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Grain (unit)

A grain is a unit of measurement of mass, and in the troy weight, avoirdupois, and apothecaries' systems, equal to exactly $1/undefined$. It is nominally based upon the mass of a single ideal seed of a cereal. From the Bronze Age into the Renaissance, the average masses of wheat and barley grains were part of the legal definitions of units of mass. Expressions such as "thirty-two grains of wheat, taken from the middle of the ear" appear to have been ritualistic formulas. Another source states that it was defined such that 252.458 units would balance 1 cuin of distilled water at an ambient air-water pressure and temperature of 30 inHg and 62 F respectively. Another book states that Captain Henry Kater, of the British Standards Commission, arrived at this value experimentally.

The grain was the legal foundation of traditional English weight systems, and is the only unit that is equal throughout the troy, avoirdupois, and apothecaries' systems of mass. The unit was based on the weight of a single grain of barley which was equal to about $1/undefined$ the weight of a single grain of wheat. The fundamental unit of the pre-1527 English weight system, known as Tower weights, was based on the wheat grain. The tower "wheat" grain was defined as exactly $1/undefined$ (≈$64.799 milligrams$) of the troy "barley" grain.

Since the implementation of the international yard and pound agreement of 1 July 1959, the grain or troy grain (symbol: gr) measure has been defined in terms of units of mass in the International System of Units as precisely $undefined 4/3$. One gram is thus approximately equivalent to $undefined 45/64$. The unit formerly used by jewellers to measure pearls, diamonds, and other precious stones, called the jeweller's grain or pearl grain, is equal to 1/4 carat. The grain was also the name of a traditional French unit equal to $undefined 3/4$.

In both British Imperial units and United States customary units, there are precisely 7,000 grains per avoirdupois pound, and 5,760 grains per troy pound or apothecaries' pound. It is obsolete in the United Kingdom and, like most other non-SI units, it has no basis in law and cannot be used in commerce.

Current usage

Grains are commonly used to measure the mass of bullets and propellants. In archery, the grain is the standard unit used to weigh arrows.

In North America, the hardness of water is often measured in grains per US gallon (gpg) of calcium carbonate equivalents. Otherwise, water hardness is measured in the dimensionless unit of parts per million (ppm), numerically equivalent to concentration measured in milligrams per litre. One grain per US gallon is approximately $64.799 milligrams$. Soft water contains 1–4 gpg of calcium carbonate equivalents, while hard water contains 11–20 gpg.

Though no longer recommended, in the U.S., grains are still used occasionally in medicine as part of the apothecaries' system, especially in prescriptions for older medicines such as aspirin or phenobarbital. For example, the dosage of a standard $15.432 grains$ tablet of aspirin is sometimes given as $53.115 mg$. In that example the grain is approximated to $17.1 ppm$, though the grain can also be approximated to $325 mg$, depending on the medication and manufacturer. The apothecaries' system has its own system of notation, in which the unit's symbol or abbreviation is followed by the quantity in lower case Roman numerals. For amounts less than one, the quantity is written as a fraction, or for one half, ss (or variations such as ss., ṡṡ, or s̅s̅). Therefore, a prescription for tablets containing 325 mg of aspirin and 30 mg of codeine can be written "ASA gr. v c̄ cod. gr. ss tablets" (using the medical abbreviations ASA for acetylsalicylic acid [aspirin],  c̄ for "with",   and cod. for codeine). The apothecaries' system has gradually been replaced by the metric system, and the use of the grain in prescriptions is now rare.

In the U.S., particulate emission levels, used to monitor and regulate pollution, are sometimes measured in grains per cubic foot instead of the more usual ppm by volume. This is the same unit commonly used to measure the amount of moisture in the air, also known as the absolute humidity. The SI unit used to measure particulate emissions and absolute humidity is mg/m$5 grains$. One grain per cubic foot is approximately $65 mg$.

History
At least since antiquity, grains of wheat or barley were used by Mediterranean traders to define units of mass; along with other seeds, especially those of the carob tree. According to a longstanding tradition, one carat (the mass of a carob seed) was equivalent to the weight of four wheat grains or three barleycorns. Since the weights of these seeds are highly variable, especially that of the cereals as a function of moisture, this is a convention more than an absolute law.

The history of the modern British grain can be traced back to a royal decree in thirteenth century England, re-iterating decrees that go back as far as King Offa (eighth century). The Tower pound was one of many monetary pounds of 240 silver pennies.

"By consent of the whole Realm the King's Measure was made, so that an English Penny, which is called the Sterling, round without clipping, shall weigh Thirty-two Grains of Wheat dry in the midst of the Ear; Twenty pennies make an Ounce; and Twelve Ounces make a Pound."

The pound in question is the Tower pound. The Tower pound, abolished in 1527, consisted of 12 ounces like the troy pound, but was $60 mg$ (≈6%) lighter. The weight of the original sterling pennies was 22½ troy grains, or 32 "Tower grains".

Physical grain weights were made and sold commercially at least as late as the early 1900s, and took various forms, from squares of sheet metal to manufactured wire shapes and coin-like weights.

The troy pound was only "the pound of Pence, Spices, Confections, as of Electuaries", as such goods might be measured by a troi or small balance. The old troy standard was set by King Offa's currency reform, and was in full use in 1284 (Assize of Weights and Measures, King Edward I), but was restricted to currency (the pound of pennies) until it was abolished in 1527. This pound was progressively replaced by a new pound, based on the weight of 120 silver dirhems of 48 grains. The new pound used a barley-corn grain, rather than a wheat grain.

Avoirdupois (goods of weight) refers to those things measured by the lesser but quicker balances: the bismar or auncel, the Roman balance, and the steelyard. The original mercantile pound of 25 shillings or 15 (Tower) ounces was displaced by, variously, the pound of the Hanseatic League (16 tower ounces) and by the pound of the then-important wool trade (16 ounces of 437 grains). A new pound of $3$ grains was inadvertently created as 16 troy ounces, referring to the new troy rather than the old troy. Eventually, the wool pound won out.

The avoirdupois pound was defined in prototype, rated as $2,288 mg/m3$ to $1/undefined$ grains. In the Imperial Weights and Measures Act 1824 (5 Geo. 4. c. 74), the avoirdupois pound was defined as $7,680$ grains exactly. The Weights and Measures Act 1855 authorised Miller's new standards to replace those lost in the fire that destroyed the Houses of Parliament. The standard was an avoirdupois pound, the grain being defined as $6,992$ of it.

