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Exponential distribution

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.

The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions.

Probability density function
The probability density function (pdf) of an exponential distribution is

 * $$ f(x;\lambda) = \begin{cases}

\lambda e^{ - \lambda x} & x \ge 0, \\ 0 & x < 0. \end{cases}$$

Here λ > 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval $[0, ∞)$. If a random variable X has this distribution, we write $X ~ Exp(λ)$.

The exponential distribution exhibits infinite divisibility.

Cumulative distribution function
The cumulative distribution function is given by

 * $$F(x;\lambda) = \begin{cases}

1-e^{-\lambda x} & x \ge 0, \\ 0 & x < 0. \end{cases}$$

Alternative parametrization
The exponential distribution is sometimes parametrized in terms of the scale parameter $β = 1/λ$, which is also the mean: $$f(x;\beta) = \begin{cases} \frac{1}{\beta} e^{-x/\beta} & x \ge 0, \\ 0 & x < 0. \end{cases} \qquad\qquad F(x;\beta) = \begin{cases} 1- e^{-x/\beta} & x \ge 0, \\ 0 & x < 0. \end{cases} $$

Mean, variance, moments, and median

The mean or expected value of an exponentially distributed random variable X with rate parameter λ is given by $$\operatorname{E}[X] = \frac{1}{\lambda}.$$

In light of the examples given below, this makes sense; a person who receives an average of two telephone calls per hour can expect that the time between consecutive calls will be 0.5 hour, or 30 minutes.

The variance of X is given by $$\operatorname{Var}[X] = \frac{1}{\lambda^2},$$ so the standard deviation is equal to the mean.

The moments of X, for $$n\in\N$$ are given by $$\operatorname{E}\left[X^n\right] = \frac{n!}{\lambda^n}.$$

The central moments of X, for $$n\in\N$$ are given by $$\mu_n = \frac{!n}{\lambda^n} = \frac{n!}{\lambda^n}\sum^n_{k=0}\frac{(-1)^k}{k!}.$$ where !n is the subfactorial of n

The median of X is given by $$\operatorname{m}[X] = \frac{\ln(2)}{\lambda} < \operatorname{E}[X],$$ where $ln$ refers to the natural logarithm. Thus the absolute difference between the mean and median is $$\left|\operatorname{E}\left[X\right] - \operatorname{m}\left[X\right]\right| = \frac{1 - \ln(2)}{\lambda} < \frac{1}{\lambda} = \operatorname{\sigma}[X],$$

in accordance with the median-mean inequality.

Memorylessness property of exponential random variable
An exponentially distributed random variable T obeys the relation $$\Pr \left (T > s + t \mid T > s \right ) = \Pr(T > t), \qquad \forall s, t \ge 0.$$

This can be seen by considering the complementary cumulative distribution function: $$ \begin{align} \Pr\left(T > s + t \mid T > s\right) &= \frac{\Pr\left(T > s + t \cap T > s\right)}{\Pr\left(T > s\right)} \\[4pt] &= \frac{\Pr\left(T > s + t \right)}{\Pr\left(T > s\right)} \\[4pt] &= \frac{e^{-\lambda(s + t)}}{e^{-\lambda s}} \\[4pt] &= e^{-\lambda t} \\[4pt] &= \Pr(T > t). \end{align} $$

When T is interpreted as the waiting time for an event to occur relative to some initial time, this relation implies that, if T is conditioned on a failure to observe the event over some initial period of time s, the distribution of the remaining waiting time is the same as the original unconditional distribution. For example, if an event has not occurred after 30 seconds, the conditional probability that occurrence will take at least 10 more seconds is equal to the unconditional probability of observing the event more than 10 seconds after the initial time.

The exponential distribution and the geometric distribution are the only memoryless probability distributions.

The exponential distribution is consequently also necessarily the only continuous probability distribution that has a constant failure rate.

Quantiles

The quantile function (inverse cumulative distribution function) for Exp(λ) is $$F^{-1}(p;\lambda) = \frac{-\ln(1-p)}{\lambda},\qquad 0 \le p < 1$$

The quartiles are therefore:

 * first quartile: ln(4/3)/λ
 * median: ln(2)/λ
 * third quartile: ln(4)/λ

And as a consequence the interquartile range is ln(3)/λ.

Conditional Value at Risk (Expected Shortfall)
The conditional value at risk (CVaR) also known as the expected shortfall or superquantile for Exp(λ) is derived as follows:

$$\begin{align} \bar{q}_\alpha (X) &= \frac{1}{1-\alpha} \int_{\alpha}^{1} q_p (X) dp \\ &= \frac{1}{(1-\alpha)} \int_{\alpha}^{1} \frac{-\ln (1 - p )}{\lambda}  dp \\ &= \frac{-1}{\lambda(1-\alpha)} \int_{1-\alpha}^{0} -\ln (y )  dy \\ &= \frac{-1}{\lambda(1-\alpha)} \int_{0}^{1 - \alpha} \ln (y )  dy \\ &=  \frac{-1}{\lambda(1-\alpha)}  [  ( 1-\alpha) \ln(1-\alpha) - (1-\alpha) ] \\ &=  \frac{ - \ln(1-\alpha) + 1 } { \lambda} \\ \end{align} $$

Buffered Probability of Exceedance (bPOE)
The buffered probability of exceedance is one minus the probability level at which the CVaR equals the threshold $$x$$. It is derived as follows:

$$\begin{align} \bar{p}_x (X) &= \{ 1 - \alpha | \bar{q}_\alpha (X) = x \} \\ &= \{ 1 - \alpha |\frac{ - \ln(1-\alpha) + 1 } { \lambda} = x \} \\ &= \{ 1 - \alpha |  \ln(1-\alpha)  =  1-\lambda x \} \\ &= \{ 1 - \alpha |  e^{\ln(1-\alpha)}  =  e^{1-\lambda x} \} =  \{ 1 - \alpha |  1-\alpha =  e^{1-\lambda x} \} = e^{1-\lambda x} \end{align} $$

Kullback–Leibler divergence
The directed Kullback–Leibler divergence in nats of $$e^\lambda$$ ("approximating" distribution) from $$e^{\lambda_0}$$ ('true' distribution) is given by $$\begin{align} \Delta(\lambda_0 \parallel \lambda) &= \mathbb{E}_{\lambda_0}\left( \log \frac{p_{\lambda_0}(x)}{p_\lambda(x)}\right)\\ &= \mathbb{E}_{\lambda_0}\left( \log \frac{\lambda_0 e^{\lambda_0 x}}{\lambda e^{\lambda x}}\right)\\ &= \log(\lambda_0) - \log(\lambda) - (\lambda_0 - \lambda)E_{\lambda_0}(x)\\ &= \log(\lambda_0) - \log(\lambda) + \frac{\lambda}{\lambda_0} - 1. \end{align} $$

Maximum entropy distribution
Among all continuous probability distributions with support $[0, ∞)$ and mean μ, the exponential distribution with λ = 1/μ has the largest differential entropy. In other words, it is the maximum entropy probability distribution for a random variate X which is greater than or equal to zero and for which E[X] is fixed.

Distribution of the minimum of exponential random variables
Let X1, …, Xn be independent exponentially distributed random variables with rate parameters λ1, …, λn. Then $$\min\left\{X_1, \dotsc, X_n \right\}$$ is also exponentially distributed, with parameter $$\lambda = \lambda_1 + \dotsb + \lambda_n.$$

This can be seen by considering the complementary cumulative distribution function: $$\begin{align} &\Pr\left(\min\{X_1, \dotsc, X_n\} > x\right) \\ ={} &\Pr\left(X_1 > x, \dotsc, X_n > x\right) \\ ={} &\prod_{i=1}^n \Pr\left(X_i > x\right) \\ ={} &\prod_{i=1}^n \exp\left(-x\lambda_i\right) = \exp\left(-x\sum_{i=1}^n \lambda_i\right). \end{align}$$

The index of the variable which achieves the minimum is distributed according to the categorical distribution $$\Pr\left(X_k = \min\{X_1, \dotsc, X_n\}\right) = \frac{\lambda_k}{\lambda_1 + \dotsb + \lambda_n}.$$

A proof can be seen by letting $$I = \operatorname{argmin}_{i \in \{1, \dotsb, n\}}\{X_1, \dotsc, X_n\}$$. Then, $$\begin{align} \Pr (I = k) &= \int_{0}^{\infty} \Pr(X_k = x) \Pr(\forall_{i\neq k}X_{i} > x ) \,dx \\ &= \int_{0}^{\infty} \lambda_k e^{- \lambda_k x} \left(\prod_{i=1, i\neq k}^{n} e^{- \lambda_i x}\right) dx \\ &= \lambda_k \int_{0}^{\infty} e^{- \left(\lambda_1 + \dotsb  +\lambda_n\right) x}  dx \\ &= \frac{\lambda_k}{\lambda_1 + \dotsb + \lambda_n}. \end{align}$$

Note that $$\max\{X_1, \dotsc, X_n\}$$ is not exponentially distributed, if X1, …, Xn do not all have parameter 0.

Joint moments of i.i.d. exponential order statistics
Let $$ X_1, \dotsc, X_n $$ be $$ n $$ independent and identically distributed exponential random variables with rate parameter λ. Let $$ X_{(1)}, \dotsc, X_{(n)} $$ denote the corresponding order statistics. For $$ i < j $$, the joint moment $$ \operatorname E\left[X_{(i)} X_{(j)}\right] $$ of the order statistics $$ X_{(i)} $$ and $$ X_{(j)} $$ is given by $$\begin{align} \operatorname E\left[X_{(i)} X_{(j)}\right] &= \sum_{k=0}^{j-1}\frac{1}{(n - k)\lambda} \operatorname E\left[X_{(i)}\right] + \operatorname E\left[X_{(i)}^2\right] \\ &= \sum_{k=0}^{j-1}\frac{1}{(n - k)\lambda}\sum_{k=0}^{i-1}\frac{1}{(n - k)\lambda} + \sum_{k=0}^{i-1}\frac{1}{((n - k)\lambda)^2} + \left(\sum_{k=0}^{i-1}\frac{1}{(n - k)\lambda}\right)^2. \end{align}$$

This can be seen by invoking the law of total expectation and the memoryless property: $$\begin{align} \operatorname E\left[X_{(i)} X_{(j)}\right] &= \int_0^\infty \operatorname E\left[X_{(i)} X_{(j)} \mid X_{(i)}=x\right] f_{X_{(i)}}(x) \, dx \\ &= \int_{x=0}^\infty x \operatorname E\left[X_{(j)} \mid X_{(j)} \geq x\right] f_{X_{(i)}}(x) \, dx     &&\left(\textrm{since}~X_{(i)} = x \implies X_{(j)} \geq x\right) \\ &= \int_{x=0}^\infty x \left[ \operatorname E\left[X_{(j)}\right] + x \right] f_{X_{(i)}}(x) \, dx     &&\left(\text{by the memoryless property}\right) \\ &= \sum_{k=0}^{j-1}\frac{1}{(n - k)\lambda} \operatorname E\left[X_{(i)}\right] + \operatorname E\left[X_{(i)}^2\right]. \end{align}$$

The first equation follows from the law of total expectation. The second equation exploits the fact that once we condition on $$ X_{(i)} = x $$, it must follow that $$ X_{(j)} \geq x $$. The third equation relies on the memoryless property to replace $$\operatorname E\left[ X_{(j)} \mid X_{(j)} \geq x\right]$$ with $$\operatorname E\left[X_{(j)}\right] + x$$.

