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Geometric distribution

In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions:

 * The probability distribution of the number $$X$$ of Bernoulli trials needed to get one success, supported on $$\mathbb{N} = \{1,2,3,\ldots\}$$;
 * The probability distribution of the number $$Y=X-1$$ of failures before the first success, supported on $$\mathbb{N}_0 = \{0, 1, 2, \ldots \} $$.

These two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of $$X$$); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.

The geometric distribution gives the probability that the first occurrence of success requires $$k$$ independent trials, each with success probability $$p$$. If the probability of success on each trial is $$p$$, then the probability that the $$k$$-th trial is the first success is

 * $$\Pr(X = k) = (1-p)^{k-1}p$$

for $$k=1,2,3,4,\dots$$

The above form of the geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success:

 * $$\Pr(Y=k) =\Pr(X=k+1)= (1 - p)^k p$$

for $$k=0,1,2,3,\dots$$

The geometric distribution gets its name because its probabilities follow a geometric sequence. It is sometimes called the Furry distribution after Wendell H. Furry.

Definition
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support. When supported on $$ \mathbb{N} $$, the probability mass function is$$P(X = k) = (1 - p)^{k-1} p$$where $$k = 1, 2, 3, \dotsc$$ is the number of trials and $$p$$ is the probability of success in each trial.

The support may also be $$\mathbb{N}_0$$, defining $$Y=X-1$$. This alters the probability mass function into$$P(Y = k) = (1 - p)^k p$$where $$k = 0, 1, 2, \dotsc$$ is the number of failures before the first success.

An alternative parameterization of the distribution gives the probability mass function$$P(Y = k) = \left(\frac{P}{Q}\right)^k \left(1-\frac{P}{Q}\right)$$where $$P = \frac{1-p}{p}$$ and $$Q = \frac{1}{p}$$.

An example of a geometric distribution arises from rolling a six-sided die until a "1" appears. Each roll is independent with a $$1/6$$ chance of success. The number of rolls needed follows a geometric distribution with $$p=1/6$$.

Memorylessness
The geometric distribution is the only memoryless discrete probability distribution. It is the discrete version of the same property found in the exponential distribution. The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success. Expressed in terms of conditional probability, $$\Pr(X>m+n\mid X>n)=\Pr(X>m)$$where $$m$$ and $$n$$ are natural numbers. The equality is still true when ≥ is substituted.

Moments and cumulants
The expected value and variance of a geometrically distributed random variable $$X$$ defined over $$\mathbb{N}$$ is $$\operatorname{E}(X) = \frac{1}{p}, \qquad\operatorname{var}(X) = \frac{1-p}{p^2}.$$ When a geometrically distributed random variable $$Y$$ defined over $$\mathbb{N}_0$$, the expected value changes into$$\operatorname{E}(Y) = \frac{1-p} p,$$while the variance stays the same.

For example, when rolling a six-sided die until landing on a "1", the average number of rolls needed is $$\frac{1}{1/6} = 6$$ and the average number of failures is $$\frac{1 - 1/6}{1/6} = 5$$.

The moment generating function of the geometric distribution when defined over $$ \mathbb{N} $$ and $$\mathbb{N}_0$$ respectively is $$\begin{align} M_X(t) &= \frac{pe^t}{1-(1-p)e^t} \\ M_Y(t) &= \frac{p}{1-(1-p)e^t}, t < -\ln(1-p) \end{align}$$The moments for the number of failures before the first success are given by

\begin{align} \mathrm{E}(Y^n) & {} =\sum_{k=0}^\infty (1-p)^k p\cdot k^n \\ & {} =p \operatorname{Li}_{-n}(1-p) & (\text{for }n \neq 0) \end{align} $$

where $$ \operatorname{Li}_{-n}(1-p) $$ is the polylogarithm function.

The cumulant generating function of the geometric distribution defined over $$\mathbb{N}_0$$ is $$K(t) = \ln p - \ln (1 - (1-p)e^t)$$The cumulants $$\kappa_r$$ satisfy the recursion$$\kappa_{r+1} = q \frac{\delta\kappa_r}{\delta q}, r=1,2,\dotsc$$where $$q = 1-p$$, when defined over $$\mathbb{N}_0$$.

Proof of expected value
Consider the expected value $$\mathrm{E}(X)$$ of X as above, i.e. the average number of trials until a success. On the first trial, we either succeed with probability $$p$$, or we fail with probability $$1-p$$. If we fail the remaining mean number of trials until a success is identical to the original mean. This follows from the fact that all trials are independent. From this we get the formula:

\operatorname E(X) = p \cdot 1 + (1-p) \cdot (1 + \mathrm{E}(X)), $$

which, if solved for $$ \mathrm{E}(X) $$, gives:

 * $$\operatorname E(X) = \frac{1}{p}.$$

The expected value of $$Y$$ can be found from the linearity of expectation, $$\mathrm{E}(Y) = \mathrm{E}(X-1) = \mathrm{E}(X) - 1 = \frac 1 p - 1 = \frac{1-p}{p}$$. It can also be shown in the following way:

\begin{align} \operatorname E(Y) & {} =\sum_{k=0}^\infty (1-p)^k p\cdot k \\ & {} =p\sum_{k=0}^\infty(1-p)^k k \\ & {} = p (1-p) \sum_{k=0}^\infty (1-p)^{k-1}\cdot k\\ & {} = p (1-p) \left[\frac{d}{dp}\left(-\sum_{k=0}^\infty (1-p)^k\right)\right] \\ & {} =p(1-p)\frac{d}{dp}\left(-\frac{1}{p}\right)=\frac{1-p}{p}. \end{align} $$

The interchange of summation and differentiation is justified by the fact that convergent power series converge uniformly on compact subsets of the set of points where they converge.

Summary statistics
The mean of the geometric distribution is its expected value which is, as previously discussed in § Moments and cumulants, $$\frac{1}{p}$$ or $$\frac{1-p}{p}$$ when defined over $$\mathbb{N}$$ or $$\mathbb{N}_0$$ respectively.

The median of the geometric distribution is $$\left\lceil -\frac{\log 2}{\log(1-p)} \right\rceil$$when defined over $$\mathbb{N}$$ and $$\left\lfloor-\frac{\log 2}{\log(1-p)}\right\rfloor$$ when defined over $$\mathbb{N}_0$$.

The mode of the geometric distribution is the first value in the support set. This is 1 when defined over $$\mathbb{N}$$ and 0 when defined over $$\mathbb{N}_0$$.

The skewness of the geometric distribution is $$\frac{2-p}{\sqrt{1-p}}$$.

The kurtosis of the geometric distribution is $$9 + \frac{p^2}{1-p}$$. The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution, $$3$$. Therefore, the excess kurtosis of the geometric distribution is $$6 + \frac{p^2}{1-p}$$. Since $$\frac{p^2}{1-p} \geq 0$$, the excess kurtosis is always positive so the distribution is leptokurtic. In other words, the tail of a geometric distribution decays faster than a Gaussian.

