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Sanhedrin

The Sanhedrin (Hebrew and Middle Aramaic סַנְהֶדְרִין, a loanword from, 'assembly,' 'sitting together,' hence 'assembly' or 'council') was a legislative and judicial assembly of either 23 or 71 elders, existing at both a local and central level in the ancient Land of Israel.

There were two classes of Rabbinite courts called sanhedrins: Greater and Lesser. A lesser Sanhedrin of 23 judges was appointed to sit as a tribunal in each city. There was only one Great Sanhedrin of 71 judges, which, among other roles, acted as a supreme court, taking appeals from cases that lesser courts decided. In general usage, the Sanhedrin without qualifier usually refers to the Great Sanhedrin, which was presided over by the Nasi, who functioned as its head or representing president, and was a member of the court; the Av Beit Din or the chief of the court, who was second to the nasi; and 69 general members.

In the Second Temple period, the Great Sanhedrin met in the Temple in Jerusalem, in a building called the Hall of Hewn Stones. The Great Sanhedrin convened every day except festivals and the sabbath day (Shabbat).

After the destruction of the Second Temple and the failure of the Bar Kokhba revolt, the Great Sanhedrin moved to Galilee, which became part of the Roman province of Syria Palaestina. In this period, the Sanhedrin was sometimes called the Galilean Patriarchate or Patriarchate of Palaestina, the governing legal body of Galilean Jewry. In the late 200s CE, to avoid persecution, the name Sanhedrin was dropped and its decisions were issued under the name of Beit HaMidrash (house of learning). The last universally binding decision of the Great Sanhedrin appeared in 358 when the Hebrew calendar was established. The Great Sanhedrin was finally disbanded in 425.

Over the centuries, attempts have been made to revive the institution, such as the Grand Sanhedrin convened by Napoleon Bonaparte and modern attempts in Israel.

Hebrew Bible
In the Hebrew Bible, Moses and the Israelites were commanded by God to establish courts of judges. They were also commanded to establish a "supreme court" located at the central sanctuary (after arriving in the Land of Israel), to handle cases too difficult for local courts.

When Moses declared that the task of leading the people was too difficult for him, God had him appoint 70 elders (zekenim) to share the burden of leadership with him. According to the Mishnah, these 70 elders plus Moses himself are the source for the 71 judges of the "Great Sanhedrin". These elders are described as "the elders of the people and its officers", according to a midrash, they were the same officers who were beaten in Egyptian slavery for failing to meet Pharaoh's quota of bricks, and after the Exodus were rewarded with membership on the first Sanhedrin.

The 23 judges of the "Lesser Sanhedrin" are derived from the following exegesis: it must be possible for a "community" to vote for both conviction and exoneration. The minimum size of a "community" is 10 men, thus 10 vs 10. One more is required to achieve a majority (11 vs. 10), but a simple majority cannot convict, and so an additional judge is required (12 vs. 10). Finally, a court should have an odd number of judges to prevent deadlocks; thus 23 rather than 22.

Early Sanhedrin
The first historic mention of a Synedrion (Greek: Συνέδριον) occurs in the Psalms of Solomon (17:49), a Jewish religious book translated into Greek.

The Hasmonean court in Judea, presided over by Alexander Jannaeus, until 76 BCE, followed by his wife, Queen Salome Alexandra, was called Synhedrion or Sanhedrin. The exact nature of this early Sanhedrin is not clear. It may have been a body of sages or priests, or a political, legislative and judicial institution. The first historical record of the body was during the administration of Aulus Gabinius, who, according to Josephus, organized five synedra in 57 BCE as Roman administration was not concerned with religious affairs unless sedition was suspected. Only after the destruction of the Second Temple was the Sanhedrin made up only of sages.

Josephus describes a synhedrion for the first time in connection with the decree of the Roman governor of Syria, Aulus Gabinius (57 BCE), who abolished the constitution and the then existing form of government of Palestine and divided the country into five provinces, at the head of each of which a synhedrion was placed; Jerusalem was the seat of one of these. Later, Josephus describes Herod (at the time governor of Galilee) as being summoned before the synhedrion, led by High Priest Hyrcanus II, due to having executed alleged criminals without permission from the synhedrion. Eventually, though, Herod would go on to kill many members of this synhedrion.

The Mishnah describes the Sanhedrin in this period further. The Great Sanhedrin met in the Hall of Hewn Stones in the Temple in Jerusalem. It convened every day except festivals and Shabbat. Its members included priests, Levites, and ordinary Jews whose families had a pure lineage such that their daughters were allowed to marry priests.