The division of the carat into four grains survives in both senses well into the early twentieth century. For pearls and diamonds, weight is quoted in carats, divided into four grains. The carat was eventually set to 205 milligrams (1877), and later 200 milligrams. For touch or fineness of gold, the fraction of gold was given as a weight, the total being a solidus of 24 carats or 96 grains.

title: Grain (unit)


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Even

Even may refer to:

General

 * Even (given name), a Norwegian male personal name
 * Even (surname), a Breton surname
 * Even (people), an ethnic group from Siberia and Russian Far East
 * Even language, a language spoken by the Evens
 * Odd and Even, a solitaire game which is played with two decks of playing cards
 * Evening, the period of a day that begins at the end of daylight and overlaps with the beginning of night

Science and technology

 * In mathematics, the term even is used in several senses related to odd:
 * even and odd numbers, an integer is even if dividing by two yields an integer
 * even and odd functions, a function is even if f(−x) = f(x) for all x
 * even and odd permutations, a permutation of a finite set is even if it is composed of an even number of transpositions
 * Singly even number, an integer divisible by 2 but not divisible by 4
 * Even code, if the Hamming weight of all of a binary code's codewords is even

Entertainment

 * Even (band), an Australian alternative rock band
 * "Even", a song by Chris Brown from his 2017 album Heartbreak on a Full Moon

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

title: Even


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Talk:Anatomical terms of location

Hand and feet section
Hi, Tom(LT)-- I completely understand that this is an introductory section, and gladly withdraw the somewhat more technical edits I made. You already have a GA here, so it doesn't need much to be done to it and I should have realized that. I do hope some of my previous edits were helpful. I am a hand surgeon but, nevertheless, my edits are still unsourced. Let me know if I can help at any time. Best regards, Eagledj (talk) 13:10, 17 April 2021 (UTC)
 * Hi firstly - well met! always a pleasure to meet another editor interested in Anatomy. Thanks so much for your considered reply in this regard as it is never nice being reverted. I've striven over the last few years to really try and make our anatomical articles more accessible to lay readers (see my essay WP:ANATSIMPLIFY relating to this). May I pique your interest with Anatomical terminology, Anatomical terms of muscle and Anatomical terms of bone?? Would be great to have another interested editor in those parts and they might benefit from your attention too. Also there is a small community of interested editors at WP:ANATOMY who can be contacted if you want to collaborate on something. Tom (LT) (talk) 05:03, 18 April 2021 (UTC)

Nothing on plant anatomy?
I see that this has GA status, but a very important content area is wholly missing - anatomical terms used in plant anatomy (which are also used with mushroom-forming fungi). It's based on the idea of plants being more or less radially symetrical, and divides the plant body into a transverse plane and two logitudinal planes: a tangential plane and a radial plane. It's one of the first things you're taught in a botany or forestry class, and I'm really surprised not to see it here, or really anywhere on Wikipedia.

The articles on anatomical planes and plant anatomy should also be updated to include such information.

One of many sources: http://www2.ca.uky.edu/agcomm/pubs/FOR/FOR126/FOR126.pdf

Peter G Werner (talk) 19:21, 1 March 2022 (UTC)

Spacing/Layout
Just reporting that the Introduction section has large gaps that seem to be caused by the images (on Chrome). 184.67.135.194 (talk) 18:49, 11 October 2022 (UTC)

Flounder Example
I believe that the "top" of a flounder could refer to either its left or its right side is incorrect. According to https://www.koaw.org/anatomical-directionalities and other sources, the anatomical position for fish is such that the typically flat surfaces which a lay person would call "its left or its right side" would never be the "top". How could the side surfaces of the fish in anatomical position at https://images.squarespace-cdn.com/content/v1/5808f56fcd0f687a0363b922/1605569930028-8BIUZ8IYRGME9Y2W2FQC/Anatomical+Directionalities+of+Fishes+Fish+Ventral+Dorsal+Anterior+Posterior+Koaw+Nature.png?format=2500w possibly be described as at the "top"? It's also problematic and circular to describe "top" in terms of "left" or "right" when the purpose is to define what top, left, right, etc. are. IMO the description should be in terms of some other characteristics (such as organs located in that direction). — Preceding unsigned comment added by Blaine-dev (talk • contribs) 22:11, 26 July 2023 (UTC)

title: Talk:Anatomical terms of location


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Malayalam calendar

The Malayalam Calendar is a sidereal solar calendar used in Kerala. The origin of the calendar has been dated to 825 CE, the beginning of the Kollam Era.

There are many theories regarding the origin of the era, but according to recent scholarship, it commemorated the foundation of Kollam after the liberation of the southern Chera kingdom (known as Venadu) from the Chola dynasty's rule by or with the assistance of the Chera emperor at Kodungallur. The origin of the Kollam Era has been dated to 825 CE, at the end of the three year-long great convention in Kollam held at the behest of the Venadu King Kulasekharan. Scholars from west and east were present in the convention, and the Tamil Kanakku (Calendar) was adopted.

Kollam was the capital of Venadu and an important port town of the Chera Kingdom in that period. Kollam Aandu was adapted in the entire Chera Kingdom (the contemporary states of Tamil Nadu, Karnataka, and Kerala), the majority of which is now in Kerala. In Malayalam-speaking Kerala, it is now called the Malayalam Era or 'Kollavarsham’ (Kollam Thontri Aandu). The earliest available record mentioning the Kollam Era is a royal decree by Sri Vallavan Goda, the King of Venadu, dated to c. 973 CE (Kollam Era 149). In the inscription, the phrase "Kollam Thontri Aandu" is employed. Another era, referred to as "Kollam Aḻintha Aandu", counting from 1097 CE, was reckoned by the Cholas for some time. It is tentatively calculated that the Chola overlords captured the port of Kollam in 1097 CE.

History
The origin of the Kollam Era has been dated to 825 CE, when the great convention in Kollam was held at the behest of King Kulashekharan. Kollam was an important town in that period, and the Malayalam Era is called 'Kollavarsham'.

There are multiple conflicting accounts regarding the origins of the Malayalam calendar, some of which are mentioned below:

 * The Kollam era is attributed to the legend of the hero Paraśurāma, an avatar (incarnation) of the god Vishnu. It is sometimes divided into cycles of 1,000 years reckoned from 1176 BCE. Thus, 825 CE would have been the first year of the era's third millennium.
 * The news of the physical disappearance of Sri Adi Shankaracharya in 820 CE at Kedarnath reached Kerala only a few years later. It is believed that Kerala began the Malayalam era, also called the Kollam era, in 825 CE in his memory.
 * According to Hermann Gundert, Kollavarsham started as part of erecting a new Shiva Temple in Kollam and because of the strictly local and religious background, the other regions did not follow this system at first. Once Kollam port emerged as an important trade center, however, the other countries also started to follow the new system of calendar. This theory backs the remarks of Ibn Battuta as well.
 * It is also believed that the era started as part of erection of the Thirupalkadal Sreekrishnaswamy Temple, family temple of Venad located at Keezhperoor or Kil-perur. Keezhperoor is a place located near Kilimanoor, which is used as prefix along with name of Venad and Travancore monarchs and is believed to be the maternal home of Kulasekhara Alvar.