General properties
X $$ and $$ Y $$ defined over $$ \mathbb{N} $$ and $$ \mathbb{N}_0 $$ are, respectively,
 * The probability generating functions of geometric random variables $$
 * $$\begin{align}

G_X(s) & = \frac{s\,p}{1-s\,(1-p)}, \\[10pt] G_Y(s) & = \frac{p}{1-s\,(1-p)}, \quad |s| < (1-p)^{-1}. \end{align}$$

\mathbb{N} $$ and $$ \mathbb{N}_0 $$ respectively, is $$\begin{align} \varphi_X(t) &= \frac{pe^{it}}{1-(1-p)e^{it}},\\[10pt] \varphi_Y(t) &= \frac{p}{1-(1-p)e^{it}}. \end{align}$$ \mathbb{N}_0 $$ is infinitely divisible, that is, for any positive integer $$n$$, there exist $$n$$ independent identically distributed random variables whose sum is also geometrically distributed. This is because the negative binomial distribution can be derived from a Poisson-stopped sum of logarithmic random variables.
 * The characteristic function $$\varphi(t)$$ is equal to $$G(e^{it})$$ so the geometric distribution's characteristic function, when defined over $$
 * The entropy of a geometric distribution with parameter $$p$$ is $$-\frac{p \log_2 p + (1-p) \log_2 (1-p)}{p}$$
 * Given a mean, the geometric distribution is the maximum entropy probability distribution of all discrete probability distributions. The corresponding continuous distribution is the exponential distribution.
 * The geometric distribution defined on $$
 * The decimal digits of the geometrically distributed random variable Y are a sequence of independent (and not identically distributed) random variables. For example, the hundreds digit D has this probability distribution:

 * $$\Pr(D=d) = {q^{100d} \over 1 + q^{100} + q^{200} + \cdots + q^{900}},$$
 * where q = 1 − p, and similarly for the other digits, and, more generally, similarly for numeral systems with other bases than 10. When the base is 2, this shows that a geometrically distributed random variable can be written as a sum of independent random variables whose probability distributions are indecomposable.

 * Golomb coding is the optimal prefix code for the geometric discrete distribution.

Related distributions

 * The sum of $$r$$ independent geometric random variables with parameter $$p$$ is a negative binomial random variable with parameters $$r$$ and $$p$$. The geometric distribution is a special case of the negative binomial distribution, with $$r=1$$.

 * The geometric distribution is a special case of discrete compound Poisson distribution.
 * The minimum of $$n$$ geometric random variables with parameters $$p_1, \dotsc, p_n$$ is also geometrically distributed with parameter $$1 - \prod_{i=1}^n (1-p_i)$$.

 * Suppose 0 < r < 1, and for k = 1, 2, 3, ... the random variable Xk has a Poisson distribution with expected value rk/k. Then

 * $$\sum_{k=1}^\infty k\,X_k$$

 * has a geometric distribution taking values in $$\mathbb{N}_0$$, with expected value r/(1 − r).

 * The exponential distribution is the continuous analogue of the geometric distribution. Applying the floor function to the exponential distribution with parameter $$\lambda$$ creates a geometric distribution with parameter $$p=1-e^{-\lambda}$$ defined over $$\mathbb{N}_0$$. This can be used to generate geometrically distributed random numbers as detailed in § Random variate generation.

\begin{align} \Pr(X/n>a)=\Pr(X>na) & = (1-p)^{na} = \left(1-\frac 1 n \right)^{na} = \left[ \left( 1-\frac 1 n \right)^n \right]^{a} \\ & \to [e^{-1}]^{a} = e^{-a} \text{ as } n\to\infty. \end{align} $$More generally, if p = λ/n, where λ is a parameter, then as n→ ∞ the distribution of X/n approaches an exponential distribution with rate λ:$$\Pr(X>nx)=\lim_{n \to \infty}(1-\lambda /n)^{nx}=e^{-\lambda x}$$ therefore the distribution function of X/n converges to $$1-e^{-\lambda x}$$, which is that of an exponential random variable.
 * If p = 1/n and X is geometrically distributed with parameter p, then the distribution of X/n approaches an exponential distribution with expected value 1 as n → ∞, since$$
 * The index of dispersion of the geometric distribution is $$\frac{1}{p}$$ and its coefficient of variation is $$\frac{1}{\sqrt{1-p}}$$. The distribution is overdispersed.

Statistical inference
The true parameter $$p$$ of an unknown geometric distribution can be inferred through estimators and conjugate distributions.

Method of moments
Provided they exist, the first $$l$$ moments of a probability distribution can be estimated from a sample $$x_1, \dotsc, x_n$$ using the formula$$m_i = \frac{1}{n} \sum_{j=1}^n x^i_j$$where $$m_i$$ is the $$i$$th sample moment and $$1 \leq i \leq l$$. Estimating $$\mathrm{E}(X)$$ with $$m_1$$ gives the sample mean, denoted $$ \bar{x} $$. Substituting this estimate in the formula for the expected value of a geometric distribution and solving for $$ p $$ gives the estimators $$ \hat{p} = \frac{1}{\bar{x}} $$ and $$ \hat{p} = \frac{1}{\bar{x}+1} $$ when supported on $$\mathbb{N}$$ and $$\mathbb{N}_0$$ respectively. These estimators are biased since $$\mathrm{E}\left(\frac{1}{\bar{x}}\right) > \frac{1}{\mathrm{E}(\bar{x})} = p$$ as a result of Jensen's inequality.

Maximum likelihood estimation
The maximum likelihood estimator of $$p$$ is the value that maximizes the likelihood function given a sample. By finding the zero of the derivative of the log-likelihood function when the distribution is defined over $$\mathbb{N}$$, the maximum likelihood estimator can be found to be $$\hat{p} = \frac{1}{\bar{x}}$$, where $$\bar{x}$$ is the sample mean. If the domain is $$\mathbb{N}_0$$, then the estimator shifts to $$\hat{p} = \frac{1}{\bar{x}+1}$$. As previously discussed in § Method of moments, these estimators are biased.

Regardless of the domain, the bias is equal to

b \equiv \operatorname{E}\bigg[\;(\hat p_\mathrm{mle} - p)\;\bigg] = \frac{p\,(1-p)}{n} $$

which yields the bias-corrected maximum likelihood estimator,

\hat{p\,}^*_\text{mle} = \hat{p\,}_\text{mle} - \hat{b\,} $$

Bayesian inference
In Bayesian inference, the parameter $$p$$ is a random variable from a prior distribution with a posterior distribution calculated using Bayes' theorem after observing samples. If a beta distribution is chosen as the prior distribution, then the posterior will also be a beta distribution and it is called the conjugate distribution. In particular, if a $$\mathrm{Beta}(\alpha,\beta)$$ prior is selected, then the posterior, after observing samples $$k_1, \dotsc, k_n \in \mathbb{N}$$, is $$p \sim \mathrm{Beta}\left(\alpha+n,\ \beta+\sum_{i=1}^n (k_i-1)\right). \!$$Alternatively, if the samples are in $$\mathbb{N}_0$$, the posterior distribution is $$p \sim \mathrm{Beta}\left(\alpha+n,\beta+\sum_{i=1}^n k_i\right).$$Since the expected value of a $$\mathrm{Beta}(\alpha,\beta)$$ distribution is $$\frac{\alpha}{\alpha+\beta}$$, as $$\alpha$$ and $$\beta$$ approach zero, the posterior mean approaches its maximum likelihood estimate.

Unbiased estimator
An unbiased estimator of $$p$$ will, on average, equal the true parameter. Expressed in terms of expectation, the unbiased estimator $$T(x)$$ satisfies $$\mathrm{E}(T(x)) = p$$. For the geometric distribution, the unbiased estimator would need to satisfy:$$\sum_{x=1}^\infty T(x) p(1-p)^{x-1} = p$$The only solution to this equation is,$$T(x) = \begin{cases} 1 & x=1 \\ 0 & x \geq 2 \end{cases}$$This estimator is not useful when $$p$$ is not close to 0 or 1.

Random variate generation
The geometric distribution can be generated experimentally from i.i.d. standard uniform random variables by finding the first such random variable to be less than or equal to $$p$$. However, the number of random variables needed is also geometrically distributed and the algorithm slows as $$p$$ decreases.

Random generation can be done in constant time by truncating exponential random numbers. An exponential random variable $$E$$ can become geometrically distributed with parameter $$p$$ through $$\lceil -E/\log(1-p) \rceil$$. In turn, $$E$$ can be generated from a standard uniform random variable $$U$$ altering the formula into $$\lceil \log(U) / \log(1-p)\rceil$$.