Sum of two independent exponential random variables
The probability distribution function (PDF) of a sum of two independent random variables is the convolution of their individual PDFs. If $$X_1$$ and $$X_2$$ are independent exponential random variables with respective rate parameters $$\lambda_1$$ and $$\lambda_2,$$ then the probability density of $$Z=X_1+X_2$$ is given by $$ \begin{align} f_Z(z) &= \int_{-\infty}^\infty f_{X_1}(x_1) f_{X_2}(z - x_1)\,dx_1\\ &= \int_0^z \lambda_1 e^{-\lambda_1 x_1} \lambda_2 e^{-\lambda_2(z - x_1)} \, dx_1 \\ &= \lambda_1 \lambda_2 e^{-\lambda_2 z} \int_0^z e^{(\lambda_2 - \lambda_1)x_1}\,dx_1 \\ &= \begin{cases} \dfrac{\lambda_1 \lambda_2}{\lambda_2-\lambda_1} \left(e^{-\lambda_1 z} - e^{-\lambda_2 z}\right) & \text{ if } \lambda_1 \neq \lambda_2 \\[4 pt] \lambda^2 z e^{-\lambda z} & \text{ if } \lambda_1 = \lambda_2 = \lambda. \end{cases} \end{align} $$ The entropy of this distribution is available in closed form: assuming $$\lambda_1 > \lambda_2$$ (without loss of generality), then $$\begin{align} H(Z) &= 1 + \gamma + \ln \left( \frac{\lambda_1 - \lambda_2}{\lambda_1 \lambda_2} \right) + \psi \left( \frac{\lambda_1}{\lambda_1 - \lambda_2} \right) , \end{align}$$ where $$\gamma$$ is the Euler-Mascheroni constant, and $$\psi(\cdot)$$ is the digamma function.

In the case of equal rate parameters, the result is an Erlang distribution with shape 2 and parameter $$\lambda,$$ which in turn is a special case of gamma distribution.

The sum of n independent Exp(λ) exponential random variables is Gamma(n, λ) distributed.

Related distributions

 * If X ~ Laplace(μ, β−1), then |X − μ| ~ Exp(β).
 * If X ~ Pareto(1, λ), then log(X) ~ Exp(λ).
 * If X ~ SkewLogistic(θ), then $$\log\left(1 + e^{-X}\right) \sim \operatorname{Exp}(\theta)$$.
 * If Xi ~ U(0, 1) then $$\lim_{n \to \infty}n \min \left(X_1, \ldots, X_n\right) \sim \operatorname{Exp}(1)$$
 * The exponential distribution is a limit of a scaled beta distribution: $$\lim_{n \to \infty} n \operatorname{Beta}(1, n) = \operatorname{Exp}(1).$$
 * The exponential distribution is a special case of type 3 Pearson distribution.
 * The exponential distribution is the special case of a Gamma distribution with shape parameter 1.
 * If X ~ Exp(λ) and X$i$ ~ Exp(λ$i$) then:
 * $$kX \sim \operatorname{Exp}\left(\frac{\lambda}{k}\right)$$, closure under scaling by a positive factor.
 * 1 + X ~ BenktanderWeibull(λ, 1), which reduces to a truncated exponential distribution.
 * keX ~ Pareto(k, λ).
 * e−X ~ Beta(λ, 1).
 * $1⁄k$e$X$ ~ PowerLaw(k, λ)
 * $$\sqrt{X} \sim \operatorname{Rayleigh} \left(\frac{1}{\sqrt{2\lambda}}\right)$$, the Rayleigh distribution
 * $$X \sim \operatorname{Weibull}\left(\frac{1}{\lambda}, 1\right)$$, the Weibull distribution
 * $$X^2 \sim \operatorname{Weibull}\left(\frac{1}{\lambda^2}, \frac{1}{2}\right)$$
 * μ − β log(λX) ∼ Gumbel(μ, β).
 * $$\lfloor X\rfloor \sim \operatorname{Geometric}\left(1-e^{-\lambda}\right)$$, a geometric distribution on 0,1,2,3,...
 * $$\lceil X\rceil \sim \operatorname{Geometric}\left(1-e^{-\lambda}\right)$$, a geometric distribution on 1,2,3,4,...
 * If also Y ~ Erlang(n, λ) or$$Y \sim \Gamma\left(n, \frac{1}{\lambda}\right)$$ then $$\frac{X}{Y} + 1 \sim \operatorname{Pareto}(1, n)$$
 * If also λ ~ Gamma(k, θ) (shape, scale parametrisation) then the marginal distribution of X is Lomax(k, 1/θ), the gamma mixture
 * λ$1$X$1$ − λ$2$Y$2$ ~ Laplace(0, 1).
 * min{X1, ..., Xn} ~ Exp(λ1 + ... + λn).
 * If also λ$i$ = λ then:
 * $$X_1 + \cdots + X_k = \sum_i X_i \sim$$ Erlang(k, λ) = Gamma(k, λ−1) = Gamma(k, λ) (in (k, θ) and (α, β) parametrization, respectively) with an integer shape parameter k.
 * If $$T = (X_1 + \cdots + X_n ) = \sum_{i=1}^n X_i$$, then $$2 \lambda T \sim \chi^2_{2n}$$.
 * X$i$ − X$j$ ~ Laplace(0, λ−1).
 * If also X$i$ are independent, then:
 * $$\frac{X_i}{X_i + X_j}$$ ~ U(0, 1)
 * $$Z = \frac{\lambda_i X_i}{\lambda_j X_j}$$ has probability density function $$f_Z(z) = \frac{1}{(z + 1)^2}$$. This can be used to obtain a confidence interval for $$\frac{\lambda_i}{\lambda_j}$$.
 * If also λ = 1:
 * $$\mu - \beta\log\left(\frac{e^{-X}}{1 - e^{-X}}\right) \sim \operatorname{Logistic}(\mu, \beta)$$, the logistic distribution
 * $$\mu - \beta\log\left(\frac{X_i}{X_j}\right) \sim \operatorname{Logistic}(\mu, \beta)$$
 * μ − σ log(X) ~ GEV(μ, σ, 0).
 * Further if $$Y \sim \Gamma\left(\alpha, \frac{\beta}{\alpha}\right)$$ then $$\sqrt{XY} \sim \operatorname{K}(\alpha, \beta)$$ (K-distribution)
 * If also λ = 1/2 then X ∼ χ$2 2$; i.e., X has a chi-squared distribution with 2 degrees of freedom. Hence: $$\operatorname{Exp}(\lambda) = \frac{1}{2\lambda} \operatorname{Exp}\left(\frac{1}{2} \right) \sim \frac{1}{2\lambda} \chi_2^2\Rightarrow \sum_{i=1}^n \operatorname{Exp}(\lambda) \sim \frac{1}{2\lambda }\chi_{2n}^2$$
 * If $$X \sim \operatorname{Exp}\left(\frac{1}{\lambda}\right)$$ and $$Y \mid X$$ ~ Poisson(X) then $$Y \sim \operatorname{Geometric}\left(\frac{1}{1 + \lambda}\right)$$    (geometric distribution)
 * The Hoyt distribution can be obtained from exponential distribution and arcsine distribution
 * The exponential distribution is a limit of the κ-exponential distribution in the $$\kappa = 0$$ case.
 * Exponential distribution is a limit of the κ-Generalized Gamma distribution in the $$\alpha = 1$$ and $$\nu = 1$$ cases:
 * $$\lim_{(\alpha,\nu)\to(0,1)} p_\kappa(x) = (1+\kappa\nu)(2\kappa)^\nu \frac{\Gamma\Big(\frac{1}{2\kappa}+\frac{\nu}{2}\Big)}{\Gamma\Big(\frac{1}{2\kappa}-\frac{\nu}{2}\Big)} \frac{\alpha \lambda^\nu}{\Gamma(\nu)} x^{\alpha\nu-1}\exp_\kappa(-\lambda x^\alpha) = \lambda e^{ - \lambda x} $$

Other related distributions:
 * Hyper-exponential distribution – the distribution whose density is a weighted sum of exponential densities.
 * Hypoexponential distribution – the distribution of a general sum of exponential random variables.
 * exGaussian distribution – the sum of an exponential distribution and a normal distribution.

Statistical inference
Below, suppose random variable X is exponentially distributed with rate parameter λ, and $$x_1, \dotsc, x_n$$ are n independent samples from X, with sample mean $$\bar{x}$$.

Parameter estimation
The maximum likelihood estimator for λ is constructed as follows.

The likelihood function for λ, given an independent and identically distributed sample x = (x1, …, xn) drawn from the variable, is: $$ L(\lambda) = \prod_{i=1}^n\lambda\exp(-\lambda x_i) = \lambda^n\exp\left(-\lambda \sum_{i=1}^n x_i\right) = \lambda^n\exp\left(-\lambda n\overline{x}\right), $$

where: $$\overline{x} = \frac{1}{n}\sum_{i=1}^n x_i$$ is the sample mean.

The derivative of the likelihood function's logarithm is: $$ \frac{d}{d\lambda} \ln L(\lambda) = \frac{d}{d\lambda} \left( n \ln\lambda - \lambda n\overline{x} \right) = \frac{n}{\lambda} - n\overline{x}\ \begin{cases} > 0, & 0 < \lambda < \frac{1}{\overline{x}}, \\[8pt] = 0, & \lambda = \frac{1}{\overline{x}}, \\[8pt] < 0, & \lambda > \frac{1}{\overline{x}}. \end{cases} $$

Consequently, the maximum likelihood estimate for the rate parameter is: $$\widehat{\lambda}_\text{mle} = \frac{1}{\overline{x}} = \frac{n}{\sum_i x_i}$$

This is an unbiased estimator of $$\lambda,$$ although $$\overline{x}$$  an unbiased MLE estimator of $$1/\lambda$$ and the distribution mean.

