text:
Talk:Chastity

Pagan Beliefs?
The section on Paganism under "Eastern Religion" should be removed. Paganism is not one religion and it does not include only eastern religions. Furthermore how can you generalize over a category of unrelated religions like this? 202.89.191.178 (talk) 08:55, 21 November 2008 (UTC)

 * I assume that new-agers and neopagans (predominantly actually living in Western countries) is what is meant... AnonMoos (talk) 12:33, 21 November 2008 (UTC)

Older comments
In wikipedia, it is definitely okay to describe different points of view in the articles, but I think we should try to avoid stating these views as facts. Alkas 17:43, 14 September 2007 (UTC)
 * I felt the clothing section needed rewording to maintain npov. The sentence "Premarital sexual abstinence, which should be easy and natural to maintain..." seems like an opinion to me.
 * I also removed the reference to virgins, as it seemed arbitrary.

I tried to explain the part about virgins better. I believe it is relevant for this article to point out how the chastity of virgins can be undermined by immodest dress. Jpritikin 12:24, 15 September 2007 (UTC)

Removed two paragraphs: - One paragraph about clothing. This seems unrelated to me. Please refrain from straying away from the main article. If you feel that the clothing issue needs to be addressed, please add a section rather then including this paragraph in the intro.

- One paragraph about the virtues of chastity. I understand your point of view, but I feel that this is your personal opinion rather than a definition of chastity. If you feel that this issue needs to be addressed in this article, please think about adding a section. In this section you can describe these opinions. However, please try to avoid stating opinions as facts, instead describe them as opinions of certain social groups. Alkas 20:58, 13 September 2007 (UTC)

The terms "pederasty" and "pedagogy" are reversed- pederasty is sexual, not pedagogy. -- 04:19, 30 June 2007 24.128.51.174

I think the first sentence isn't NPOV in proclaiming chastity as the "state of sexual purity", without qualification along the lines of "according to most mainstream Christian doctrine" (or something more accurate if that isn't viewed accurate). Alternatively, would it be fair to just delete references to "sexual purity" and just stick to the facts - no sex if you're not married, sex only with your spouse if you are? --Robert Merkel

This most seems to duplicate sexual abstinence... I ponder merging. Martin

Merge away Martin.

I removed

"Chastity" can be used to refer to other sexual recommendations:
 * Sex should be solely for the purpose of biological reproduction. This form of chastity limits sexual activity to fertile heterosexual couples who are not using contraception.

This is recommended by some groups, but I have never heard of a case where 'chastity' is used to describe whether or not you are using contraception.

DJ Clayworth 15:56, 4 Dec 2003 (UTC)

 * I did the merge. :) Martin 00:19, 15 Feb 2004 (UTC)

Oh dear, I think the merge is just a radical misconception. But I won't argue, it's so obvious... Pfortuny 17:25, 15 Feb 2004 (UTC)

Undid redirect, wrote article
I though redirecting chastity to sexual abstinence addresses a very superficial and narrow point-of-view, so I wrote an article which I think is fairly NPOV. For those of you who would like to see an example of chastity as part of a documented system of ethics, look here.

The article is very brief. Please expand to include examples from other ethical systems. In particular, I have little knowledge of far eastern ethical systems and religions. --Mm35173 14:31, 19 September 2005 (UTC)

 * I'm afraid I don't quite understand how "coitus within the context of marital fidelity" can be considered chastity. Also, while I know many Baptist groups prohibit dancing, I don't know whether they'd consider it a violation of chastity. If so, it might be added to the list of possible offenses against chastity. --Angr/undefined 22:31, 17 October 2005 (UTC)
 * "The acts in marriage by which the intimate and chaste union of the spouses takes place are noble and honorable; the truly human performance of these acts fosters the self-giving they signify and enriches the spouses in joy and gratitude." Sexuality is a source of joy and pleasure:" - Catechism of the Catholic Church. Also, St. Ambrose said, "There are three forms of the virtue of chastity: the first is that of spouses, the second that of widows, and the third that of virgins. We do not praise any one of them to the exclusion of the others. . . . This is what makes for the richness of the discipline of the Church." The Baptists' proscription of dancing is very interesting. Is that because they think that dancing is an expression of sexuality which is contrary to God's plan, or is it merely a mechanism to prevent temptation? If it is the former, then yes, it would be unchaste in the Catholic sense of the word, but if it is the latter, then it is not. --24.176.68.73 14:25, 19 October 2005 (UTC)
 * Maybe we should be more explicit about what is a Roman Catholic definition of "chastity" on this page then. Merriam-Webster's dictionary has two relevant definitions: "abstention from any sexual intercourse reprobated by religion or condemned by morality" (by which definition married people can engage in sex and still be chaste; the R.C. definition) and "abstention from all sexual intercourse" (by which definition they can't; not the R.C. definition). As for the Baptists' proscription on dancing, I can't say for sure because I'm not a Baptist, and not all Baptists prohibit it (there are as many different Baptist theologies as there are Baptist churches, because they're organized congregationally), but I think those that do condemn it do so because they fear it will arouse lust, rather than because dancing is itself a sexual act. I suspect even married people aren't allowed to dance with each other, though. --Angr/undefined 17:09, 19 October 2005 (UTC)

Since the very word (and the notion) predates christianity, and is not limited to Abrahamic religions, it is only linguistic logic that the word remains in use as (at least historically, forever) a moral/religious concept, while a more distant, descriptive term as sexual abstinence belongs in a different, profane semantic register, so DON'T merge, whatever you do; and yes, the precise implemenatation does differ per religion, and may even shift over time Fastifex 12:23, 21 October 2005 (UTC)
 * To what I said above I might add that the "abstention from all sexual intercourse" defintion of chastity might well be the Shaker view; at any rate they didn't marry and could only have children by adopting them. I don't know whether they used the word "chastity" to define their insistence on celibacy, though. --Angr/undefined 12:39, 21 October 2005 (UTC)
 * It seems they did, according to, so I'm adding the information. --Angr/undefined 12:46, 21 October 2005 (UTC)

Removed portions
The paragraph on vows of chastity originally read:
 * Vows of chastity can also be taken by laymen, either as part of an argoasied religious life (such as Catholic beguins and begards) or on an individual basis, as a voluntary act of devotion and/or as part of an ascetic lifestyle, often devoted to contemplation.

I edited this to remove the words "argoasied" (which seems to be a typo, but I can't tell for what), "beguin" (which means "infatuation" and so makes no sense in this context), and "begard" (which as far as I can tell is not a word of English). --Angr (t·c) 06:21, 14 December 2005 (UTC)

 * I would guess that "argoasied" was originally meant to be "organized", as it's the only word I can think of that would work in that context and shares a number of letters and letter combonations (nearly all; o, a, i, rg, ed. Also, in the British spelling system, sometimes s is used for what in the American spelling system is spelled with a z). It would make perfect sense in that context, as I've never really heard of "Vows of Chastity" being taken outside of the context of a religious organization or group (I have seen the term "Abstinence Pledge" used in reference to sexual abstinence and used in secular contexts, usually as a part of sex ed, especially abstinence-only sex ed, though). Your guess is still as good as mine on "begards", though. :P Runa27 05:09, 15 July 2006 (UTC)

 * Good guessing- organized is right; the other pair you couldn't guess, it refers to a Catholic type of open convent-life without formal vows (so technically not clergy) predominantly found in the Low Countries, where they are called in my native Dutch Begijnen (most are women, still o few 'begijnhoven'=convents) and Begarden (men), but tanslations into French vary, and I guess also in English - Catholic Encyclopaedia and Etymology On Line both use Beguines & Beghards, so that's probably the best choice. Fastifex 13:46, 15 July 2006 (UTC)
 * Thanks, Fastifex. I've restored the bit about beguines and beghards now that you've explained what they are, and added links to the relevant articles. User:Angr 14:58, 15 July 2006 (UTC)

Natural Family Planning an Offense Against Chastity?
Is their a source for this, because this surely is NOT the Catholic view, or any other Christian view that supports NFP as far as I know. NFP would be seen as promoting chastity not violating it. (Assuming no argument, will change this portion later) -- Jbamb 20:56, 18 December 2005 (UTC)

Never mind, the organization was unclear and I misread. -- Jbamb 20:59, 18 December 2005 (UTC)

Celibacy is not Chastity is not Abstinence
This page is one big muddle. Although in common usage today celibacy chastity and abstinence all pretty much just mean "not having sex" that is not their historical or current religious meaning, which is what the page is supposedly here to explain.

 * Celibacy means renunciation of marriage (and necessarily includes abstinence)
 * Chastity means godly sexual behavior according to your position in life. Historically that has meant virginity and modesty before marriage, monogamous fertility within marriage, and abstinence for those in religious order
 * Abstinence means not having sex, and is always part of celibacy but not always part of chastity.

