is, generating a finite cycle). Let r be the order of the cycle C (its number of points) and let $$z^*$$ be a point in C. We have $$f(f(\dots f(z^*))) = z^*$$ (the r-fold composition), and we define the complex number α by

 * $$\alpha = (d(f(f(\dots f(z))))/dz)_{z=z^*}.$$

If the points of C are $$z_i, i = 1, \dots, r (z_1 = z^*)$$, α is the product of the r numbers $$f'(z_i)$$. The real number 1/|α| is the attraction of the cycle, and our assumption that the cycle is neither neutral nor super-attracting, means that $c = 1 − φ$. The point $$z^*$$ is a fixed point for $$f(f(\dots f(z)))$$, and near this point the map $$f(f(\dots f(z)))$$ has (in connection with field lines) character of a rotation with the argument β of α (that is, $$\alpha = |\alpha|e^{\beta i}$$).

In order to colour the Fatou domain, we have chosen a small number ε and set the sequences of iteration $$z_k (k = 0, 1, 2, \dots, z_0 = z)$$ to stop when $$|z_k - z^*| < \epsilon$$, and we colour the point z according to the number k (or the real iteration number, if we prefer a smooth colouring). If we choose a direction from $$z^*$$ given by an angle θ, the field line issuing from $$z^*$$ in this direction consists of the points z such that the argument ψ of the number $$z_k - z^*$$ satisfies the condition that

 * $$\psi - k\beta = \theta \mod \pi. \, $$

For if we pass an iteration band in the direction of the field lines (and away from the cycle), the iteration number k is increased by 1 and the number ψ is increased by β, therefore the number $$\psi - k\beta \mod \pi$$ is constant along the field line.

A colouring of the field lines of the Fatou domain means that we colour the spaces between pairs of field lines: we choose a number of regularly situated directions issuing from $$z^*$$, and in each of these directions we choose two directions around this direction. As it can happen that the two field lines of a pair do not end in the same point of the Julia set, our coloured field lines can ramify (endlessly) in their way towards the Julia set. We can colour on the basis of the distance to the center line of the field line, and we can mix this colouring with the usual colouring. Such pictures can be very decorative (second picture).

A coloured field line (the domain between two field lines) is divided up by the iteration bands, and such a part can be put into a one-to-one correspondence with the unit square: the one coordinate is (calculated from) the distance from one of the bounding field lines, the other is (calculated from) the distance from the inner of the bounding iteration bands (this number is the non-integral part of the real iteration number). Therefore, we can put pictures into the field lines (third picture).

Plotting the Julia set
Methods :
 * Distance Estimation Method for Julia set (DEM/J)
 * Inverse Iteration Method (IIM)

Using backwards (inverse) iteration (IIM)
As mentioned above, the Julia set can be found as the set of limit points of the set of pre-images of (essentially) any given point. So we can try to plot the Julia set of a given function as follows. Start with any point z we know to be in the Julia set, such as a repelling periodic point, and compute all pre-images of z under some high iterate $$f^n$$ of f.

Unfortunately, as the number of iterated pre-images grows exponentially, this is not feasible computationally. However, we can adjust this method, in a similar way as the "random game" method for iterated function systems. That is, in each step, we choose at random one of the inverse images of f.

For example, for the quadratic polynomial fc, the backwards iteration is described by

 * $$z_{n-1} = \sqrt{z_n - c} .$$

At each step, one of the two square roots is selected at random.

Note that certain parts of the Julia set are quite difficult to access with the reverse Julia algorithm. For this reason, one must modify IIM/J ( it is called MIIM/J) or use other methods to produce better images.

Using DEM/J
As a Julia set is infinitely thin we cannot draw it effectively by backwards iteration from the pixels. It will appear fragmented because of the impracticality of examining infinitely many startpoints. Since the iteration count changes vigorously near the Julia set, a partial solution is to imply the outline of the set from the nearest color contours, but the set will tend to look muddy.

A better way to draw the Julia set in black and white is to estimate the distance of pixels (DEM) from the set and to color every pixel whose center is close to the set. The formula for the distance estimation is derived from the formula for the potential function φ(z). When the equipotential lines for φ(z) lie close, the number $$|\varphi'(z)|$$ is large, and conversely, therefore the equipotential lines for the function $$\delta(z) = \varphi(z)/|\varphi'(z)|$$ should lie approximately regularly. It has been proven that the value found by this formula (up to a constant factor) converges towards the true distance for z converging towards the Julia set.

We assume that f(z) is rational, that is, $$f(z) = p(z)/q(z)$$ where p(z) and q(z) are complex polynomials of degrees m and n, respectively, and we have to find the derivative of the above expressions for φ(z). And as it is only $$z_k$$ that varies, we must calculate the derivative $$z'_k$$ of $$z_k$$ with respect to z. But as $$z_k = f(f(\cdots f(z)))$$ (the k-fold composition), $$z'_k$$ is the product of the numbers $$f'(z_k)$$, and this sequence can be calculated recursively by $$z'_{k+1} = f'(z_k)z'_k$$, starting with $$z'_0 = 1$$ (before the calculation of the next iteration $$z_{k+1} = f(z_k)$$).

For iteration towards ∞ (more precisely when $size=100%$, so that ∞ is a super-attracting fixed point), we have

 * $$|\varphi'(z)| = \lim_{k\to\infty} \frac{|z'_k|}{|z_k|d^k},$$

($c = 0.285 + 0i$) and consequently:

 * $$\delta(z) = \varphi(z)/|\varphi'(z)| = \lim_{k\to\infty} \log|z_k||z_k|/|z'_k|. \, $$

For iteration towards a finite attracting cycle (that is not super-attracting) containing the point $c$ and having order r, we have

 * $$|\varphi'(z)| = \lim_{k\to\infty} |z'_{kr}|/(|z_{kr} - z^*|^{2}\alpha^{k}), \, $$

and consequently:

 * $$\delta(z) = \varphi(z)/|\varphi'(z)| = \lim_{k\to\infty} |z_{kr} - z^*|/|z'_{kr}|. \, $$

For a super-attracting cycle, the formula is:

 * $$\delta(z) = \lim_{k\to\infty} \log|z_{kr} - z^*|^2/|z'_{kr}|. \, $$

We calculate this number when the iteration stops. Note that the distance estimation is independent of the attraction of the cycle. This means that it has meaning for transcendental functions of "degree infinity" (e.g. sin(z) and tan(z)).

Besides drawing of the boundary, the distance function can be introduced as a 3rd dimension to create a solid fractal landscape.

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

title: Julia set


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Obesity

Obesity is a medical condition, sometimes considered a disease,  in which excess body fat has accumulated to such an extent that it can potentially have negative effects on health. People are classified as obese when their body mass index (BMI)—a person's weight divided by the square of the person's height—is over $30 kg/m2$; the range $30 kg/m2$ is defined as overweight. Some East Asian countries use lower values to calculate obesity. Obesity is a major cause of disability and is correlated with various diseases and conditions, particularly cardiovascular diseases, type 2 diabetes, obstructive sleep apnea, certain types of cancer, and osteoarthritis.

Obesity has individual, socioeconomic, and environmental causes. Some known causes are diet, physical activity, automation, urbanization, genetic susceptibility, medications, mental disorders, economic policies, endocrine disorders, and exposure to endocrine-disrupting chemicals.

While a majority of obese individuals at any given time attempt to lose weight and are often successful, maintaining weight loss long-term is rare. There is no effective, well-defined, evidence-based intervention for preventing obesity. Obesity prevention requires a complex approach, including interventions at societal, community, family, and individual levels. Changes to diet as well as exercising are the main treatments recommended by health professionals. Diet quality can be improved by reducing the consumption of energy-dense foods, such as those high in fat or sugars, and by increasing the intake of dietary fiber, if these dietary choices are available, affordable, and accessible. Medications can be used, along with a suitable diet, to reduce appetite or decrease fat absorption. If diet, exercise, and medication are not effective, a gastric balloon or surgery may be performed to reduce stomach volume or length of the intestines, leading to feeling full earlier, or a reduced ability to absorb nutrients from food.

Obesity is a leading preventable cause of death worldwide, with increasing rates in adults and children. In 2022, over 1 billion people were obese worldwide (879 million adults and 159 million children), representing more than a double of adult cases (and four times higher than cases among children) registered in 1990. Obesity is more common in women than in men. Today, obesity is stigmatized in most of the world. Conversely, some cultures, past and present, have a favorable view of obesity, seeing it as a symbol of wealth and fertility. The World Health Organization, the US, Canada, Japan, Portugal, Germany, the European Parliament and medical societies, e.g. the American Medical Association, classify obesity as a disease. Others, such as the UK, do not.