Applications
The geometric distribution is used in many disciplines. In queueing theory, the M/M/1 queue has a steady state following a geometric distribution. In stochastic processes, the Yule Furry process is geometrically distributed. The distribution also arises when modeling the lifetime of a device in discrete contexts. It has also been used to fit data including modeling patients spreading COVID-19.

title: Geometric distribution


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Talk:Farmer in the Sky/Archive 1

Vicki, do you remember what happened to the stepmother's daughter? I remember she had trouble adjusting to the low pressure. Did the family ever move out to the farm?

And we must mention the appleseed theme. It's key, in an anarchic sort of neighborly way.

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

title: Talk:Farmer in the Sky/Archive 1


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Talk:Gaia philosophy

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Merger Discussion
Request received to merge articles: Gaian Greens into Gaia philosophy; dated: {June/2022}. Proposer's Rationale: The article is poorly sourced and it pretty much has similar content to whatever it is covering in gaian philosophy regarding politics. Discuss here. Waltzingmogumogupeach (talk) 18:13, 8 June 2022 (UTC)
 * Delete Gaian Greens as an unreferenced neologism or term that hasn't become established through reliable sources. Klbrain (talk) 08:53, 12 November 2022 (UTC)

More philosophical
I edited the lead to make it more philosophical hmmm, that we all live on a planet now...Arnbiology (talk) 23:59, 17 January 2023 (UTC)

title: Talk:Gaia philosophy


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Talk:Between Planets

Untitled
This story features the first use of a cell phone, does it not? While out riding a horse? Someone check your copy: it's on the first page, then send it to Technovelgy. -- Paw Yigh Lee

No, no! I confused this book with Podkayne of Mars!!!

"Why, I bet Captain Blaine would space a man for that." -- Max

Heinlein has cell phones in Space Cadet, which appeared two books before this one. Cdixon 20:11, 10 November 2006 (UTC)

There is mention of "a stereotelephone no bigger than a pack of cigarettes" in Have Space Suit—Will Travel. Not the first mention of mobile phones for sure, but the size spect is worth a mention. 88.105.88.140 (talk) 20:38, 12 February 2009 (UTC)

title: Talk:Between Planets


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Podkayne of Mars

Podkayne of Mars is a science-fiction novel by American writer Robert A. Heinlein, originally serialised in Worlds of If (November 1962, January, March 1963), and published in hardcover in 1963. The novel features a teenage girl named Podkayne "Poddy" Fries and her younger brother, Clark, who leave their home on Mars to take a trip on a spaceliner to visit Earth, accompanied by their great-uncle.

Plot summary
The book is a first-person narrative consisting of the diary of Podkayne Fries, a 15-year-old (Earth years) girl living on Mars with her parents and 11-year-old brother Clark. Due to the unscheduled "uncorking" (birth) of their three test-tube babies, Podkayne's parents cancel a much-anticipated trip to Earth. Disappointed, Podkayne confesses her misery to her uncle, Senator Tom Fries, an elder statesman of the Mars government. Tom arranges for Clark and Podkayne, escorted by himself, to get upgraded passage on a luxury liner to Earth.

During boarding, Clark is asked by a customs official "Anything to declare?" and facetiously answers "Two kilos of happy dust!" As he anticipated, his seemingly flippant remark gets him taken away and searched. This ploy serves to divert attention away from Podkayne's luggage, where he has hidden a package he was paid to smuggle aboard. Podkayne suspects the reason behind her brother's behavior, but cannot prove it. Clark was told it was a present for the captain, but is far too cynical to be taken in. He later carefully opens the package and finds a nuclear bomb, which he disarms and keeps.

Much of the description of the voyage is based on Heinlein's own experiences as a naval officer and world traveler. Clark's ploy is taken from a real-life incident, related in Heinlein's Tramp Royale, in which his wife answers the same question with "heroin" substituted for the fictitious, but equally illegal, happy dust.

Once aboard, they are befriended by "Girdie", an attractive, capable, experienced woman left impoverished by her late husband. Much to Podkayne's surprise, the normally very self-centered Clark contracts a severe case of puppy love.

Podkayne overhears fellow passengers calling the Frieses "criminals" (Mars had been a convict colony) and "savages" (the Frieses have Māori ancestry).

The liner makes a stop at Venus, which is depicted as a latter-day Las Vegas gone ultra-capitalistic. The planet is controlled by a single corporation; the dream of most of the frantically enterprising residents is to earn enough to buy a single share in it, which guarantees lifelong financial security. Just about anything goes, as long as one can pay for it. The penalty for murder is a fine paid to the corporation for the victim's estimated value plus his projected future earnings. On a less serious level, Heinlein anticipated, by over forty years, television ads in taxicabs (in the book, holographic), which have since been implemented in taxicabs in major cities worldwide.

The Frieses are given VIP treatment by the Venus Corporation and Podkayne is escorted by Dexter Cunha, the Chairman's dashing son. She begins to realize that Tom is much more than just her pinochle-playing uncle. When Clark vanishes and even the corporation is unable to find him, Tom reveals that he is on a secret diplomatic mission, as the accredited representative of the Martian government to a vital conference on Luna (the Moon). The children have been his protective coloration—Tom appearing to be a doddering uncle escorting two young people on a tour of the solar system. Clark has been kidnapped by members of a political faction opposed to Tom.

Podkayne makes an ill-judged attempt to rescue Clark by herself and falls into the kidnappers' clutches as well—only to find her uncle caught too. The captors' scheme is to use the children to blackmail the uncle into doing their bidding at the Luna conference. They return Uncle Tom to Venusberg after showing him that they have the children. Clark realizes that once Uncle Tom is released, no matter what happens, their kidnappers will have little reason to keep their prisoners alive. He is prepared, however: he engineers an escape, kills his captors, but forgets to disable the nuclear bomb he had intended to go off only if they failed in their escape.

Two versions of the ending
In Heinlein's original ending, Podkayne is killed. This did not please his publisher, who demanded and got a rewrite over the author's bitter objections. In a letter to Lurton Blassingame, his literary agent, Heinlein complained that it would be like "revising Romeo and Juliet to let the young lovers live happily ever after." He also declared that changing the end "isn't real life, because in real life, not everything ends happily."

In the original ending, after they escape from the kidnappers to a safe distance, Podkayne remembers that a semi-intelligent Venerian "fairy" baby has been left behind, and returns to rescue it. When the bomb that Clark leaves for the kidnappers blows up, Podkayne is killed, shielding the young fairy with her body. Clark takes over the narrative for the last chapter. The story ends with a hint of hope for him, as he admits his responsibility for what happened to Podkayne—that he "fubbed it, mighty dry"—then shows some human feeling by regretting his inability to cry and describes his plan to raise the fairy himself.

In the revised version, Podkayne is badly injured by the bomb, but not fatally. Uncle Tom, in a phone conversation with Podkayne's father, blames the parents—especially the mother—for neglecting the upbringing of the children. Uncle Tom feels that Clark is dangerous and maladjusted, and attributes this to the mother giving priority to her career. Clark still takes over as the narrator, and, again, regrets that Podkayne was hurt and plans to take care of the fairy, this time because Podkayne will want to see it when she is better. This is the ending that appeared when the book was published in 1963.

The 1993 Baen edition included both endings (which differ only on the last page) and featured a "pick the ending" contest, in which readers were asked to submit essays on which ending they preferred. The 1995 edition included both endings, Jim Baen's own postlude to the story, and twenty-seven of the essays. The ending in which Podkayne dies was declared the winner. Among the reasons readers favored this ending were that they felt Heinlein should have been free to create his own story, and they believed the changed ending turned a tragedy into a mere adventure, and not a very well constructed one at that. This ending has appeared in all subsequent editions.

title: Podkayne of Mars


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Dark Angel (American TV series)

Dark Angel is an American science fiction drama television series that premiered on the Fox network on October 3, 2000. Created by James Cameron and Charles H. Eglee, it stars Jessica Alba in her breakthrough role. Set in 2019, the series chronicles the life of Max Guevara (Alba), a runaway genetically enhanced supersoldier who escapes from a covert military facility as a child. In a dystopian near-future Seattle, she tries to lead a normal life while eluding capture by government agents and searching for her brothers and sisters scattered in the aftermath of their escape. Dark Angel was the only show produced by the company Cameron/Eglee Productions, and was filmed in Vancouver at Lions Gate Studios.