These different categories really need to be explained. DanB DanD 18:25, 9 August 2006 (UTC)

 * The problem is, the definitions are different from culture to culture and religion to religion. Somewhere on this talk page I've mentioned two dictionary definitions of "chastity", and the fact that for the Shakers at least, "chastity" entails both celibacy and abstinence, while for Roman Catholics it does not. We cannot stick to just one definition and chastity and still retain an NPOV. User:Angr 18:51, 9 August 2006 (UTC)

 * Well, I think an NPoV would view the idea historically, and a historical view would acknowledge the dominance of a Catholic-and-Orthodox-shaped conception of sexual morality--the Shakers are cool but they didn't exactly make Western culture. And they were consciously reacting against a culture that meant something different by "chastity" than they did.
 * Not sure what to do about a non-Western context. The word is specifically European, but should there be a goal of finding analogous concepts in other cultures, or treat the article as specifically about one evolving cultural form?, with separate articles about sexual rules in other religions and cultures where they occur? Trouble is it's unlikely any wiki-folk know enough about non-western cultures to say much that's useful about their traditions. —The preceding unsigned comment was added by DanB DanD (talk • contribs) 19:36, 9 August 2006 (UTC)
 * Certainly more space can be given to Catholic and Orthodox views of chastity than to Shaker views, but we should also be careful not to define chastity only in terms of one group's definition. And certainly the article should not be written in such a way as to preclude the possibility of non-Western views being added in the future, even if you and I aren't able to add anything. Even Westerners can go to the library and do some research on non-Western views of chastity. User:Angr 19:55, 9 August 2006 (UTC)

 * Actually, having now read through the sexual abstinence page, I think that's where non-Western perspectives should go--or on a more general "religion and sexuality" page, or a specific page of their own if the treatment is in-depth.
 * It was decided to keep a separate page for "Chastity" instead of merging it with sexual abstinence, so I think to justify the separation this page ought to be a detailed study of a culturally specific concept. "Chastity" is a Christian/European-derived conception of right sexual behavior, so I (now) don't think it would be accurate to try to fold ideas from other cultures into that.
 * One thing the page does need is pre-Christian conceptions of sexual morality in Europe that influenced the idea of chastity--Lucretia in Rome and so on.
 * DanB DanD 20:16, 9 August 2006 (UTC)

Cultural bias
Article is missing the Islamic sense of chastity which is quite strong and part of the Sharia Law.

In addition, there is the whole Mediterranean sense of "honor" that is not associated with any one country or people but which seems to (historically in most places and still today in some places) require a substantial protection of women.

--Blue Tie 14:05, 18 September 2006 (UTC)

Then site your Islamic beliefs and sources. Site your Islamic leaders exegesis regarding chastity. This is the Catholic belief as handed down from the time of Jesus before Muhammed by 600 years. And please explain how you can have more than one wife, and please explain why killing is part of Islamic holy tradition.

Here is the difference and I hope resolution to this mark: IF needed I can make this a multi-part series.

Chastity is stateless. Sexually this means no sexual activity. Celibacy is related to the state you are in:

Being Celibate in the single life or holy priestly office means no masturbation or fornication, and forcing your will to remove such thoughts from your brain. Jesus says,"If you look at a woman with lust, you have already committed adultery with her in your heart." This means we need complete renewal of mind and body.

Celibacy to the married life means being faithful to your spouse, meaning only having sex with your spouse. This is celibacy in marriage.

This philosohpy has many citings. Lets start with the Catechism of the Catholic Church then we will cite the sources from that book, which is the Bible.

Proof for the state of marriage and the allowance of sex in marriage CoCC (Page 446, Article 7, The Sacrament of Matrimony 1601)

"The matrimonial covenant, by which a man and a woman establish between themselves a partnership of the whole of life, is by its nature ordered toward the good of the spouses and the procreation and education of offspring; this covenant between baptized persons has been raised by Christ the Lord to the dignity of the Sacrament" (CIC, can. 1055 paragraph 1; cf. 48 paragraph 1. )

We are formed in the image and likeness of God, Rev 19:7,9; cf. Gen 1:26-27

Marriage as the order of creation: "Be fruitful and multiply"  Gen 1:28; cf 1:31

It is not good that man should be alone Gen 2:18 The woman, "flesh of his flesh" his equal, his nearest in all things, is given to him by God as a "helpmate"; thus she represents God from whom all help comes and into which the man pours his love into. Gen 2:18-25 "Therefore a man leaves his father and his mother and cleaves to his wife, and they become one flesh!" Gen 2:24 "They are no longer two but one flesh" in the NT, Mt 19:6 Sex after marriage joins the man and a woman into one flesh and an unbreakable bond. This is celibacy in marriage. — Preceding unsigned comment added by 68.197.136.111 (talk) 20:47, 30 May 2011 (UTC)

Clerics and Catholicism
I edited/reworked this section, hopefully makeing it more clear. I also corrected/updated the current law ref the promise of celibacy, and included the footnote for Anglicans being received as Catholics. I doubt anyone actually wants to read all the specific decrees of various nations, and they do change, but if so, I can provide refs for the United States and Great Britian.DaveTroy 09:39, 10 March 2007 (UTC)

POV
I believe the statement "While lewd clothing may contribute to successful courtship, such clothing has far reaching implications on society as a whole." to be a POV, that is stated as fact.

Jpritikin claims that POV can't be removed - which policy are you referring to? Please see WP:NPOV.

The paragraph that follows is also full of unsupported claims; but even if we phrase it as "what some cultures believe", that is different from stating that clothing has "far reaching implications" as a fact. Mdwh 21:12, 24 September 2007 (UTC)

Of course it would be nice to be able to cite research supporting these claims but I don't think I am claiming anything that isn't particularly obvious. If there are other POVs then they should be included. The NPOV policy is to include all POV. Jpritikin 01:43, 26 September 2007 (UTC)

 * Well I disagree with it, for one. And the problem isn't that a POV is being included - but that the POV is being stated as fact, rather than attributed to a particular point of view. Mdwh 02:36, 26 September 2007 (UTC)

Feel free to include your opinion as well. With two opinions, it will be easier to present them as opinions, not as facts. Jpritikin 17:27, 26 September 2007 (UTC)

Promiscuity
Is it not inaccurate to say that the opposite of chastity is promiscuity? Chastity refers to adherence to a particular value system, whereas promiscuity is something that really has less of a dependence on a value system. Also, one can be neither promiscuous nor chaste in a given value system. I think this sentence ought to be removed. Cazort (talk) 12:57, 26 November 2007 (UTC)

Islam paragraph
This paragraph is extremely POV. I am not able to fix it myself but I'd rather have no Islam related information than what's there now. Even better if someone could fix it of course. I think this speaks for itself. --86.88.18.236 22:35, 20 October 2007 (UTC)
 * 1) Islam has been careful to distance people from their animalistic desires and Satanic manners
 * 2) The chastity of Islam is what restrains the human behaviour from deteriorating into the following of despicable desires.
 * 3) Fornication is incompatible with the characteristics of the faithful muslim believer and repulsive to the pious and the God-fearing

I removed the entire section since the information was already more generally included under Abrahamic religions. Str1977 (talk) 18:56, 21 October 2007 (UTC)

Nice improvement Str1977. Jpritikin 19:19, 21 October 2007 (UTC)

Chastity belts?
I noticed in this whole article on chastity with a section that has clothing on it that there is no mention of a chastity belt. Perhaps we should include it in the "see also" section? ZtObOr 21:30, 27 November 2007 (UTC)

 * Well, the role of Chastity belts in actual history (as opposed to apocryphal legends) is rather minor, but I wouldn't object to a simple "See also" link... AnonMoos (talk) 22:20, 28 November 2007 (UTC)

 * Well, now that I think about it, it doesn't belong. And I wonder which "apocryphcal legends" are being referred to here... ZtObOr 23:15, 22 February 2009 (UTC)

 * That knights going off to the crusades slapped chastity belts on the wives they left behind... AnonMoos (talk) 13:57, 23 February 2009 (UTC)

 * That, they did. But it's still not relevant to the article. ZtObOr 02:05, 10 April 2009 (UTC)

2021

 * What about the modern use of chastity belts? And chastity, as absurd as it may sound, in a modern sexual content in general? -- Preceding unsigned comment added by 2001:16B8:A0DC:B00:8C25:693B:B1FE:A481 (talk) 16:33, 26 February 2021 (UTC)

 * I'm very very late in replying to Ztobor, but crusaders did NOT use chastity belts (which were much more of a Renaissance phenomenon than medieval). AnonMoos (talk) 01:49, 3 May 2021 (UTC)

This article is way in need revision
Chasity is having respect for sex as being primarily a means of reproduction. Indeed, chastity across different cultures is the same thing - sexual restraint to the purpose of bringing human beings into the world. Chastity is a conservative value, as it conserves sexual energies. None of this information is new... it's been known for thousands of years. 74.195.25.78 (talk) 00:29, 7 January 2008 (UTC)

WHY IS "CHASTISE" REDIRECTED TO "CHASTITY"?
Why does the word "Chastise" redirect to the word "Chastity" when no reference to the word "Chastise" is mentioned? The dictionary definitions of "chastise" are, 1) to inflict punishment on (as by whipping), and, 2) to censure severely. Please correct this error. -- PiPhD (talk) 08:55, 12 May 2008 (UTC)

There is a problem with Intro
It's diluted. Being chaste isn't just about being acceptable, but rather by being pure and by being unencumbered by excessive sexual pursuits. -- 21:47, 21 February 2009 74.195.28.79

Pretentious pseudo-scholar talk
"The particular ethical system may not prescribe each of these. For example, within the scope of Christian ethic, ..."
 * Does anyone endorse this writing style? patsw (talk) 01:03, 11 July 2011 (UTC)

Islam as an Eastern Religion?
Islam developed in what is technically the east, the middle part of it more specifically, but it is without a doubt an Abrahamic religion. I'm going to move it to the Abrahamic section, if anyone has a problem with it please note it here. — Preceding unsigned comment added by 108.92.161.161 (talk) 02:48, 26 August 2015 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Chastity. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20090304123934/http://www.vatican.va/archive/catechism/p3s2c2a6.htm to http://www.vatican.va/archive/catechism/p3s2c2a6.htm

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.— InternetArchiveBot  (Report bug) 19:47, 20 November 2016 (UTC)

In Christianity
I have no idea of the meaning of "sexual purity" .Chiloa (talk) 13:35, 6 May 2018 (UTC)

Definition
In heterosexual marriage, are sexual practices not directed toward reproduction against chastity ? — Preceding unsigned comment added by Chiloa (talk • contribs) 13:51, 6 May 2018 (UTC)

 * They're against celibacy, but if you define chastity as limiting all sexual acts exclusively within marriage (i.e. with one's lawfully-wedded spouse only), and keeping one's sexual thoughts and feelings under control and in what was considered to be their proper place (i.e. not letting them dominate one's life), they're not against chastity... AnonMoos (talk) 05:03, 12 May 2018 (UTC)

Artifice?
When I read the article and the word it capitalize, must it not be qualified as "artificial"? The head says that its root is "the seven virtues" but there sex is not mentioned. Many people "yes especially those "simple-minds" relate it to clean neat and tidy". And that is far more important because in that sexual behavior eventual finds its place.