Months
Makaram month (middle of January) was the starting of the Kollam Aandu (year). It was similar to the other calendars followed in the Pandya and Chola Kingdoms. The Chera kingdom had two harvests, one in Makaram and the other in Kanni, so the year started in Makaram, the harvesting month. Later, in the 20th century, after Venadu (the Travancore Kingdom) joined the Indian Union, the Calendar was aligned with that of the Sanskrit Calendar to have the Year Starting in Medam (April middle).

The Malayalam months and the Sanskritic Sauramāsa (solar month) are almost the same, raising many doubts that which came first. If you see, Chingam is a month in Kollam Era. Sanskrit also has the solar month, the Simham, and so on. This is unlike the case in Tulu calendar which follow the names of lunar months. The following are the months of the astronomical Malayalam calendar:

Days
The days of the week in the Malayalam calendar are suffixed with Aazhcha (ആഴ്ച), meaning week.

Like the months above, there are twenty seven stars starting from Aswati (Ashvinī in Sanskrit) and ending in Revatī. The 365 days of the year are divided into groups of fourteen days called Ñattuvela (ഞാറ്റുവേല), each one bearing the name of a star.

Significant dates

 * Vishu (1st Medam): Malayali New Year (traditional)
 * Onam
 * 1st Chingam: Malayali New Year (as per the Kollam Era calendar)

Vishu (വിഷു), celebrated on the first day of Medam, and Onam (ഓണം), celebrated on the star Thiruvonam in the month of Chingam, are two of the major festivals. The first day of Chingam is celebrated as the Kerala New Year, replacing Vishu (വിഷു), which was considered the beginning of a year until 825 CE. Vishu is still celebrated as the traditional Malayali New Year, particularly in erstwhile Malabar and South Canara areas, as it is astronomically significant, 'Medam' being the first among the 12 rashis (the zodiac signs corresponding to the 12 months of a solar year).

The Makaravilakku festival is celebrated in the Ayyappa Temple at Sabarimala on the first day of Makaram month. This marks the grand finale of the two-month period to the Sabarimala pilgrimage. The 1st of Makaram marks the winter Solstice (Uttarayanam) and the 1st of Karkaṭakam marks the summer solstice (Dakshinayanam) according to the Malayalam calendar (according to the astronomical calendar, the summer solstice is on 21 June, and the winter solstice on 21 December).

Chaitram 1 (usually coinciding with 20 March) or Medam 1 (mostly coinciding with 14 April, for 2019 it was on 15 April), both in the proximity of the date of the vernal equinox (21 March), mark the beginning of the new year in many traditional Indian calendars such as the Indian national calendar and the Tamil calendar. When the Government of Kerala adopted Kolla Varsham as the regional calendar, the first of Chingam, the month of the festival of Onam, was accepted as the Malayalam New Year instead.

Derived names
Many events in Kerala are related to the dates in the Malayalam calendar.

The agricultural activities of Kerala are centred on the seasons. The southwest monsoon which starts around 1 June is known as Etavappathi, meaning mid of month Etavam. The northeast monsoon which starts during mid October is called thulavarsham (rain in the month of thulam). The two harvests of paddy are called Kannikkoythu and Makarakkoythu (harvests in the months kanni and makaram) respectively.

title: Malayalam calendar


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Michael Williams (actor)

Michael Leonard Williams (9 July 1935 – 11 January 2001) was a British actor who played both classical and comedy roles. He was best known for co-starring in the sitcom A Fine Romance with his wife Dame Judi Dench, and for voicing Dr. Watson in the long-running Sherlock Holmes adaptations for BBC Radio.

Biography
Williams was born in Salford, Lancashire, England.

Williams married Judi Dench on 5 February 1971, the same year in which they co-starred in a stage production of John Webster's The Duchess of Malfi. They had one daughter, Finty Williams, who is also an actress. Williams was also godfather to the actor Rory Kinnear.

Williams was the President of the Roman Catholic Actors' Guild.

Shortly before his death from lung cancer aged 65, Williams was appointed a Knight of St Gregory (KSG) by Pope John Paul II for his contribution to Catholic life in Britain. The honour was officially bestowed upon him at home on 10 January 2001. He died the next day, and was buried in the churchyard of St Leonard's, the Anglican parish church of Charlecote, Warwickshire. Williams was a fan of Everton FC.

Stage roles
Principal stage appearances; mostly with the Royal Shakespeare Company: • A Midsummer Night's Dream (1963)

• The Beggar's Opera (1963)

• The Representative (1963)

• King Lear (1964)

• The Comedy of Errors  (1964)

• Marat/Sade (1964)

• The Jew of Malta  (1964)

• Don't Make Me Laugh (1965)

• Timon of Athens (1965)

• Hamlet (1965)

• Tango (1966)

• The Taming of the Shrew (1967)

• As You Like It (1967)

• Troilus and Cressida  (1968)

• London Assurance (1970)

• The Merchant of Venice  (1971)

• The Duchess of Malfi (1971)

• Henry V (1971)

• Toad of Toad Hall (1972)

• Content to Whisper  (1973)

• Jingo (1975)

• Too True to Be Good  (1975)

• The Comedy of Errors (1976)

• The Winter's Tale  (1976)

• Schweik in the Second World War  (1977)

• The Montrous Regiment (1978)

• A Village Wooing  (1981)

• Quartermaine's Terms (1982)

• Pack of Lies (1983/4)

• Two into One (1984)

• Mr and Mrs Nobody (1986/7)

• Out of Order (1990)

• The Tempest (1995)

• The Round Dozen (1996)

• Brief Lives   (1997/8)

• The Forest (1999) Also appeared in the Royal Shakespeare Company's Theatre-Go-Round Festival, Round House Theatre, London, 1970.

title: Michael Williams (actor)


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Talk:Parity (mathematics)

Redirection
Maybe merge & redirect to Parity? -- Tarquin 23:30 Jan 16, 2003 (UTC)

It was rather ridiculous that Even, Even integer, and Even number all redirected to Odd number. So, I've expanded the content and moved it to the generic "Even and odd numbers". -- Minesweeper 01:10 3 Jun 2003 (UTC)

 * I second your decision. Sometimes it is meaingless to have two seprate articles for some pair of concepts.

Integers only
Anyway, I know this is too detailed but the opening setence says:
 * any integer can be either even or odd. A number is called an even number if it can be evenly divided by two.

The readers might wonder so what's exactly difference between integer and number? Any integer can be even or odd and a number dividable by 2 is an even number. What about integers? -- Taku 03:37 3 Jun 2003 (UTC)

I wonder can a real number be even or odd? -- Taku 04:10 3 Jun 2003 (UTC)

 * Well, if the real number in question happens to be an integer, it can. ;) -- Oliver P. 04:13 3 Jun 2003 (UTC)

Whata about 1.2? It's not an integer but a real number and even. -- Taku 12:44 3 Jun 2003 (UTC)

Eh? How 1.2 an even number? No fraction can be an even number by definition.