The high-budget pilot episode marked Cameron's television debut and was heavily promoted by Fox, reaching 17.4 million viewers. The first season, which was shown on Tuesday nights in the United States, received mainly positive reviews and won several awards, including the People's Choice Award for Favorite New TV Drama, and averaged 10.4 million viewers per episode. Alba's portrayal of Max also received mostly positive reviews and several awards. For the second season, the show was moved to the less desirable air time of Friday night and received some criticism for new plot elements. It suffered from a drop in ratings, averaging 6 million viewers per episode, and was canceled.

A series of novels continued the storyline, and a video game adaptation was also released. Dark Angel is considered to have gothic and female empowerment themes; Max followed a long line of strong female characters in Cameron's work, including Sarah Connor and Ellen Ripley. Cameron was also influenced by the manga Battle Angel Alita. Dark Angel is considered to be part of a wave of shows in the late 1990s and early 2000s that feature strong female characters, alongside Xena: Warrior Princess, Buffy the Vampire Slayer, La Femme Nikita, and Alias.

Season one
In February 2009, a genetically enhanced nine-year-old female supersoldier designated as X5-452 (Geneva Locke) escapes along with eleven others from a secret U.S. government institution code-named Manticore, where they were born, raised, and trained to be soldiers and assassins. On June 1, 2009, months after the twelve X5s' escape, terrorists detonate an electromagnetic pulse weapon in the atmosphere over the U.S., which destroys the vast majority of computer and communication systems, throwing the country into chaos.

Ten years later in 2019, the now 19-year-old X5-452 (Jessica Alba), who calls herself Max Guevara, struggles to search for her Manticore brothers and sisters. In the recovering United States, which is now barely more than a developing country, she tries to live a relatively normal life and evade capture by Manticore, which wishes to recover its lost asset. Logan Cale (Michael Weatherly), an underground cyber-journalist with the alias Eyes Only, attempts to recruit her to help fight corruption in the post-Pulse world. She initially refuses but accepts after Cale is rendered a paraplegic while attempting the assignment for which he was attempting to recruit her. A romantic interest buds between the two. While assisting Cale, Max also makes a living as a bicycle messenger at Jam Pony, a courier company, along with her friends Original Cindy (Valarie Rae Miller), Herbal Thought (Alimi Ballard), and Sketchy (Richard Gunn). Other X5s are periodically introduced, most significantly the unit leader Zack (William Gregory Lee). The Manticore hunt for the escaped X5s is led by Colonel Donald Lydecker (John Savage). Near the end of the season, Lydecker is betrayed by his superior, the even more ruthless Elizabeth Renfro (Nana Visitor), and he defects from Manticore. He aids Max and Zack in an assault on Manticore headquarters. Max is badly wounded and captured. Zack, who has also been captured, commits suicide to provide Max with his heart, as she needs an X5 heart transplant to survive.

Season two
Cale exposes Manticore to the world. Renfro decides to burn the facility to cover up the evidence and is killed in the process. Aided by Joshua (Kevin Durand), a transgenic with conspicuous canine DNA, Max escapes the facility and frees the other transgenics, including Alec (Jensen Ackles), a fellow X5 and clone of Max's brother Ben (also Jensen Ackles) whom she was forced to kill in the first season, who later joins Jam Pony. When Max is reunited with Cale he immediately becomes ill and almost dies. Max discovers that Manticore has infected her with a virus specifically designed to kill Cale, and the two must avoid all physical contact to keep him alive. Max learns that Joshua was the first transgenic created by Sandeman, Manticore's founder. Over the course of the season, it is revealed that a millennia-old breeding cult has bred their own advanced humans who rival the Manticore-produced transgenics in their abilities. Ames White (Martin Cummins), a government agent tasked with eliminating the freed transgenics, is revealed to be a member of the cult. When a strange message written in Max's genetic code makes an appearance on her skin it is revealed that Sandeman is a renegade from the breeding cult and Ames White is his son. White is still loyal to the cult and hates his father's transgenic creations with a passion. Believing that the special sequences Sandeman buried in Max's DNA are a threat to the breeding cult's plans for the extinction of normal humanity, they attempt to kill her, but she escapes to Terminal City, an abandoned part of Seattle where hundreds of outcast transgenics have been hiding. When the police begin to surround Terminal City Max convinces the other transgenics to stand their ground rather than run. The series ends with the military surrounding Terminal City as the residents raise their newly designed flag from one of the buildings, and wait for a possible invasion.

Cast and characters

The first season introduced Jessica Alba as the main character Max Guevara (X5-452), a genetically enhanced transgenic super-soldier who escaped from a government facility named Manticore. She works as a bike messenger for the courier company Jam Pony during the day and as a cat burglar at night. Michael Weatherly played Logan Cale, the show's second most prominent character. Cale is a wealthy cyber-journalist and vigilante who operates under the alias Eyes Only. He recruits Max to assist with his campaign against corruption and crime in return for helping her find information on her fellow Manticore escapees. Main roles were given to several of the couriers at Jam Pony, including Valarie Rae Miller as Cynthia "Original Cindy" McEachin, Richard Gunn as Calvin "Sketchy" Theodore, and Alimi Ballard as Herbal Thought. J. C. MacKenzie played Reagan "Normal" Ronald, the company's boss, and Jennifer Blanc played Kendra Maibaum, Max's first roommate, and John Savage played the main antagonist, Col. Donald Lydecker, who is trying to recapture Max and the other Manticore escapees.

The Lydecker character is written out of the series early in the second season, and Herbal Thought and Kendra Maibaum do not appear at all. Season two introduces Kevin Durand as Joshua, an experimental creature from Manticore who has distinct canine facial features. It also brings back Jensen Ackles as Alec McDowell (X5-494), who is an identical twin of Ben (X5-493), one of the original 12 escapees from Manticore, and introduces Ashley Scott as Asha Barlow, a resistance fighter who has a romantic interest in Cale. Martin Cummins portrayed the season's main antagonist Ames White, a National Security Agency agent tasked with destroying the Manticore escapees.

Background

Following his success with the film Titanic, director James Cameron teamed up with Charles H. Eglee with whom he had previously worked on projects including Piranha II: The Spawning. The two formed a production company, Cameron/Eglee Productions, and began working on ideas for a television series. They considered several options, including a family drama, before deciding on the idea of Dark Angel. Cameron said they began with the idea that Max would be a genetic construct who "looked normal on the outside but was different on the cellular, genetic level. We explore what that could mean." Cameron was influenced by the manga Battle Angel Alita, which he was originally intending to adapt into a film after completing Dark Angel.

Dark Angel would be the first and only work by Cameron/Eglee Productions. Max followed a long line of strong female characters in Cameron's work, including Sarah Connor and Ellen Ripley. Cameron said "it's a win/win situation" as "women respond to characters who appear strong and capable" and young male audiences "want to see girls kick ass". Later they decided to set the series in a post-social collapse world, saying that the hysteria surrounding Y2K served as inspiration; in the series, an electromagnetic pulse previously destroyed every computer in the United States. Working titles for the series included "Experimental Girl" and "Maximum Girl". The project marked Cameron's television debut; he worked mainly as a writer and executive producer for the series.