The bias of $$ \widehat{\lambda}_\text{mle} $$ is equal to $$B \equiv \operatorname{E}\left[\left(\widehat{\lambda}_\text{mle} - \lambda\right)\right] = \frac{\lambda}{n - 1} $$ which yields the bias-corrected maximum likelihood estimator $$\widehat{\lambda}^*_\text{mle} = \widehat{\lambda}_\text{mle} - B.$$

An approximate minimizer of mean squared error (see also: bias–variance tradeoff) can be found, assuming a sample size greater than two, with a correction factor to the MLE: $$\widehat{\lambda} = \left(\frac{n - 2}{n}\right) \left(\frac{1}{\bar{x}}\right) = \frac{n - 2}{\sum_i x_i}$$ This is derived from the mean and variance of the inverse-gamma distribution, $\mbox{Inv-Gamma}(n, \lambda)$.

Fisher information
The Fisher information, denoted $$\mathcal{I}(\lambda)$$, for an estimator of the rate parameter $$\lambda$$ is given as: $$\mathcal{I}(\lambda) = \operatorname{E} \left[\left. \left(\frac{\partial}{\partial\lambda} \log f(x;\lambda)\right)^2\right|\lambda\right] = \int \left(\frac{\partial}{\partial\lambda} \log f(x;\lambda)\right)^2 f(x; \lambda)\,dx$$

Plugging in the distribution and solving gives: $$ \mathcal{I}(\lambda) = \int_{0}^{\infty} \left(\frac{\partial}{\partial\lambda} \log \lambda e^{-\lambda x}\right)^2 \lambda e^{-\lambda x}\,dx = \int_{0}^{\infty} \left(\frac{1}{\lambda} - x\right)^2 \lambda e^{-\lambda x}\,dx = \lambda^{-2}.$$

This determines the amount of information each independent sample of an exponential distribution carries about the unknown rate parameter $$\lambda$$.

Confidence intervals
An exact 100(1 − α)% confidence interval for the rate parameter of an exponential distribution is given by: $$\frac{2n}{\widehat{\lambda}_{\textrm{mle}} \chi^2_{\frac{\alpha}{2},2n} }< \frac{1}{\lambda} < \frac{2n}{\widehat{\lambda}_{\textrm{mle}} \chi^2_{1-\frac{\alpha}{2},2n}}\,,$$ which is also equal to $$\frac{2n\overline{x}}{\chi^2_{\frac{\alpha}{2},2n}} < \frac{1}{\lambda} < \frac{2n\overline{x}}{\chi^2_{1-\frac{\alpha}{2},2n}}\,,$$ where $χ2 p,v$ is the $100(p)$ percentile of the chi squared distribution with v degrees of freedom, n is the number of observations and x-bar is the sample average. A simple approximation to the exact interval endpoints can be derived using a normal approximation to the $χ2 p,v$ distribution. This approximation gives the following values for a 95% confidence interval: $$\begin{align} \lambda_\text{lower} &= \widehat{\lambda}\left(1 - \frac{1.96}{\sqrt{n}}\right) \\ \lambda_\text{upper} &= \widehat{\lambda}\left(1 + \frac{1.96}{\sqrt{n}}\right) \end{align}$$

This approximation may be acceptable for samples containing at least 15 to 20 elements.

Bayesian inference
The conjugate prior for the exponential distribution is the gamma distribution (of which the exponential distribution is a special case). The following parameterization of the gamma probability density function is useful:

$$\operatorname{Gamma}(\lambda; \alpha, \beta) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} \lambda^{\alpha-1} \exp(-\lambda\beta).$$

The posterior distribution p can then be expressed in terms of the likelihood function defined above and a gamma prior:

$$\begin{align} p(\lambda) &\propto L(\lambda) \Gamma(\lambda; \alpha, \beta) \\ &= \lambda^n \exp\left(-\lambda n\overline{x}\right) \frac{\beta^{\alpha}}{\Gamma(\alpha)} \lambda^{\alpha-1} \exp(-\lambda \beta) \\ &\propto \lambda^{(\alpha+n)-1} \exp(-\lambda \left(\beta + n\overline{x}\right)). \end{align}$$

Now the posterior density p has been specified up to a missing normalizing constant. Since it has the form of a gamma pdf, this can easily be filled in, and one obtains:

$$p(\lambda) = \operatorname{Gamma}(\lambda; \alpha + n, \beta + n\overline{x}).$$

Here the hyperparameter α can be interpreted as the number of prior observations, and β as the sum of the prior observations. The posterior mean here is: $$\frac{\alpha + n}{\beta + n\overline{x}}.$$

Occurrence of events
The exponential distribution occurs naturally when describing the lengths of the inter-arrival times in a homogeneous Poisson process.

The exponential distribution may be viewed as a continuous counterpart of the geometric distribution, which describes the number of Bernoulli trials necessary for a discrete process to change state. In contrast, the exponential distribution describes the time for a continuous process to change state.

In real-world scenarios, the assumption of a constant rate (or probability per unit time) is rarely satisfied. For example, the rate of incoming phone calls differs according to the time of day. But if we focus on a time interval during which the rate is roughly constant, such as from 2 to 4 p.m. during work days, the exponential distribution can be used as a good approximate model for the time until the next phone call arrives. Similar caveats apply to the following examples which yield approximately exponentially distributed variables:

 * The time until a radioactive particle decays, or the time between clicks of a Geiger counter
 * The time between receiving one telephone call and the next
 * The time until default (on payment to company debt holders) in reduced-form credit risk modeling

Exponential variables can also be used to model situations where certain events occur with a constant probability per unit length, such as the distance between mutations on a DNA strand, or between roadkills on a given road.

In queuing theory, the service times of agents in a system (e.g. how long it takes for a bank teller etc. to serve a customer) are often modeled as exponentially distributed variables. (The arrival of customers for instance is also modeled by the Poisson distribution if the arrivals are independent and distributed identically.) The length of a process that can be thought of as a sequence of several independent tasks follows the Erlang distribution (which is the distribution of the sum of several independent exponentially distributed variables). Reliability theory and reliability engineering also make extensive use of the exponential distribution. Because of the memoryless property of this distribution, it is well-suited to model the constant hazard rate portion of the bathtub curve used in reliability theory. It is also very convenient because it is so easy to add failure rates in a reliability model. The exponential distribution is however not appropriate to model the overall lifetime of organisms or technical devices, because the "failure rates" here are not constant: more failures occur for very young and for very old systems.

In physics, if you observe a gas at a fixed temperature and pressure in a uniform gravitational field, the heights of the various molecules also follow an approximate exponential distribution, known as the Barometric formula. This is a consequence of the entropy property mentioned below.

In hydrology, the exponential distribution is used to analyze extreme values of such variables as monthly and annual maximum values of daily rainfall and river discharge volumes.

 * The blue picture illustrates an example of fitting the exponential distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.

In operating-rooms management, the distribution of surgery duration for a category of surgeries with no typical work-content (like in an emergency room, encompassing all types of surgeries).

Prediction
Having observed a sample of n data points from an unknown exponential distribution a common task is to use these samples to make predictions about future data from the same source. A common predictive distribution over future samples is the so-called plug-in distribution, formed by plugging a suitable estimate for the rate parameter λ into the exponential density function. A common choice of estimate is the one provided by the principle of maximum likelihood, and using this yields the predictive density over a future sample xn+1, conditioned on the observed samples x = (x1, ..., xn) given by $$p_{\rm ML}(x_{n+1} \mid x_1, \ldots, x_n) = \left( \frac1{\overline{x}} \right) \exp \left( - \frac{x_{n+1}}{\overline{x}} \right).$$

The Bayesian approach provides a predictive distribution which takes into account the uncertainty of the estimated parameter, although this may depend crucially on the choice of prior.

A predictive distribution free of the issues of choosing priors that arise under the subjective Bayesian approach is

$$p_{\rm CNML}(x_{n+1} \mid x_1, \ldots, x_n) = \frac{ n^{n+1} \left( \overline{x} \right)^n }{ \left( n \overline{x} + x_{n+1} \right)^{n+1} },$$

which can be considered as
 * 1) a frequentist confidence distribution, obtained from the distribution of the pivotal quantity $${x_{n+1}}/{\overline{x}}$$;
 * 2) a profile predictive likelihood, obtained by eliminating the parameter λ from the joint likelihood of xn+1 and λ by maximization;
 * 3) an objective Bayesian predictive posterior distribution, obtained using the non-informative Jeffreys prior 1/λ;
 * 4) the Conditional Normalized Maximum Likelihood (CNML) predictive distribution, from information theoretic considerations.

The accuracy of a predictive distribution may be measured using the distance or divergence between the true exponential distribution with rate parameter, λ0, and the predictive distribution based on the sample x. The Kullback–Leibler divergence is a commonly used, parameterisation free measure of the difference between two distributions. Letting Δ(λ0||p) denote the Kullback–Leibler divergence between an exponential with rate parameter λ0 and a predictive distribution p it can be shown that

$$\begin{align} \operatorname{E}_{\lambda_0} \left[ \Delta(\lambda_0\parallel p_{\rm ML}) \right] &= \psi(n) + \frac{1}{n-1} - \log(n) \\ \operatorname{E}_{\lambda_0} \left[ \Delta(\lambda_0\parallel p_{\rm CNML}) \right] &= \psi(n) + \frac{1}{n} - \log(n) \end{align}$$

where the expectation is taken with respect to the exponential distribution with rate parameter λ0 ∈ (0, ∞), and ψ( · ) is the digamma function. It is clear that the CNML predictive distribution is strictly superior to the maximum likelihood plug-in distribution in terms of average Kullback–Leibler divergence for all sample sizes n > 0.

Random variate generation
A conceptually very simple method for generating exponential variates is based on inverse transform sampling: Given a random variate U drawn from the uniform distribution on the unit interval $(0, 1)$, the variate

$$T = F^{-1}(U)$$

has an exponential distribution, where F is the quantile function, defined by

$$F^{-1}(p)=\frac{-\ln(1-p)}{\lambda}.$$

Moreover, if U is uniform on (0, 1), then so is 1 − U. This means one can generate exponential variates as follows:

$$T = \frac{-\ln(U)}{\lambda}.$$

Other methods for generating exponential variates are discussed by Knuth and Devroye.

A fast method for generating a set of ready-ordered exponential variates without using a sorting routine is also available.

title: Exponential distribution


text:
Beyond This Horizon

Beyond This Horizon is a science fiction novel by American writer Robert A. Heinlein. It was originally published as a two-part serial in Astounding Science Fiction (April, May 1942, under the pseudonym Anson MacDonald) and then as a single volume by Fantasy Press in 1948. It was awarded a Retro-Hugo award for best novel in 2018.