Classification
Obesity is typically defined as a substantial accumulation of body fat that could impact health. Medical organizations tend to classify people as obese based on body mass index (BMI) – a ratio of a person's weight in kilograms to the square of their height in meters. For adults, the World Health Organization (WHO) defines "overweight" as a BMI 25 or higher, and "obese" as a BMI 30 or higher. The U.S. Centers for Disease Control and Prevention (CDC) further subdivides obesity based on BMI, with a BMI 30 to 35 called class 1 obesity; 35 to 40, class 2 obesity; and 40+, class 3 obesity.

For children, obesity measures take age into consideration along with height and weight. For children aged 5–19, the WHO defines obesity as a BMI two standard deviations above the median for their age (a BMI around 18 for a five-year old; around 30 for a 19-year old). For children under five, the WHO defines obesity as a weight three standard deviations above the median for their height.

Some modifications to the WHO definitions have been made by particular organizations. The surgical literature breaks down class II and III or only class III obesity into further categories whose exact values are still disputed.
 * Any BMI ≥ 35 or 40 kg/m2 is severe obesity.
 * A BMI of ≥ 35 kg/m2 and experiencing obesity-related health conditions or ≥ 40 or 45 kg/m2 is morbid obesity.
 * A BMI of ≥ 45 or 50 kg/m2 is super obesity.

As Asian populations develop negative health consequences at a lower BMI than Caucasians, some nations have redefined obesity; Japan has defined obesity as any BMI greater than 25 kg/m2 while China uses a BMI of greater than 28 kg/m2.

The preferred obesity metric in scholarly circles is the body fat percentage (BF%) – the ratio of the total weight of person's fat to his or her body weight, and BMI is viewed merely as a way to approximate BF%. According to American Society of Bariatric Physicians, levels in excess of 32% for women and 25% for men are generally considered to indicate obesity.

BMI ignores variations between individuals in amounts of lean body mass, particularly muscle mass. Individuals involved in heavy physical labor or sports may have high BMI values despite having little fat. For example, more than half of all NFL players are classified as "obese" (BMI ≥ 30), and 1 in 4 are classified as "extremely obese" (BMI ≥ 35), according to the BMI metric. However, their mean body fat percentage, 14%, is well within what is considered a healthy range. Similarly, Sumo wrestlers may be categorized by BMI as "severely obese" or "very severely obese" but many Sumo wrestlers are not categorized as obese when body fat percentage is used instead (having <25% body fat). Some Sumo wrestlers were found to have no more body fat than a non-Sumo comparison group, with high BMI values resulting from their high amounts of lean body mass.

Effects on health
Obesity increases a person's risk of developing various metabolic diseases, cardiovascular disease, osteoarthritis, Alzheimer disease, depression, and certain types of cancer. Depending on the degree of obesity and the presence of comorbid disorders, obesity is associated with an estimated 2–20 year shorter life expectancy. High BMI is a marker of risk for, but not a direct cause of, diseases caused by diet and physical activity.

Mortality
Obesity is one of the leading preventable causes of death worldwide. The mortality risk is lowest at a BMI of 20–25 kg/m2 in non-smokers and at 24–27 kg/m2 in current smokers, with risk increasing along with changes in either direction. This appears to apply in at least four continents. Other research suggests that the association of BMI and waist circumference with mortality is U- or J-shaped, while the association between waist-to-hip ratio and waist-to-height ratio with mortality is more positive. In Asians the risk of negative health effects begins to increase between 22 and 25 kg/m2. In 2021, the World Health Organization estimated that obesity caused at least 2.8 million deaths annually. On average, obesity reduces life expectancy by six to seven years, a BMI of 30–35 kg/m2 reduces life expectancy by two to four years, while severe obesity (BMI ≥ 40 kg/m2) reduces life expectancy by ten years.

Morbidity
Obesity increases the risk of many physical and mental conditions. These comorbidities are most commonly shown in metabolic syndrome, a combination of medical disorders which includes: diabetes mellitus type 2, high blood pressure, high blood cholesterol, and high triglyceride levels. A study from the RAK Hospital found that obese people are at a greater risk of developing long COVID. The CDC has found that obesity is the single strongest risk factor for severe COVID-19 illness.

Complications are either directly caused by obesity or indirectly related through mechanisms sharing a common cause such as a poor diet or a sedentary lifestyle. The strength of the link between obesity and specific conditions varies. One of the strongest is the link with type 2 diabetes. Excess body fat underlies 64% of cases of diabetes in men and 77% of cases in women.

Health consequences fall into two broad categories: those attributable to the effects of increased fat mass (such as osteoarthritis, obstructive sleep apnea, social stigmatization) and those due to the increased number of fat cells (diabetes, cancer, cardiovascular disease, non-alcoholic fatty liver disease). Increases in body fat alter the body's response to insulin, potentially leading to insulin resistance. Increased fat also creates a proinflammatory state, and a prothrombotic state.

Metrics of health
Newer research has focused on methods of identifying healthier obese people by clinicians, and not treating obese people as a monolithic group. Obese people who do not experience medical complications from their obesity are sometimes called (metabolically) healthy obese, but the extent to which this group exists (especially among older people) is in dispute. The number of people considered metabolically healthy depends on the definition used, and there is no universally accepted definition. There are numerous obese people who have relatively few metabolic abnormalities, and a minority of obese people have no medical complications. The guidelines of the American Association of Clinical Endocrinologists call for physicians to use risk stratification with obese patients when considering how to assess their risk of developing type 2 diabetes.

In 2014, the BioSHaRE–EU Healthy Obese Project (sponsored by Maelstrom Research, a team under the Research Institute of the McGill University Health Centre) came up with two definitions for healthy obesity, one more strict and one less so:

To come up with these criteria, BioSHaRE controlled for age and tobacco use, researching how both may effect the metabolic syndrome associated with obesity, but not found to exist in the metabolically healthy obese. Other definitions of metabolically healthy obesity exist, including ones based on waist circumference rather than BMI, which is unreliable in certain individuals.

Another identification metric for health in obese people is calf strength, which is positively correlated with physical fitness in obese people. Body composition in general is hypothesized to help explain the existence of metabolically healthy obesity—the metabolically healthy obese are often found to have low amounts of ectopic fat (fat stored in tissues other than adipose tissue) despite having overall fat mass equivalent in weight to obese people with metabolic syndrome.

Survival paradox
Although the negative health consequences of obesity in the general population are well supported by the available research evidence, health outcomes in certain subgroups seem to be improved at an increased BMI, a phenomenon known as the obesity survival paradox. The paradox was first described in 1999 in overweight and obese people undergoing hemodialysis and has subsequently been found in those with heart failure and peripheral artery disease (PAD).

In people with heart failure, those with a BMI between 30.0 and 34.9 had lower mortality than those with a normal weight. This has been attributed to the fact that people often lose weight as they become progressively more ill. Similar findings have been made in other types of heart disease. People with class I obesity and heart disease do not have greater rates of further heart problems than people of normal weight who also have heart disease. In people with greater degrees of obesity, however, the risk of further cardiovascular events is increased. Even after cardiac bypass surgery, no increase in mortality is seen in the overweight and obese. One study found that the improved survival could be explained by the more aggressive treatment obese people receive after a cardiac event. Another study found that if one takes into account chronic obstructive pulmonary disease (COPD) in those with PAD, the benefit of obesity no longer exists.

Causes
The "a calorie is a calorie" model of obesity posits a combination of excessive food energy intake and a lack of physical activity as the cause of most cases of obesity. A limited number of cases are due primarily to genetics, medical reasons, or psychiatric illness. In contrast, increasing rates of obesity at a societal level are felt to be due to an easily accessible and palatable diet, increased reliance on cars, and mechanized manufacturing.

Some other factors have been proposed as causes towards rising rates of obesity worldwide, including insufficient sleep, endocrine disruptors, increased usage of certain medications (such as atypical antipsychotics), increases in ambient temperature, decreased rates of smoking, demographic changes, increasing maternal age of first-time mothers, changes to epigenetic dysregulation from the environment, increased phenotypic variance via assortative mating, social pressure to diet, among others. According to one study, factors like these may play as big of a role as excessive food energy intake and a lack of physical activity; however, the relative magnitudes of the effects of any proposed cause of obesity is varied and uncertain, as there is a general need for randomized controlled trials on humans before definitive statement can be made.

According to the Endocrine Society, there is "growing evidence suggesting that obesity is a disorder of the energy homeostasis system, rather than simply arising from the passive accumulation of excess weight".