Casting and filming

More than a thousand young actresses were considered for the part of Max. Cameron started reviewing audition tapes when the field had been narrowed down to twenty or thirty applicants. He was initially not impressed with Alba's audition tape, saying "she had her head down, she was reading out of the script ... she didn't present herself all that well. But there was something about the way she read the script that copped an attitude that I liked." Cameron continually reviewed the audition tapes but kept coming back to Alba's, eventually deciding that he needed to meet her. Alba was hired for the role before the script was written. Eglee said: "We had the benefit of being able to write a script kind of backward, we were writing for this actress, with her cadences and her rhythms and her sensibilities and her attitude and her slang." To train for the role, Alba spent a year doing martial arts and gymnastics and riding motorcycles.

The two-hour premiere episode cost up to $10 million to produce, and Cameron reportedly "brought the pilot in on time and on budget". Subsequent episodes had a considerably smaller budget. Fox spent heavily on the promotional campaign for the premiere, paying for theatrical trailers, billboards, and guerilla marketing. Cameron took a "very basic view" of the show's chance of success, saying: "If it flies, it flies. If it doesn't, it doesn't ... If people connect with it, which I hope they will, fine. If we don't find an audience, we deserve to be off the air. It's that simple." Eglee admitted the series had been "routinely over budget" in the first season, and feared that this would be a factor in whether or not the show was renewed for a second season, though Cameron downplayed these concerns.

Fox "just barely" renewed the series for a second season. The budget for episodes in season two was $1.3 million each. After the intended director of the final episode did not work out, Cameron decided to step in and fill the position. He did this partially for the experience but also to show the network the potential for a third season. It was his first experience directing a TV drama.

The producers were initially told a third season had been approved, but two days later Fox informed them that the series had been canceled.

"They called us on Saturday and told us we were on schedule and we'd been picked up. We got together Saturday night and celebrated. Sunday goes by, and Monday morning we get a call saying, 'No, you're not on the schedule! It's been changed.' I've never heard of that happening. But then, I'd never been around television. ... We were supposed to be on a plane on Monday to go to the [network] upfront in New York on Tuesday. They called us that day and told us not to go! I was pissed!"

Dark Angel was set in Seattle, and filmed in Vancouver, British Columbia at Lions Gate Studios. Other filming locations included the Vancouver Art Gallery, as well as Buntzen Lake and Riverview Hospital, also in British Columbia.

Unproduced season
In the DVD commentary for "Freak Nation", the series finale, Charles H. Eglee explained what had been planned for season three. The intention was to bring together the storylines of seasons one ("Manticore") and two ("Breeding Cult") and reveal the mythology of Dark Angel. The season would reveal that thousands of years ago, Earth passed through a comet's tail which deposited viral material that killed 97% of the human race. The breeding cult preserved the survivors' genetic immunity so that when the comet returned, only members of the cult would survive. Sandeman, a cult member, and Max's creator betrayed the cult and decided to give this genetic immunity to the rest of humanity through Max, who would be the savior of the human race. There were multiple ideas on how to spread Max's immunity, including an air burst that would disperse the antibody through the atmosphere, or attaching the immunity to a common cold virus (Eglee detailed how a scene would show Original Cindy sneezing as part of the beginning of the immunity spread). This storyline is expanded upon in the final Dark Angel novel After the Dark though when the comet returns nobody falls ill, and it is believed that the cult simply had a false prediction.

Broadcast history
The first season premiered in the United States on Tuesday, October 3, 2000, from 9:00 pm until 11:00 pm. Fox had to obtain agreements from its affiliates to broadcast past 10:00 pm, as most of them air local news programs at this time. In subsequent weeks the show aired from 9:00 pm till 10:00 pm Tuesdays. During its first season, the show was preempted on several occasions, including by the 2000 World Series, the Billboard Music Awards and coverage of the presidential election. The frequent preemptions became a running joke on the set. Dark Angel's scheduled air time put it in direct competition with Angel on The WB. Critics debated which of the similarly named shows would dominate the time-slot. Jonathon Storm from Philadelphia Media Network believed that Dark Angel would prove victorious, while Brad Adgate, a research director at Horizon Media, predicted that Dark Angel would only initially take the lead in the ratings, as Angel's strong fanbase would prevail in the long run. Brad Turrell, executive vice-president of Network Communication for the WB conceded that the heavy promotion for Dark Angel would give it higher initial ratings at first but believed that as Angel was a "better show" it would not be affected long-term. Concerned that there might be confusion between the two shows, the WB took out a full page ad in TV Guide, which read "There is only ONE. David Boreanaz is ANGEL." Angel won the time slot when Fox moved the broadcast time of Dark Angel to 8:00 pm on Fridays for its second season, where it preceded the new series Pasadena.

The final episode of the series aired on May 3, 2002, as a special 90-minute episode. Dark Angel has been syndicated on Syfy and the El Rey Network in the United States and on E4 and the Horror Channel in the UK.

Music
The score for the Dark Angel pilot was composed and conducted by Joel McNeely. The pilot score track "Bicycle Ride" was used in the end credits for the duration of the series. The pilot score was released in full as part of the original publicity press kit, titled Dark Angel: Complete Score from the Dark Angel Pilot. The 37-track CD was for promotional use only and not for resale. McNeely returned to score the entire series, making frequent use of "grumbling timpani rolls, bass drum beats and shrill brass and violin crescendos that familiarly sketch the action arcs of the narrative." Traditional orchestral elements are integrated with innovative electronic sounds and female vocals to create a sense of Max's "otherworldliness", "haunting wind chimes, pseudo-Orientalist refrains and extenuated high-pitched eerie sounds" evoke Max's super-human abilities, and "driving hip hop bass beats with heavy percussive effects [and] high-pitched feedback and reverberation" convey Max's struggles with violence and her memories of Manticore. The theme song for the series was composed by Chuck D and Gary G-Wiz. Both McNeely and G-Wiz cited Dark Angel as an opportunity to push sonic boundaries; G-Wiz stated that Eglee and music supervisor Randy Gerston kept calling him and telling him to make the theme song "crazier". McNeely said scoring the series was "like the difference between jazz and classical music. I'm a jazz player, so Dark Angel is as free form and as weird as we want to get."

A soundtrack album consisting of hip hop and R&B songs was released on April 23, 2002, through Artemis Records. Eglee explained that he and Cameron began with the idea that they could do a "hip hop youth ensemble thing", noting that "hip hop had become the dominant influence in the country [and] in the world" and that they saw an opportunity to give the future of Dark Angel the soundtrack of contemporary American popular culture. In the soundtrack's liner notes, Eglee writes:"Reminiscent of another time and place ... that part of the Bronx in the late 1970s known as Fort Apache: a place that for white America, defined lack and limitation, violence and hopelessness. What white Americans couldn't see or hear then was the beautiful thing being birthed there, which, years later, would come to be known as Hip Hop. ... This album remembers the foundations of Hip Hop as it contemplates its future." Randy Gerston said that because of the near future setting of the series, he avoided any major hit songs as these would not sound futuristic. This gave them the opportunity to discover new talent instead. The album features predominately female hip hop and neo soul artists whose lyrics typically "focus on the expression of female agency and power – particularly with regard to sexuality." It peaked at No. 50 on the Top Independent Albums chart. Jason Birchmeier of AllMusic gave the soundtrack three out of five stars. He noted the lack of major artists on the album and commented that it "seems to be a female-orientated soundtrack, perhaps because of the show's female lead character". Birchmeier said many of the songs were "quite impressive" and that it "exceeds your expectations for a television show soundtrack".

Themes
Dark Angel is considered to be in the cyberpunk genre. Writing in Reconstruction: Studies in Contemporary Culture, Lorna Jowett considered Dark Angel to be a "hybrid of science fiction, Gothic, and action" which incorporated forms and themes from all three genres. Jowett compared Dark Angel to the Gothic novel Frankenstein, saying that Max's genetic engineering makes her a "postmodern Frankenstein's monster, blurring boundaries between human and monster". Kathleen McConnell in Gothic Studies also compared Max's unconventional conception to Frankenstein's monster, and cited several other Gothic themes in the series. She states that Max fits the model of a Gothic heroine who "ostensibly appear[s] to be conforming to their accepted role within the patriarchy but who actually subvert the father's power at every possible occasion." In her book Post-feminist Impasses in Popular Heroine Television, Alison Horbury theorizes that Dark Angel, along with the shows Alias, La Femme Nikita, and Dollhouse have themes of abduction, physical and symbolic rape, motherlessness, and the discovery of a sister.