145.129.136.48 (talk) 23:44, 22 February 2019 (UTC)

Abrahamic religions
The sentence "Sexual acts outside or apart from marriage... are considered immoral..." does not apply to all Abrahamic religions. In Judaism, premarital sex is strongly discouraged, but (unlike adultery and incest) it is not halachically forbidden, and therefore not inherently sinful. --ABehrens (talk) 04:52, 21 June 2020 (UTC)

Lack of References
There are no references whatsoever in the "Sharia" subtitle. — Preceding unsigned comment added by WikiJoe24 (talk • contribs) 04:18, 1 May 2021 (UTC)

Sexual pleasure
Should there be a section on kink acts involving chasitity?147.134.92.125 (talk) 02:27, 30 November 2021 (UTC)

 * We have an article Erotic sexual denial... -- AnonMoos (talk) 14:48, 30 November 2021 (UTC)

title: Talk:Chastity


text:
Concentration

In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes and solvents in solutions. The molar (amount) concentration has variants, such as normal concentration and osmotic concentration. Dilution is reduction of concentration, e.g. by adding solvent to a solution. The verb to concentrate means to increase concentration, the opposite of dilute.

Etymology
Concentration-, concentratio, action or an act of coming together at a single place, bringing to a common center, was used in post-classical Latin in 1550 or earlier, similar terms attested in Italian (1589), Spanish (1589), English (1606), French (1632).

Qualitative description

Often in informal, non-technical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" for solutions of relatively low concentration and "concentrated" for solutions of relatively high concentration. To concentrate a solution, one must add more solute (for example, alcohol), or reduce the amount of solvent (for example, water). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are miscible, there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur. Instead, phase separation will occur, leading to coexisting phases, either completely separated or mixed as a suspension. The point of saturation depends on many variables, such as ambient temperature and the precise chemical nature of the solvent and solute.

Concentrations are often called levels, reflecting the mental schema of levels on the vertical axis of a graph, which can be high or low (for example, "high serum levels of bilirubin" are concentrations of bilirubin in the blood serum that are greater than normal).

Quantitative notation
There are four quantities that describe concentration:

Mass concentration
The mass concentration $$\rho_i$$ is defined as the mass of a constituent $$m_i$$ divided by the volume of the mixture $$V$$:

 * $$\rho_i = \frac {m_i}{V}.$$

The SI unit is kg/m3 (equal to g/L).

Molar concentration
The molar concentration $$c_i$$ is defined as the amount of a constituent $$n_i$$ (in moles) divided by the volume of the mixture $$V$$:

 * $$c_i = \frac {n_i}{V}.$$

The SI unit is mol/m3. However, more commonly the unit mol/L (= mol/dm3) is used.

Number concentration
The number concentration $$C_i$$ is defined as the number of entities of a constituent $$N_i$$ in a mixture divided by the volume of the mixture $$V$$:

 * $$C_i = \frac{N_i}{V}.$$

The SI unit is 1/m3.

Volume concentration
The volume concentration $$\sigma_i$$ (not to be confused with volume fraction ) is defined as the volume of a constituent $$V_i$$ divided by the volume of the mixture $$V$$:

 * $$\sigma_i = \frac {V_i}{V}.$$

Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%; its unit is 1.

There seems to be no standard notation in the English literature. The letter $$\sigma_i$$ used here is normative in German literature (see Volumenkonzentration).

Related quantities
Several other quantities can be used to describe the composition of a mixture. These should not be called concentrations.

Normality
Normality is defined as the molar concentration $$c_i$$ divided by an equivalence factor $$f_\mathrm{eq}$$. Since the definition of the equivalence factor depends on context (which reaction is being studied), the International Union of Pure and Applied Chemistry and National Institute of Standards and Technology discourage the use of normality.

Molality
The molality of a solution $$b_i$$ is defined as the amount of a constituent $$n_i$$ (in moles) divided by the mass of the solvent $$m_\mathrm{solvent}$$ (not the mass of the solution):

 * $$b_i = \frac{n_i}{m_\mathrm{solvent}}.$$

The SI unit for molality is mol/kg.

Mole fraction
The mole fraction $$x_i$$ is defined as the amount of a constituent $$n_i$$ (in moles) divided by the total amount of all constituents in a mixture $$n_\mathrm{tot}$$:

 * $$x_i = \frac {n_i}{n_\mathrm{tot}}.$$

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole fractions.

Mole ratio
The mole ratio $$r_i$$ is defined as the amount of a constituent $$n_i$$ divided by the total amount of all other constituents in a mixture:

 * $$r_i = \frac{n_i}{n_\mathrm{tot}-n_i}.$$

If $$n_i$$ is much smaller than $$n_\mathrm{tot}$$, the mole ratio is almost identical to the mole fraction.

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole ratios.

Mass fraction
The mass fraction $$w_i$$ is the fraction of one substance with mass $$m_i$$ to the mass of the total mixture $$m_\mathrm{tot}$$, defined as:

 * $$w_i = \frac {m_i}{m_\mathrm{tot}}.$$

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass fractions.

Mass ratio
The mass ratio $$\zeta_i$$ is defined as the mass of a constituent $$m_i$$ divided by the total mass of all other constituents in a mixture:

 * $$\zeta_i = \frac{m_i}{m_\mathrm{tot}-m_i}.$$

If $$m_i$$ is much smaller than $$m_\mathrm{tot}$$, the mass ratio is almost identical to the mass fraction.

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass ratios.

Dependence on volume and temperature
Concentration depends on the variation of the volume of the solution with temperature, due mainly to thermal expansion.

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

title: Concentration


text:
Talk:Complex number

Calligraphic font for Re and Im
The article currently uses the calligraphic  font for the Re and Im operators:
 * $$\mathcal{Re}(z)$$ and $$\mathcal{Im}(z)$$

While not exactly wrong this strikes me as unusal and unconventional, and I think
 * $$\operatorname{Re}(z)$$ and $$\operatorname{Im}(z)$$

is much more common. – Tea2min (talk) 10:10, 16 April 2021 (UTC)

 * We could also use
 * $$\mathrm{Re}(z)$$ and $$\mathrm{Im}(z)$$
 * which looks the same on Chrome.— Anita5192 (talk) 16:39, 16 April 2021 (UTC)
 * The macro \mathrm must be avoided for operators, since it generates wrong spaces. Compare $$a \mathrm{Re} (z)$$ (with \mathrm) with $$a \operatorname{Re} (z)$$ (with \operatorname). Things are even worse if parentheses are omitted for the argument: $$\mathrm{Re} z$$ vs. $$\operatorname{Re} z.$$ Similarly \operatorname must also be used (in many cases) with \mathcal (for example \operatorname{\mathcal{Re}}). Compare $$a \mathcal{Re} (z)$$ with $$a\operatorname{\mathcal{Re}} (z).$$ D.Lazard (talk) 09:04, 17 April 2021 (UTC)

History of applications
This article could use a secton on the history of the applications of complex numbers (which I myself am completely UNqualified to develop). For example, I came to this article, out of curiosity, to learn how and when complex numbers were first used to describe electrical impedance, and other electromagnetic phenomena. (I still do not know...) Acwilson9 (talk) 05:56, 9 January 2022 (UTC)

 * You probably have a good point, but I don't think the article specifically needs an entire section devoted to "the history of applications." It already has a history section and an applications section. Perhaps the history section could describe the history of the applications mentioned elsewhere in the article.—Anita5192 (talk) 07:07, 9 January 2022 (UTC)

"Complex getal" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Complex getal and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 February 15 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. User:1234qwer1234qwer4 (talk) 20:28, 15 February 2022 (UTC)

"Nombre complexe" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Nombre complexe and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 February 15 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. User:1234qwer1234qwer4 (talk) 20:29, 15 February 2022 (UTC)

Geometric interpretation of the multiplication of complex numbers

I'm looking for a better source for the geometric interpretation of multiplication, preferably a textbook. This interpretation seems to be well known e.g. it featured in this desmos course by Luke Walsh on complex numbers: #REDIRECT [], Grant Sanders heavily uses in his video on complex numbers: #REDIRECT []. Grant refers to #REDIRECT [] by Ben Sparks. But I did not find a text book that features it. The only source beside these I found was deemed not reliable enough.