Diet
1961 2001–03 Map of dietary energy availability per person per day in 1961 (left) and 2001–2003 (right) Calories per person per day (kilojoules per person per day)

{{legend|#b3b3b3| No data }} {{legend|#ffff65| <1,600 (<6,700) }} {{legend|#fff200| 1,600–1,800 (6,700–7,500) }} {{legend|#ffdc00| 1,800–2,000 (7,500–8,400) }} {{legend|#ffc600| 2,000–2,200 (8,400–9,200) }} {{legend|#ffb000| 2,200–2,400 (9,200–10,000) }} {{legend|#ff9a00| 2,400–2,600 (10,000–10,900) }}

{{legend|#ff8400| 2,600–2,800 (10,900–11,700) }} {{legend|#ff6e00| 2,800–3,000 (11,700–12,600) }} {{legend|#ff5800| 3,000–3,200 (12,600–13,400) }} {{legend|#ff4200| 3,200–3,400 (13,400–14,200) }} {{legend|#ff2c00| 3,400–3,600 (14,200–15,100) }} {{legend|#cb0000| >3,600 (>15,100) }}

Excess appetite for palatable, high-calorie food (especially fat, sugar, and certain animal proteins) is seen as the primary factor driving obesity worldwide, likely because of imbalances in neurotransmitters affecting the drive to eat. Dietary energy supply per capita varies markedly between different regions and countries. It has also changed significantly over time. From the early 1970s to the late 1990s the average food energy available per person per day (the amount of food bought) increased in all parts of the world except Eastern Europe. The United States had the highest availability with 3654 Cal per person in 1996. This increased further in 2003 to 3754 Cal. During the late 1990s, Europeans had 3394 Cal per person, in the developing areas of Asia there were 2648 Cal per person, and in sub-Saharan Africa people had 2176 Cal per person. Total food energy consumption has been found to be related to obesity. The widespread availability of dietary guidelines has done little to address the problems of overeating and poor dietary choice. From 1971 to 2000, obesity rates in the United States increased from 14.5% to 30.9%. During the same period, an increase occurred in the average amount of food energy consumed. For women, the average increase was 335 Cal per day (1542 Cal in 1971 and 1877 Cal in 2004), while for men the average increase was 168 Cal per day (2450 Cal in 1971 and 2618 Cal in 2004). Most of this extra food energy came from an increase in carbohydrate consumption rather than fat consumption. The primary sources of these extra carbohydrates are sweetened beverages, which now account for almost 25 percent of daily food energy in young adults in America, and potato chips. Consumption of sweetened beverages such as soft drinks, fruit drinks, and iced tea is believed to be contributing to the rising rates of obesity and to an increased risk of metabolic syndrome and type 2 diabetes. Vitamin D deficiency is related to diseases associated with obesity.

As societies become increasingly reliant on energy-dense, big-portions, and fast-food meals, the association between fast-food consumption and obesity becomes more concerning. In the United States, consumption of fast-food meals tripled and food energy intake from these meals quadrupled between 1977 and 1995.

Agricultural policy and techniques in the United States and Europe have led to lower food prices. In the United States, subsidization of corn, soy, wheat, and rice through the U.S. farm bill has made the main sources of processed food cheap compared to fruits and vegetables. Calorie count laws and nutrition facts labels attempt to steer people toward making healthier food choices, including awareness of how much food energy is being consumed.

Obese people consistently under-report their food consumption as compared to people of normal weight. This is supported both by tests of people carried out in a calorimeter room and by direct observation.

Sedentary lifestyle
A sedentary lifestyle may play a significant role in obesity. Worldwide there has been a large shift towards less physically demanding work,  and currently at least 30% of the world's population gets insufficient exercise. This is primarily due to increasing use of mechanized transportation and a greater prevalence of labor-saving technology in the home. In children, there appear to be declines in levels of physical activity (with particularly strong declines in the amount of walking and physical education), likely due to safety concerns, changes in social interaction (such as fewer relationships with neighborhood children), and inadequate urban design (such as too few public spaces for safe physical activity). World trends in active leisure time physical activity are less clear. The World Health Organization indicates people worldwide are taking up less active recreational pursuits, while research from Finland found an increase and research from the United States found leisure-time physical activity has not changed significantly. Physical activity in children may not be a significant contributor.

In both children and adults, there is an association between television viewing time and the risk of obesity. Increased media exposure increases the rate of childhood obesity, with rates increasing proportionally to time spent watching television.

Genetics
Like many other medical conditions, obesity is the result of an interplay between genetic and environmental factors. Polymorphisms in various genes controlling appetite and metabolism predispose to obesity when sufficient food energy is present. As of 2006, more than 41 of these sites on the human genome have been linked to the development of obesity when a favorable environment is present. People with two copies of the FTO gene (fat mass and obesity associated gene) have been found on average to weigh 3–4 kg more and have a 1.67-fold greater risk of obesity compared with those without the risk allele. The differences in BMI between people that are due to genetics varies depending on the population examined from 6% to 85%.

Obesity is a major feature in several syndromes, such as Prader–Willi syndrome, Bardet–Biedl syndrome, Cohen syndrome, and MOMO syndrome. (The term "non-syndromic obesity" is sometimes used to exclude these conditions.) In people with early-onset severe obesity (defined by an onset before 10 years of age and body mass index over three standard deviations above normal), 7% harbor a single point DNA mutation.

Studies that have focused on inheritance patterns rather than on specific genes have found that 80% of the offspring of two obese parents were also obese, in contrast to less than 10% of the offspring of two parents who were of normal weight. Different people exposed to the same environment have different risks of obesity due to their underlying genetics.

The thrifty gene hypothesis postulates that, due to dietary scarcity during human evolution, people are prone to obesity. Their ability to take advantage of rare periods of abundance by storing energy as fat would be advantageous during times of varying food availability, and individuals with greater adipose reserves would be more likely to survive famine. This tendency to store fat, however, would be maladaptive in societies with stable food supplies. This theory has received various criticisms, and other evolutionarily-based theories such as the drifty gene hypothesis and the thrifty phenotype hypothesis have also been proposed.

Other illnesses
Certain physical and mental illnesses and the pharmaceutical substances used to treat them can increase risk of obesity. Medical illnesses that increase obesity risk include several rare genetic syndromes (listed above) as well as some congenital or acquired conditions: hypothyroidism, Cushing's syndrome, growth hormone deficiency, and some eating disorders such as binge eating disorder and night eating syndrome. However, obesity is not regarded as a psychiatric disorder, and therefore is not listed in the DSM-IVR as a psychiatric illness. The risk of overweight and obesity is higher in patients with psychiatric disorders than in persons without psychiatric disorders. Obesity and depression influence each other mutually, with obesity increasing the risk of clinical depression, and also depression leading to a higher chance of developing obesity.

Drug-induced obesity
Certain medications may cause weight gain or changes in body composition; these include insulin, sulfonylureas, thiazolidinediones, atypical antipsychotics, antidepressants, steroids, certain anticonvulsants (phenytoin and valproate), pizotifen, and some forms of hormonal contraception.

Social determinants

While genetic influences are important to understanding obesity, they cannot completely explain the dramatic increase seen within specific countries or globally. Though it is accepted that energy consumption in excess of energy expenditure leads to increases in body weight on an individual basis, the cause of the shifts in these two factors on the societal scale is much debated. There are a number of theories as to the cause but most believe it is a combination of various factors.

The correlation between social class and BMI varies globally. Research in 1989 found that in developed countries women of a high social class were less likely to be obese. No significant differences were seen among men of different social classes. In the developing world, women, men, and children from high social classes had greater rates of obesity. In 2007 repeating the same research found the same relationships, but they were weaker. The decrease in strength of correlation was felt to be due to the effects of globalization. Among developed countries, levels of adult obesity, and percentage of teenage children who are overweight, are correlated with income inequality. A similar relationship is seen among US states: more adults, even in higher social classes, are obese in more unequal states.

Many explanations have been put forth for associations between BMI and social class. It is thought that in developed countries, the wealthy are able to afford more nutritious food, they are under greater social pressure to remain slim, and have more opportunities along with greater expectations for physical fitness. In undeveloped countries the ability to afford food, high energy expenditure with physical labor, and cultural values favoring a larger body size are believed to contribute to the observed patterns. Attitudes toward body weight held by people in one's life may also play a role in obesity. A correlation in BMI changes over time has been found among friends, siblings, and spouses. Stress and perceived low social status appear to increase risk of obesity.

Smoking has a significant effect on an individual's weight. Those who quit smoking gain an average of 4.4 kilograms (9.7 lb) for men and 5.0 kilograms (11.0 lb) for women over ten years. However, changing rates of smoking have had little effect on the overall rates of obesity.