Overview
The novel depicts a world in which genetic selection for increased health, longevity, and intelligence has become so widespread that the unmodified "control naturals" are a carefully managed and protected minority. Duels and the carrying of arms are socially accepted ways of maintaining civility in public. A man can wear distinctive clothing to show his unwillingness to duel, but this results in an inferior social status. The world has become an economic utopia; the "economic dividend" is so high that work has become optional. The chief economic problem uses up the economic surplus: many high-quality goods actually cost less than those of lower quality. Many people use lower-quality goods as status symbols. The government invests heavily in scientific research, but it has the side effect of further increasing productivity a decade or more later, and so long-term projects with no expected economic return are favored above anything but medical research, on the theory that longer lifespans will consume more surplus.

The story's protagonist, Hamilton Felix (surname first), is the archetypal übermensch. He is the penultimate step in a "star line" designed to breed for the highest-quality human characteristics. However, he lacks eidetic memory, which disqualifies him for what many consider to be humanity's most important occupation: that of an "encyclopedic synthesist", who analyzes the sum total of human knowledge for untapped potential. As such, he finds his life and the society in which he lives to be enjoyable but meaningless. However, when one of the synthesists seeks him out and inquires when he plans to continue his line, he finds himself drawn into an adventure that gives him purpose and also convinces him that his society is worth saving after all.

Major themes in the novel are reincarnation, the immortality of the soul, and telepathy. Felix is the product of generations of genetic engineering. He is almost but not quite the perfect human. In the second half of the book, his genetically engineered son is born, the climax of generations of genetic engineering and selective breeding and a genetically perfect human. As the son grows, he begins to develop almost-superhuman mental abilities and a surprising telepathic ability.

As the novel draws to a close, it becomes apparent that the son senses that Hamiton Felix's second child, a daughter, is the reincarnation of a wise elderly government official, who foresaw her own death and arranged to die shortly before Felix's daughter was born. The official understood that the soul is reincarnated, and in preparation for her own death and reincarnation, she was instrumental in the genetic engineering of the son and the daughter.

Reception
Anthony Boucher and J. Francis McComas characterized Beyond This Horizon as among "the finest science fiction novels of the modern crop". P. Schuyler Miller reviewed the novel favorably, saying: "in true Heinlein manner the basic theme of the book smashes the screen of action only in the closing pages".

In popular culture
In the Japanese visual novel Eden*, the term "Felix" is used in the setting to refer to genetically engineered humans with abilities similar to those described in the book, and the connection to Heinlein's work is referred to in dialogue.

Mordan Claude’s quote "An armed society is a polite society" is often cited by pro-gun groups in justifying the proposal of universal carrying of arms. The context of the quote is usually omitted, though: "Well, in the first place an armed society is a polite society. Manners are good when one may have to back up his acts with his life. For me, politeness is a sine qua non of civilization. That’s a personal evaluation only. But gun-fighting has a strong biological use. We do not have enough things that kill off the weak and the stupid these days. But to stay alive as an armed citizen a man has to be either quick with his wits or with his hands, preferably both."

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

title: Beyond This Horizon


text:
Rocket Ship Galileo

Rocket Ship Galileo, a juvenile science-fiction novel by the American writer Robert A. Heinlein, published in 1947, features three teenagers who participate in a pioneering flight to the Moon. It was the first in the Heinlein juveniles, a long and successful series of science-fiction novels published by Scribner's. Heinlein originally envisioned the novel as the first of a series of books called "Young Rocket Engineers". Publishers initially rejected the script, judging going to the Moon as "too far out".

Plot summary
After World War II, three teenage rocket experimenters are recruited by one boy's uncle, Dr. Cargraves, a renowned physicist who had worked on the Manhattan Project, to refit a conventionally powered surplus "mail rocket". It is to be converted to run on a thorium nuclear pile which boils zinc as a propellant. They use a cleared area in a military weapons test range in the desert for their work, despite prying and sabotage attempts by unknown agents.

Upon completion of the modifications, they stock the rocket, which they name the Galileo, and take off for the Moon, taking approximately three days to arrive. After establishing a semi-permanent structure based on a Quonset hut, they claim the Moon on behalf of the United Nations.

As they set up a radio to communicate with the Earth they pick up a local transmission, the sender of which promises to meet them. Instead, their ship is bombed. However, they are able to hole up undetected in their hut and succeed in ambushing the other ship when it lands, capturing the pilot. They discover that there is a Nazi base on the Moon. They bomb it from their captured ship and land. One survivor is found, revived, and questioned.

The boys also find evidence of an ancient lunar civilization, and postulate that the craters of the Moon were formed not by impacts from space, but by nuclear bombs that destroyed the alien race.

When the base's Nazi leader shoots the pilot in order to silence him, Cargraves convenes a trial and finds him guilty of murder. Cargraves prepares to execute the prisoner by ejecting him into vacuum, mostly as a bluff for information on how to fly the base's spaceship. The Nazi capitulates in the airlock and teaches them how to fly the ship back to Earth.

The boys radio the location of the hidden Nazi base on Earth to the authorities, leading to its destruction; they return as heroes.

Adaptations
The 1950 movie Destination Moon was loosely based on Rocket Ship Galileo, and Heinlein was one of three co-authors of the script. The film's plot also resembles that of "The Man Who Sold the Moon", which Heinlein wrote in 1949 but did not publish until 1951.

Critical reception
Surveying Heinlein's juvenile novels, Jack Williamson noted that while Rocket Ship Galileo remains "readable, with Heinlein's familiar themes already emerging," it was a "sometimes fumbling experiment. ... The plot is often trite, and the characters are generally thin stereotypes." Robert Wilfred Franson said that "Heinlein wants there always to be young people of the right mind and character to seize such opportunities. His novels went a long way toward educating such a class of people, and still are doing so." Andrew Baker wrote: "'Rocket Ship Galileo' shares with numerous works composed before the advent of the actual Space Program a gross underestimation of the huge costs and investment of resources needed for any jaunt outside Earth's gravitational field. (...) The idea of private people (boys in this case) being able to just take off to the Moon on their own can ultimately be traced - like so many Science Fiction themes - to the fertile mind of H. G. Wells and to the two English gentlemen quietly taking off to the Moon in The First Men in the Moon. (...) The politics of 'Galileo' are still those of the World War II anti-Nazi Alliance, not of the emerging Cold War. Had it been written a few years later, the villains would have likely been Russian Communists".

title: Rocket Ship Galileo


text:
Space Cadet

Space Cadet is a 1948 science fiction novel by Robert A. Heinlein about Matt Dodson, who joins the Interplanetary Patrol to help preserve peace in the Solar System. The story translates the standard military academy story into outer space: a boy from Iowa goes to officer school, sees action and adventure, shoulders responsibilities far beyond his experience, and becomes a man. It was published as the second of the series of Heinlein juveniles and inspired the media franchise around the character Tom Corbett, including the 1950s television series Tom Corbett, Space Cadet and radio show which made "Space Cadet" a household phrase whose meaning later shifted in popular culture.

Plot summary
In 2075, teenager Matt Dodson applies to join the prestigious Interplanetary Patrol. After a number of physical, mental, and ethics tests, he is accepted as a cadet. He makes friends with fellow recruits William "Tex" Jarman, Venus-born Oscar Jensen, and Pierre Armand from Ganymede. His first roommate is Girard Burke, the arrogant son of a wealthy spaceship builder. They are transported to the orbiting school ship PRS James Randolph for further training. Burke eventually either resigns or is asked to leave, and goes into the merchant service, but the remainder do well enough to be assigned to working Patrol ships.

Dodson, Jarman and Jensen ship out on the Aes Triplex. Their first real mission is to help search for a missing research vessel, the Pathfinder, in the asteroid belt. They find it, but all aboard are dead, the unlucky victims of a fast-moving object that punctured the ship when the armored outer airlock door was open. Before the accident, a researcher on the Pathfinder had found evidence that the planet which blew up to form the asteroids was inhabited by an intelligent species, and that the explosion had been artificial. The captain of the Aes Triplex transfers half the crew to the repaired Pathfinder so that they can take the ship and the news of the startling discovery back to Earth quickly. With the remainder (including all three cadets), he plots a slower, fuel-efficient, elliptical voyage back to Earth.

Then, he receives an urgent message to investigate an incident on Venus. He sends Lieutenant Thurlow and the cadets to the planet's surface. The lander touches down on a sinkhole, giving the crew barely enough time to get out before it disappears in the mud. With Thurlow comatose, injured when the lander fell over, Jensen assumes command. He contacts the sentient, usually friendly Venerians, but the entire party is taken captive. They soon find out why.

These particular natives had never seen human beings before, until old classmate Burke showed up in a prospecting ship. He had taken the matriarch of the local clan hostage when she refused to give him permission to exploit a rich deposit of radioactive ores. The locals promptly attacked the ship and killed his crew; Burke managed to send a message for help before being taken prisoner.

Jensen gains the matriarch's trust and convinces her that they are honorable and civilized, unlike Burke, and the Patrolmen are released. Unfortunately, neither the lander nor Burke's ship is flightworthy. To their amazement, the matriarch takes the stranded humans to the carefully preserved Astarte, the legendary first ship to set out for Venus over a century before and thought to have been lost en route. According to the log, the crew perished from disease. With the help of the natives, the cadets recommission the ship and fly it back to Venus's South Pole colony. Dodson is initially disappointed when they are not treated as heroes, but then realizes that what they accomplished was simply what was expected of Patrolmen.

Themes
The Patrol is entrusted by the worldwide Earth government with a monopoly on nuclear weapons, and is expected to maintain a credible threat to drop them on Earth from orbit as a deterrent against breaking the peace. Matt, on a visit home, causes a family argument when his parents refuse to believe that the Patrol—and especially their son—would actually bomb Iowa.

The cadets are expected to renounce their loyalty to their respective countries and replace it by a wider allegiance to humanity as a whole and to the sentient species of the Solar System. They are told the stories of four Patrol heroes/martyrs who exemplify this quality. One of them, Rivera, leaves orders to annihilate his hometown if he is held captive there during negotiations. Heinlein later expanded another of these anecdotes into "The Long Watch".

The young, idealistic Matt feels that he should be able, if the need arose, to emulate Rivera and destroy his own Iowa hometown. His father tells him such a need would never arise, since the Patrol's cosmopolitan allegiance is little more than a sham and in fact it is controlled by the "North American Federation" and serves its interests. Later, Matt's mentor in the Patrol makes him understand that if such an unlikely dilemma should arise, his commanding officer would lock him in his room rather than expect him to participate in the attack. The mentor uses this scenario to force Matt to confront the personal and political issues involved in the institutional control of atomic weapons in a more mature way.