Note: The illustration below for $$ab$$ and by Luke Walsh distributes $$b$$ to $$a = x + yi$$, i.e. $$ab = xb + yib$$, while Grant Sanderson and Ben Sparks in their visualizations distribute $$a$$ to $$b = u + vi$$, i.e. $$ab = ua + vib$$, but due to commutativity this does really matter. (In other words their presentations of $$ab$$ match mine and Luke Walsh's of $$ba$$.)

This is a bit (together with two pictures) I'd like to add in the section Complex_number.

 * The distributive property of multiplication over addition can be used to visualize multiplication geometrically. In particular, distributing $ab$ to $$a = x + yi$$:
 * $$a\,b = (x+yi)\, b= xb+ yib.$$
 * and using the visualization of complex numbers in the complex plane, multiplication can be given the following geometric interpretation: the product of two complex numbers $a$ and $b$ is the point that has the same coordinates as the point $ib$ in the complex plane but in a new scaled and rotated Cartesian coordinate system that has the x-axis and y-axis going through $ba$ and $b$ and a unit of measure $$|b|$$.

Happy for any suggestion. Qerez (talk) 11:31, 20 February 2022 (UTC)

 * The proposed addition would certainly be confusing and too technical for most readers (I, a professional mathematician, have difficulties for understanding the logic behind the explanation), and the reference (a communication in a minor conference) is certainly not a reliable source for a subject covered by hundreds of textbooks. D.Lazard (talk) 12:02, 20 February 2022 (UTC)
 * I had more or less the same objections and suggested user Qerez to come here. My comments are available at User talk:Qerez. - DVdm (talk) 12:38, 20 February 2022 (UTC)

Lazy revert by D. Lazzard
Aside from a lazy reversion of several improvements in my edits, we're back to an opening sentence that's unclear:

 * "In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit, and satisfying the equation i2 = −1."

It needs to be clearly expressed, even if experts can wade through it to extract the correct meaning.
 * (1) is it "an element" or "a number system" that contains the real numbers and a specific element denoted i, called the imaginary unit? It needs to be unambiguous.
 * (2) what is "satisfying" the equation i2 = −1? Is it "the imaginary unit" or "a complex number", or both "the real numbers and a specific element denoted i, called the imaginary unit"?

Tony (talk)  08:08, 4 July 2022 (UTC)
 * Reverting the introduction of grammar errors is not a lazy revert.
 * Point (2): it is $a$ that satisfies $$i^2=-1.$$ Nothing confusing here.
 * Point (1): the usual rule is that "that" refers to the last preceding noun, that is, "number system". Also, an element is not a set, and thus does not contain anything.
 * Nevertheless, I have replaced "that contains the real numbers and a specific element denoted $ia$" with "that extends the real numbers with a specific element denoted $ab$", hoping that this will be clearer. D.Lazard (talk) 09:09, 4 July 2022 (UTC)
 * In accusing, you appear to have misread my opening above: "Aside from a lazy reversion of several improvements in my edits, we're back to an opening sentence that's unclear:" (my italics).
 * "an element is not a set" – you're making it up. Depends on scale. In many areas, elements can have internal components. You're not talking just to experts who will be able to decipher your text because they know the subject already. We can't be expected to know what you're assuming.
 * "the usual rule is that "that" refers to the last preceding noun" – your source for that?
 * Back to the problematic sentence in the article: "that extends the real numbers with a specific element denoted i, called the imaginary unit, and satisfying the equation i2 = −1". But you say "Nothing confusing here".
 * If it's i that satisfies the equation, you need at the very least to get rid of the confusing comma after "unit"; or perhaps better, either (a) or (b):
 * (a) "with a specific element denoted i (called the imaginary unit) that satisfies the equation i2 = −1"
 * (b) "with a specific element denoted i (called the imaginary unit), which satisfies the equation i2 = −1."
 * I don't know which of (a) or (b) is correct: you need to decide that, based on whether i inherently satisfies the equation (which), or not inherently (that).
 * Precision is central, especially at the opening. Tony (talk)  10:08, 4 July 2022 (UTC)

 * Parentheses are not convenient for an essential clause. The comma is an old-standing typo that I have fixed. D.Lazard (talk) 10:46, 4 July 2022 (UTC)

For what it’s worth, I think this lead section is pretty mediocre, suffering from a common problem of math textbooks of elevating formal definitions ahead of meaning. The #1 key thing to know about the complex numbers is that while multiplication by a "real number" represents scaling, multiplication by a complex number represents both scaling and planar rotation (Needham calls this an "amplitwist"). Here, the words “rotate”, “rotation”, etc. don’t occur until 1200 words into the article, and even then the explanation is that multiplication is "adding the angles" (To lay readers, this does not obviously and immediately come across as meaning rotation.) A proper explanation doesn’t come until about 4000 words into the article. The lead section says that multiplication is "a similarity" with a hyperlink: this is not remotely lay-accessible; most readers are going to skip right past that without understanding what is meant.

The #2 key thing to know about the imaginary unit i (after #1 knowing that it squares to –1) is that it represents some kind of movement or position at a right angle from the "straight" real-number direction. But words like "perpendicular", "orthogonal", "right angle" don’t show up anywhere here, and again, multiplication of a complex number by i corresponds to rotating the position vector counterclockwise by a quarter turn (90°) about the origin doesn’t show up until 1200 words in.

The lead image here is also not sufficient for the article. Just showing that a complex number can be pictured as a 2-dimensional Euclidean point or an arrow from the origin (representing a Euclidean planar vector) in a diagram with axes labeled Re and Im instead of x and y doesn’t explain anything. The key geometrical features of complex numbers are that they add tip-to-tail like a geometric vector and that they multiply by “amplitwisting”. Both of these key features can be easily depicted in a diagram or two.

Even when getting to formalities, this article somewhat picks sides. Defining complex numbers as a quotient ring is not wrong, but it is just one of many possible definitions. The definition from linear algebra (a certain class of matrices), the definition from geometric algebra (the even sub-algebra of the geometric algebra of the Euclidean plane), and others are equally valid. As Clifford (and Grassmann!) figured out, a complex number is best thought of conceptually as the ratio of two planar vectors. Grassmann (1844): “From this all imaginary expressions now acquire a purely ge- ometric meaning, and can be described by geometric constructions.... it is likewise now evident how, according to the meaning of the imaginaries thus discovered, one can derive the laws of analysis in the plane; however it is not possible to derive the laws for space as well by means of imaginaries. In addition there are general difficulties in considering the angle in space, for the solution of which I have not yet had sufficient leisure.”

Wikipedia math articles about basic topics should try to lead with a lay-accessible definition/explanation, ideally with a figure that gets the main point(s) across, and then follow up (possibly soon) after with the formalities. –jacobolus (t) 12:01, 4 July 2022 (UTC)

 * I agree with Tony that the opening sentence is pretty clumsy as it stands.
 * I agree with Jacobolus that many Wikipedia math articles are harmed by a textbookish insistence of having a rigorous definition in the opening sentence. I wish that we could get past that, as a community. And I agree that, when several definitions are equally valid, more accessible ones should be presented first.
 * I disagree with Jacobolus's #1 and #2 key-thing opinions. That geometry does not require the invention of the complex numbers. Complex numbers exist because of algebraic closure.
 * Anyway, if we were willing to set aside rigor in the opening sentence, we would have much more freedom in writing succinct sentences that satisfy the typical reader's needs. Mgnbar (talk) 13:15, 4 July 2022 (UTC)
 * (P.S. Okay, in addition to algebraic closure, complex numbers are popular because they provide a handy calculational framework for quantum theory and other physics. Mgnbar (talk) 13:19, 4 July 2022 (UTC))
 * Why complex numbers were first invented/discovered (solving cubic polynomials) and why mathematicians enjoy them (they are commutative, unlike higher-dimensional analogs) is not the same as why they are important (having an algebra for planar similarity transformations (including inside an algebra for rotations on the circle that doesn’t involve so many transcendental functions as classical trigonometry) is essential all over science, engineering, and mathematics). –jacobolus (t) 13:25, 4 July 2022 (UTC)
 * Well, I disagree, but maybe we should not debate it here, until it impinges on how we edit the opening sentence. Mgnbar (talk) 13:41, 4 July 2022 (UTC)
 * The application of complex numbers to plane geometry is important, but not more than the non-geometric applications, such as, among many, the fundamental theorem of algebra, Euler's formula (and its applications in acoustics and electrical engineering through Fourier analysis), the concept of holomorphic functions, etc. D.Lazard (talk) 13:57, 4 July 2022 (UTC)
 * “Euler’s formula” (the complex exponential), Fourier analysis, and holomorphic functions are all essentially geometrical, and are useful in math and in applications for geometrical reasons. The complex logarithm is a way of taking the multiplicative structure of complex numbers (scaling and rotation) and transplanting it by a conformal map from the plane to the infinite cylinder, where it turns into complex addition (translation). When limited to the unit circle, this just recovers the traditional way of thinking about goniometry (angle measures) from the more natural multiplicative structure in the complex plane: that multiplicative structure was already implicit in the angle-sum formulas ($\cos(a + b) = \cos a\, \cos b - \sin a\, \sin b$ and  $\sin(a + b) = \cos a\, \sin b + \sin a\, \cos b$ ) from antiquity, long before anyone defined complex numbers per se. Notice that historically the more general complex logarithm showed up first geometrically as the relation between the stereographic projection and Mercator projection, long before the relevant mathematical formalisms were developed. Fourier analysis is all about representing periodic signals by considering the independent variable to be a point on a conceptual circle (or a conceptual angle measure) and then approximating them as trigonometric polynomials (each term of which represents spinning around the circle at some integer frequency). It turns out periodic (or nearly periodic) motions and signals show up all over the place so this is a very generally useful tool. Historically the first example of this general idea is approximating planetary motions by epicycles. Holomorphic functions are a representation of those maps from the plane to the plane (or more generally between two locally planar surfaces) which locally preserve complex multiplication (similarity transformations). Historically these also first showed up in cartography. –jacobolus (t) 14:24, 4 July 2022 (UTC)
 * Almost all mathematics can be interpreted geometrically, but the converse is also true, as shown by René Descartes (Cartesian coordinates) and Felix Klein (Erlangen program): all geometry can be interpreted algebraically. To assert, as you do that one direction is more important than the other, you must provide reliable sources. Otherwise this is only your opinion, and Wikipedia is not the place to discuss it. (By the way, your characterization of holomorphic functions is wrong, and I cannot imagine how to interpret geometrically the fundamental theorem of holomorphic functions, which asserts that a complex function is derivable if and only if it equals the sum of its Taylor series.) D.Lazard (talk) 14:55, 4 July 2022 (UTC)
 * Nobody says that the symbolic/algebraic structure of complex numbers is unimportant, but only that (a) this article is currently woefully deficient in describing the basic geometry (especially for an encyclopedia article aimed at a wide audience for many of whom visual/spatial reasoning is clearer than symbol twiddling), and (b) complex numbers are fundamentally the algebra of rotation-and-scaling transformations of the plane, which can (as one possibility) serve as their basic definition and which provides much of their power. Many other situations in mathematics turn out to have the same structure as rotation-and-scaling of the plane, and we can learn much by interpreting other questions as a kind of conceptual plane and operating on them there using the tools of complex numbers. As for holomorphic functions: a holomorphic function f:U → V is a function with a complex derivative, which means that if you zoom in on a very tiny piece of U, the function f applied to that tiny piece looks locally complex-linear, i.e. like a similarity transformation.  f(z + dz) - f(z) = dz f′(z), which is to say, displacements in f(z) preserve the complex-multiplicative structure present among very small displacements of z.
 * As for sources, Tristan Needham thought this interpretation of the meaning of holomorphic functions was so important that he literally wrote a whole book about it (Needham (1997), Visual Complex Analysis)! At least some other people agree – the book has been cited >1000 times in the academic literature. –jacobolus (t) 18:17, 4 July 2022 (UTC)