In the United States, the number of children a person has is related to their risk of obesity. A woman's risk increases by 7% per child, while a man's risk increases by 4% per child. This could be partly explained by the fact that having dependent children decreases physical activity in Western parents.

In the developing world urbanization is playing a role in increasing rate of obesity. In China overall rates of obesity are below 5%; however, in some cities rates of obesity are greater than 20%. In part, this may be because of urban design issues (such as inadequate public spaces for physical activity). Time spent in motor vehicles, as opposed to active transportation options such as cycling or walking, is correlated with increased risk of obesity.

Malnutrition in early life is believed to play a role in the rising rates of obesity in the developing world. Endocrine changes that occur during periods of malnutrition may promote the storage of fat once more food energy becomes available.

Gut bacteria
The study of the effect of infectious agents on metabolism is still in its early stages. Gut flora has been shown to differ between lean and obese people. There is an indication that gut flora can affect the metabolic potential. This apparent alteration is believed to confer a greater capacity to harvest energy contributing to obesity. Whether these differences are the direct cause or the result of obesity has yet to be determined unequivocally. The use of antibiotics among children has also been associated with obesity later in life.

An association between viruses and obesity has been found in humans and several different animal species. The amount that these associations may have contributed to the rising rate of obesity is yet to be determined.

Other factors
Not getting enough sleep is also associated with obesity. Whether one causes the other is unclear. Even if short sleep does increase weight gain, it is unclear if this is to a meaningful degree or if increasing sleep would be of benefit.

Some have proposed that chemical compounds called "obesogens" may play a role in obesity.

Certain aspects of personality are associated with being obese. Loneliness, neuroticism, impulsivity, and sensitivity to reward are more common in people who are obese while conscientiousness and self-control are less common in people who are obese. Because most of the studies on this topic are questionnaire-based, it is possible that these findings overestimate the relationships between personality and obesity: people who are obese might be aware of the social stigma of obesity and their questionnaire responses might be biased accordingly. Similarly, the personalities of people who are obese as children might be influenced by obesity stigma, rather than these personality factors acting as risk factors for obesity.

In relation to globalization, it is known that trade liberalization is linked to obesity; research, based on data from 175 countries during 1975-2016, showed that obesity prevalence was positively correlated with trade openness, and the correlation was stronger in developing countries.

Pathophysiology

Two distinct but related processes are considered to be involved in the development of obesity: sustained positive energy balance (energy intake exceeding energy expenditure) and the resetting of the body weight "set point" at an increased value. The second process explains why finding effective obesity treatments has been difficult. While the underlying biology of this process still remains uncertain, research is beginning to clarify the mechanisms.

At a biological level, there are many possible pathophysiological mechanisms involved in the development and maintenance of obesity. This field of research had been almost unapproached until the leptin gene was discovered in 1994 by J. M. Friedman's laboratory. While leptin and ghrelin are produced peripherally, they control appetite through their actions on the central nervous system. In particular, they and other appetite-related hormones act on the hypothalamus, a region of the brain central to the regulation of food intake and energy expenditure. There are several circuits within the hypothalamus that contribute to its role in integrating appetite, the melanocortin pathway being the most well understood. The circuit begins with an area of the hypothalamus, the arcuate nucleus, that has outputs to the lateral hypothalamus (LH) and ventromedial hypothalamus (VMH), the brain's feeding and satiety centers, respectively.

The arcuate nucleus contains two distinct groups of neurons. The first group coexpresses neuropeptide Y (NPY) and agouti-related peptide (AgRP) and has stimulatory inputs to the LH and inhibitory inputs to the VMH. The second group coexpresses pro-opiomelanocortin (POMC) and cocaine- and amphetamine-regulated transcript (CART) and has stimulatory inputs to the VMH and inhibitory inputs to the LH. Consequently, NPY/AgRP neurons stimulate feeding and inhibit satiety, while POMC/CART neurons stimulate satiety and inhibit feeding. Both groups of arcuate nucleus neurons are regulated in part by leptin. Leptin inhibits the NPY/AgRP group while stimulating the POMC/CART group. Thus a deficiency in leptin signaling, either via leptin deficiency or leptin resistance, leads to overfeeding and may account for some genetic and acquired forms of obesity.

Management
The main treatment for obesity consists of weight loss via lifestyle interventions, including prescribed diets and physical exercise. Although it is unclear what diets might support long-term weight loss, and although the effectiveness of low-calorie diets is debated, lifestyle changes that reduce calorie consumption or increase physical exercise over the long term also tend to produce some sustained weight loss, despite slow weight regain over time.

Although 87% of participants in the National Weight Control Registry were able to maintain 10% body weight loss for 10 years, the most appropriate dietary approach for long term weight loss maintenance is still unknown. In the US, intensive behavioral interventions combining both dietary changes and exercise are recommended. Intermittent fasting has no additional benefit of weight loss compared to continuous energy restriction. Adherence is a more important factor in weight loss success than whatever kind of diet an individual undertakes.

Several hypo-caloric diets are effective. In the short-term low carbohydrate diets appear better than low fat diets for weight loss. In the long term, however, all types of low-carbohydrate and low-fat diets appear equally beneficial. Heart disease and diabetes risks associated with different diets appear to be similar.

Promotion of the Mediterranean diets among the obese may lower the risk of heart disease. Decreased intake of sweet drinks is also related to weight-loss. Success rates of long-term weight loss maintenance with lifestyle changes are low, ranging from 2–20%. Dietary and lifestyle changes are effective in limiting excessive weight gain in pregnancy and improve outcomes for both the mother and the child. Intensive behavioral counseling is recommended in those who are both obese and have other risk factors for heart disease.

Health policy
Obesity is a complex public health and policy problem because of its prevalence, costs, and health effects. As such, managing it requires changes in the wider societal context and effort by communities, local authorities, and governments. Public health efforts seek to understand and correct the environmental factors responsible for the increasing prevalence of obesity in the population. Solutions look at changing the factors that cause excess food energy consumption and inhibit physical activity. Efforts include federally reimbursed meal programs in schools, limiting direct junk food marketing to children, and decreasing access to sugar-sweetened beverages in schools. The World Health Organization recommends the taxing of sugary drinks. When constructing urban environments, efforts have been made to increase access to parks and to develop pedestrian routes.

Mass media campaigns seem to have limited effectiveness in changing behaviors that influence obesity, but may increase knowledge and awareness regarding physical activity and diet, which might lead to changes in the long term. Campaigns might also be able to reduce the amount of time spent sitting or lying down and positively affect the intention to be active physically. Nutritional labelling with energy information on menus might be able to help reducing energy intake while dining in restaurants. Some call for policy against ultra-processed foods.

Medication
Since the introduction of medicines for the management of obesity in the 1930s, many compounds have been tried. Most of them reduce body weight by small amounts, and several of them are no longer marketed for obesity because of their side effects. Out of 25 anti-obesity medications withdrawn from the market between 1964 and 2009, 23 acted by altering the functions of chemical neurotransmitters in the brain. The most common side effects of these drugs that led to withdrawals were mental disturbances, cardiac side effects, and drug abuse or drug dependence. Deaths were reportedly associated with seven products.

Five medications beneficial for long-term use are: orlistat, lorcaserin, liraglutide, phentermine–topiramate, and naltrexone–bupropion. They result in weight loss after one year ranged from 3.0 to 6.7 kg (6.6-14.8 lbs) over placebo. Orlistat, liraglutide, and naltrexone–bupropion are available in both the United States and Europe, phentermine–topiramate is available only in the United States. European regulatory authorities rejected lorcaserin and phentermine-topiramate, in part because of associations of heart valve problems with lorcaserin and more general heart and blood vessel problems with phentermine–topiramate. Lorcaserin was available in the United States and then removed from the market in 2020 due to its association with cancer. Orlistat use is associated with high rates of gastrointestinal side effects and concerns have been raised about negative effects on the kidneys. There is no information on how these drugs affect longer-term complications of obesity such as cardiovascular disease or death; however, liraglutide, when used for type 2 diabetes, does reduce cardiovascular events.

In 2019 a systematic review compared the effects on weight of various doses of fluoxetine (60 mg/d, 40 mg/d, 20 mg/d, 10 mg/d) in obese adults. When compared to placebo, all dosages of fluoxetine appeared to contribute to weight loss but lead to increased risk of experiencing side effects such as dizziness, drowsiness, fatigue, insomnia and nausea during period of treatment. However, these conclusions were from low certainty evidence. When comparing, in the same review, the effects of fluoxetine on weight of obese adults, to other anti-obesity agents, omega-3 gel and not receiving a treatment, the authors could not reach conclusive results due to poor quality of evidence.