Written almost a decade before the American Civil Rights Movement, and at a time when non-white characters were almost entirely absent from science fiction, the book also explores the theme of racism, both literally, in discussions about the cosmopolitan racial makeup of the (all-male) Patrol, and metaphorically, in its description of conflict with the Venerians. Venus is described as intensely hot and (incorrectly, as is now known) swampy, but habitable. The Venerians are at first thought to be primitive, but it is later revealed that they have a high level of technological sophistication, though developed along radically different lines than that of humans.

There is also a subplot revolving around the issue of what it means to be a good soldier. Discouraged by the intellectual demands of his Patrol training, and attracted to the glamor and esprit de corps of the Marines, Matt requests a transfer, but is dissuaded by his mentor. The mentor, dividing human motivations into three types, explains that the Patrol, which has the responsibility of holding the ultimate weapon and keeping overall peace, is manned by a certain sort of person, the man of ideals (its motto is Quis custodiet ipsos custodes?). In contrast, the Marines, the service branch which deals with ordinary military affairs, are trained to prize unquestioning loyalty and bravery as the highest ideals, and are deliberately recruited from the type of person who seeks glory and excitement. Matt belongs to the former category. The Merchant Service, by implication, is for a third category, those motivated by economic concerns — which is where Burke fits in.

The novel contains an early description of a mobile phone:

"Matt dug a candy bar out of his pouch, split it and gave half to Jarman, who accepted it gratefully. "You're a pal, Matt, I've been living on my own fat ever since breakfast -- and that's risky. Say, your telephone is sounding.

"Oh!" Matt fumbled in his pouch and got out his phone. "Hello?""

The phone "was limited by its short range to the neighborhood of an earth-side [i.e. terrestrial] relay office". A cadet avoids having to talk to his family while traveling by packing his phone in luggage.

Critical reception
Surveying Heinlein's juvenile novels, Jack Williamson characterized Space Cadet as "a long step forward. ... The characters are stronger [and] the background is carefully built, original, and convincing, the story suspenseful enough." Williamson noted that Heinlein was "perfecting the bildungsroman form that shapes the whole series."

P. Schuyler Miller gave the book a favorable review as "a first-rate historical novel of the near future," saying "So subtly has the scientific detail been interwoven with plot and action that the reader never realizes how painstakingly it has been worked out."

Tom Corbett, Space Cadet
The novel inspired Joseph Greene of Grosset & Dunlap to develop the Tom Corbett, Space Cadet comic books, television series, radio show, comic strip, and novels that were popular in the early 1950s. Greene had originally submitted a radio script for "Tom Ranger and the Space Cadets" on January 16, 1946, but it remained unperformed when Heinlein's novel was published. Heinlein influenced the evolution of "Tom Ranger" into "Tom Corbett" and launched his student astronaut title's common mention; they share credit for the popularity of both formal and later slang uses of "space cadet."

In popular culture
The Tom Corbett, Space Cadet television series and radio show made "space cadet" a household phrase. By 1955, Jackie Gleason spoke the phrase on The Honeymooners television show in an episode called "TV or Not to TV," original airdate October 1, 1955.

The popular meanings of "space cadet" later shifted in popular culture away from astronaut-in-training to indicate, by the 1960s, an "eccentric person disconnected with reality" (often implying an intimacy with hallucinogenic drugs) although by the 2010s, drug use was rarely implied by this phrase, nor was low intelligence implied; "space cadet" was more simply associated with "spacing out," wandering from present concerns, especially of others present, and being a "space case." Both the "trainee astronaut" and "person regarded as being out of touch with reality" entered the Oxford English Dictionary, though by 2014 Oxford noted that, in American English, the phrase had also recouped the positive connotations originally meant by Heinlein and Joseph Greene, the Tom Corbett, Space Cadet writer: "An enthusiast for space travel, typically a young person."

title: Space Cadet


text:
Red Planet

Red Planet is a nickname for the planet Mars, due to its surface color. It may also refer to:

 * Mission: Red Planet, a 2005 boardgame by Bruno Cathala and Bruno Faidutti
 * Red Planet (novel) by Robert A. Heinlein (1949)
 * Red Planet (miniseries), a 1994 animated adaptation of the novel
 * Red Planet, the source of the J-Jewel in The King of Braves GaoGaiGar
 * Red Planet (film), a 2000 film starring Val Kilmer
 * Red Planet (game), a BattleTech game scenario (ca. 1993)
 * Red Planet Hotels, a regional hotel chain in Indonesia, Japan, the Philippines and Thailand
 * Red Planet Mars a 1952 film based on a 1932 play Red Planet
 * "Red Planet", an episode in the game Angry Birds Space
 * "Red Planet", a song by Little Mix featuring T-Boz from their debut album, DNA (2012)
 * "Red Planet", a song by the Canadian indie band Alvvays from their eponymous debut album (2014)
 * The Red Planet, an album by Rick Wakeman (2020)

title: Red Planet


text:
Talk:Natural capital

Discussion
addition is necessary - maybe not complete.

It's a bit more than "land as capital" since air, watersheds, genes, etc., would all classify as natural capital. The "land" definition includes them... soil in particular. But soil is confined to land in a way that air, water, and genes are not.

It's this inadequacy that led to the theory of natural capital itself - land is a glaring exception sitting in the theory of economics. In fact Adam Smith and contemporaries made the point over and over again that everything they said didn't apply to land - that there was nothing good to be said about land ownership if the owner wasn't "improving" it.

Today we might interpret that as improving its soil sustainability, air and water filtration capacity, genetic diversity, etc., rather than simply its human housing and food production capacity. But it's the same principle... just a different valuation ethic.

When refactoring or adding I think we need to address and link to the more traditional militant conservative view of industrial behomeths who view exploitation as pre-eminent use of all god given natural resources .... this practice and view is still pre-eminent or "natural" would not be so scarce and still diminishing.

Another nugget. There is a stock fund firm or venture investment firm based in Seattle that invests in "green" firms because their analysis shows they have small consistent edge of .... 3% .... additional gain over time. I saw this on television .... illustrates Natural Capitalism's point about trends. I will google and see if I can find the firm's name.

http://seattletimes.nwsource.com/news/business/html98/greenf07_20000911.html

user:mirwin

Natural capital refers to the mineral, plant, and animal formations of the Earth's biosphere when viewed as a means of production of oxygen, water filter, erosion preventer, or provider of other natural services?

I think it is not clear that air and water are part of the natural capital. Shouldn't it be added ?

It is one approach to ecosystem valuation?, an alternative to the traditional view of all non-human life as passive natural resources.

all non-human life, as well as non-living parts of the planetary system - rocks, ocean and atmosphere. An ecosystem is a group of biological communities, which share an environment. Water, air, soil, living life, including human life, interact to form the ecosystem. Not only non-human life.

 * Natural Capital connects to Ecological economics and Deep Ecology, lets develop this article --Swedenborg 05:34, 18 May 2006 (UTC)

 * Can we take away "An editor has expressed a concern that the topic of this article may be unencyclopedic" tag? I see no reason to keep it on this page! --Swedenborg 21:27, 18 May 2006 (UTC)

Unencyclopedic
This article reads like an essay. Example:

"However, human knowledge and understanding of the natural environment is never complete, and therefore the boundaries of natural capital expand or contract as knowledge is gained or lost."

This type of wording has no place in an encyclopedia. 67.171.34.5 06:27, 21 May 2006 (UTC)

 * Topic is encyclopedic; execution is not. "Natural capital" is actually an economic term, very closely related to "natural resource". However, I agree that this article needs some heavy editing. I suggest to either merge this with natural resource or put up a  tag, for a start. —Matveims 23:46, 21 May 2006 (UTC)

 * Leave Topic is encyclopedic! Agree that it needs editing. Invite critics to help to develop instead of promoting deleteationastic approach. --Swedenborg 13:42, 27 May 2006 (UTC)

Can we take away unencyclopedic tag?
This article is Encyclopedic but needs cleanup and structure. I put an ecology stub notion in the end maybe that is enough? Or change the top tag to something more appropriate. I will come back later when I have some time and do some work here. --Swedenborg 09:17, 28 May 2006 (UTC)

This article and this terminology are ridiculous
The best thing I can say for this article is that it illustrates the length to which pretenders and wannabe economists will go in order to defile the classical distinction between natural resources and produced commodities. "natural capital" is a contradiction in terms intended to allow Marxists and neoclassical nincompoops to MUNGE the word "capital" to suit their political agendas.The Trucker (talk) 02:59, 29 January 2014 (UTC)

This article and this terminology are indeed ridiculous
I can only agree with Mikcob. The article reads like a weak undergraduate essay, and it would be far better to delete it than try to improve it.

Among many other problems are problems of fact. For example, the term "natural capital" was first used not by Schumacher in 1973 but by Frank Adams in 1914, in his Presidential address before the Royal Society of Canada. He used the metaphor in a context (owned and managed forests) in which it actually made sense. Its present users seem to have no need for such subtlety.

Furthermore any article on natural capital should contain a section on critical views - such as, for example, that nature has not one single attribute of capital. It is not owned, it is free, it is not inert, it cannot be increased or decreased without changing its nature, if left alone it does not depreciate, changes are generally irreversible, it is not fungible, and humans cannot create it. So in what sense is natural capital "capital"? — Preceding unsigned comment added by 213.89.210.34 (talk) 16:21, 29 September 2014 (UTC)

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SEEA EA
In March 2021, at its 52nd session, the United Nations Statistical Commission adopted CHAPTERS 1-7 of the SEEA Ecosystem Accounting (SEEA EA) "describing the accounting framework and the physical accounts", as an "international statistical standard". Concerning the parts on valuation of ecosystem services (the Natural Capital aspect of ecosystems) it "recognized that, Chapters 8-11 of the SEEA Ecosystem Accounting describe internationally recognized statistical principles and recommendations" and requested "to promptly resolve the outstanding methodological aspects in chapters 8-11 as identified in the research agenda” as well as "to make clear the different statuses" of the different chapters 1-7", thus acknowledging the great methodological uncertainties of this aspect of the natural capital concept. — Preceding unsigned comment added by 193.204.91.31 (talk) 10:03, 22 May 2022 (UTC)

Natural capital as environmental
Contains 45.127.89.47 (talk) 11:44, 25 January 2023 (UTC)

title: Talk:Natural capital


text:
Humpty Dumpty

Humpty Dumpty is a character in an English nursery rhyme, probably originally a riddle and one of the best known in the English-speaking world. He is typically portrayed as an anthropomorphic egg, though he is not explicitly described as such. The first recorded versions of the rhyme date from late eighteenth-century England and the tune from 1870 in James William Elliott's National Nursery Rhymes and Nursery Songs. Its origins are obscure, and several theories have been advanced to suggest original meanings.