Before discussing lead sentences, I would like to hear your opinion on whether to merge imaginary numbers into this page. If we didn't merge, I think we can omit some explanations about imaginary numbers. Also, I think the section of Relations and operations will be explained before section of visualization.--SilverMatsu (talk) 15:36, 4 July 2022 (UTC)

 * There's not much at Imaginary number, and I'm not sure what should be added. The imaginary numbers do have their own existence as the Lie algebra of the unitary group U(1), but that's not much. Is there any other reason why imaginary numbers should be treated on their own, separately from the complex numbers? Mgnbar (talk) 17:25, 4 July 2022 (UTC)
 * Thank you your reply. I haven't found any reason other than the example you gave. It seems that wikipedia already has an imaginary unit as a separate article from the imaginary number. If merge, there isn't much to add to this article, I think just redirecting the Imaginary number to this article will complete the merge. --SilverMatsu (talk) 05:40, 6 July 2022 (UTC)
 * I don’t think they should necessarily be merged. Among other potential topics, Imaginary number seems like a better place to talk at greater length about the confusion about whether "real" and "imaginary" numbers are really "real" or "imaginary" under the conventional lay connotations of those terms. There can also be some discussion about which quantities should best be thought of as "pure imaginary" and why (for example, angle measures are naturally "imaginary” (bivector-valued) quantities, which is why we exponentiate them as $$\exp \theta i$$). Imaginary number should probably link to (and discuss) bivector, and maybe include some material about the “imaginary” part of a quaternion and its (somewhat confusing) use in representing both vectors and bivectors. –jacobolus (t) 08:33, 6 July 2022 (UTC)
 * If more place is needed for explaining the lay connotations of "real" and "imaginary", then "complex" and "hypercomplex" must also be included. As far as I know (without historical references), the word "complex" is used because the complex numbers have two parts, as opposite to (simple) numbers that have a single part. "Hypercomplex" means thus more than two parts.
 * IMO this information has its place in this article. D.Lazard (talk) 09:22, 6 July 2022 (UTC)
 * Yes this is correct, “complex” is used in the sense of “composite” (etymologically, complect = “braid together”). “Hypercomplex” numbers “split complex” numbers, “dual” numbers, (and possibly Clifford algebras, etc.) should probably also just be called “complex” by standards of ordinary language, but I suspect that by the time the term “hypercomplex” was introduced, the idea of “complex numbers” had already become ingrained as a single chunk referring only to one specific number system with most users of the term not ever thinking too hard about what “complex” means as a plain-language word per se.
 * Talking about the history of the name “imaginary” is relevant enough here at complex number to briefly mention, but belaboring the point here starts to become a distraction, whereas I think you could easily put an extended history/language lesson at imaginary number. –jacobolus (t) 19:38, 6 July 2022 (UTC)

 * I arrived at the article last week to remind myself of what a complex number is, after encountering it in a YouTube physics video. I didn't find the opening helpful. (But of course it must become too technical for me, further down.) Tony (talk)  12:11, 8 July 2022 (UTC)

Revert by user:D.Lazard on 13.03.23
Dear D.Lazard, your $$(a + bi)\, i = -b + ai$$ does not fit the current graphic. Nomen4Omen (talk) 15:50, 13 March 2023 (UTC)

 * I do not know what you call the “current graphic”, as there is no figure illustrating the rotation that is the subject of this section. The central dot is not used in this article, and the real and imaginary parts are called a and b in all previous sections. So changing a and b to x and y could be confusing. D.Lazard (talk) 16:23, 13 March 2023 (UTC)

Special nature of X^2+1 as ideal
From Google Gemini:

Clarifying Isomorphism and Topological Properties:

Isomorphism in the context of fields refers to structural equivalence. Two fields are considered isomorphic if there exists a one-to-one correspondence between their elements that preserves all the field operations (addition, subtraction, multiplication, and division) under the corresponding operations in the other field.

Topological properties, such as connectedness and local compactness, are distinct characteristics from the purely algebraic structure of a field. These properties are related to the way elements in a field are "close" to each other and how sets of elements within the field can be organized.

In the case of constructing the complex numbers, using different irreducible polynomials (like X^2 + a and X^2 + b) leads to isomorphic fields in the sense that their algebraic structure (addition, subtraction, multiplication, and division) is identical. However, these isomorphic fields might not inherit the same topological properties from the real numbers when constructing them as quotient fields.

Example:

 * As we discussed previously, the field of complex numbers (C) constructed using the polynomial X^2 + 1 exhibits both connectedness and local compactness as a topological field.
 * However, if we construct a field using a different irreducible polynomial, like X^2 + 2, the resulting quotient field would be isomorphic to the complex numbers in terms of its algebraic structure but would not be connected or locally compact.

I haven't taken a math course for 40 years now, and this surprises me, but I don't find it implausible. I was taught that X^2 + 1 was not algebraically special, and I thought that meant everything, with no consideration that topology might think different.

Bear in mind that yesterday Gemini insisted:

As a result of this shift, the Euler gamma function doesn't directly match the factorial values at positive integers. For example:
 * Γ(1) = Γ(2) = 1, while 1! = 1.
 * Γ(2) = Γ(3) = 2, while 2! = 2.
 * Γ(3) = Γ(4) = 6, while 3! = 6.

This nonsense continued until I confronted it rather sternly:

Your error runs deeper than that. Somehow you have processed the true statement that Gamma(n) = (n-1)! as implying that Gamma(n) = Gamma(n-1) which immediately leads to nonsense. From Legendre, the correct recurrence for Gamma is that Gamma(z+1) = z * Gamma(z).

At which point Gemini found the light:

You're absolutely right, and I apologize for the repeated errors in my previous responses. My understanding of the relationship between the Gamma function and factorial function was flawed, leading to inaccurate statements and misleading information.

My Mistakes:

 * I incorrectly stated that the Euler Gamma Function (Γ(z)) and the factorial function (n!) directly interpolate each other, leading to the erroneous claim that Γ(2) = 1.
 * I falsely implied that the true statement Γ(n) = (n-1)! somehow implied Γ(n) = Γ(n-1), which is not only incorrect but also mathematically illogical.

Correct Information:

 * The Euler Gamma Function extends the concept of factorial to non-integer and complex numbers. It does not directly interpolate the factorial function at positive integers due to a specific definition involving a shift in the argument (Γ(n) ≠ n! for most positive integers n).
 * The correct recurrence relation for the Gamma function is Γ(z + 1) = z * Γ(z), as you accurately pointed out, referencing Legendre's work.