Several academics have considered Dark Angel to be part of a wave of shows in the late 90s and early 2000s including Buffy the Vampire Slayer, Xena: Warrior Princess, and La Femme Nikita that feature strong female characters. Writing in Science Fiction Film & Television, Clarice Butkus noted Max has been considered to be a "distinctly millennial post-third-wave feminist warrior. She also felt that Max's relationship and dialogue with Original Cindy, an African American lesbian, conveyed female empowerment. For example, Cindy encourages Max not to feel guilt over her sexual behaviour and instead to embrace a traditionally masculine approach to sex. McConnell and Jowett also cited Max as an example of female empowerment; Jowett considered Max to be the "usual postmodern, postfeminist representation of the female action hero with [at least] a reversal or [at most] a mixture of traditional gender traits."

Butkus stated that Dark Angel repeatedly paid homage to the film Blade Runner. Lydecker, the "flawed antagonist" of Dark Angel is said to be a transposition of Deckard, the "flawed hero" of Blade Runner. Alec McDowell/X5-494's love interest is named Rachel, believed to be a reference to the replicant Rachael, though in Dark Angel it is McDowell and not Rachel who is bio-engineered. His flashbacks of this traumatic relationship use piano music similar to that used in Blade Runner to denote memories and a desire for former times. Alec's genetic memory enhancements enable him, with only a few hours practice, to play a detailed piano piece by Frédéric Chopin, the composer originally scripted for the scene in Blade Runner where Rachael inexplicably finds herself able to play the piano; both characters are considered to be pre-programmed by state forces to master superhuman skills.

Reception and legacy
Initial reaction to the series and Max's character was mostly positive, with favorable reviews in Rolling Stone and Time. Hal Boedeker of the Orlando Sentinel said: "Television's newest warrior woman possesses skills worthy of Catwoman, Xena, Emma Peel, and Wonder Woman." Howard Rosenberg said: "If pouty faces and sexy walks could destroy, the highly arresting Max would be wiping out the entire planet." However Joyce Millman said Max was "little more than lips and ass" and considered the series to be an expensive Britney Spears music video. People ran a negative review of the Pilot episode in October 2000, though in December they listed Alba's portrayal of Max as among the "breakthrough" performances of 2000.

The first episode was behind only CSI: Crime Scene Investigation as the most watched new show of the week, albeit in a week with fewer new shows because of the presidential debate coverage. Fox chose to debut Dark Angel instead of airing the first presidential debate, a move which TV analyst Marc Berman praised, saying: "The people who watch the debates aren't the people who'll tune into Dark Angel anyway", though he predicted that the premiere's high ratings would not hold up as the show competed against more varied competition in subsequent weeks. It was the tenth most popular show overall that week, attracting 17.4 million viewers. The first season averaged 10.4 million viewers per episode, ranking number 59 for the 2000–01 season. Cameron said he did not know if the broadcast time change for the second season would have a positive or negative effect on the show's ratings, though R. D. Heldenfels of the Sun Journal noted the poor ratings of Friday night television, especially the low viewing rates among 18 to 24-year-olds, the age-group that Dark Angel was most popular with. The new time slot saw a ratings drop; for the second season Dark Angel averaged 6 million viewers, ranking number 114 for the 2001–02 season in the Nielsen ratings.

Commenting on the release of the second season, Cynthia Fuchs of PopMatters said the first season of Dark Angel was one of the "few straight-up successes, a ratings hit among the coveted 'youth' demographic." She praised the series but clarified: "I'm not getting carried away: Jim Cameron is not going to be making revolutionary art anytime soon." Michael Sauter of Entertainment Weekly gave the first season a B+ and spoke highly of Alba, saying that "for a while [she was] TV's hottest kick-butt heroine". Elka Karl of Common Sense Media gave the entire series 3 out of 5 stars, saying: "While the dialogue sometimes falls flat, overall the show is well-scripted and well acted, and Alba does an excellent job of carrying the series. Dark Angel isn't perfect by any stretch of the imagination, but it is compelling television that teen sci-fi fans will enjoy." While praising the first season, Randy Dankievitch of TVOvermind labelled the second season "silly", criticizing "dumb stories" like Max's dream episode "Boo", the virus that prevents Logan and Max having physical contact, and the various half-animal Manticore experiments that are revealed.

Writing in his book The Encyclopedia of Superheroes on Film and Television, John Kenneth Muir said it was necessary for Cameron to set Dark Angel in the future because the prosperity of the U.S. in 2000 "offered little possibility for crime, squalor and other societal problems". While criticizing certain plot elements in the second season as contributing to the show's downfall, Muir said that larger factors in ratings dropping were the September 11 attacks, the Enron scandal, and the depletion of the U.S. government's surplus, which changed Dark Angel's "futuristic vision of recession in a Third-World America" from an interesting, far-fetched premise to a "depressing reminder that things could still get worse".

In 2004, Max was ranked number 17 on TV Guide's list of the 25 Greatest Sci-Fi Legends, and in 2012, Dave Golder of GamesRadar ranked her number 49 on his list of the 100 sexiest women in sci-fi. In 2009, AfterEllen ranked Original Cindy number 6 on their list of the Top 11 Lesbian/Bi Sidekicks. In 2015, Kayti Burt of Den of Geek included Dark Angel at the top of her list of "10 Sci-Fi Shows That Don't Get Enough Love". In 2016, it was recognized that Dark Angel was the first American television series to feature an openly transgender actress playing a transgender character. In the season one episode "Out", transgender actress Jessica Crockett portrayed "Louise", a young woman on a date with Normal.

The 2007 film Hitman re-used footage of Max and other Manticore children in training from Dark Angel. It was used to portray the Hitman protagonist Agent 47, a cloned assassin who, like the Manticore children, has a barcode on the back of his head.

Accolades
In its first season Dark Angel won the Favorite Television New Dramatic Series award at the 27th People's Choice Awards, and was nominated for Best Television by the International Horror Guild Awards. The production team was nominated for the Excellence in Production Design Award by the Art Directors Guild. Editor Stephen Mark won Best Edited Motion Picture for Commercial Television at the Eddie Awards for the pilot episode, and the pilot was also nominated for Outstanding Special Visual Effects for the 53rd Primetime Emmy Awards and "Best Visual Effects: Dramatic Series" by the Leo Awards. Dark Angel was nominated for the 2001 Golden Reel Award for Best Sound Editing – Television Movies and Specials – Dialogue & ADR, and for Choice Drama at the 2001 Teen Choice Awards.

Jessica Alba won Best Actress on Television at the 27th Saturn Awards, Breakout Star of the Year at the TV Guide Awards, Outstanding Actress in a New Television Series at the ALMA Awards, and Choice Actress at the 2001 Teen Choice Awards. She also received nominations for Best Actress – Television Series Drama for the 58th Golden Globe Awards and Best Performance in a TV Drama Series – Leading Young Actress for the 22nd Young Artist Awards.

Dark Angel was nominated for fewer awards in its second season. It was nominated for Choice Drama/Action Adventure for the 2002 Teen Choice Awards, where Alba was also nominated for Choice Actress, Drama. Alba was also nominated for Outstanding Actress in a Television Series for the ALMA Awards. At the Leo Awards the episode "Boo" received a nomination for Best Visual Effects: Dramatic Series, and David Geddes won Best Cinematography: Dramatic Series for the episode "Two".