Among antipsychotic drugs for treating schizophrenia clozapine is the most effective, but it also has the highest risk of causing the metabolic syndrome, of which obesity is the main feature. For people who gain weight because of clozapine, taking metformin may reportedly improve three of the five components of the metabolic syndrome: waist circumference, fasting glucose, and fasting triglycerides.

Surgery
The most effective treatment for obesity is bariatric surgery. The types of procedures include laparoscopic adjustable gastric banding, Roux-en-Y gastric bypass, vertical-sleeve gastrectomy, and biliopancreatic diversion. Surgery for severe obesity is associated with long-term weight loss, improvement in obesity-related conditions, and decreased overall mortality; however, improved metabolic health results from the weight loss, not the surgery. One study found a weight loss of between 14% and 25% (depending on the type of procedure performed) at 10 years, and a 29% reduction in all cause mortality when compared to standard weight loss measures. Complications occur in about 17% of cases and reoperation is needed in 7% of cases.

Epidemiology

In earlier historical periods obesity was rare and achievable only by a small elite, although already recognised as a problem for health. But as prosperity increased in the Early Modern period, it affected increasingly larger groups of the population. Prior to the 1970s, obesity was a relatively rare condition even in the wealthiest of nations, and when it did exist it tended to occur among the wealthy. Then, a confluence of events started to change the human condition. The average BMI of populations in first-world countries started to increase, and consequently there was a rapid increase in the proportion of people overweight and obese.

In 1997, the WHO formally recognized obesity as a global epidemic. As of 2008, the WHO estimates that at least 500 million adults (greater than 10%) are obese, with higher rates among women than men. The global prevalence of obesity more than doubled between 1980 and 2014. In 2014, more than 600 million adults were obese, equal to about 13 percent of the world's adult population. The percentage of adults affected in the United States as of 2015–2016 is about 39.6% overall (37.9% of males and 41.1% of females). In 2000, the World Health Organization (WHO) stated that overweight and obesity were replacing more traditional public health concerns such as undernutrition and infectious diseases as one of the most significant cause of poor health.

The rate of obesity also increases with age at least up to 50 or 60 years old and severe obesity in the United States, Australia, and Canada is increasing faster than the overall rate of obesity. The OECD has projected an increase in obesity rates until at least 2030, especially in the United States, Mexico and England with rates reaching 47%, 39% and 35%, respectively.

Once considered a problem only of high-income countries, obesity rates are rising worldwide and affecting both the developed and developing world. These increases have been felt most dramatically in urban settings.

Sex- and gender-based differences also influence the prevalence of obesity. Globally there are more obese women than men, but the numbers differ depending on how obesity is measured.

Etymology
Obesity is from the Latin obesitas, which means "stout, fat, or plump". Ēsus is the past participle of edere (to eat), with ob (over) added to it. The Oxford English Dictionary documents its first usage in 1611 by Randle Cotgrave.

Historical attitudes
Ancient Greek medicine recognizes obesity as a medical disorder and records that the Ancient Egyptians saw it in the same way. Hippocrates wrote that "Corpulence is not only a disease itself, but the harbinger of others". The Indian surgeon Sushruta (6th century BCE) related obesity to diabetes and heart disorders. He recommended physical work to help cure it and its side effects. For most of human history, mankind struggled with food scarcity. Obesity has thus historically been viewed as a sign of wealth and prosperity. It was common among high officials in Ancient East Asian civilizations. In the 17th century, English medical author Tobias Venner is credited with being one of the first to refer to the term as a societal disease in a published English language book.

With the onset of the Industrial Revolution, it was realized that the military and economic might of nations were dependent on both the body size and strength of their soldiers and workers. Increasing the average body mass index from what is now considered underweight to what is now the normal range played a significant role in the development of industrialized societies. Height and weight thus both increased through the 19th century in the developed world. During the 20th century, as populations reached their genetic potential for height, weight began increasing much more than height, resulting in obesity. In the 1950s, increasing wealth in the developed world decreased child mortality, but as body weight increased, heart and kidney disease became more common. During this time period, insurance companies realized the connection between weight and life expectancy and increased premiums for the obese.

Many cultures throughout history have viewed obesity as the result of a character flaw. The obesus or fat character in Ancient Greek comedy was a glutton and figure of mockery. During Christian times, food was viewed as a gateway to the sins of sloth and lust. In modern Western culture, excess weight is often regarded as unattractive, and obesity is commonly associated with various negative stereotypes. People of all ages can face social stigmatization and may be targeted by bullies or shunned by their peers.

Public perceptions in Western society regarding healthy body weight differ from those regarding the weight that is considered ideal – and both have changed since the beginning of the 20th century. The weight that is viewed as an ideal has become lower since the 1920s. This is illustrated by the fact that the average height of Miss America pageant winners increased by 2% from 1922 to 1999, while their average weight decreased by 12%. On the other hand, people's views concerning healthy weight have changed in the opposite direction. In Britain, the weight at which people considered themselves to be overweight was significantly higher in 2007 than in 1999. These changes are believed to be due to increasing rates of adiposity leading to increased acceptance of extra body fat as being normal.

Obesity is still seen as a sign of wealth and well-being in many parts of Africa. This has become particularly common since the HIV epidemic began.

The arts
The first sculptural representations of the human body 20,000–35,000 years ago depict obese females. Some attribute the Venus figurines to the tendency to emphasize fertility while others feel they represent "fatness" in the people of the time. Corpulence is, however, absent in both Greek and Roman art, probably in keeping with their ideals regarding moderation. This continued through much of Christian European history, with only those of low socioeconomic status being depicted as obese.

During the Renaissance some of the upper class began flaunting their large size, as can be seen in portraits of Henry VIII of England and Alessandro dal Borro. Rubens (1577–1640) regularly depicted heavyset women in his pictures, from which derives the term Rubenesque. These women, however, still maintained the "hourglass" shape with its relationship to fertility. During the 19th century, views on obesity changed in the Western world. After centuries of obesity being synonymous with wealth and social status, slimness began to be seen as the desirable standard. In his 1819 print, The Belle Alliance, or the Female Reformers of Blackburn!!!, artist George Cruikshank criticised the work of female reformers in Blackburn and used fatness as a means to portray them as unfeminine.

Economic impact
In addition to its health impacts, obesity leads to many problems, including disadvantages in employment and increased business costs. These effects are felt by all levels of society, from individuals, to corporations, to governments.

In 2005, the medical costs attributable to obesity in the US were an estimated $190.2 billion or 20.6% of all medical expenditures, while the cost of obesity in Canada was estimated at CA$2 billion in 1997 (2.4% of total health costs). The total annual direct cost of overweight and obesity in Australia in 2005 was A$21 billion. Overweight and obese Australians also received A$35.6 billion in government subsidies. The estimated range for annual expenditures on diet products is $40 billion to $100 billion in the US alone.

The Lancet Commission on Obesity in 2019 called for a global treaty—modelled on the WHO Framework Convention on Tobacco Control—committing countries to address obesity and undernutrition, explicitly excluding the food industry from policy development. They estimate the global cost of obesity $2 trillion a year, about or 2.8% of world GDP.

Obesity prevention programs have been found to reduce the cost of treating obesity-related disease. However, the longer people live, the more medical costs they incur. Researchers, therefore, conclude that reducing obesity may improve the public's health, but it is unlikely to reduce overall health spending. Sin taxes such as a sugary drink tax have been implemented in certain countries globally to curb dietary and consumer habits, and as an effort to offset the economic tolls.

Obesity can lead to social stigmatization and disadvantages in employment. When compared to their normal weight counterparts, obese workers on average have higher rates of absenteeism from work and take more disability leave, thus increasing costs for employers and decreasing productivity. A study examining Duke University employees found that people with a BMI over 40 kg/m2 filed twice as many workers' compensation claims as those whose BMI was 18.5–24.9 kg/m2. They also had more than 12 times as many lost work days. The most common injuries in this group were due to falls and lifting, thus affecting the lower extremities, wrists or hands, and backs. The Alabama State Employees' Insurance Board approved a controversial plan to charge obese workers $25 a month for health insurance that would otherwise be free unless they take steps to lose weight and improve their health. These measures started in January 2010 and apply to those state workers whose BMI exceeds 35 kg/m2 and who fail to make improvements in their health after one year.

Some research shows that obese people are less likely to be hired for a job and are less likely to be promoted. Obese people are also paid less than their non-obese counterparts for an equivalent job; obese women on average make 6% less and obese men make 3% less.