 * Right. non-integers are neither even nor odd by definition. -- Taku

But it can be evenly divided by 2: 1.2/2 = 0.6. ^_^
 * How long has 0.6 been an integer?

-- Toby Bartels 05:37 12 Jun 2003 (UTC)
 * You're a wild and crazy guy. -- Cimon Avaro on a pogo stick 05:43 12 Jun 2003 (UTC)

 * By the definition that mathematicians come up with, only is an integer an even number. But it may be wrong in practice. Because to me, 1.2 or 0.6 look like an even number while 1.3 may be odd. -- Taku

I guess that the point is that "evenly divided" is ambiguous until you specify what the quotient is allowed to be. But we say "multiple", which works fine. As for Taku's perceptions, 1.2 is an even multiple of 0.1, while 1.3 is an odd multiple ... but 1.3 = 1.30 is an even multiple of 0.01! -- Toby Bartels 05:53 12 Jun 2003 (UTC)

And if you write 1.2 in binary instead, you get 1.0011001100110011001... which suddenly makes it look not at all even any more... :) -- Oliver P. 06:08 12 Jun 2003 (UTC)
 * Rather depends where you stop writing it out (it's an infinitely recurring binary fraction; the number you wrote out is not equal to 1.2). mfc 17:03, 2 Dec 2004 (UTC)

I still think we should move this to parity and open with something like: "the parity of an integer is whether it is even or odd ... " -- Tarquin 09:13 12 Jun 2003 (UTC)

I don't want to think about combinging those, but I ceratinly won't stop you if you want to do it. -- Toby Bartels 09:37 12 Jun 2003 (UTC)

Is the odd / even parity of numbers natural or man made ? Eg. one / many is a "natural" distinction and I would argue, so is prime / non-prime. But parity depends on choosing 2 at the start - why not 3 or 5 ?46.208.181.195 (talk) 18:51, 17 June 2012 (UTC)

I think 1.2 should not be considered as even because, in this analogy, 3 which may also be written as 3.0 will also be an even number, and this way we will lose all the odds. So, no. The fractional numbers do not fall into the category of even or odd. — Preceding unsigned comment added by 14.139.50.90 (talk) 09:05, 25 November 2021 (UTC)

Music theory
Seriously though, could someone who knows wind instruments please clarify what fundamental means in that context. Thanks. (and do it by editing the article) -- Cimon Avaro on a pogo stick 05:49 12 Jun 2003 (UTC)

Evenness (or non-evenness?) of 0
"The number zero is even, because it is equal to two multiplied by zero."

But wouldn't zero then also be considered an odd number since zero is also equal to one multiplied by zero?

n * 0 = 0. Thus, regardless of what number n is, the result is always 0? —The preceding unsigned comment was added by Kindragon (talk • contribs).

One multiplied by zero does equal zero, but one multiplied by 987348792834 equals 987348792834 and 987348792834 is even. Multiplying something by one does not make it odd. Catch my drift? Rsercher (talk) 19:32, 20 June 2011 (UTC)

 * As the article says, an odd number is 2*n+1, where n is an integer. You can't write 0 that way, so it's not odd. "Odd" does NOT mean "2 times another odd number" —dcclark (talk) 06:57, 27 December 2005 (UTC)

 * Zero is an even number, as Dr. Math (a.k.a. Dr. Rick) states. – TTD [[Image:Thetorpedodogwiki.png|16px|Mocha!]] Bark! (pawprints) 06:50, 8 August 2006 (UTC)

 * Zero is an even number because two divides 0.--Jersey Devil 00:28, 6 May 2007 (UTC)

 * See Evenness of zero. Melchoir 06:56, 14 September 2007 (UTC)

Parity
It would be nice to see the word "parity" used in a few sentences to get a sense of its usage. I've seen that numbers are said to have "even parity", the quality of being even, or "odd parity", the quality of being odd. What about numbers that aren't even or odd -- do they have "no parity", "neither parity", or "imparity"? Would one say that integers "have parity" but non-integers "do not have parity"? Would one say that "the parity of 53 is odd" or is that an invalid grammatical construction? Zeroparallax 20:44, 25 March 2007 (UTC)

 * That is better suited for a dictionary, not an encyclopedia. --Cheeser1 08:58, 23 August 2007 (UTC)

Number Theory
In number theory, Nielsen proved the following. An odd positive number N such that :$$\sigma_{1}(N)/ N = n/d $$ ( n,d ∈ N * ) and ω(N)= k is less than $$ (d+1)^{4^{k}} $$. —Preceding unsigned comment added by 218.133.184.93 (talk) 19:41, 16 September 2007 (UTC)
 * In case anyone here is not familiar with this case: Requests for comment/WAREL; Category:Suspected Wikipedia sockpuppets of WAREL. —David Eppstein 19:48, 16 September 2007 (UTC)

Arithmetic rules of parity
I removed from the subsection on multiplicative parity the following remark:
 * These rules only hold because 2 is a prime number; the analogous rules for divisibility by a composite number would be more complex.

I removed it because this is not an adequate explanation of parity rules. The rules for primes larger than 2 are also more complex. 2 and parity occupy a special place, not generalized directly to other numbers. Zaslav (talk) 21:16, 24 February 2008 (UTC)

Prime Connection
I think it would be very germane to mention the connection to prime numbers via Goldbach's. thus, odd+odd = even  [via GC =prime + prime]  and odd+odd = even [via GC =prime + prime] I understand it is not "proven", but is widely believed to hold, and really drives home the connections between all of the positive integers.--Billymac00 (talk) 21:31, 6 March 2008 (UTC)

Parity in culture?
Is it worth to mention that in many cultures even numbers were associtated with bad luck, and odd numbers were supposed to bring luck? — Preceding unsigned comment added by Ilya-42 (talk • contribs) 08:37, 28 June 2011 (UTC)

Title
It is weird that there is no article named Even number and Odd number on English Wikipedia (they are only redirect pages), even MathWorld has these.

I think the current title "Parity (mathematics)", which refers to the evenness or oddness, is too technical and unfamiliar for non-mathematicians. So I suggest moving this article to "Even and odd numbers", which is also avoids a parenthetical disambiguation. (I think it is unnecessary to divide it into Even number and Odd number.) --Minawa Yukino (talk) 09:06, 22 September 2012 (UTC)

 * I would actually support this suggested rename as a better-known description of the concept described, and as being less ambigiuous. The concept of parity (as described in the last section of the article) is a common use of the term, but is a distinct meaning: the hamming weight of a bit string modulo-2; it is only indirectly related to the topic of this article. As per WP:NAD, we should not be covering distinct uses of a term in one article. In a sense, the topic is really oddness and evenness of numbers, but this makes for a clumsy title. —Quondum 23:49, 1 May 2015 (UTC)

Parity of any rational number can be determined
http://math.stackexchange.com/questions/92451/can-decimal-numbers-be-considered-even-or-odd What I gathered from Patrick Da Silva's answer is such: Any rational number a can be represented as a fraction n/d. If n is even, a is even. If n is odd, a is odd.