Humpty Dumpty was popularized in the United States on Broadway by actor George L. Fox in the pantomime musical Humpty Dumpty. The show ran from 1868 to 1869, for a total of 483 performances. As a character and literary allusion, Humpty Dumpty has appeared or been referred to in many works of literature and popular culture, particularly English author Lewis Carroll's 1871 book Through the Looking-Glass, in which he was described as an egg. The rhyme is listed in the Roud Folk Song Index as No. 13026.

Lyrics and melody
The rhyme is one of the best known in the English language. The common text from 1882 is: Humpty Dumpty sat on a wall. Humpty Dumpty had a great fall. All the king's horses and all the king's men Couldn't put Humpty together again.

It is a single quatrain with external rhymes that follow the pattern of AABB and with a trochaic metre, which is common in nursery rhymes. The melody commonly associated with the rhyme was first recorded by composer and nursery rhyme collector James William Elliott in his National Nursery Rhymes and Nursery Songs (London, 1870), as outlined below:

Origins
The earliest known version was published in Samuel Arnold's Juvenile Amusements in 1797 with the lyrics: Humpty Dumpty sat on a wall, Humpty Dumpty had a great fall. Four-score Men and Four-score more, Could not make Humpty Dumpty where he was before.

A manuscript addition to a copy of Mother Goose's Melody published in 1803 has the modern version with a different last line: "Could not set Humpty Dumpty up again". It was published in 1810 in a version of Gammer Gurton's Garland. (Note: Original spelling variations left intact.) Humpty Dumpty sate on a wall, Humpti Dumpti had a great fall; Threescore men and threescore more, Cannot place Humpty dumpty as he was before.

In 1842, James Orchard Halliwell published a collected version as: Humpty Dumpty lay in a beck. With all his sinews around his neck; Forty Doctors and forty wrights Couldn't put Humpty Dumpty to rights!

Evidence of an alternative American version closer to the modern received rhyme quoted above is given by William Carey Richards in the issue of a children's magazine for 1843, where he comments that he had come across it as a riddle when he was five-years old and that the answer was "an egg". Humpty-dumpty sit upon a wall, Humpty-dumpty had a great fall; All the king's horses and all the king's men Couldn't put humpty-dumpty together again.

According to the Oxford English Dictionary, in the 17th century, the term "humpty dumpty" referred to a drink of brandy boiled with ale. The riddle probably exploited, for misdirection, the fact that "humpty dumpty" was also eighteenth-century reduplicative slang for a short and clumsy person. The riddle may depend upon the assumption that a clumsy person falling off a wall might not be irreparably damaged, whereas an egg would be. The rhyme is no longer posed as a riddle, since the answer is now so well known. Similar riddles have been recorded by folklorists in other languages, such as "Boule Boule" in French, "Lille Trille" in Swedish and Norwegian, and "Runtzelken-Puntzelken" or "Humpelken-Pumpelken" in different parts of Germany—although none is as widely known as Humpty Dumpty is in English.

Meaning
The rhyme does not explicitly state that the subject is an egg, possibly because it may have been originally posed as a riddle. There are also various theories of an original "Humpty Dumpty". One, advanced by Katherine Elwes Thomas in 1930 and adopted by Robert Ripley, posits that Humpty Dumpty is King Richard III of England, depicted as hunchbacked in Tudor histories and particularly in Shakespeare's play, and who was defeated, despite his armies, at Bosworth Field in 1485.

In 1785, Francis Grose's Classical Dictionary of the Vulgar Tongue noted that a "Humpty Dumpty" was "a short clumsey [sic] person of either sex, also ale boiled with brandy"; no mention was made of the rhyme.

Punch in 1842 suggested jocularly that the rhyme was a metaphor for the downfall of Cardinal Wolsey; just as Wolsey was not buried in his intended tomb, so Humpty Dumpty was not buried in his shell.

Professor David Daube suggested in The Oxford Magazine of 16 February 1956 that Humpty Dumpty was a "tortoise" siege engine, an armored frame, used unsuccessfully to approach the walls of the Parliamentary-held city of Gloucester in 1643 during the Siege of Gloucester in the English Civil War. This was on the basis of a contemporary account of the attack, but without evidence that the rhyme was connected. The theory was part of an anonymous series of articles on the origin of nursery rhymes and was widely acclaimed in academia, but it was derided by others as "ingenuity for ingenuity's sake" and declared to be a spoof. The link was nevertheless popularized by a children's opera All the King's Men by Richard Rodney Bennett, first performed in 1969.

From 1996, the website of the Colchester tourist board attributed the origin of the rhyme to a cannon recorded as used from the church of St Mary-at-the-Wall by the Royalist defenders in the siege of 1648. In 1648, Colchester was a walled town with a castle and several churches and was protected by the city wall. The story given was that a large cannon, which the website claimed was colloquially called Humpty Dumpty, was strategically placed on the wall. A shot from a Parliamentary cannon succeeded in damaging the wall beneath Humpty Dumpty, which caused the cannon to tumble to the ground. The Royalists (or Cavaliers, "all the King's men") attempted to raise Humpty Dumpty on to another part of the wall, but the cannon was so heavy that "All the King's horses and all the King's men couldn't put Humpty together again". Author Albert Jack claimed in his 2008 book Pop Goes the Weasel: The Secret Meanings of Nursery Rhymes that there were two other verses supporting this claim. Elsewhere, he claimed to have found them in an "old dusty library, [in] an even older book", but did not state what the book was or where it was found. It has been pointed out that the two additional verses are not in the style of the seventeenth century or of the existing rhyme, and that they do not fit with the earliest printed versions of the rhyme, which do not mention horses and men.

Adaptations
American actor George L. Fox (1825–1877) helped to popularise the nursery rhyme character in nineteenth-century stage productions of pantomime versions, music, and rhyme. The character is also a common literary allusion, particularly to refer to a person in an insecure position, something that would be difficult to reconstruct once broken, or a short and fat person.

Lewis Carroll's Through the Looking-Glass

Humpty Dumpty also makes an appearance in Lewis Carroll's Through the Looking-Glass (1871). There Alice remarks that Humpty is "exactly like an egg", which Humpty finds to be "very provoking" in the looking-glass world. Alice clarifies that she said he looks like an egg, not that he is one. They then go on discuss semantics and pragmatics when Humpty Dumpty says, "my name means the shape I am".

A. J. Larner suggested that Carroll's Humpty Dumpty had prosopagnosia on the basis of his description of his finding faces hard to recognise:

""The face is what one goes by, generally," Alice remarked in a thoughtful tone.

"That's just what I complain of," said Humpty Dumpty. "Your face is the same as everybody has—the two eyes,—" (marking their places in the air with his thumb) "nose in the middle, mouth under. It's always the same. Now if you had the two eyes on the same side of the nose, for instance—or the mouth at the top—that would be some help.""

James Joyce's Finnegans Wake
James Joyce used the story of Humpty Dumpty as a recurring motif of the Fall of Man in the 1939 novel Finnegans Wake. One of the most easily recognizable references is at the end of the second chapter, in the first verse of the Ballad of Persse O'Reilly:

In science
Humpty Dumpty has been used to demonstrate the second law of thermodynamics. The law describes a process known as entropy, a measure of the number of specific ways in which a system may be arranged, often taken to be a measure of "disorder". The higher the entropy, the higher the disorder. After his fall and subsequent shattering, the inability to put him together again is representative of this principle, as it would be highly unlikely (though not impossible) to return him to his earlier state of lower entropy, as the entropy of an isolated system never decreases.

title: Humpty Dumpty


text:
Between Planets

Between Planets is a juvenile science fiction novel by American writer Robert A. Heinlein, originally serialized in Blue Book magazine in 1951 as "Planets in Combat". It was published in hardcover that year by Scribner's as part of the Heinlein juveniles.

Plot summary
Don Harvey's scientist parents withdraw him from his high school in New Mexico in the middle of the term so that he can join them on Mars. The headmaster suggests that they want him out of a potential war zone, where he might be viewed suspiciously because of doubts about his loyalties. At his parents' behest, he visits an old family friend who asks him to deliver a ring to his father; security forces later arrest both of them. Harvey is released and given his ring back, after it has been examined; he is told that his friend has died of "heart failure". Only later does he realize that all deaths can be described that way.

Harvey boards a shuttle to a space station orbiting Earth. The station doubles as a transshipment terminus and a military base, armed with missiles to keep restive nations in check. On the trip up, he befriends another passenger, a Venerian "dragon" calling himself "Sir Isaac Newton". Sir Isaac, a renowned physicist, can vocalize English using a portable device.

Harvey gets caught up in the Venerian war of independence when colonial forces capture the station in a surprise raid. Most of the other travelers are sent back to Earth, while a few decide to join the rebels. Harvey is in a quandary. The spaceship to Mars has been confiscated, but he remains determined to get there, by way of Venus if necessary. Because he was born in space, with one parent from Venus and the other from Earth, he claims Venerian citizenship; more importantly, Sir Isaac vouches for him. He is allowed to tag along, which turns out to be very fortunate for Harvey. The rebels blow up the station to stir up trouble for the Earth government. When the shuttle returns to Earth with its radios disabled, the military assumes it has been booby-trapped and destroys it, killing all aboard.

On his arrival on Venus, Harvey finds that his Earth-backed money is now worthless. A banker lends him money, telling him to pay it forward. He gets a job washing dishes for his keep for Charlie, a Chinese immigrant who runs a small restaurant. He befriends a young woman, Isobel, when he tries to send a message to his parents. However, communication with Mars has been cut due to the hostilities. Harvey settles in to wait out the war, but the war comes to him.

Earth sends a force to put down the rebellion on Venus. The Venerian ships are destroyed in orbit and the ground forces are routed. Charlie is killed resisting the occupying soldiers. Harvey is rounded up and questioned by a senior security officer, who is very eager to get his hands on Harvey's ring. Luckily, Harvey had given it to Isobel for safekeeping; he does not know where she is or whether she is even alive. Before he can be interrogated with drugs, he escapes and joins the Venerian guerrilla forces.

Harvey joins the army of the Republic and becomes an effective commando. In time, he is tracked down by the leaders of the resistance, who are also looking for the ring. Isobel and her father (an important member of the rebels) are safe at the very base where Harvey is taken.

The seemingly valueless ring turns out to contain the secret of scientific breakthroughs resulting from archaeological studies of an extinct alien civilization on Mars. With Sir Isaac's assistance, the rebels use the information to build an advanced spaceship that is much faster than any other vessel in existence, with revolutionary weapons and defenses also derived from the new technology. As a combat veteran, Harvey is recruited for the maiden voyage of Little David, manning a dead man's switch with strict orders to blow up the ship if it is in danger of capture. Little David intercepts and defeats a task force of warships on their way to Mars to crush the revolt there.