Specific industries, such as the airline, healthcare and food industries, have special concerns. Due to rising rates of obesity, airlines face higher fuel costs and pressures to increase seating width. In 2000, the extra weight of obese passengers cost airlines US$275 million. The healthcare industry has had to invest in special facilities for handling severely obese patients, including special lifting equipment and bariatric ambulances. Costs for restaurants are increased by litigation accusing them of causing obesity. In 2005, the US Congress discussed legislation to prevent civil lawsuits against the food industry in relation to obesity; however, it did not become law.

With the American Medical Association's 2013 classification of obesity as a chronic disease, it is thought that health insurance companies will more likely pay for obesity treatment, counseling and surgery, and the cost of research and development of fat treatment pills or gene therapy treatments should be more affordable if insurers help to subsidize their cost. The AMA classification is not legally binding, however, so health insurers still have the right to reject coverage for a treatment or procedure.

In 2014, The European Court of Justice ruled that morbid obesity is a disability. The Court said that if an employee's obesity prevents them from "full and effective participation of that person in professional life on an equal basis with other workers", then it shall be considered a disability and that firing someone on such grounds is discriminatory.

In low-income countries, obesity can be a signal of wealth. A 2023 experimental study found that obese individuals in Uganda were more likely to access credit.

Size acceptance

The principal goal of the fat acceptance movement is to decrease discrimination against people who are overweight and obese. However, some in the movement are also attempting to challenge the established relationship between obesity and negative health outcomes.

A number of organizations exist that promote the acceptance of obesity. They have increased in prominence in the latter half of the 20th century. The US-based National Association to Advance Fat Acceptance (NAAFA) was formed in 1969 and describes itself as a civil rights organization dedicated to ending size discrimination.

The International Size Acceptance Association (ISAA) is a non-governmental organization (NGO) which was founded in 1997. It has more of a global orientation and describes its mission as promoting size acceptance and helping to end weight-based discrimination. These groups often argue for the recognition of obesity as a disability under the US Americans With Disabilities Act (ADA). The American legal system, however, has decided that the potential public health costs exceed the benefits of extending this anti-discrimination law to cover obesity.

Industry influence on research
In 2015, the New York Times published an article on the Global Energy Balance Network, a nonprofit founded in 2014 that advocated for people to focus on increasing exercise rather than reducing calorie intake to avoid obesity and to be healthy. The organization was founded with at least $1.5M in funding from the Coca-Cola Company, and the company has provided $4M in research funding to the two founding scientists Gregory A. Hand and Steven N. Blair since 2008.

Reports
Many organizations have published reports pertaining to obesity. In 1998, the first US Federal guidelines were published, titled "Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults: The Evidence Report". In 2006, the Canadian Obesity Network, now known as Obesity Canada published the "Canadian Clinical Practice Guidelines (CPG) on the Management and Prevention of Obesity in Adults and Children". This is a comprehensive evidence-based guideline to address the management and prevention of overweight and obesity in adults and children.

In 2004, the United Kingdom Royal College of Physicians, the Faculty of Public Health and the Royal College of Paediatrics and Child Health released the report "Storing up Problems", which highlighted the growing problem of obesity in the UK. The same year, the House of Commons Health Select Committee published its "most comprehensive inquiry [...] ever undertaken" into the impact of obesity on health and society in the UK and possible approaches to the problem. In 2006, the National Institute for Health and Clinical Excellence (NICE) issued a guideline on the diagnosis and management of obesity, as well as policy implications for non-healthcare organizations such as local councils. A 2007 report produced by Derek Wanless for the King's Fund warned that unless further action was taken, obesity had the capacity to debilitate the National Health Service financially. In 2022 the National Institute for Health and Care Research (NIHR) published a comprehensive review of research on what local authorities can do to reduce obesity.

The Obesity Policy Action (OPA) framework divides measure into upstream policies, midstream policies, and downstream policies. Upstream policies have to do with changing society, while midstream policies try to alter behaviors believed to contribute to obesity at the individual level, while downstream policies treat currently obese people.

Childhood obesity
The healthy BMI range varies with the age and sex of the child. Obesity in children and adolescents is defined as a BMI greater than the 95th percentile. The reference data that these percentiles are based on is from 1963 to 1994 and thus has not been affected by the recent increases in rates of obesity. Childhood obesity has reached epidemic proportions in the 21st century, with rising rates in both the developed and the developing world. Rates of obesity in Canadian boys have increased from 11% in the 1980s to over 30% in the 1990s, while during this same time period rates increased from 4 to 14% in Brazilian children. In the UK, there were 60% more obese children in 2005 compared to 1989. In the US, the percentage of overweight and obese children increased to 16% in 2008, a 300% increase over the prior 30 years.

As with obesity in adults, many factors contribute to the rising rates of childhood obesity. Changing diet and decreasing physical activity are believed to be the two most important causes for the recent increase in the incidence of child obesity. Advertising of unhealthy foods to children also contributes, as it increases their consumption of the product. Antibiotics in the first 6 months of life have been associated with excess weight at age seven to twelve years of age. Because childhood obesity often persists into adulthood and is associated with numerous chronic illnesses, children who are obese are often tested for hypertension, diabetes, hyperlipidemia, and fatty liver disease.

Treatments used in children are primarily lifestyle interventions and behavioral techniques, although efforts to increase activity in children have had little success. In the United States, medications are not FDA approved for use in this age group. Brief weight management interventions in primary care (e.g. delivered by a physician or nurse practitioner) have only a marginal positive effect in reducing childhood overweight or obesity. Multi-component behaviour change interventions that include changes to dietary and physical activity may reduce BMI in the short term in children aged 6 to 11 years, although the benefits are small and quality of evidence is low.

Other animals
Obesity in pets is common in many countries. In the United States, 23–41% of dogs are overweight, and about 5.1% are obese. The rate of obesity in cats was slightly higher at 6.4%. In Australia, the rate of obesity among dogs in a veterinary setting has been found to be 7.6%. The risk of obesity in dogs is related to whether or not their owners are obese; however, there is no similar correlation between cats and their owners.

title: Obesity


text:
Infrared astronomy

Infrared astronomy is a sub-discipline of astronomy which specializes in the observation and analysis of astronomical objects using infrared (IR) radiation. The wavelength of infrared light ranges from 0.75 to 300 micrometers, and falls in between visible radiation, which ranges from 380 to 750 nanometers, and submillimeter waves.

Infrared astronomy began in the 1830s, a few decades after the discovery of infrared light by William Herschel in 1800. Early progress was limited, and it was not until the early 20th century that conclusive detections of astronomical objects other than the Sun and Moon were made in infrared light. After a number of discoveries were made in the 1950s and 1960s in radio astronomy, astronomers realized the information available outside the visible wavelength range, and modern infrared astronomy was established.

Infrared and optical astronomy are often practiced using the same telescopes, as the same mirrors or lenses are usually effective over a wavelength range that includes both visible and infrared light. Both fields also use solid state detectors, though the specific type of solid state photodetectors used are different. Infrared light is absorbed at many wavelengths by water vapor in the Earth's atmosphere, so most infrared telescopes are at high elevations in dry places, above as much of the atmosphere as possible. There have also been infrared observatories in space, including the Spitzer Space Telescope, the Herschel Space Observatory, and more recently the James Webb Space Telescope.

History
The discovery of infrared radiation is attributed to William Herschel, who performed an experiment in 1800 where he placed a thermometer in sunlight of different colors after it passed through a prism. He noticed that the temperature increase induced by sunlight was highest outside the visible spectrum, just beyond the red color. That the temperature increase was highest at infrared wavelengths was due to the spectral response of the prism rather than properties of the Sun, but the fact that there was any temperature increase at all prompted Herschel to deduce that there was invisible radiation from the Sun. He dubbed this radiation "calorific rays", and went on to show that it could be reflected, transmitted, and absorbed just like visible light.

Efforts were made starting in the 1830s and continuing through the 19th century to detect infrared radiation from other astronomical sources. Radiation from the Moon was first detected in 1856 by Charles Piazzi Smyth, the Astronomer Royal for Scotland, during an expedition to Tenerife to test his ideas about mountain top astronomy. Ernest Fox Nichols used a modified Crookes radiometer in an attempt to detect infrared radiation from Arcturus and Vega, but Nichols deemed the results inconclusive. Even so, the ratio of flux he reported for the two stars is consistent with the modern value, so George Rieke gives Nichols credit for the first detection of a star other than our own in the infrared.

The field of infrared astronomy continued to develop slowly in the early 20th century, as Seth Barnes Nicholson and Edison Pettit developed thermopile detectors capable of accurate infrared photometry and sensitive to a few hundreds of stars. The field was mostly neglected by traditional astronomers until the 1960s, with most scientists who practiced infrared astronomy having actually been trained physicists. The success of radio astronomy during the 1950s and 1960s, combined with the improvement of infrared detector technology, prompted more astronomers to take notice, and infrared astronomy became well established as a subfield of astronomy.