I found this after wondering about the function y=x^(1/a), which is an easy way to determine whether a number is odd or even. If a is an even number, such as 2, the graph includes only real values of y when x>=0. If a is an odd number, such as 3, the graph of the function includes real values of y when x<0. Here we find that any rational number follows the same rules, not just integers. When a is a number such as 2/5, or 0.4, the graph will include only real values of y when x>=0. When a is a number such as 3/5, or 0.6, the graph will include real values of y when x<0

To summarize: A fraction is even if the numerator is, therefore all rational numbers have parity.

For another explanation, with visual effects, visit https://www.desmos.com/calculator/okiivdqo94 Zekava (talk) 23:08, 3 August 2015 (UTC)
 * While you can define the parity of fractions in this way (or in any other way that pleases you), it is problematic. In particular, consider the case 1/8 + 1/8 = 1/4. Shouldn't we have a rule that adding an odd number to itself produces an even one? To my mind, the correct generalization is to go from binary values (is it odd or even) to integer values (what is the smallest integer k such that 2k times the given number is an integer), or in fancier terms the 2-adic valuation. —David Eppstein (talk) 23:43, 3 August 2015 (UTC)
 * PS If you stick to rational numbers n/d for which d is odd, the rule you describe for calling them even or odd produces results that are much more consistent with integer arithmetic. One way to explain this is that in 2-adic arithmetic, these numbers are actually (2-adic) integers. —David Eppstein (talk) 08:01, 4 August 2015 (UTC)

Are there more even numbers than odd, more odd numbers than even, an equal number of odd and even numbers, or is it unknown which is greater?
I once conjectured that not all infinities were equal, and asked a mathematician friend to see if my conjecture was correct. He confirmed it was, pointing out to me that the set of all even numbers was not as great as the set of all integers, which in turn is not as great as the set of all real numbers, despite all three of these sets being infinite. This meant that the latter infinities were larger than the former. That made sense. Unfortunately, one thing this article does not discuss is whether the set of all even numbers is infinitesimally larger than, infinitesimally smaller than, or equal to the set of all odd numbers. Here's why this appears to me a conundrum: Obviously, zero is even, always even, and nothing but even. This is completely obvious. Nothing in the history of humankind, in fact, has ever been so obvious. But, unlike every other even number, zero lacks a negative counterpart. In other words, +0 and −0 are the same number, viz., zero; the value they represent is identical. If there were no zero, then we could easily conclude that there were an even number of even and odd numbers, exactly the same infinite number of each, with exactly half of each being on the positive side and the other half of each being on the negative side. But the fact that zero exists throws what appears at least to me to be a wrench in our count. At first, the solution appears simple enough. Since there is a negative one and a positive one, both of which are negative, and a negative two and a positive two, both of which are positive, if there were no zero, we might conclude that, starting at the ones and moving out to the twos, we are even, with exactly two evens and two odds. If we move forward a couple more steps, to include both the positive and negative threes and fours, we're still even, just as we are if we extend out to the tens, the quadrillions, or infinity—again, if there were no zero. And, since there is a zero, and since it is even, we would then conclude that the set of even numbers is infinitesimally larger than the set of odd numbers. At first, that solution appears pretty convincing. But, then I got to thinking, that's because I'm starting with the ones and adding the zero at the end. But, I get a very different result if I acknowledge and start with the zero from the start. Remember, negative zero is not a different number than zero; they're the same number, by which I mean, they occupy the same exact point on any graph, not two separate points. They are but one number. So, if I start with the zero, I can either throw it in with my count of the positive evens or with my count of the negative evens, but I can't throw it into both, for by doing so, I treat it as two separate points, when it is only a single point. I throw it in with the positive evens because, well, why not? I've got to throw it in with one side, and both sides are just as good as the other. Certainly, the count isn't going to be effected regardless of on which side I throw it; either way, it's a single even number, not two even numbers. So, zero is an even number, while both negative one and positive one are odd numbers. Right now, odds and beating even two-to-one. If we move forward a couple more steps, to include both the positive and negative twos and threes, we still have one more odd number than even, just as we have if we extend out by another ten steps, another quadrillion steps, or another infinite steps. This way of looking at it would lead us to concluding that the set of odd numbers is infinitesimally larger than the set of even numbers. And, yet, there is yet a third way to look at this pattern. We start with an even integer, and add to it two odd integers (viz., one and negative one), making odd lead two-to-one. We add to that two positive integers (viz., two and negative two), making even lead three-to-two. Next, odd leads four-to-three, then even five-to-four, odd six-to-five, and so on, creating a wave-pattern in which the number in the lead constantly fluctuates back and fourth across the median. In this way of thinking about it, either the odds nor the evens have a lead at infinity, which might lead us to thinking that there are ultimately an equal number of even and odd numbers, that the two infinities are equal in size. Unfortunately, I see nothing about the ratio of odd to even numbers being discussed in this article. If there is an answer to this, consider improving the article by adding the information and its proof. allixpeeke (talk) 08:25, 11 March 2017 (UTC)

 * Not sure that you heard your mathematician friend correctly or whether they just made a mistake, but the number (in the sense of cardinality) of even integers is the same as that of all the integers. The proof of this is given informally in the introductory section of countable set. The rest of that statement (that the number of reals is larger than the number of integers) is correct. The type of counting that you discuss above is a never ending process and there is no way to make a conclusion about what happens when it's over, because it is never over! A different way of thinking about this issue is needed and this is discussed in cardinality. Also, when talking about infinite sets, it is not a good idea to refer to the "number" of elements ... that is a concept that works fine for finite sets but does not extend very well to infinite sets. The term "cardinality" is used for both finite and infinite sets, agrees with the idea of "number" for finite sets and makes sense for infinite sets.--Bill Cherowitzo (talk) 23:40, 11 March 2017 (UTC)

even/odd notations
I noticed that the set descriptions for even/odd were in math markup, instead of using the unicode like in the sets article (https://en.wikipedia.org/wiki/Set_(mathematics) )

Does anyone prefer it the current way, or would using the unicode be better?

Smallest even number
Sir would you tell me that "what is the smallest even number?" Don't use -ve or +ve even number. Only u tell me-Smallest Even number. Baji0071 (talk) 11:03, 23 August 2018 (UTC)

Airline flight numbers
According to https://www.johndcook.com/blog/2019/09/20/airline-flight-parity/, the accuracy of the following statement (sourced to this book) is questionable:
 * ''Among airline flight numbers, even numbers typically identify eastbound or northbound flights, and odd numbers typically identify westbound or southbound flights.