Astronomy
Like many science fiction works of its period, the novel depicts both Venus and Mars as suitable for human habitation. Since no interplanetary space probes had been launched at the time, neither the extreme pressure and temperature at the surface of Venus, nor the extremely low atmospheric pressure at the surface of Mars, were known to science. Even the length of the day on Venus was not yet known.

Reception
Groff Conklin reviewed the novel favorably, calling it "a magnificently real and vivid Picture of the Possible". Boucher and McComas named it among the best sf novels of 1951, characterizing it as "more mature than most 'adult' science fiction". P. Schuyler Miller praised the novel as "very smoothly and logically put together", although he noted that it lacked the level of "elaboration of background detail" that he expected from Heinlein.

Surveying Heinlein's juvenile novels, Jack Williamson characterized Between Planets as "mov[ing] the series still farther from its juvenile origins toward grownup concerns". Although describing the plot as "pretty traditional space opera", he praised the novel for its "ably drawn" characters, its "well-imagined" background, and its "story told with zest". Williamson also noted that Heinlein closed the novel "with a vigorous statement of his unhappiness with 'the historical imperative' leading to the loss of individual freedom as governmental organizations grew".

Cartoon
Between Planets was serialized in Boys' Life magazine in 1978 as a monthly cartoon series. The story took some liberties — for instance, the "Dragons" of Venus were portrayed as humanoids and the planets' names were changed — but the spirit of the story was relatively faithful.

title: Between Planets


text:
Academy Award for Best Dance Direction

The Academy Award for Best Dance Direction was presented from 1935 to 1937, after which it was discontinued due to pressure from the directors' branch. It is the only category for which a Marx Brothers film received an Oscar nomination, for the dance number All God's Chillun Got Rhythm in A Day at the Races (1937).

title: Academy Award for Best Dance Direction


text:
Augusta, Maine

Augusta is the capital of the U.S. state of Maine and the county seat of and most populous city in Kennebec County. Augusta is included in the Lewiston-Auburn, Maine metropolitan New England city and town area. The city's population was 18,899 at the 2020 census, making it the 12th most populous city in Maine, and 3rd least populous state capital in the United States after Montpelier, Vermont, and Pierre, South Dakota.

The area was explored in 1607 by English settlers from the Popham Colony at the mouth of the Kennebec River. Before European settlement, Algonquian-speaking Indians lived in the area. In 1625, representatives of Plymouth Colony chose the east shore of the Kennebec for a trading post, which was likely built in 1628 and became known as "Cushnoc". The Kennebec Proprietors, successors to the Plymouth Company, built Fort Western near the site of the abandoned trading post in 1754 and began settlement efforts. The new village was incorporated as Hallowell in 1771, and the upriver part of town separated in 1797 to form the town of Harrington. On June 9, 1797, Harrington changed its name to Augusta and, in 1827, it was designated capital of Maine.

Augusta is the easternmost state capital in the United States. Located on the Kennebec River at the head of tide, it is the principal city in the Augusta-Waterville micropolitan statistical area and home to the University of Maine at Augusta. Because of the city's position on the Kennebec, downtown Augusta is vulnerable to floods in spring. The Maine flood of 1987, known as the "Great Flood", affected the city. Bond Brook runs from northwest to southeast through the city center, and has been called the "Home of wild Atlantic Salmon".

The city has five different residential areas, including the "west side", a historic neighborhood north of the state capitol complex, and the "east side", which is situated on the opposite side of the Kennebec. The city's northwest quadrant includes both a retail center and neighborhoods.

Augusta State Airport serves the city, offering both commercial service and general aviation. Although the airport is owned by the State of Maine, it is managed and operated by the city. Interstate 95 passes by the western outskirts of Augusta, and both U.S. 202 and U.S. 201 run through the city.

History
The area was first explored by the English of the short-lived Popham Colony in September 1607. Twenty-one years later, English settlers from the Plymouth Colony settled in the area in 1628 as part of a trading post on the Kennebec River. The settlement was known by its Native American name Cushnoc (or Coussinoc or Koussinoc), meaning "head of the tide". Fur trading was at first profitable, but because of Native uprisings and declining revenues, Plymouth Colony sold the Kennebec Patent in 1661. Cushnoc would remain unoccupied for the next 75 years.

The area around Cushnoc was inhabited by the Kennebec, a band of the larger Abenaki nation. During the 17th century, they were on friendly terms with the English settlers in the region.

A hotbed of Abenaki hostility toward British settlements was located further up the Kennebec at Norridgewock. In 1722, the tribe and its allies attacked Fort Richmond (now Richmond) and destroyed Brunswick. In response, English forces sacked Norridgewock in 1724 during Dummer's War, when the English gained tentative control of the Kennebec.

During the height of the French and Indian War, in 1754, the English colonists built a blockhouse named Fort Western at Cushnoc on the eastern bank of the Kennebec River. It was intended as a supply depot for Fort Halifax upriver, as well as a regional defense from French attack. Later, during the American Revolutionary War, Benedict Arnold and his 1,100 troops would use Fort Western as a staging area before continuing their journey up the Kennebec to the Battle of Quebec.

Cushnoc was incorporated as part of Hallowell in 1771. Known as "the Fort", it was set off and incorporated by the Massachusetts General Court in February 1797 as Harrington. In August, however, the name was changed to Augusta after Pamela Augusta Dearborn, daughter of Henry Dearborn. In 1799, it was designated as the county seat for the newly created Kennebec County.

Maine became a state in 1820 as a result of the Missouri Compromise. Augusta was designated as its capital in 1827, over the current capital of Portland, and rival communities Brunswick and Hallowell. The Maine State Legislature continued meeting in Portland, however, until the completion of the Maine State House in 1832, designed by Charles Bulfinch. Augusta was incorporated as a city in 1849. After being named the state capital and the introduction of new industry, the city flourished. In 1840 and 1850, the city ranked among the 100 largest urban populations in the country. During the next decade, however, the city was quickly bypassed by rapidly growing metropolises in the Midwest.

Excellent soil provided for agriculture, and water power from streams provided for the industry. In 1837, a dam was built across the Kennebec where the falls drop 15 feet at the head of a tide. By 1838, 10 sawmills were contracted. With the arrival of the Kennebec & Portland Railroad in 1851, Augusta became an even more productive mill town. In 1883, the property of A. & W. Sprague Company was purchased by the Edwards Manufacturing Company, which erected extensive brick mills for manufacturing cotton textiles. They imported cotton from the South for processing and export to Europe. In the late 19th century, a paper and pulp plant was constructed.

Other Augusta firms produced lumber, sash, doors, window shutters, broom handles, stone cutters' tools, shoes, headstones, ice and furniture. The city developed as a publishing and shipping center. Today, government and post-secondary education are important businesses.

Since the mid-eighteenth century, there has been a military presence in Augusta. Fort Western has not had troops garrisoned there since the 1790s, but in 1828, the U.S. Government built an arsenal to protect their interests from Britain. During the Civil War, Augusta was a rendezvous point for Union soldiers traveling to the front. Many of the soldiers camped on the green in front of the capitol building. In 1862, Camp E.D. Keyes was established in the northwestern portion of the city.

During World War I, Camp Keyes was used as a mobilization and training camp for soldiers. The camp eventually became a headquarters for the Maine National Guard. In 1929, the state legislature approved the placement of the Augusta State Airport next to the camp. As the airport grew, the use of the camp as a training facility was no longer possible. Today, it is still used for administrative and logistical purposes by the National Guard.

In the 19th century, Augusta got a regular steamboat service and the railroad. The city installed gas lights in 1859. A telephone service was available in 1880 and a local hospital in 1898. In the early 20th century, Augusta built two movie houses and a film production studio.

Downtown revitalization
For much of Augusta's history, the central business district was on and near Water Street on the west bank of the Kennebec River. The street, laid out in the late 1700s, was the location of the area's commercial and industrial life. Many fires damaged this concentrated area, including one in 1865 that destroyed nearly 100 buildings. In 1890, the first trolley line began operation down Water Street, connecting Augusta with Gardiner and Hallowell to the south.

In 1932, buses replaced the trolley line. With the completion of the Maine Turnpike and Interstate 95 in 1955, local commercial developments began to move away from Water Street and closer to the highway. Among the results was a storefront vacancy rate downtown of about 60 percent.

Since the late 2000s, there has been a renewed and ongoing focus by city officials, the Augusta Downtown Alliance, and private developers to revitalize the downtown area.

Geography
Augusta is located at 44.31056°N, -69.77944°W, making it the easternmost state capital in the United States. According to the United States Census Bureau, the city has a total area of 58.03 sqmi, of which 55.13 sqmi is land and 2.90 sqmi is water. Augusta is drained by Bond's Brook, Woromontogus Stream and the Kennebec River.

Roads
The city is crossed by Interstate 95, U.S. Route 201, State Route 11, U.S. Route 202, State Route 9, State Route 3, State Route 100, State Route 27, State Route 8, State Route 104, and State Route 105.

Bordering
Augusta borders the towns of Manchester to its west, Sidney and Vassalboro to its north, Windsor to its east, Chelsea to its south, and the city of Hallowell to its southwest.

Climate
Augusta's climate is classified as a humid continental climate (Köppen: Dfb). Summers are typically warm, rainy, and humid, while winters are cold, windy, and snowy. Spring and fall are usually mild, but conditions are widely varied, depending on wind direction and jet stream positioning.

The hottest month is July, with an average high temperature of 80 °F. The coldest month is January, with an average low of 10 °F. Most snowfall occurs from December through March. There is usually little or no snow in April and November, and snow is rare in May and October.

2010 census
As of the census of 2010, there were 19,136 people, 8,802 households, and 4,490 families residing in the city. The population density was 347.1 PD/sqmi. There were 9,756 housing units at an average density of 177.0 /sqmi. The racial makeup of the city was 94.1% White, 1.1% African American, 0.7% Native American, 1.5% Asian, 0.1% Pacific Islander, 0.4% from other races, and 2.3% from two or more races. Hispanic or Latino of any race were 1.8% of the population.

There were 8,802 households, of which 23.0% had children under the age of 18 living with them, 35.2% were married couples living together, 11.8% had a female householder with no husband present, 4.0% had a male householder with no wife present, and 49.0% were non-families. 39.8% of all households were made up of individuals, and 13.6% had someone living alone who was 65 years of age or older. The average household size was 2.08 and the average family size was 2.76.

The median age in the city was 43.2 years. 18.3% of residents were under the age of 18; 8.1% were between the ages of 18 and 24; 26% were from 25 to 44; 29.4% were from 45 to 64; and 18% were 65 years of age or older. The gender makeup of the city was 48.6% male and 51.4% female.