Infrared space telescopes entered service. In 1983, IRAS made an all-sky survey. In 1995, the European Space Agency created the Infrared Space Observatory. Before this satellite ran out of liquid helium in 1998, it discovered protostars and water in our universe (even on Saturn and Uranus).

On 25 August 2003, NASA launched the Spitzer Space Telescope, previously known as the Space Infrared Telescope Facility. In 2009, the telescope ran out of liquid helium and lost the ability to see far infrared. It had discovered stars, the Double Helix Nebula, and light from extrasolar planets. It continued working in 3.6 and 4.5 micrometer bands. Since then, other infrared telescopes helped find new stars that are forming, nebulae, and stellar nurseries. Infrared telescopes have opened up a whole new part of the galaxy for us. They are also useful for observing extremely distant things, like quasars. Quasars move away from Earth. The resulting large redshift make them difficult targets with an optical telescope. Infrared telescopes give much more information about them.

During May 2008, a group of international infrared astronomers proved that intergalactic dust greatly dims the light of distant galaxies. In actuality, galaxies are almost twice as bright as they look. The dust absorbs much of the visible light and re-emits it as infrared light.

Modern infrared astronomy

Infrared radiation with wavelengths just longer than visible light, known as near-infrared, behaves in a very similar way to visible light, and can be detected using similar solid state devices (because of this, many quasars, stars, and galaxies were discovered). For this reason, the near infrared region of the spectrum is commonly incorporated as part of the "optical" spectrum, along with the near ultraviolet. Many optical telescopes, such as those at Keck Observatory, operate effectively in the near infrared as well as at visible wavelengths. The far-infrared extends to submillimeter wavelengths, which are observed by telescopes such as the James Clerk Maxwell Telescope at Mauna Kea Observatory.

Like all other forms of electromagnetic radiation, infrared is utilized by astronomers to study the universe. Indeed, infrared measurements taken by the 2MASS and WISE astronomical surveys have been particularly effective at unveiling previously undiscovered star clusters. Examples of such embedded star clusters are FSR 1424, FSR 1432, Camargo 394, Camargo 399, Majaess 30, and Majaess 99. Infrared telescopes, which includes most major optical telescopes as well as a few dedicated infrared telescopes, need to be chilled with liquid nitrogen and shielded from warm objects. The reason for this is that objects with temperatures of a few hundred kelvins emit most of their thermal energy at infrared wavelengths. If infrared detectors were not kept cooled, the radiation from the detector itself would contribute noise that would dwarf the radiation from any celestial source. This is particularly important in the mid-infrared and far-infrared regions of the spectrum.

To achieve higher angular resolution, some infrared telescopes are combined to form astronomical interferometers. The effective resolution of an interferometer is set by the distance between the telescopes, rather than the size of the individual telescopes. When used together with adaptive optics, infrared interferometers, such as two 10 meter telescopes at Keck Observatory or the four 8.2 meter telescopes that make up the Very Large Telescope Interferometer, can achieve high angular resolution.

The principal limitation on infrared sensitivity from ground-based telescopes is the Earth's atmosphere. Water vapor absorbs a significant amount of infrared radiation, and the atmosphere itself emits at infrared wavelengths. For this reason, most infrared telescopes are built in very dry places at high altitude, so that they are above most of the water vapor in the atmosphere. Suitable locations on Earth include Mauna Kea Observatory at 4205 meters above sea level, the Paranal Observatory at 2635 meters in Chile and regions of high altitude ice-desert such as Dome C in Antarctic. Even at high altitudes, the transparency of the Earth's atmosphere is limited except in infrared windows, or wavelengths where the Earth's atmosphere is transparent. The main infrared windows are listed below:

As is the case for visible light telescopes, space is the ideal place for infrared telescopes. Telescopes in space can achieve higher resolution, as they do not suffer from blurring caused by the Earth's atmosphere, and are also free from infrared absorption caused by the Earth's atmosphere. Current infrared telescopes in space include the Herschel Space Observatory, the Spitzer Space Telescope, the Wide-field Infrared Survey Explorer and the James Webb Space Telescope. Since putting telescopes in orbit is expensive, there are also airborne observatories, such as the Stratospheric Observatory for Infrared Astronomy and the Kuiper Airborne Observatory. These observatories fly above most, but not all, of the atmosphere, and water vapor in the atmosphere absorbs some of infrared light from space.

Infrared technology
One of the most common infrared detector arrays used at research telescopes is HgCdTe arrays. These operate well between 0.6 and 5 micrometre wavelengths. For longer wavelength observations or higher sensitivity other detectors may be used, including other narrow gap semiconductor detectors, low temperature bolometer arrays or photon-counting Superconducting Tunnel Junction arrays.

Special requirements for infrared astronomy include: very low dark currents to allow long integration times, associated low noise readout circuits and sometimes very high pixel counts.

Low temperature is often achieved by a coolant, which can run out. Space missions have either ended or shifted to "warm" observations when the coolant supply used up. For example, WISE ran out of coolant in October 2010, about ten months after being launched. (See also NICMOS, Spitzer Space Telescope)

Space observatories
Many space telescopes detect electromagnetic radiation in a wavelength range that overlaps at least to some degree with the infrared wavelength range. Therefore it is difficult to define which space telescopes are infrared telescopes. Here the definition of "infrared space telescope" is taken to be a space telescope whose main mission is detecting infrared light.

Eight infrared space telescopes have been operated in space. They are:

 * Infrared Astronomical Satellite (IRAS), operated 1983 (10 months). A joint mission of US (NASA), UK and the Netherlands.
 * Infrared Space Observatory (ISO), operated 1995-1998, ESA mission.
 * Midcourse Space Experiment (MSX), operated 1996-1997, BMDO mission.
 * Spitzer Space Telescope, operated 2003-2020, NASA mission.
 * Akari, operated 2006-2011, JAXA mission.
 * Herschel Space Observatory, operated 2009-2013, ESA mission.
 * Wide-field Infrared Survey Explorer (WISE), operated 2009-, NASA mission.
 * James Webb Space Telescope (JWST), operated 2022-, NASA mission.
 * Euclid telescope, operated 2023-, ESA mission.

In addition, SPHEREx is a telescope scheduled for launch in 2025. NASA is also planning to launch the Nancy Grace Roman Space Telescope (NGRST), originally known as the Wide Field InfraRed Space Telescope (WFIRST), in 2027.

Many other smaller space-missions and space-based detectors of infrared radiation have been operated in space. These include the Infrared Telescope (IRT) that flew with the Space Shuttle.

The Submillimeter Wave Astronomy Satellite (SWAS) is sometimes mentioned as an infrared satellite, although it is a submillimeter satellite.

Infrared instruments on space telescopes
For many space telescopes, only some of the instruments are capable of infrared observation. Below are listed some of the most notable of these space observatories and instruments:

 * Cosmic Background Explorer (COBE) satellite (1989-1993) Diffuse Infrared Background Experiment (DIRBE) instrument
 * Hubble Space Telescope (1990-) Near Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument (1997-1999, 2002-2008)
 * Hubble Space Telescope Wide Field Camera 3 (WFC3) camera (2009-) observes infrared.

Airborne Observatories
Three airplane-based observatories have been used (other aircraft have also been used occasionally to host infrared space studies) to study the sky in infrared. They are:

 * Galileo Observatory, a NASA mission. Was active 1965-1973.
 * Kuiper Airborne Observatory, a NASA mission. Was active 1974-1995.
 * SOFIA, a NASA-DLR mission. Was active 2010-2022.

Ground-based observatories
Many ground-based infrared telescopes exist around the world. The largest are:

 * VISTA
 * UKIRT
 * IRTF
 * WIRO

title: Infrared astronomy


text:
Akhnaten (opera)

Akhnaten is an opera in three acts based on the life and religious convictions of the Egyptian pharaoh Akhenaten (Amenhotep IV), written by the American composer Philip Glass in 1983. The libretto is by Philip Glass in association with Shalom Goldman, Robert Israel, Richard Riddell, and Jerome Robbins. According to the composer, this work is the culmination of a trilogy including his two other biographical operas, Einstein on the Beach (about Albert Einstein) and Satyagraha (about Mahatma Gandhi). These three people were all driven by an inner vision which altered the age in which they lived: Akhenaten in religion, Einstein in science, and Gandhi in politics.