(CCing David Eppstein who appears to have authored this sentence.)

Regards, HaeB (talk) 17:59, 21 September 2019 (UTC)
 * I wouldn't have written that if it weren't in the source, but Google Books isn't giving me access to that page currently so I can't quote it for you. I suppose it could also vary from airline to airline. In any case, we have to go by what's in published reliable sources, not by personal observations on blogs. —David Eppstein (talk) 18:18, 21 September 2019 (UTC)
 * I wasn't able to access that page either, but Google Books lists another edition which I could read, and it says that the practice does indeed vary from airline to airline. "In his piece, Owen points out that some airlines will number their flights from east to west with odd numbers, and those from west to east with even numbers, but he explains that Southwest doesn't do this because its route network is so dense that they could not get that type of system to work efficiently." XOR'easter (talk) 19:16, 21 September 2019 (UTC)

Inscrutable sentence in intro
The intro stated: "In particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0." Unless all binary numbers are odd—and I'm quite confident they aren't—this isn't the case. I'm simply lopping off everything after the 'and' for the time being. If anybody knows what this sentence is trying to convey, please add that information back in. — Preceding unsigned comment added by HamartiaProsciuttoPharos (talk • contribs) 23:33, 26 February 2020 (UTC)
 * I do not see what difficulty you are having with the original sentence. 0110 is even but 01001 is odd. Last digit refers to the least significant digit and is in the rightmost position. What assumption are you making that is making this confusing?--Bill Cherowitzo (talk) 23:50, 26 February 2020 (UTC)
 * Here's my reading of the sentence: "In particular, a number expressed in the binary numeral system is odd if that number's last digit is 1 and even if that number's last digit is 0." These are inherently contradictory; a number's last digit cannot be both 1 and 0. Maybe it's the use of the demonstrative that's giving me trouble, but I'm not sure how else the sentence could be read.HamartiaProsciuttoPharos (talk) 05:16, 27 February 2020 (UTC)
 * EDIT: Oh jeez. I just realized what was wrong with my reading. I was stuck on the phrase "and even if"—i.e, "it is odd if its last digit is 0, and is still odd even if its last digit is 1." Foolish mistake on my part. I'm going to make an edit to the sentence structure to remove any ambiguity. HamartiaProsciuttoPharos (talk) 05:22, 27 February 2020 (UTC)
 * I suspected that that might be the problem, but did not want to put words in your mouth. The fix is fine. --Bill Cherowitzo (talk) 22:43, 27 February 2020 (UTC)

title: Talk:Parity (mathematics)


text:
Opium Wars

The Opium Wars were two conflicts waged between China and Western powers during the mid-19th century.

The First Opium War was fought from 1839 to 1842 between China and Britain. It was triggered by the Chinese government's campaign to enforce its prohibition of opium, which included destroying opium stocks owned by British merchants and the British East India Company. The British government responded by sending a naval expedition to force the Chinese government to pay reparations and allow the opium trade. The Second Opium War was waged by Britain and France against China from 1856 to 1860, and consequently resulted in China being forced to legalise opium.

In each war, the superior military advantages enjoyed by European forces led to several easy victories over the Chinese military, with the consequence that China was compelled to sign the unequal treaties to grant favourable tariffs, trade concessions, reparations and territory to Western powers. The two conflicts, along with the various treaties imposed during the century of humiliation, weakened the Chinese government's authority and forced China to open specified treaty ports (including Shanghai) to Western merchants. In addition, China ceded sovereignty over Hong Kong to the British Empire, which maintained control over the region until 1997. During this period, the Chinese economy also contracted slightly as a result of the wars, though the Taiping Rebellion and Dungan Revolt had a much larger economic effect.

First Opium War
The First Opium War broke out in 1839 between China and Britain and was fought over trading rights (including the right of free trade) and Britain's diplomatic status among Chinese officials. In the eighteenth century, China enjoyed a trade surplus with Europe, trading porcelain, silk, and tea in exchange for silver. By the late 18th century, the British East India Company (EIC) expanded the cultivation of opium in the Bengal Presidency, selling it to private merchants who transported it to China and covertly sold it on to Chinese smugglers. By 1797, the EIC was selling 4,000 chests of opium (each weighing 77 kg) to private merchants per annum.

In earlier centuries, opium was utilised as a medicine with anesthetic qualities, but new Chinese practices of smoking opium recreationally increased demand tremendously and often led to smokers developing addictions. Successive Chinese emperors issued edicts making opium illegal in 1729, 1799, 1814, and 1831, but imports grew as smugglers and colluding officials in China sought profit. Some American merchants entered the trade by smuggling opium from Turkey into China, including Warren Delano Jr., the grandfather of twentieth-century American President Franklin D. Roosevelt, and Francis Blackwell Forbes; in American historiography this is sometimes referred to as the Old China Trade. By 1833, the Chinese opium trade soared to 30,000 chests. British and American merchants sent opium to warehouses in the free-trade port of Canton, and sold it to Chinese smugglers.

In 1834, the EIC's monopoly on British trade with China ceased, and the opium trade burgeoned. Partly concerned with moral issues over the consumption of opium and partly with the outflow of silver, the Daoguang Emperor charged Governor General Lin Zexu with ending the trade. In 1839, Lin published in Canton an open letter to Queen Victoria requesting her cooperation in halting the opium trade. The letter never reached the Queen. It was later published in The Times as a direct appeal to the British public for their cooperation. An edict from the Daoguang Emperor followed on 18March, emphasising the serious penalties for opium smuggling that would now apply henceforth. Lin ordered the seizure of all opium in Canton, including that held by foreign governments and trading companies (called factories), and the companies prepared to hand over a token amount to placate him. Charles Elliot, Chief Superintendent of British Trade in China, arrived 3 days after the expiry of Lin's deadline, as Chinese troops enforced a shutdown and blockade of the factories. The standoff ended after Elliot paid for all the opium on credit from the British government (despite lacking official authority to make the purchase) and handed the 20,000 chests (1,300 metric tons) over to Lin, who had them destroyed at Humen.

Elliott then wrote to London advising the use of military force to resolve the dispute with the Chinese government. A small skirmish occurred between British and Chinese warships in the Kowloon Estuary on 4 September 1839. After almost a year, the British government decided, in May 1840, to send a military expedition to impose reparations for the financial losses experienced by opium traders in Canton and to guarantee future security for the trade. On 21 June 1840, a British naval force arrived off Macao and moved to bombard the port of Dinghai. In the ensuing conflict, the Royal Navy used its superior ships and guns to inflict a series of decisive defeats on Chinese forces.