If Gemini's topological claims rise above the hallucination floor, it seems like something this article might profit from pointing out as a footnote-ish addition to the bottom of the relevant section concerning the extra topological specialness of X2 + 1. — MaxEnt 01:46, 28 February 2024 (UTC)

 * Presently, no AI can be a reliable source for mathematical assertions, and this is not a place for discussing their ability to state fallacies. D.Lazard (talk) 02:38, 28 February 2024 (UTC)
 * Questions about AI nonsense should be removed to Reference desk/Mathematics to the extent they belong on Wikipedia at all. Some other forum would probably be better still. –jacobolus (t) 03:04, 28 February 2024 (UTC)
 * I am thinking that "if we construct a field using a different irreducible polynomial, like X^2 + 2, the resulting quotient field ... would not be connected or locally compact." is just false. But sure, if you can find a reliable notable source to back this statement then we could add it. — Q uantling (talk | contribs) 15:12, 28 February 2024 (UTC)

Image of symbol
This article and the articles for real number, rational number, integer, and possibly others, have a large image of the symbol (in this article, $$\mathbb C$$) even though the symbol is defined in the lead. This is redundant. I think these large images should be removed.—Anita5192 (talk) 14:18, 26 March 2024 (UTC)

 * As a general rule, good images enhance the visual appeal of Wikipedia. Without them, Wikipedia is paragraphs of text, which are informative but not attractive. This specific image is not very appealing, and it's certainly not useful. So the question for me is: Is it better than nothing? And I guess my answer is a weak "no". Mgnbar (talk) 14:41, 26 March 2024 (UTC)

 * I agree that good images enhance the visual appeal of Wikipedia. However, I approve of images of real objects, scenery, mathematical objects, etc. that help readers visualize the subject matter.  I think an image of a symbol is usually redundant, especially if it is already in the text.—Anita5192 (talk) 15:22, 26 March 2024 (UTC)

 * If this article had no images at all, and no prospects for good images, then I might support having this image in the article, just for the sake of having something. But that doesn't apply here, so I agree with you. Mgnbar (talk) 16:41, 26 March 2024 (UTC)
 * Speaking as the person who substantially wrote the current version of our article Blackboard bold, I think you should feel free to take it out. We can make better images describing and explaining complex numbers. If really necessary an image of a $b$ symbol could go in the section . –jacobolus (t) 17:18, 26 March 2024 (UTC)

 * ✅, and also for real number, rational number, and integer—Anita5192 (talk) 17:36, 26 March 2024 (UTC)

More justification and intuition, please!
This article is very good from a mathematical perspective. Definitions, algebraic rules and so on are well explained. But I miss more emphasis on WHY. It would be much more inspiring for a reader to go through all those algebraic rules if the reader had a clue about what complex numbers can be used for. There isn't even a mention about a pendulum here!?

Complex numbers are often useful when a phenomenon can change between manifesting itself in two different ways.

One example is a pendulum where energy can be kinetic energy when the pendulum is moving fast at the bottom of its trajectory and positional energy at the highest points of a its trajectory. As the pendulum swings back and forth, the same energy changes in revealing itself in two different dimensions. One of the dimensions can be called "real", and the other then becomes "imaginary".

Another example is in an oscillating electrical circuit, where the same energy can change between revealing itself as a current flowing through a conductor or as a charge in a capacitor.

Another example is sound waves, where a sound measured at one point can change between revealing itself as a air pressure deviation and as a motion in the air.

Thus, two different manifestations or aspects of something can be modelled using just one complex number.

(If something like this had been told me when I started learning about complex number, this would have made my learning easier and more fun) Joreberg (talk) 21:05, 14 April 2024 (UTC)

 * Some of this is mentioned in the Applications section. It would be great if you could add some of the others you list (with Reliable sources of course).

 * In some of your examples, I can't tell whether the object under discussion is the space C of complex numbers or the space R2 of pairs of real numbers. This article should restrict its attention to the former. Mgnbar (talk) 11:53, 15 April 2024 (UTC)
 * I venture that an original motivation for complex numbers is analysis of harmonic oscillators and Fourier analysis in general, so I'd want those featured prominently — which they already are to some extent. — Q uantling (talk | contribs) 15:03, 15 April 2024 (UTC)
 * You seem to be especially interested in uniform circular motion and simple harmonic motion (which can be modeled as a projection of uniform circular motion). These are worth discussing somewhere, but I don't think we should belabor the point at the start of the article. –jacobolus (t) 19:56, 15 April 2024 (UTC)

title: Talk:Complex number


text:
Christine Lavin

Christine Lavin (born January 2, 1952) is a New York City-based singer-songwriter and promoter of contemporary folk music. She has recorded numerous solo albums, and has also recorded with other female folk artists under the name Four Bitchin' Babes. She is known for her sense of humor, which is expressed in both her music and her onstage performances. Many of her songs alternate between comedy and emotional reflections on romance.

Lavin worked at Caffe Lena in Saratoga Springs, New York until Dave Van Ronk convinced her to move to New York City and make a career as a singer-songwriter. She followed his advice and accepted his offer of guitar lessons. She was the original host of Sunday Breakfast on WFUV in New York City and a founding member of the Four Bitchin' Babes when they were formed in 1990.

She is a lifelong astrophysics hobbyist and has included those themes in her music.

Awards

 * The ASCAP 43rd Annual Deems Taylor Award for her book Cold Pizza For Breakfast: A Mem-Wha??, 2011
 * The ASCAP Foundation Jamie deRoy and Friends Award, 2010
 * Top 100 of the Most Influential Artists in the Last 15 Years, Singer Songwriter Magazine
 * Top 30 iPod Singer/Songwriters of Choice, WUMB, Boston 2006
 * ASCAP Composer Award 1992, 1993, 1996, 1998, 1999, 2004, 2005, 2006
 * Singer/Songwriter of the Year, Backstage Magazine, NYC 2001
 * Honorable Mention, NAIRD Singer / Songwriter Album of the Year, 1996: Please Don’t Make Me Too Happy
 * New York Music Award Folk Artist of the Year 1990, 1992
 * World Folk Music Association Kate Wolf Memorial Award 1990
 * NAIRD Folk Album of the Year, 1988: Good Thing He Can’t Read My Mind

Discography

 * Absolutely Live (1981; re-issued by Winthrop, 2000)
 * Future Fossils (Philo, 1984)
 * Beau Woes and Other Problems of Modern Life (Philo, 1986)
 * Another Woman's Man (Philo, 1987)
 * Good Thing He Can't Read My Mind (Philo, 1988)
 * Attainable Love (Philo, 1990)
 * Compass (Philo, 1991)
 * Live at the Cactus Cafe: What Was I Thinking? (Philo, 1993)
 * Please Don't Make Me Too Happy (Shanachie, 1995)
 * Shining My Flashlight on the Moon (Shanachie, 1997)
 * One Wild Night in Concert (1998)
 * Getting in Touch With My Inner Bitch (Christine Lavin, 1999)
 * The Bellevue Years (Philo, 2000)
 * The Subway Series (Christine Lavin, 2001)
 * Final Exam (2001)
 * I Was in Love With a Difficult Man (Redwing, 2002)
 * The Runaway Christmas Tree (2003)
 * Sometimes Mother Really Does Know Best [Live] (Appleseed, 2004)
 * folkZinger (Appleseed, 2005)
 * One Meat Ball (Appleseed, 2006)
 * The Runaway Christmas Tree (Appleseed, 2006)
 * Happydance of the Xenophobe (2007)
 * I Don't Make This Stuff Up, I Just Make It Rhyme (2008)
 * Cold Pizza for Breakfast (Yellow Tail Records, 2009)
 * If You're Drunk You Cannot Buy A Puppy (Christine Lavin, 2014)
 * Spaghettification (Christine Lavin, 2017)
 * On My Way To Hooterville (2020)

title: Christine Lavin


text:
Cutter Expansive Classification

The Cutter Expansive Classification system is a library classification system devised by Charles Ammi Cutter. The system was the basis for the top categories of the Library of Congress Classification.

History of the Expansive Classification
Charles Ammi Cutter (1837–1903), inspired by the decimal classification of his contemporary Melvil Dewey, and with Dewey's initial encouragement, developed his own classification scheme for the Winchester, Massachusetts town library and then the Boston Athenaeum, at which he served as librarian for twenty-four years. He began work on it around the year 1880, publishing an overview of the new system in 1882. The same classification would later be used, but with a different notation, also devised by Cutter, at the Cary Library in Lexington, Massachusetts.

Many libraries found this system too detailed and complex for their needs, and Cutter received many requests from librarians at small libraries who wanted the classification adapted for their collections. While numbers and letters are required in large library classifications, small libraries did not need their classification system to be too specific. He devised the Expansive Classification in response, to meet the needs of growing libraries, and to address some of the complaints of his critics. Cutter completed and published an introduction and schedules for the first six classifications of his new system (Expansive Classification: Part I: The First Six Classifications), but his work on the seventh was interrupted by his death in 1903.

The Cutter Expansive Classification, although adopted by comparatively few libraries, has been called one of the most logical and scholarly of American classifications. Library historian Leo E. LaMontagne writes:

"Cutter produced the best classification of the nineteenth century. While his system was less 'scientific' than that of J. P. Lesley, its other key features – notation, specificity, and versatility – make it deserving of the praise it has received."

Its top level divisions served as a basis for the Library of Congress classification, which also took over some of its features. It did not catch on as did Dewey's system because Cutter died before it was completely finished, making no provision for the kind of development necessary as the bounds of knowledge expanded and scholarly emphases changed throughout the twentieth century.

Structure of the Expansive Classification
The Expansive Classification uses seven separate schedules, each designed to be used by libraries of different sizes. After the first, each schedule was an expansion of the previous one, and Cutter provided instructions for how a library might change from one expansion to another as it grows.

First classification
The first classification is meant for very small libraries. The first classification has only seven top-level classes, and only eight classes in total:

 * A Works of reference and general works which include several of the following sections, and so could not go in any one.
 * B Philosophy and Religion
 * E Biography
 * F History and Geography and Travels
 * H Social sciences
 * L Natural sciences and Arts
 * Y Language and Literature
 * YF Fiction

Further classifications
Further expansions add more top level classes and subdivisions. Many subclasses arranged systematically, with common divisions, such as those by geography and language, following a consistent system throughout.