Home media
20th Century Fox Home Entertainment released seasons 1 and 2 of Dark Angel on DVD in region 1 (R1), as well as a dual-coded region 2 and 4 (R2/4) set in 2003, as six-disc sets packaged in cardboard sleeves containing three DVD cases each of two discs. Season 1 was released in R2/4 in February and R1 in May, and season 2 was released in R2/4 in June and R1 in October.

The R1 releases contain several special features, including four episodes with optional commentary in each season, bloopers, deleted scenes, and featurettes. The R2/4 releases contain no commentaries and fewer other special features, but the episodes are presented in anamorphic widescreen, while R1 releases are fullscreen. Adam Tyner of DVD Talk gave the R1 first season three out of five stars for audio and video, and three and a half stars for special features. Shannon Nutt of DVD Talk gave the R1 second season three stars out of five for audio and video, and two and a half stars for extras, stating: "it appears [to have] a decent number of features, but then you discover the length of each one and really feel short-changed by Fox". She also noted the episode's commentary was mainly by writers and producers, and did not feature James Cameron or any of the actors.

Both seasons were re-released in R1 on June 5, 2007, with slim packaging consisting of one plastic case containing all six discs (which were unchanged in content and cosmetics).

Related media
A video game of the same name based on the series was developed by Radical Entertainment, published by Sierra Entertainment and released for PlayStation 2 on November 18, 2002, and later on Xbox. Alba and Weatherly voiced their respective characters in the game. Development of the game started before the series was cancelled, and the game was met with mixed to negative reception upon release. Brett Todd of GameSpot gave the game 3.8 out of 10, saying: "Although it's impossible to say whether or not the developers' morale was affected by the cancellation of the series, this third-person action adventure plays like it was cranked out to fulfill a contract" and concluded "the development of this game probably should have been cancelled at the same time as the television series". Duke Ferris from Game Revolution gave the game a 'D+', saying that while fans of Dark Angel would enjoy it as it "mirrors an episode of the show almost exactly", anybody else was likely to find it boring.

Three original novels written by Max Allan Collins expand upon the Dark Angel television series, with two picking up directly where the series ended, and another serving as a prequel. A companion book, Dark Angel: The Eyes Only Dossier, was written by D.A. Stern.
 * Dark Angel: Before the Dawn (2002) is a prequel to the television series, detailing Max's life after her escape from Manticore in 2009. After witnessing footage taken in Seattle of a man she believes to be one of her X5 siblings, Max moves from Los Angeles to Seattle, meeting Original Cindy and Kendra on the way, before finding employment at Jam Pony. Max eventually discovers the man in the footage is her brother Seth, who unbeknown to her has been working for Logan as a personal agent. Shortly after being reunited with him at the Space Needle, Seth, who has been injured, commits suicide by falling from it to avoid being captured by Lydecker. Max begins returning to the Space Needle to think and "to be with Seth".
 * Dark Angel: Skin Game (2003) immediately follows the events of "Freak Nation", the final episode of season two, describing days in May 2021. Skin Game focuses on a killer terrorizing the streets of Seattle and the growing suspicion and evidence that the killer could be transgenic. As the killings escalate, the U.S. Army and National Guard prepare themselves for an invasion of Terminal City. Max uncovers that the killer is a shapeshifting transgenic named Kelpy, though he has been unwillingly given a drug by Ames White that is causing his psychosis. When Max reveals this information to the public through Eyes Only, Ames White goes into hiding, and the invasion of Terminal City is called off. When Kelpy takes on Logan's form he is killed by the virus Max carries which was designed to kill Logan.
 * Dark Angel: After the Dark (2003) follows Skin Game. It is revealed that Max's virus is gone, the most likely explanation being that when the virus killed Kelpy it went dormant as it believed its mission to kill Logan was accomplished. However, Logan and Max's relationship is thrown into turmoil when he reveals that he inadvertently caused Seth's death by sending him on an assignment. Just as Max is ready to forgive him, Logan is kidnapped by Ames White and the breeding cult, who are preparing for the coming of a comet they believe will destroy everyone except cult-members and transgenics through depositing viral material into Earth's atmosphere. They are trying to kill Max as they believe she possesses a genetic code that will save ordinary humans from the comet's viral material. With the aid of a team of transgenics, Max eventually rescues Logan and destroys the headquarters of the breeding cult; Joshua kills Ames White. When the comet arrives, nobody falls ill, and it is believed the cult's prediction was false. Max finds Lydecker in a prison cell at the cult's headquarters. He promises to help her find her mother if she saves him, and she agrees. The book ends with Logan and Max finally consummating their relationship.

The companion book, Dark Angel: The Eyes Only Dossier, begins with a letter written by Logan Cale during the stand-off at Terminal City. It is addressed to Detective Matt Sung, a recurring character from the series who aides Logan, instructing him that the package he is sending him contains documents pertaining to the four most critical Eyes Only investigations. If he is killed by the potential invasion of Terminal City, Logan wants Sung to carry on the investigations. The rest of the book contains the documents relating to the four investigations.

title: Dark Angel (American TV series)


text:
List of index fossils

Index fossils (also known as guide fossils or indicator fossils) are fossils used to define and identify geologic periods (or faunal stages). Index fossils must have a short vertical range, wide geographic distribution and rapid evolutionary trends. Another term, "zone fossil", is used when the fossil has all the characters stated above except wide geographical distribution; thus, they correlate the surrounding rock to a biozone rather than a specific time period.

title: List of index fossils


text:
Talk:BDSM

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 15:07, 25 January 2023 (UTC)
 * BDSM Collar and Chain.jpg

Madonna - Erotica / Sex
The Section under music refers only to songs released post 2010, whereas Madonna released the ground-breaking S&M-themed song 'Erotica' in 1992. The video contains nudity, Madonna dressed as a dominatrix and S&M imagery. While the lyrics refer to S&M, pain as pleasure, infantilism and the female as the dominant partner. https://en.wikipedia.org/wiki/Erotica_(song) As well as this, she released the photograph book 'Sex' which is full of imagery of S&M & domination (female on female, female on male, male on female). https://en.wikipedia.org/wiki/Sex_(book) This was incredibly shocking in 1992, by the time Rihanna and Aguilera released their S&M-themed songs, the subject was already somewhat tame. Please give Madonna the credit she deserves for bringing the topic to the mainstream. 2A02:8309:2183:7800:BDFA:D66C:2D23:B424 (talk) 07:04, 19 March 2023 (UTC)

Madonna - Hanky Panky / Human Nature
Furthermore, Madonna's 1990 single "Hanky Panky" is all about BDSM, with lyrics about spanking, bondage, domination. https://en.wikipedia.org/wiki/Hanky_Panky_(Madonna_song) The video for her 1995 single "Human Nature" also contained BDSM elements, with Madonna dressed in a rubber bodysuit, chained to a chair and also dominating bound male and female dancers and wielding a riding crop. https://en.wikipedia.org/wiki/Human_Nature_(Madonna_song) 86.49.231.136 (talk) 09:45, 19 March 2023 (UTC)

Edit Request: "Addiction" section on masochism is absurd and offensive. Remove it.
The section on sadomasochism that describes it as an addiction was added by someone with an axe to grind and no sources to back them up. One citation suffers from every imaginable bias (a "phenomenological study" of 9 criminals in prison is hardly a scientific endeavor), and the other isn't even relevant (it's about gambling, and the supposed link is not apparent in the data). 50.47.99.220 (talk) 15:48, 24 June 2023 (UTC)
 * The latter statement (correlating gambling) feels like OR/conclusion of the reader, so that has been removed. The study, I'm unsure about -- I've heard others speak of the addictive quality, so it's not entirely untrue, but I'll let someone else weigh in on the validity here. HalJor (talk) 21:40, 25 June 2023 (UTC)

Wow! Just some full-frontal nudity on this page huh.
Just a full set of titties and a vulva right on here. Stopchewingyourcuticles (talk) 10:59, 29 November 2023 (UTC)