The war was concluded by the Treaty of Nanking (Nanjing) in 1842, the first of the Unequal treaties between China and Western powers. The treaty ceded the Hong Kong Island and surrounding smaller islands to Britain, and established five cities as treaty ports open to Western traders: Shanghai, Canton, Ningbo, Fuzhou, and Xiamen (Amoy). The treaty also stipulated that China would pay a twenty-one million dollar payment to Britain as reparations for the destroyed opium, with six million to be paid immediately, and the rest through specified installments thereafter. Another treaty the following year gave most favoured nation status to Britain and added provisions for British extraterritoriality, making Britain exempt from Chinese law. France secured several of the same concessions from China in the Treaty of Whampoa in 1844.

Second Opium War

In 1853, northern China was convulsed by the Taiping Rebellion, which established its capital at Nanjing. In spite of this, a new Imperial Commissioner, Ye Mingchen, was appointed at Canton, determined to stamp out the opium trade, which was still technically illegal. In October 1856, he seized the Arrow, a ship claiming British registration, and threw its crew into chains. Sir John Bowring, Governor of British Hong Kong, called up Rear Admiral Sir Michael Seymour's East Indies and China Station fleet, which, on 23 October, bombarded and captured the Pearl River forts on the approach to Canton and proceeded to bombard Canton itself, but had insufficient forces to take and hold the city. On 15 December, during a riot in Canton, European commercial properties were set on fire and Bowring appealed for military intervention. The execution of a French missionary inspired support from France. The United States and Russia also intervened in the war.

Britain and France now sought greater concessions from China, including the legalization of the opium trade, expanding of the transportation of coolies to European colonies, opening all of China to British and French citizens and exempting foreign imports from internal transit duties. The war resulted in the 1858 Treaty of Tientsin (Tianjin), in which the Chinese government agreed to pay war reparations for the expenses of the recent conflict, open a second group of ten ports to European commerce, legalize the opium trade, and grant foreign traders and missionaries rights to travel within China. This also included China being required to bend to Western diplomatic behaviors instead of their normal way of conducting business through a tribute system. This treaty led to the era in Chinese history known as the "Century of Humiliation", this term referring to how China lost control of many territories to its enemies after being forced into treaties which were unfair in their own regard. After a second phase of fighting which included the sack of the Old Summer Palace and the occupation of the Forbidden City palace complex in Beijing, the treaty was confirmed by the Convention of Peking in 1860.

The impact of the Opium War on cultural relics
In February 1860, the British and French imperialist authorities again appointed Elgin and Grotto as plenipotentiaries respectively, leading more than 15,000 British troops and about 7,000 French troops to expand the war against China. The British and French forces invaded Beijing, and the Qing emperor fled to Chengde. The British and French forces broke into the Old Summer Palace, looted jewelry, and burned it. Among the cultural relics that were looted were the well-known Old Summer Palace bronze heads. On the morning of October 7, the French army broke into the Old Summer Palace and began to rob it. British soldiers who arrived in the afternoon also joined the robbery, and the most precious things in the Old Summer Palace were looted. All twelve bronze statues of animal heads began to be lost overseas. On October 18, the Old Summer Palace was burned down by British soldiers, and France refused to provide aid. The fire burned for three days and nights, razing the buildings of the Old Summer Palace to the ground and destroying nearby royal properties.

As of December 2020, seven of the twelve bronze statues have been found and returned to China. The whereabouts of the remaining five are still unknown.

Cited references and further reading

 * Beeching, Jack. The Chinese Opium Wars (Harvest Books, 1975)
 * Gelber, Harry G. Opium, Soldiers and Evangelicals: Britain's 1840–42 War with China, and its Aftermath. Palgrave Macmillan, 2004.
 * Hanes, W. Travis and Frank Sanello. The Opium Wars: The Addiction of One Empire and the Corruption of Another (2014)
 * Kitson, Peter J. "The Last War of the Romantics: De Quincey, Macaulay, the First Chinese Opium War". Wordsworth Circle (2018) 49#3.
 * Lovell, Julia. The Opium War: Drugs, Dreams, and the Making of Modern China(2011).
 * Marchant, Leslie R. "The War of the Poppies", History Today (May 2002) Vol. 52 Issue 5, pp 42–49, online popular history
 * 556 pp.
 * Kenneth Pomeranz, "Blundering into War" (review of Stephen R. Platt, Imperial Twilight: The Opium War and the End of China's Last Golden Age, Vintage), The New York Review of Books, vol. LXVI, no. 10 (6 June 2019), pp. 38–41.
 * Polachek, James M., The inner opium war (Harvard Univ Asia Center, 1992).
 * Waley, Arthur, ed. The Opium War Through Chinese Eyes (1960).
 * Wong, John Y. Deadly Dreams: Opium, Imperialism, and the Arrow War (1856–1860) in China. (Cambridge UP, 2002)
 * Yu, Miles Maochun. "Did China Have a Chance to Win the Opium War?" Military History in the News, July 3, 2018.
 * Wong, John Y. Deadly Dreams: Opium, Imperialism, and the Arrow War (1856–1860) in China. (Cambridge UP, 2002)
 * Yu, Miles Maochun. "Did China Have a Chance to Win the Opium War?" Military History in the News, July 3, 2018.

title: Opium Wars


text:
Talk:Information hiding

Old copy
In computer science and object-oriented programming, encapsulation or modularity refers to how objects contain and manipulate data. Encapsulation (also referred to as, "information hiding") is the practice of hiding the data structures which represent the internal state of an object from access by anything other than the publicly-exposed methods of that object. This ensures that objects cannot change the internal state of other objects in unexpected ways, minimizing the complexity of putting together modules of code from different sources.

Encapsulated code can generally be rewritten without any need to rewrite the encapsulating code.

The two main advantages of encapsulation are:

 * 1) The data structure that represents the state can be reimplemented without affecting the implementation of the other objects. For example if the state of a point is represented internally with Cartesian coordinates then this might be changed to Polar coordinates without changing the interface of the object, i.e, without changing which messages with which arguments are understood by the object and what the type of the result of these messages will be.
 * 2) The state of the object can be guarded by the methods. The data structure that represents the state of the object may allow certain values that are not considered meaningful, e.g., a percentage may be represented by an integer that allows numbers larger than 100. The methods that update this integer can then ensure that it never rises above 100.

Many languages allow the programmer to bypass encapsulation, or to specify varying degrees of encapsulation for specific object types. In Java, for example, a class might be defined like this:

class Cow extends Mammal { public Tail m_tail; private Horns m_horns; public void eat(Food f) { super.eat(f); chewcud; }   private void chewcud { . . .   }  }

With the Cow type as defined above, some piece of code external to Cow's implementation would be allowed to access m_tail directly, without going through any of the methods that Cow has chosen to expose as its interface. Such code would not, however, be able to access m_horns. Likewise, the method eat is exposed as part of the Cow's interface, so any other object would be able to cause the cow object to eat by calling that method, passing it the offered food item as an argument to the method. External code would not be able to directly cause the cow to call its chewcud method (nor would it even know such a method existed; only the cow itself knows or cares that eating involves chewing its cud).