By the fifth classification all the letters of the alphabet are in use for top level classes. These are:

 * A General Works
 * B Philosophy
 * C Christianity and Judaism
 * D Ecclesiastical History
 * E Biography
 * F History, Universal History
 * G Geography and Travels
 * H Social Sciences
 * I Demotics, Sociology
 * J Civics, Government, Political Science
 * K Legislation
 * L Science and Arts together
 * M Natural History
 * N Botany
 * O Zoology
 * P Anthropology and Ethnology
 * Q Medicine
 * R Useful arts, Technology
 * S Constructive arts (Engineering and Building)
 * T Manufactures and Handicrafts
 * U Art of War
 * V Recreative arts, Sports, Games, Festivals
 * W Art
 * X English Language
 * Y English and American literature
 * Z Book arts

These schedules were not meant to be fixed, but were to be adapted to meet the needs of each library. For example, books on the English language may be put in X, and books on language in general in a subclass of X, or this can be reversed. The first option is less logical, but results in shorter marks for most English language libraries.

Construction of call numbers
Most call numbers in the Expansive Classification follow conventions offering clues to the book's subject. The first line represents the subject, the second the author (and perhaps title), the third and fourth dates of editions, indications of translations, and critical works on particular books or authors. All numbers in the Expansive Classification are (or should be) shelved as if in decimal order.

Size of volumes is indicated by points (.), pluses (+), or slashes (/ or //).

For some subjects a numerical geographical subdivision follows the classification letters on the first line. The number 83 stands for the United States—hence, F83 is U.S. history, G83 U.S. travel, JU83 U.S. politics, WP83 U.S. painting. Geographical numbers are often further expanded decimally to represent more specific areas, sometimes followed by a capital letter indicating a particular city.

The second line usually represents the author's name by a capital letter plus one or more numbers arranged decimally. This may be followed by the first letter or letters of the title in lower-case, and/or sometimes the letters a, b, c indicating other printings of the same title. When appropriate, the second line may begin with a 'form' number—e.g., 1 stands for history and criticism of a subject, 2 for a bibliography, 5 for a dictionary, 6 for an atlas or maps, 7 for a periodical, 8 for a society or university publication, 9 for a collection of works by different authors.

On the third line a capital Y indicates a work about the author or book represented by the first two lines, and a capital E (for English—other letters are used for other languages) indicates a translation into English. If both criticism and translation apply to a single title, the number expands into four lines.

Cutter numbers (Cutter codes)
One of the features adopted by other systems, including Library of Congress, is the Cutter number. It is an alphanumeric device to code text so that it can be arranged in alphabetical order using the fewest characters. It contains one or two initial letters and Arabic numbers, treated as a decimal. To construct a Cutter number, a cataloguer consults a Cutter table as required by the classification rules. Although Cutter numbers are mostly used for coding the names of authors, the system can be used for titles, subjects, geographic areas, and more.

Initial letters Qa–Qt are assigned Q2–Q29, while entries beginning with numerals have a Cutter number A12–A19, therefore sorting before the first A entry.

So to make the three-digit Cutter number for "Cutter", one would start with "C", then looking under other consonants, find that "u" gives the number 8, and under additional letters, "t" is 8, giving a Cutter number of "C88".

title: Cutter Expansive Classification


text:
Cem Karaca

Muhtar Cem Karaca (5 April 1945 – 8 February 2004) was a prominent Turkish rock musician and one of the most important figures in the Anatolian rock movement. He was a graduate of Robert College. He worked with various Turkish rock bands such as Apaşlar, Kardaşlar, Moğollar and Dervişan. With these bands, he brought a new understanding and interpretation to Turkish rock.

Biography
He was the only child of Mehmet İbrahim Karaca, a theatre actor of Azerbaijani origin, and İrma Felekyan, a popular opera, theatre, and movie actress of Armenian origin. His first group was called Dynamites and was a classic rock cover band. Later he joined Jaguars, an Elvis Presley cover band. In 1967, he started to write his own music, joining the band Apaşlar (The Rowdies), his first Turkish language group. The same year, he participated in the Golden Microphone (Altın Mikrofon) contest, a popular music contest in which he won second place with his song Emrah. In 1969, Karaca and bass-player Serhan Karabay left Apaşlar and started an original Anatolian group called Kardaşlar (The Brothers).

In 1972, Karaca joined the group Moğollar (The Mongols) and wrote one of his best-known songs, "Namus Belası". However, Cahit Berkay, the leader of Moğollar, wanted an international reputation for his band, and he left for France to take the group to the next level. Karaca, who wanted to continue his Anatolian beat sound, left Moğollar and started his own band Dervişan (Dervishes) in 1974. Karaca and Dervişan sang poetic and progressive songs.

In the 1970s, Turkey was dealing with political violence between supporters of the left and the right, separatist movements and the rise of Islamism. As the country fell into chaos, the government suspected Cem Karaca of involvement in rebel organisations. He was accused of treason for being a separatist thinker and a Marxist-Leninist. The Turkish government tried to portray Karaca as a man who was unknowingly writing songs to start a revolution. One politician was quoted as saying, "Karaca is simply calling citizens to a bloody war against the state." Dervişan was ultimately dissolved at the end of 1977. In 1978, he founded Edirdahan, an acronym for "from Edirne to Ardahan"; the westernmost and the easternmost provinces of Turkey. He recorded one LP with Edirdahan called "Safinaz".

In early 1979, Karaca left for Cologne, West Germany for business reasons. In 1980 he began singing in German with the song Nazim Hikmet - Kız Çocuğu (Little girl): Cem performed the German verses alternating with his best friend, manager, producer, arranger and bandleader/bass player/keyboarder/drummer, guitar player Ralf Mähnhöfer accompanying him on grand piano, solo or with the band Anatology, singing the song in the Turkish language.

Turkey continued to spin out of control with military curfews and the 1980 Turkish coup d'état on September 12, 1980. General Kenan Evren took over the government and temporarily banned all the nation's political parties. After the coup, many intellectuals, including writers, artists and journalists, were arrested. A warrant was issued for the arrest of Karaca by the government of Turkey.

The state invited Karaca back several times, but Karaca, not knowing what would happen upon his return, decided not to come back.

While Karaca was in Germany his father died, but he could not return to attend the funeral. After some time, the Turkish government decided to strip Cem Karaca of his Turkish citizenship, keeping the arrest warrant active.

Several years later, in 1987, the prime minister and leader of the Turkish Motherland Party, Turgut Özal, issued an amnesty for Karaca. Shortly afterwards, he returned to Turkey. His return also brought a new album with it, Merhaba Gençler ve Her Zaman Genç Kalanlar ("Hello, The Young and The Young at Heart"), one of his most influential works. His return home was received cheerfully by his fans, but during his absence Karaca had lost the young audience and acquired only a few new listeners. He died of a heart attack on February 8, 2004, and was interred at Karacaahmet Cemetery in the Üsküdar district of Istanbul.

45s

 * Emrah/Karacaoğlan (1967) (with Apaşlar)
 * Hudey / Vahşet / Bang Bang / Shakin' All Over (1967) (with Apaşlar)
 * Emrah / Hücum / Karacaoğlan / Ayşen (1967) (with Apaşlar)
 * Ümit Tarlaları/Anadolu Oyun Havası/Suya Giden Allı Gelin/Nasıl Da Geçtin (1967) (with Apaşlar)
 * İstanbul'u Dinliyorum/Oy Bana Bana (1968) (with Apaşlar and Ferdy Klein Band)
 * Oy Babo/Hikaye (1968) (with Apaşlar)
 * İstanbul/Why (1968) (with Apaşlar and Ferdy Klein Band)
 * Emrah 1970/Karanlık Yollar (1968) (with Apaşlar and Ferdy Klein Band)
 * Resimdeki Gözyaşları/Emrah (1968) (with Apaşlar and Ferdy Klein Band)
 * Resimdeki Gözyaşları/Şans Çocuğu (1968) (with Apaşlar and Ferdy Klein Band)
 * Tears/No, No, No (1968) (with Apaşlar and Ferdy Klein Band)
 * Ayrılık Günümüz/Gılgamış (1969) (with Apaşlar and Ferdy Klein Band)
 * Zeyno/Niksar (1969) (with Apaşlar and Ferdy Klein Band)
 * Bu Son Olsun/Felek Beni (1969) (with Apaşlar and Ferdy Klein Band)
 * Emmioğlu/O Leyli (1970) (with Ferdy Klein Band)
 * Kendim Ettim kendim Buldum/Erenler (1970) (with Ferdy Klein Band)
 * Adsız/Unut Beni (1970) (with Ferdy Klein Band)
 * Muhtar/Baba (1970) (with Ferdy Klein Band)
 * Dadaloğlu/Kalender (1970) (with Kardaşlar)
 * Oy Gülüm Oy/Kara Sevda (1971) (with Kardaşlar)
 * Tatlı Dillim/Demedim Mi (1971) (with Kardaşlar)
 * Kara Yılan/Lümüne (1971) (with Kardaşlar)
 * Acı Doktor (Kısım 1)/Acı Doktor (Kısım 2) (1971) (with Kardaşlar)
 * Kara Üzüm/Mehmet'e Ağıt (1971) (with Kardaşlar)
 * Askaros Deresi/Üryan Geldim (1972) (with Kardaşlar)
 * Obur Dünya/El Çek Tabib (1973) (with Moğollar)
 * Gel Gel/Üzüm Kaldı (1973) (with Moğollar)
 * Namus Belası/Gurbet (1974) (with Moğollar)
 * Beyaz Atlı/Yiğitler (1974) (with Dervişan)
 * Tamirci Çırağı/Nerdesin? (1975) (with Dervişan)
 * Mutlaka Yavrum/Kavga (1975) (with Dervişan)
 * Beni Siz Delirttiniz/Niyazi (1975) (with Dervişan)
 * Parka/İhtarname (1976) (with Dervişan)
 * Mor Perşembe/Bir Mirasyediye Ağıt (1977) (with Dervişan)
 * 1 Mayıs/Durduramayacaklar Halkın Coşkun Akan Selini (1977) (with Dervişan)