 * The gender ratio on these photos is also real bad. The photos of nude women outnumber every other subject something like 10:1, and the majority of men depicted are clothed/dominant. Saying this as a researcher of the topic and former professional in the community this is not a good look for this article, doesn't represent the history of or current reality of BDSM as a culture, and it needs to be either heavily trimmed or balanced. Stopchewingyourcuticles (talk) 11:03, 29 November 2023 (UTC)

Edit request: Reference 196
This reference and it's associated URL(s) redirect to "uea.su", an old domain on the UEA Students' Union which is no longer valid. The reference should be either removed entirely, or the URL(s) updated to reflect the domain change circa February 2022 (https://www.ueasu.org); as an aside, the associated student society no longer exists, so deletion may be recommended. Union Communications (talk) 13:38, 11 December 2023 (UTC)
 * The reference includes a link to an archived version, which is appropriate for a case such as this. No action need be taken.  HalJor (talk) 21:07, 11 December 2023 (UTC)

✅ Reference has been updated. Regards, Thinker78  (talk) 01:21, 12 December 2023 (UTC)

This article being considered an LGBT studies article
Why is this article considred an LGBT studies article. BDSM is not inherently LGBT. DarknessGoth777 (talk) 02:04, 22 February 2024 (UTC)

Suggested Edit: Prevelence
Under Psychology, 3rd paragraph, it states: "The prevalence of sadomasochism within the general population is unknown."

Suggest removing the above sentence and adding a new paragraph stating:

In the U.S., a 2017 prevalence survey found that in their lifetime, 32% of adults have engaged in spanking, 23% have engaged in role-playing, 21% in tying/being tied up, and 15% in playful whipping. Attending a BDSM party was much lower, at less than 4% of the U.S. population. (Herbenick, 2017) In Canada, nearly half of the people who responded to a prevalence survey said they were interested in at least one kind of unusual sexual interest: voyeurism, fetishism, frotteurism or masochism. Men and women both expressed similar levels of interest in masochism, and masochism was significantly linked with higher satisfaction in their sexual life. (Joyal, 2016)

Citations:

Herbenick, D., Bowling, J., Fu, T. J., Dodge, B., Guerra-Reyes, L., & Sanders, S. (2017). Sexual Diversity in the United States: Results from a nationally representative probability sample of adult women and men. PloS one, 12(7), e0181198. doi:10.1371/journal.pone.0181198

Christian C. Joyal & Julie Carpentier (2016): The Prevalence of Paraphilic Interests and Behaviors in the General Population: A Provincial Survey, The Journal of Sex Research, DOI: 10.1080/00224499.2016.1139034 SusanWrightAZ (talk) 23:09, 15 July 2024 (UTC)

title: Talk:BDSM


text:
Talk:Hammond organ

Merger completed
After ages and ages of silence, I have merged this page and the B3 page, however, this article still needs some work to reduce redundancies. — Preceding unsigned comment added by FozzyMaple (talk • contribs) 19:54, 15 October 2006 (UTC)

Tonewheel generator
In a tonewheel Hammond organ, an AC synchronous motor drives all tonewheels. Earlier organ motors did not start by themselves when power was switched on; they needed an auxiliary starting motor to bring them up to speed. Power for the latter motor passed through a spring-loaded, normally off power switch next to the main switch. When switched on, the organist held the starting switch on for a few seconds to start the main motor, then released it. Later motors were self-starting synchronous types.

The whole tonewheel generator assembly extends across the width of the organ, and is roughly 35 cm from front to back; it is roughly 8 cm high. The main drive shaft (directly driven by the motor) runs through the middle, and is not continuous; it has several springs to isolate sections of the shaft (probably mechanical low-pass filtering, to reduce high-frequency torque fluctuations).

The generator assembly comprises a number of compartments which isolate neighboring tonewheels and their coils, as well as enhancing the rigidity of the structure while maintaining reasonable weight. Extending from both the front edge and the back edge are the magnets, with clamping collars and screws. These are factory adjustments, critical, to set the correct distance between the "inside" tip of the magnet and the tonewheel. They should not be readjusted without good reason and significant knowledge.

Between any given tonewheel and the main drive shaft are gears with ratios that enhance the frequency accuracy of the tones being generated. The consequence of this is that the intonation is technically just, but some frequency ratios are numerically large (such as three-digit numbers).

A few tonewheels apparently have too much harmonic content from the coil, so they have low-pass filters placed on top of the chassis.

At least some, if not all tonewheel generator chassis are normally covered by a thick felt blanket, perhaps to absorb mechanical noise, and to help keep dust from getting inside.

Some tonewheel generators have a thick non-metallic opaque coating applied to the tonewheel edges, so the teeth are not visible.

Spring reverberation unit (stub)
— Preceding unsigned comment added by Nikevich (talk • contribs) 19:14, 27 January 2010 (UTC)

Manuals, drawbars, and effects
Pianists and synthesizer players who begin playing the Hammond soon realize that authentic performance practice involves a lot more than playing the notes on the keyboard. Hammond players vary the timbre of both manuals in real time through a combination of changing drawbar settings, engaging or disengaging the vibrato and chorus effects or percussion settings, and changing the rotating Leslie speaker system's speed setting. As well, performers obtain other effects by setting the Leslie's amplifier to maximum output (and controlling the effective volume using only the organ's volume pedal) to add overdriven distortion or growl for certain passages, or by briefly switching off the organ's synchronous run motor, which produces a wobbly pitch-bend effect.

There are playing styles that are idiomatic to the Hammond organ, such as palm glissandos, rapid repetition of a single note, tremolo between two notes a third apart (typically the 5th and 7th scale degree of the current chord), percussive drumming of the keyboard, and playing a chord on the upper manual, then sliding the hand down to duplicate the chord on the lower manual. Artistic use of the foot-controlled volume pedal is an important facet of performing on the Hammond.

Bass pedalboard
Tom Vickers notes that after Jimmy Smith popularized the Hammond organ in jazz, many jazz pianists "...who thought that getting organ-ized would be a snap ...realized that the ...B-3 required not only a strong left hand, but killer coordination on those bass pedals to really get the bass groove percolating." In the 1950s, the organist Wild Bill Davis told aspiring organist Smith that it could take over a decade just to learn the bass pedals. Jazz organists such as Jimmy Smith developed the ability to perform fluent walking-bass lines on the bass pedals, mostly on ballad tempo tunes. He played up-tempo bass lines with his left hand, augmented by occasional taps on the bass pedalboard. Some organists like Barbara Dennerlein or Leon Kuijpers perform basslines on the bass pedalboard.

The organist may operate the bass pedals while either wearing standard shoes; using specially designed organ shoes; or performing barefoot. Rhoda Scott is said to have originated the barefoot playing method, which is popular with some players. — Preceding unsigned comment added by Ritchie333 (talk • contribs) 13:17, 30 July 2013 (UTC)

manuals definition
Please define the two manuals in terms of the relevant difference between them, e.g. the pitch range of each manual. Thanks. Rtdrury (talk) 19:26, 20 February 2023 (UTC)

Frequency transformers
Regarding this: "Third party companies manufacture transformers that can allow a Hammond organ designed for one region to run in the other". A transformer does not change the frequency. You would need something like an inverter to run a 60 Hz organ on 50 Hz. Does the source actually say "transformer"? GA-RT-22 (talk) 13:19, 30 November 2023 (UTC)

 * The source says "All you need is a step-down transformer to reduce the local voltage to about 100-120 volts and a frequency converter to provide a precise 60Hz frequency .... Trek II, mentioned above, sells a product that will take a line with a frequency of 25 Hz to 100Hz and convert it into a steady 60Hz source." Ritchie333 (talk) (cont)  13:24, 30 November 2023 (UTC)

title: Talk:Hammond organ