Joke

A joke is a short story or short series of words spoken or communicated with the intent of being laughed at or found humorous by the listener or reader. A practical joke differs in that the humour is not verbal, but mainly visual (e.g. putting a custard pie in somebody's face).

Most jokes contain two components: joke setup (for example, "A man walks into a bar...") and a punchline, which, when juxtaposed with the setup, provides the necessary irony to elicit laughter from the audience.

Psychology of jokes

Why we laugh has been the subject of serious academic study, examples being:

  • Sigmund Freud's "Jokes and Their Relationship to the Unconscious".
  • Marvin Minsky in Society of Mind.
  • Edward de Bono in "The mechanism of the mind" and "I am right, you are wrong".

Laughter, the intended human reaction to jokes, is healthful in moderation, uses the stomach muscles, and releases endorphins, natural happiness-inducing chemicals, into the bloodstream.

One of the most complete and informative books on different types of jokes and how to tell them is Isaac Asimov's Treasury of Humor, which encompasses several broad categories of humor, and gives useful tips on how to tell them, who to tell them to, and ways to change the joke to fit your audience.

Types of jokes

Jokes often depend for humour on the unexpected, the mildly taboo (which can include the distasteful or socially improper), or the playing on stereotypes and other cultural myths. Many jokes fit into more than one category.

Mathematical jokes

Main article: Mathematical joke

There are numerous jokes related to mathematics. Many of them are in-jokes, but may also be understandable by laymen.

A series of them parodies mathematical/logical chains of reason.

  • Mathematical proof:
  • Logic

Jokes in a certain category superficially look like math, but their essence is more akin to chemical composition.

Yo' mama jokes

Main article: The dozens. Jokes of this kind originate in the dozens, an African-American custom with West African roots in which two competitors -- usually males -- go head to head in a competition of comedic, often ribald, trash-talk. The target of the traded insults is most often the opponents' mothers, but can involve other family members as well.

  • Yo mama's so dumb when your dad said it's chilly outside, she ran out with a spoon.
  • Yo mama so dark that she can leave fingerprints on charcoal.
  • Yo mama so fat when she gets on the scale it says to be continued.
  • Yo mama so fat, when her pager goes off, people think she's backing up.
  • Yo mama's glasses are so thick, she can see the future.

Political jokes

Political jokes tell about politicians and heads of states. There are two large categories of this type of jokes. The first one makes fun of a negative attitude to political opponents or to politicians in general. The second one makes fun of political cliches, mottos, catch phrases or simply blunders of politicians.

Examples

A related subcategory is lawyer jokes plays on the commonly-held stereotypes about lawyers.

The following joke circulates for quite some time, with many different versions for <President> and <Other Country>.


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The following joke circulates for quite some time, with many different versions for <President> and <Other Country>. Note that this power spectral density corresponds to a delta function for the covariance function of w(t). A related subcategory is lawyer jokes plays on the commonly-held stereotypes about lawyers. so that w(t) is a white noise random process with zero mean and constant, unit power spectral density. The second one makes fun of political cliches, mottos, catch phrases or simply blunders of politicians. The final form of the whitening procedure is as follows:. The first one makes fun of a negative attitude to political opponents or to politicians in general. Additionally, we must be sure that H(ω) is strictly positive for all so that Hinv(ω) does not have any singularities.

There are two large categories of this type of jokes. We choose the minimum phase filter so that the resulting inverse filter is stable. Political jokes tell about politicians and heads of states. Choosing the minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then whiten x(t) with the following inverse filter. The target of the traded insults is most often the opponents' mothers, but can involve other family members as well. We factor the power spectral density Sx(ω) as described above. Main article: The dozens. Jokes of this kind originate in the dozens, an African-American custom with West African roots in which two competitors -- usually males -- go head to head in a competition of comedic, often ribald, trash-talk. We can whiten this signal using frequency domain techniques.

Jokes in a certain category superficially look like math, but their essence is more akin to chemical composition. Suppose we have a wide-sense stationary, continuous-time random process defined with the same mean μ, covariance function Kx(τ), and power spectral density Sx(ω) as above. A series of them parodies mathematical/logical chains of reason. Thus, the resultant signal has the same 2nd moment properties as the desired signal x(t). Many of them are in-jokes, but may also be understandable by laymen. where w(t) is a continuous-time, white-noise signal with the following 1st and 2nd moment properties:. There are numerous jokes related to mathematics. We can simulate x(t) by constructing the following linear, time-invariant filter.

Main article: Mathematical joke. Choosing a minimum phase H(ω) so that its poles and zeros lie inside the left half s-plane, we can then simulate x(t) with H(ω) as the transfer function of the filter. Many jokes fit into more than one category. If Sx(ω) is a rational function, we can then factor it into pole-zero form as. Jokes often depend for humour on the unexpected, the mildly taboo (which can include the distasteful or socially improper), or the playing on stereotypes and other cultural myths. if and only if Sx(ω) satisfies the Paley-Wiener criterion. One of the most complete and informative books on different types of jokes and how to tell them is Isaac Asimov's Treasury of Humor, which encompasses several broad categories of humor, and gives useful tips on how to tell them, who to tell them to, and ways to change the joke to fit your audience. Because Kx(τ) is Hermitian symmetric and positive semi-definite, it follows that Sx(ω) is real and can be factored as.