LPs

 * Apaşlar-Kardaşlar (1972)
 * Cem Karaca'nın Apaşlar, Kardaşlar, Moğollar ve Ferdy Klein Orkestrasına Teşekkürleriyle (1974)
 * Nem Kaldı (1975)
 * Parka (1977)
 * Yoksulluk Kader Olamaz (1977) (1)
 * Safinaz (1978) (2)
 * Hasret (1980) (It was sold as LP and tape)
 * Bekle Beni (1982) (It was sold as tape only)
 * Die Kanaken (1984)
 * Merhaba Gençler ve Her Zaman Genç Kalanlar (1987) (It was sold as compact cassette and CD)

Other albums

 * Töre (1988) (It was sold as CD) by Oğuz Abadan Orchestra
 * Yiyin Efendiler (1990)
 * Nerde Kalmistik (1992)
 * Bindik Bir Alamete (1999)
 * Kahpe Bizans (2000)
 * Hayvan Terli (2004) (Single)

Collection albums

 * The Best of Cem Karaca Volume 1 (1996)
 * The Best of Cem Karaca Volume 2 (1997)
 * The Best of Cem Karaca Volume 3 (2000)
 * The Best of Cem Karaca Volume 4 (2001)
 * The Best of Cem Karaca Volume 5 (2002)
 * Ölümsüzler (Immortals) (2004) (posthumously)
 * Ölümsüzler 2 (Immortals 2) (2005) (posthumously)
 * Mutlaka Yavrum (Absolutely, baby) (2006) (posthumously)

Literature

 * Martin Stokes: Music in Performance: Cem Karaca, Live. In: Virginia Danielson, Dwight Reynolds, Scott Marcus (Hrsg.): The Garland Encyclopedia of World Music. Band 6: The Middle East. Garland, London 2002, S. 243–245
 * Türkischer Akademiker- und Künstlerverein, in Berlin (author), publisher: Jürgen Kleindienst (1977): Nazim Hikmet - Sie haben Angst vor unseren Liedern, documentation, language: German-Turkish ISBN 9783885200093

title: Cem Karaca


text:
Calista Flockhart

Calista Kay Flockhart (born November 11, 1964) is an American actress. She is best known for portraying the title character on the Fox television series Ally McBeal (1997–2002), for which she received a Golden Globe Award in 1998 and was thrice nominated for the Primetime Emmy Award for Outstanding Lead Actress in a Comedy Series. From 2006 to 2011, she starred as Kitty Walker on the ABC drama series Brothers & Sisters, and between 2015 and 2021, Flockhart appeared as Cat Grant on the superhero drama Supergirl. In film, she is known for roles in The Birdcage (1996), A Midsummer Night's Dream (1999), and Things You Can Tell Just by Looking at Her (2000).

Early life
Flockhart was born in Freeport, Illinois, the daughter of Kay Calista, an English teacher, and Ronald Flockhart, a Kraft Foods executive. Her parents retired to Morristown, Tennessee, where her father lived until his death and her mother continues to reside. She has one older brother, Gary. Her mother reversed her own first and middle names in naming her Calista Kay.

Flockhart attended Mason Gross School of the Arts at Rutgers University–New Brunswick. People began recognizing Flockhart's acting ability when William Esper (Mason Gross theater director and Flockhart's acting teacher) made an exception to policy by allowing Flockhart to perform on the main stage. Though this venue usually is reserved for juniors and seniors, Harold Scott insisted that Flockhart perform there in his production of William Inge's Picnic. Flockhart graduated with a Bachelor of Fine Arts in theater in 1988 from Rutgers as one of the few students who successfully completed the acting course. Rutgers inducted her into the Hall of Distinguished Alumni on May 3, 2003.

Early career
In spring 1989, Flockhart made her first television appearance in a minor role in an episode of Guiding Light as a babysitter. She also appeared in a one-hour afternoon special for Lifestories: Families in Crisis, playing a teenager battling an eating disorder. Flockhart made her professional debut on the New York stage, appearing in Beside Herself alongside Melissa Joan Hart, at the Circle Repertory Theatre. Two years later, Flockhart appeared in the television movie Darrow. Though she later appeared in films Naked in New York (1993) and Getting In (1994), her first substantial speaking part in a film was in Quiz Show, directed by Robert Redford.

Flockhart debuted on Broadway in 1994, as Laura in The Glass Menagerie. Flockhart received a Clarence Derwent Award for her performance. In 1995, Flockhart became acquainted with actors such as Dianne Wiest and Faye Dunaway when she appeared in the movie Drunks. In 1996, Flockhart appeared as the daughter of Dianne Wiest and Gene Hackman's characters in The Birdcage. Later that year, Flockhart starred in Jane Doe as a drug addict, though it was not released until 1999, over three years after filming ended. Throughout that year, she continued to work on Broadway, playing the role of Natasha in Anton Chekhov's Three Sisters.

Ally McBeal
In 1997, Flockhart was asked to audition for the starring role in David E. Kelley's Fox television series Ally McBeal. Kelley, having heard of Flockhart, wanted her to audition for the contract part. Though she hesitated due to the necessary commitment to the show in a negotiable contract, she was swayed by the script and traveled to Los Angeles to audition for the part, which she won. She earned a Golden Globe Award for the role in 1998. Flockhart also appeared on the June 29, 1998, cover of Time magazine, placed as the newest iteration in the evolution of feminism, relating to the ongoing debate about the role depicted by her character. Flockhart starred on the show until it was canceled in 2002.

Brothers & Sisters
Flockhart performed in a starring role as Kitty Walker, opposite Sally Field, Rachel Griffiths and Matthew Rhys, in the critically acclaimed ABC prime time series Brothers & Sisters, which premiered in September 2006 in the time slot after Desperate Housewives. The show was cancelled in May 2011 after running for five years. Flockhart's character was significant throughout the series' first four years, but her appearances were reduced for the 2010–2011 season, coinciding with the departure of TV husband Rob Lowe.

Other work
Flockhart played the role of Helena in A Midsummer Night's Dream, a 1999 film version of Shakespeare's play. In 2000, she appeared in Things You Can Tell Just by Looking at Her and Bash: Latter-Day Plays, later accompanying Eve Ensler to Kenya in order to protest violence against women, particularly female genital mutilation. Flockhart also starred in the off-Broadway production of Ensler's The Vagina Monologues.

In 2004, Flockhart appeared as Matthew Broderick's deranged girlfriend in The Last Shot. In the same year, Flockhart traveled to Spain for the filming of Fragile, which premiered in September 2005 at the Venice Film Festival. She was offered the role of Susan Mayer on Desperate Housewives but declined, and the role later went to Teri Hatcher.

In 2014, Flockhart landed a role in Full Circle second season, as mob boss Ellen. It was expected to air in 2015. This had been Flockhart's first acting role in three years, after her hiatus when Brothers & Sisters ended.

In 2015, Flockhart was cast in the television series Supergirl as Cat Grant, a "self-made media magnate and founder of CatCo" and boss to Kara (Supergirl's alter ego). The series premiered on October 26, 2015, on CBS. Due to the network's wish to reduce the show's budget, it was moved to sister network The CW after its first season, along with a move to filming in Vancouver. Flockhart remained with the show (albeit as a recurring character), despite her previous aversion to working outside Los Angeles.

In 2022, she played the role of Martha opposite Zachary Quinto in Edward Albee's Who's Afraid of Virginia Woolf? at the Geffen Playhouse in Los Angeles. The production was directed by Gordon Greenberg and also starred Aimee Carrero and Graham Phillips.

In 2024, Flockhart appeared as Lee Radziwill in Capote vs. The Swans, the second season of the anthology series Feud. Regarding playing Radziwill in an interview with The New York Times, Flockhart said, “Truman Capote recognized that she was living in her sister’s shadow... and he would say things: ‘You’re so much prettier. You’re so much smarter. You’re more interesting. You have better style.’ She really needed to hear that. I think it made her really love Truman. He was fun, and she confided in him, like they all did.”

Personal life
In January 2001, Flockhart announced that she had adopted a baby boy.

Flockhart is married to actor Harrison Ford, with whom she has been in a relationship since their meeting at the Golden Globe Awards on January 20, 2002. They became engaged on Valentine's Day in 2009, and were married on June 15, 2010, in Santa Fe, New Mexico. The ceremony was presided over by New Mexico Governor Bill Richardson and New Mexico Supreme Court Chief Justice Charles W. Daniels. Flockhart and Ford share their adopted son together, Liam Flockhart Ford.

From 2004 to 2014, Flockhart served as the national spokeswoman for Peace Over Violence.

title: Calista Flockhart