The text, taken from original sources, is sung in the original languages, linked together with the commentary of a narrator in a modern language, such as English or German. Egyptian texts of the period are taken from a poem of Akhenaten himself, from the Book of the Dead, and from extracts of decrees and letters from the Amarna Period, the seventeen-year period of Akhenaten's rule. Other portions are in Akkadian and Biblical Hebrew. Akhnaten's Hymn to the Sun is sung in the language of the audience.

Performance history
Akhnaten was commissioned by Württembergische Staatstheater, Stuttgart and had its world premiere on March 24, 1984, at the Stuttgart State Theatre, under the German title Echnaton. Paul Esswood sang the title role, German director Achim Freyer staged the opera in an abstract style with highly ritualistic movements. The American premiere, directed by David Freeman, was on October 12, 1984, at the Houston Grand Opera, where Glass's opera The Making of the Representative for Planet 8 also premiered. The UK premiere, based on the American production, was on June 17, 1985, by English National Opera at the London Coliseum. This production was revived at the London Coliseum in March 1987.

The award-winning Polish premiere, directed by Henryk Baranowski, was on May 20, 2000, at the Grand Theatre in Łódź. The French premiere was on September 23, 2002, at Opéra national du Rhin in Strasbourg as a co-production with Boston Lyric Opera which had premiered the production in February 2002 A new co-production by English National Opera and LA Opera and in collaboration with Improbable directed by Phelim McDermott starring Anthony Roth Costanzo and Zachary James premiered at the London Coliseum on March 4, 2016, which won a 2017 Olivier Award, and at LA Opera on November 5, 2016. A revival of this production in London took place in March 2019 and played at the Metropolitan Opera in their 2019/2020 season, winning the 2022 Grammy Award for Best Opera Recording. The 2019 Met production was streamed online on June 20 and November 14, 2020, and February 12, 2021, and returned in 2022. A new production directed and choreographed by Nanine Linning premiered at Theater Heidelberg on June 6, 2014, another new production directed by Laura Scozzi premiered at Oper Bonn on March 11, 2018.

A November 2020 production at Opéra de Nice Côte d’Azur was performed without an audience and screened online, due to the COVID-19 pandemic. This production was produced and choreographed by longtime Glass collaborator Lucinda Childs, who conducted rehearsals remotely. She also performed the speaking roles in the opera, which were pre-recorded and projected during the performance.

Music
The orchestra's size is about the size employed for early 19th-century opera: 2 flutes (one doubling piccolo), 2 oboes (both doubling oboe d'amore), 2 clarinets, bass clarinet, 2 bassoons, 2 french horns, 2 trumpets, 2 trombones, tuba, percussion (3 players), celesta (doubling synthesizer), 12 violas, 8 celli, and 6 double basses.

Since the Stuttgart State Opera house was being restored in 1984 and the orchestra pit of the Kleines Haus at the Stuttgart State Theatre, where the premiere was to take place, was considerably smaller, Glass chose to completely leave out the violins (about 20), giving the orchestra a darker, sombre character, which fits the subject. Apart from this, this was Glass's most "conventional" opera orchestra until then (compared to Einstein on the Beach, written for the six-piece Philip Glass Ensemble, and Satyagraha, scored for woodwinds and strings only).

Synopsis
The opera is divided into three acts:

Act 1: Year 1 of Akhnaten's Reign in Thebes
Thebes, 1370 BC

Prelude, verse 1, verse 2, verse 3

Set in the key of A minor, the strings introduce a ground bass theme, with following variations. (A passacaglia). The scribe recites funeral texts from the pyramids. "Open are the double doors of the horizon; unlocked are its bolts."

Scene 1: Funeral of Akhnaten's father Amenhotep III

Heralded by hammering drums, Aye and a small male chorus chant a funeral hymn in Egyptian, later joined by the full chorus. The music is basically a march, based on the chords of A major and F♯ minor (with added major sixth), and grows to ecstatic intensity towards the end.

Scene 2: The Coronation of Akhnaten

After a lengthy orchestral introduction, during which Akhnaten appears, heralded by a solo trumpet, the High Priest, Aye, and Horemhab sing a ritual text. After that, the Narrator recites a list of royal titles bestowed upon Akhnaten, while he is crowned. After the coronation, the chorus repeats the ritual text from the beginning of the scene. Again, the main key is A minor.

Scene 3: The Window of Appearances

After an introduction in A minor, dominated by tubular bells, Akhnaten sings a praise to the Creator (in Egyptian) at the window of public appearances. This is the first time he actually sings, after he has already been on stage for 20 minutes (and 40 minutes into the opera) and the effect of his countertenor voice (which in 1983 was even more rare than nowadays) is startling. He is joined by Queen Tye, whose soprano soars high above the soon intertwining voices of the royal couple, and later by Nefertiti, who actually sings lower notes than he.

Act 2: Years 5 to 15 in Thebes and Akhetaten
Scene 1: The Temple

The scene opens again in A minor, with the High Priest and a group of priests singing a hymn to Amun, principal god of the old order, in his temple. The music becomes increasingly dramatic, as Akhnaten, together with Queen Tye and his followers, attack the temple. This scene has only wordless singing. The harmonies grow very chromatic, finally reaching A♭ major and E minor. The temple roof is removed and the sun god Aten's rays invade the temple, thus ending Amun's reign and laying the foundation for the worship of the One God: the Sun God Aten.

Scene 2: Akhnaten and Nefertiti

Two solo celli introduce a "love theme". Accompanied by a solo trombone while the harmony switches to B(sus), the Narrator recites a prayer-like poem to the sun god. The strings softly take over the music in E minor, and the same poem is recited again, this time actually as a love poem from Akhnaten to Nefertiti. Then Akhnaten and Nefertiti sing the same text to each other (in Egyptian), as an intimate love duet. After a while, the trumpet associated with Akhnaten joins them as the highest voice, turning the duet into a trio.

Scene 3: The City – Dance

The Narrator speaks a text taken from the boundary stones of the new capital of the empire, Akhet-Aten (The Horizon of Aten), describing the construction of the city, with large, light-filled spaces. After a brass fanfare, the completion of the city is celebrated in a light-hearted dance, contrasting with the stark, ritualistic music with which this act began. (In the Stuttgart premiere, the dance actually described the construction of the city.) The dance scene was omitted from the UK premiere production and its 1987 revival.

Scene 4: Hymn

What now follows is a hymn to the only god Aten, a long aria (alternating between A minor and A major) by Akhnaten, and the central piece of the opera. Notably, it is the only text sung in the language of the audience, praising the sun giving life to everything. After the aria, an off-stage chorus sings Psalm 104 in Hebrew, dating some 400 years later, which has strong resemblances to Akhnaten's Hymn, thus emphasizing Akhnaten as the first founder of a monotheistic religion.

Act 3: Year 17 and the Present
Akhnaten, 1358 BC

Scene 1: The Family

Two oboes d'amore play the "love theme" from act 2. Akhnaten, Nefertiti and their six daughters, sing wordlessly in contemplation. They are oblivious to what happens outside of the palace. As the music switches from E minor to F minor, the Narrator reads letters from Syrian vassals, asking for help against their enemies. Since the king does not send troops, his land is being seized and plundered by their enemies. The scene focuses again on Akhnaten and his family, still oblivious to the country falling apart.

Scene 2: The Attack and Fall of the City

The music moves again to a vigorous F minor. Horemhab, Aye and the High Priest of Amon instigate the people (as the chorus), singing part of the vassal's letters (in their original Akkadian language) until finally the palace is attacked, the royal family killed, and the city of the sun destroyed.

Scene 3: The Ruins

The music of the very beginning of the opera returns. The scribe recites an inscription on Aye's tomb, praising the death of "the great criminal" and the new reign of the old gods. He then describes the restoration of Amun's temple by Akhnaten's son Tutankhamun. The Prelude music grows stronger and the scene moves to present-day Egypt, to the ruins of Amarna, the former capital Akhetaten. The Narrator appears as a modern tourist guide and speaks a text from a guide book, describing the ruins. "There is nothing left of this glorious city of temples and palaces."

Scene 4: Epilogue

The ghosts of Akhnaten, Nefertiti and Queen Tye appear, singing wordlessly amongst the ruins. The funeral procession from the beginning of the opera appears on the horizon, and they join it. The music introduces a bass line from the beginning of Einstein on the Beach, the first part of Glass's "portrait" trilogy (The second one being Satyagraha and the third one Akhnaten), thus providing a musical bracket for the whole trilogy.

In popular culture

 * The fourth season of the Netflix original series Stranger Things features the tracks "Window of Appearance" and "Akhnaten and Nefertiti" in its seventh episode.

title: Akhnaten (opera)