Laughter, the intended human reaction to jokes, is healthful in moderation, uses the stomach muscles, and releases endorphins, natural happiness-inducing chemicals, into the bloodstream. We can simulate this signal using frequency domain techniques. Why we laugh has been the subject of serious academic study, examples being:. and power spectral density. . We can simulate any wide-sense stationary, continuous-time random process with constant mean μ and covariance function. Most jokes contain two components: joke setup (for example, "A man walks into a bar...") and a punchline, which, when juxtaposed with the setup, provides the necessary irony to elicit laughter from the audience. For whitening, we feed any arbitrary random signal into a specially chosen filter so that the output of the filter is a white noise signal.

putting a custard pie in somebody's face). We choose the filter so that the output signal simulates the 1st and 2nd moments of any arbitrary random process. A practical joke differs in that the humour is not verbal, but mainly visual (e.g. For simulating, we create a filter into which we feed a white noise signal. A joke is a short story or short series of words spoken or communicated with the intent of being laughed at or found humorous by the listener or reader. We can extend the same two concepts of simulating and whitening to the case of continuous time random signals or processes. Yo mama's glasses are so thick, she can see the future. Thus, with the above transformation, we can whiten the random vector to have zero mean and the identity covariance matrix.

Yo mama so fat, when her pager goes off, people think she's backing up. By diagonalizing Kxx, we get the following:. Yo mama so fat when she gets on the scale it says to be continued. and covariance matrix. Yo mama so dark that she can leave fingerprints on charcoal. Thus, the output of this transformation has expectation. Yo mama's so dumb when your dad said it's chilly outside, she ran out with a spoon. The method for whitening a vector with mean and covariance matrix Kxx is to perform the following calculation:.

Logic

. and covariance matrix. Mathematical proof:
. Thus, the output of this transformation has expectation. Edward de Bono in "The mechanism of the mind" and "I am right, you are wrong". where. Marvin Minsky in Society of Mind. We can simulate the 1st and 2nd moment properties of this random vector with mean and covariance matrix Kxx via the following transformation of a white vector :.

Sigmund Freud's "Jokes and Their Relationship to the Unconscious". where E is the orthogonal matrix of eigenvectors and Λ is the diagonal matrix of eigenvalues. Since this matrix is Hermitian symmetric and positive semidefinite, by the spectral theorem from linear algebra, we can diagonalize or factor the matrix in the following way. Suppose that a random vector has covariance matrix Kxx. These concepts are also used in data compression.

These two ideas are crucial in applications such as channel estimation and channel equalization in communications and audio. To whiten an arbitrary random vector, we transform it by a different carefully chosen matrix so that the output random vector is a white random vector. We choose the transformation matrix so that the mean and covariance matrix of the transformed white random vector matches the mean and covariance matrix of the arbitrary random vector that we are simulating. To simulate an arbitrary random vector, we transform a white random vector with a carefully chosen matrix.

Two theoretical applications using a white random vector are the simulation and whitening of another arbitrary random vector. Since this power spectral density is the same at all frequencies, we call it white as an analogy to the frequency spectrum of white light. since the Fourier transform of the delta function is equal to 1. The above autocorrelation function implies the following power spectral density.

I.e., it is a zero mean process for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function. A continuous time random process w(t) where is a white noise process if and only if its mean function and autocorrelation function satisfy the following:. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation. I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix.

A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:. White noise machines are sold as privacy enhancers and sleep aids. White noise can be used to disorient individuals prior to interrogation and may be used as part of sensory deprivation techniques. White noise is used as the basis of some random number generators.

He or she can then adjust the overall EQ to ensure a balanced mix. To set up the EQ for a concert or other performance in a venue, a short burst of pink noise is sent through the PA system and monitored from various points in the venue so that the engineer can tell if the acoustics of the building naturally boost or cut any frequencies. It is also used to generate impulse responses. It is used extensively in audio synthesis, typically to recreate percussive instruments such as cymbals which have high noise content in their frequency domain.

White noise has also been used in electronic music, where it is used either directly or as an input for a filter to create other types of noise signal. urban traffic noise). White noise is used by some sirens for emergency vehicles, due to its ability to cut through background noise (e.g. Here in order to submerge distracting, undesirable noises (for example conversations, etc.,) in interior spaces, a constant low level of noise is generated and provided as a background sound.

One use for white noise is in the field of architectural acoustics. There are also other "colors" of noise, the most commonly used being pink and brown. White noise is the generalized mean-square derivative of the Wiener process or Brownian motion. Gaussian white noise has the useful statistical property that its values are independent (see Statistical independence).

These models are used so frequently that the term additive white Gaussian noise has a standard abbreviation: AWGN. Gaussian white noise is a good approximation of many real-world situations and generates mathematically tractable models. Thus, the two words "Gaussian" and "white" are often both specified in mathematical models of systems. However, neither property implies the other.

It is often incorrectly assumed that Gaussian noise (see normal distribution) is necessarily white noise. Noise having a continuous distribution, such as a normal distribution, can of course be white. For example, a binary signal which can only take on the values 1 or 0 will be white if the sequence of zeros and ones is statistically uncorrelated. Any distribution of values is possible (although it must have zero DC component).

Being uncorrelated in time does not however restrict the values a signal can take. The image to the right displays a finite length, discrete time realization of a white noise process generated from a computer. the distribution of a signal across all angles in the night sky). The signal is then "white" in the spatial frequency domain (this is equally true for signals in the angular frequency domain, e.g.

The term white noise is also commonly applied to a noise signal in the spatial domain which has zero autocorrelation with itself over the relevant space dimensions. . In practice, a signal can be "white" with a flat spectrum over a defined frequency band. By having power at all frequencies, the total power of such a signal is infinite.

An infinite-bandwidth white noise signal is purely a theoretical construct. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. White noise () is a random signal (or process) with a flat power spectral density.

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