2000 census
As of the census of 2000, there were 18,560 people, 8,565 households, and 4,607 families residing in the city. The population density was 335.1 PD/sqmi. There were 9,480 housing units at an average density of 171.2 /sqmi. The racial makeup of the city was 96.21% White, 0.50% Black or African American, 0.48% Native American, 1.35% Asian, 0.01% Pacific Islander, 0.16% from other races, and 1.3% from two or more races. 0.86% of the population were Hispanic or Latino of any race.

There were 8,565 households, out of which 24.3% had children under the age of 18 living with them, 39.1% were married couples living together, 10.9% had a female householder with no husband present, and 46.2% were non-families. 38.3% of all households were made up of individuals, and 14.2% had someone living alone who was 65 years of age or older. The average household size was 2.10 and the average family size was 2.77.

In the city, the population was spread out, with 20.5% under the age of 18, 8.7% from 18 to 24, 28.3% from 25 to 44, 24.8% from 45 to 64, and 17.7% who were 65 years of age or older. The median age was 40 years. For every 100 females, there were 89.9 males. For every 100 females age 18 and over, there were 87.5 males.

The median income for a household in the city was $29,921, and the median income for a family was $42,230. Males had a median income of $31,209 versus $22,548 for females. The per capita income for the city was $19,145. About 11.4% of families and 15.0% of the population were below the poverty line, including 19.2% of those under age 18 and 9.8% of those age 65 or over.

Local government
Augusta is governed by a mayor and council-manager system. The City Council oversees all City government activities and establishes the legislative policies of the city, adopts and amends ordinances and local laws, appropriates municipal resources, and sets the tax rate. The City Manager serves as the chief executive officer and purchasing agent of the city. The mayor presides at all meetings of the council, and is recognized ceremonially as the official head of the city.

The city maintains a police department; it is remarkable for not having had an officer killed in the line of duty for over a century.

Political makeup
Augusta has historically been Democratic. In the 2012 presidential election, Barack Obama received 5,192 of the votes to Mitt Romney's 3,339.

In the 2020 presidential election, Joe Biden won 5,248 votes to Donald Trump's 4,155.

The city has not voted for a Republican presidential candidate since George H. W. Bush in the Republican landslide of 1988. Democrats are the majority political affiliation in all four voting wards. There are more voters who are not enrolled than there are registered Republicans in the city.

 * Voter registration

Education
There are five public schools, one private school, and one college (the University of Maine at Augusta). There are two public libraries in Augusta, the city-operated Lithgow Public Library and the Maine State Library.

Farrington, Gilbert, Hussey, and Lincoln are the four public elementary schools that are located in the city.

Cony serves students in grades 7–12 from Augusta and the surrounding towns; Cony comprises Cony Middle School and Cony High School.

St. Michaels is a private Catholic school; it charges tuition to its students.

The University of Maine at Augusta is third-largest university in the University of Maine System.

Printed media

 * Kennebec Journal, daily newspaper for capital area
 * Uncle Henry's, weekly classified adverts publication

Radio

 * WJZN, oldies
 * WMDR, religious
 * WMME-FM, top-40
 * WTOS-FM, rock
 * WVQM, talk
 * WWTP, religious

Television
Augusta is part of the Portland, Maine television market, and receives most of that market's channels. WCBB channel 10, licensed to Augusta, is the local television outlet for the Maine Public Broadcasting Network.

Transportation
Interstate 95 passes by the western outskirts of Augusta. U.S. 202 runs east–west through the city. U.S. 201 runs north–south through the city.

Augusta State Airport (AUG), in the western part of the city, has commercial flights.

Sites of interest

 * Blaine House
 * Fort Western
 * Holocaust and Human Rights Center of Maine at the University of Maine at Augusta
 * Lithgow Public Library
 * Maine State House
 * Maine State Museum
 * Viles Arboretum

Notable people

 * Ambrose Abbott, state legislator
 * Martha Ballard, midwife
 * James G. Blaine, Secretary of State and presidential nominee
 * Horatio Bridge, navy officer
 * William Bridgeo, state representative and resident of Augusta
 * Julia Clukey, 2010 Olympic luger
 * Beverly Daggett, President of the Maine Senate
 * Olive E. Dana, short-story writer, essayist, poet
 * Melville Fuller, Chief Justice of the United States Supreme Court
 * George Huntington Hartford, owner of Great Atlantic and Pacific Tea Company (A&P), the country's largest food retailer at the time of his death
 * John F. Hill, former Maine governor
 * Robert Deniston Hume, Oregon politician and businessman
 * Eastman Johnson, artist
 * Roger Katz, mayor of Augusta and state legislator
 * George W. Ladd, U.S. congressman
 * Dorianne Laux, poet
 * Sumner Lipman, state legislator and attorney
 * Henry A. McMasters, recipient of the Medal of Honor
 * Rachel Nichols, actress
 * Frederick G. Payne, Mayor of Augusta and 60th governor of Maine
 * David Peoples, athlete and golfer
 * Frederick W. Plaisted, mayor of Augusta, 48th governor of Maine
 * John F. Potter, U.S. congressman, judge
 * Travis Roy, hockey player
 * Luther Severance, publisher, U.S. congressman and senator
 * Olympia Snowe, U.S. senator
 * John L. Stevens, U.S. minister to Kingdom of Hawaii, accused of attempting to overthrow Hawaiian queen, 1893
 * Judith Tarr, fantasy and science fiction author
 * Manch Wheeler, quarterback with the Buffalo Bills
 * Gil Whitney, television news anchorman and meteorologist
 * Reuel Williams, U.S. senator
 * Willard G. Wyman, general

title: Augusta, Maine


text:
Starman Jones

Starman Jones, a 1953 science-fiction novel by Robert A. Heinlein, features a farm boy who wants to go to the stars. Charles Scribner's Sons published the book as part of the Heinlein juveniles series.

Plot summary
Max Jones works the family farm in the Ozark Mountains. With his father dead and his stepmother marrying a man he detests, Max runs away from home, taking his late uncle's astrogation manuals.

Most occupations are tightly controlled by guilds, with hereditary memberships. Since his uncle had been a member of the Astrogators' Guild and had had no children, Max hopes that before he died, his uncle had named him his heir. He begins hitchhiking towards Earthport to find out. Along the way, he finds a friendly face in hobo Sam Anderson, who later alludes to being a deserter from the Imperial Marines. Sam feeds Max and offers good advice, though he later absconds with Max's valuable manuals.

At the guild's headquarters, Max is disappointed to find that he had not been named as an heir, but he receives his uncle's substantial security deposit for his manuals. Max learns that Sam had returned the manuals and tried to claim the deposit for himself.

By chance, he runs into an apologetic Sam. With Max's money, Sam is able to finagle them jobs aboard a starship using forged records of service as crewmen aboard other starships. Max signs on as a steward's mate third class, and then he absorbs the contents of the Stewards' Guild manual using his eidetic memory. Among his duties is caring for several animals, including passengers' pets. When Eldreth "Ellie" Coburn visits her pet, an alien, semi-intelligent "spider puppy" that Max has befriended, she learns that he can play three-dimensional chess, and challenges him to a game. A champion player, she diplomatically lets him win. Meanwhile, Sam rises to the position of master-at-arms.

When, through Ellie's machinations, the ship's officers discover that Max had learned astrogation from his uncle, Max is promoted to the undermanned command deck. Under the tutelage of Chief Astrogator Hendrix and Chief Computerman Kelly, he becomes a probationary apprentice chartsman, then a probationary astrogator. In a meeting with Hendrix, Max reluctantly admits to faking his record to get into space. Hendrix defers the matter until their return to Earth. The Asgard then departs for Halcyon, a colony planet orbiting Nu Pegasi.

When Hendrix dies, the astrogation department is left dangerously shorthanded. The aging captain tries to take his place, but is not up to the task. When Max detects a critical error in his real-time calculations leading up to a transition (an instantaneous jump to another region of space), neither the captain nor Assistant Astrogator Simes believe him, and the ship becomes lost.

They locate a habitable world, which Ellie names Charity, and the passengers become colonists. Meanwhile, the crew continues to try to figure out where they are and whether they can return to Earth. Unfortunately, it turns out the planet is already inhabited by hostile centaur-like sapients. Max and Ellie are captured, but Ellie's pet is able to guide Sam to them. They escape, though Sam is killed covering their retreat. Upon his return, Max is informed that the captain has died. Simes tried to take command illegally and was killed by Sam, leaving Max as the only remaining astrogator. To make matters worse, Simes hid or destroyed the astrogation manuals.

Vastly outnumbered by the natives, the humans are forced to attempt a perilous return to known space by reversing the erroneous transition. Max must pilot the ship; he must also supply the missing astrogation tables from memory. To add to his burdens, the remaining officers inform Max that he must take command, as the captain must be an astrogator. The pressure is immense, but Max succeeds and the ship returns to known space.

Max pays heavy fines, but is allowed to join the Astrogators' Guild, and is assigned as an assistant astrogator aboard another starship. However, he loses any chance for a romantic relationship with Eldreth; she returns home to marry her boyfriend. Max accepts this with mixed feelings, but looks forward to his new career.

Reception
Groff Conklin in 1954 found the novel to be "a richly textured and thoroughly mature tale" and the best of the seven Heinlein juveniles available. Anthony Boucher and J. Francis McComas praised it for its "good character-development, rousing adventure-telling, and brilliant creation of several forms of extra-Terrestrial life". P. Schuyler Miller ranked it "close to the best in mainline science fiction".

New York Times reviewer Villiers Gerson declared Starman Jones to be "superior science-fiction. ... carefully plotted, lucidly and beautifully written".

Surveying Heinlein's juvenile novels, Jack Williamson described Starman Jones as "a classic example of the bildungsroman pattern" and noted that "with its bold symbolism, the book makes a universal appeal". Despite "coincidence and occasional melodrama" in the plotting, Williamson concluded that "the novel is a fine juvenile [which] reflects hopes and fears we all have known".

Damon Knight wrote that in Starman Jones "Heinlein is doing something more than just earning a living at the work he does supremely well: he's preparing a whole generation – the generation that will live to see the year 2000 – for the Age of Space that's as real to him now as it will be, must be, to them."

Adaptation to other media
Although Heinlein rarely permitted dramatic adaptations of his work, he authorized Douglas L. Lieberman to stage Starman Jones at the Goodman Children's Theater in Chicago. Written and directed by Lieberman, the 2-act play ran for 25 performances in 1972. The title role was played by Charles Fleischer, who later performed the voice of Roger Rabbit in Hollywood. In 1974, Avon Books published the script as part of the anthology Contemporary Children's Theater edited by Betty Jean Lifton.

title: Starman Jones