More to be said about how various languages handle encapsulation.

See also:
 * Design by contract

I disagree with this definition (what described is not encapsulation, but data hiding), but I don't want to change it unless others agree with me. This is a fairly complicated subject, because "encapsulation" is a buzzword to begin with, with no fixed definition (or many definitions that disagree with one another). Nevertheless, defining encapsulation as different from data hiding seems much more useful. There's discussion on exactly this subject going on on the c2.com wiki: http://c2.com/cgi-bin/wiki?EncapsulationIsNotInformationHiding. Please read it and form your opinion. -- Lament

I disagree too. Encapsulation is a fundamental principles of object-oriented programming, though several object-oriented languages doesn't have any "public" and "private" notions (e.g. Python, Perl, and (not sure) Smalltalk).

Encapsulation is rather the fact of putting BOTH data (= attributes) and procedures (=methods) in the same "capsule" = the "object". But the "capsule" may be transparent or not, it is still a capsule.

See Encapsulation is not information hiding : http://www.javaworld.com/javaworld/jw-05-2001/jw-0518-encapsulation.html

Jiba -- jiba@tuxfamily.org

I've removed everything from the article that is encapsulation and left only the parts that are information hiding. Hopefully, that has addressed the concerns above. However, I will add encapsulation back in as a separate section in this article since encapsulation is so closely related and as far as I know, doesn't have a separate entry.

I will also include some examples of information hiding.. in particular, one where the principle of information hiding is employed outside of an object-oriented programming language (that is, information hiding without encapsulation).

Lastly, I will include some of the history of this if I can find some good sources. I know this principle has been around long before David Parnas published his seminal paper in 1972. However, Parnas often does receive the attribution for coining the term.

Kendrick

Consider the following definitions:

 * Encapsulation is the public interface that defines how an object can be used, and how its data is derived.

 * Information Hiding prevents external objects from using the derived data altogether.

This implies that Information Hiding without Encapsulation is not possible. Consider the following examples:

No Encapsulation and no Information Hiding (severely bad):

class Mammal { public final static int EMPTY = 0; public final static int FULL = 1; public int tummy = EMPTY; }

Encapsulation and no Information Hiding (typically bad):

class Mammal { public final static int EMPTY = 0; public final static int FULL = 1; private int tummy = EMPTY; public int getTummyStatus { return this.tummy; }   public void setTummyStatus( int status ) { this.tummy = status; } }

Encapsulation and Information Hiding (good):

class Mammal { private final static int EMPTY = 0; private final static int FULL = 1; private int tummy = EMPTY; private int tummy { return this.tummy; }   private void tummy( int status ) { this.tummy = status; }   public void eat { tummy( FULL ); }   public void walk { if( tummy == FULL ) tummy( EMPTY ); else throw new ElfNeedsFoodBadly; } }

The object knows how to change itself, and does so without exposing its data to the rest of the world. As a consequence of both encapsulation and information hiding, the Mammal class may change how its tummy is used without affecting any other class in the system. For example, if hungriness was changed to a sliding scale (like gas in a car), then eat and walk could be modified to take the new sliding scale into consideration. Existing classes that used eat/walk would not need to change (whereas external classes that used either 'tummy' from the first example or 'getTummyStatus' from the second, would require changes).

Design decisions

 * In computer science, the principle of information hiding is the hiding of design decisions in a computer program that are most likely to change, thus protecting other parts of the program from change if the design decision is changed.

Aren't the decisions usually hidden implementation decisions rather than design decisions? - furrykef (Talk at me) 12:42, 6 Mar 2005 (UTC)

Very stupid article
My god, what idiotism/cretinism u can find in computer article!3 I cry. :^(

 * What the?
 * I like it how computer scientists always relate programming principles to some other kind of engineering procedure, even if the connection doesn't quite make sense. haha

Encapsulation issue.
I came to this article through the encapsulation disambiguation page. However, it seems that the very first reference to this term points back the same disambiguation page. What gives?? Folajimi(talk)
 * Be bold! I dunno.  I think I put it in, probably without looking.  Here, I'll be bold instead. --Mgreenbe 16:29, 26 January 2006 (UTC)

Another meaning for infomation hiding
What about the other meaning, where developers (usually consultants) will intentionally not divulge information to others, in an effort to make themselves appear indispensable?

what is "Example Information hiding?"
In the History section, second paragraph, the word "Example," which begins the first sentence, seems out of place, but I am not sufficiently familiar with this topic to boldly delete it. Bustter (talk) 23:08, 19 January 2010 (UTC)

Moving topic "Relation to object-oriented programming" to "Encapsulation" page
I think the Encapsulation (computer programming) page would be a better place for the section "Relation to object-oriented programming". Also, it doesn't seem to explain what it states in it's title. I will move the section until someone rejects this. Kaartic (talk) 16:06, 1 October 2016 (UTC)

Apparent conflation of implementation-hiding, information-hiding, and their applications.
Information-hiding, or data hiding, has traditionally been used for dual purposes of future-proofing (the same purpose as in implementation-hiding) and encapsulation (i.e. enforcement of invariants). This article's introduction only mentions the former. There is also a discussion on the talk page of encapsulation which promotes the conflation of data hiding and encapsulation. Encapsulation is distinct; the enforcement of invariants additionally employs exception safety (where applicable), synchronization, and a swathe of other programming constructs which are used to moderate the things that can occur both inside and outside privileged scopes. This page should present information hiding as a single, specific design construct which is used to express principles such as future-proofing and encapsulation, not as a principle in itself. 184.102.64.32 (talk) 07:52, 7 July 2020 (UTC)

Why is the change, confined to processes that follow change?
The term 'change' was used incorrectly, and connected to one action= limiting. Misdirection, rather than 'hiding information' is a clearer message. Of course how does one explain how to think abstractively, two times? And do you mean two abstract streams of thought, or thoughts, at the same time? or do you mean, two streams of abstractive thinking stacked, one on top of the other? pstract'. It has no singular or plural, as it i, and it just spirals on and out and all around from there. Do you realise thw implications of pretending to be cahleva, in these 'meaning levelling' times?times? 49.194.46.174 (talk) 07:22, 29 May 2024 (UTC)

There is no logic
Once the words 'more general' have been read, how can anyone read on? For anything to change its sliding scale of the sliding scale, one might slide, right off the flipping scale? 49.194.46.174 (talk) 07:27, 29 May 2024 (UTC)

title: Talk:Information hiding