The trial of Jesus, and early Christianity
A Synhedrion is mentioned 22 times in the Greek New Testament, including in the Gospels in relation to the trial of Jesus, and in the Acts of the Apostles, which mentions a "Great Synhedrion" in chapter 5 where rabbi Gamaliel appeared, and also in chapter 7 in relation to the stoning death of Saint Stephen. This body is described as a court led by the High Priest or leading priests, as well as the "elders" and/or Pharisees.

During Jewish–Roman Wars
After the destruction of the Second Temple in 70 CE, the Sanhedrin was re-established in Yavneh, with reduced authority, by agreement between Yochanan ben Zakai and Roman Emperor Vespasian. Vespasian agreed in part due to the perception that the Pharisees had not participated in the first revolt to the extent that other groups had. Thus the Sanhedrin in Yavneh was comprised almost exclusively of pharisaic scholars. The imperial Roman government recognized the Sanhedrin. They regarded the head of the Sanhedrin as their own paid government official with the status of a prefect. Roman legislation severely reduced the scope of its authority, but confirmed the body's ultimate authority in religious matters. In an attempt to quash revolutionary elements, Rome in effect declared one form of Judaism to be the only recognized form of religion. This led to persecution of sectarian groups, and attempts by these groups to find fault with the Sanhedrin before the Roman government.

The seat of the Patriarchate moved to Usha under the presidency of Gamaliel II in 80 CE. In 116 it moved back to Yavneh, and then again back to Usha.

After Bar Kokhba Revolt
Rabbinic texts indicate that following the Bar Kokhba revolt, southern Galilee became the seat of rabbinic learning in the Land of Israel. This region was the location of the court of the Patriarch which was situated first at Usha, then at Bet Shearim, later at Sepphoris and finally at Tiberias.

The Great Sanhedrin moved in 140 to Shefaram under the presidency of Shimon ben Gamliel II, and subsequently to Beit She'arim and later to Sepphoris, under the presidency of Judah ha-Nasi (165–220). Finally, it moved to Tiberias in 220, under the presidency of Gamaliel III (220–230), a son of Judah ha-Nasi, where it became more of a consistory, but still retained, under the presidency of Judah II (230–270), the power of excommunication.

During the presidency of Gamaliel IV (270–290), due to Roman persecution, it dropped the name Sanhedrin; and its authoritative decisions were subsequently issued under the name of Beth HaMidrash.

In the year 363, the emperor Julian (r. 355–363 CE), an apostate from Christianity, ordered the Temple rebuilt. The project's failure has been ascribed to the Galilee earthquake of 363, and to the Jews' ambivalence about the project. Sabotage is a possibility, as is an accidental fire. Divine intervention was the common view among Christian historians of the time. As a reaction against Julian's pro-Jewish stance, the later emperor Theodosius I (r. 379–395 CE) forbade the Sanhedrin to assemble and declared ordination illegal. Capital punishment was prescribed for any Rabbi who received ordination, as well as complete destruction of the town where the ordination occurred.

However, since the Hebrew calendar was based on witnesses' testimony, which had become far too dangerous to collect, rabbi Hillel II recommended change to a mathematically based calendar that was adopted at a clandestine, and maybe final, meeting in 358 CE. This marked the last universal decision made by the Great Sanhedrin.

Gamaliel VI (400–425) was the Sanhedrin's last president. With his death in 425, Theodosius II outlawed the title of Nasi, the last remains of the ancient Sanhedrin. An imperial decree of 426 diverted the patriarchs' tax (post excessum patriarchorum) into the imperial treasury. The exact reason for the abrogation of the patriarchate is not clear, though Gamaliel VI, the last holder of the office who had been for a time elevated by the emperor to the rank of prefect, may have fallen out with the imperial authorities. Thereafter, Jews were gradually excluded from holding public office. A law dated to 429, however, refers to the existence of a Sanhedrin in each of the Eastern Roman provinces of Palestine.

Powers
The Talmud tractate Sanhedrin identifies two classes of rabbinical courts called Sanhedrin, a Great Sanhedrin (בית דין הגדול) and a Lesser Sanhedrin (בית דין הקטן). Each city could have its own lesser Sanhedrin of 23 judges, but there could be only one greater Sanhedrin of 71, which among other roles acted as the Supreme Court, taking appeals from cases decided by lesser courts. The uneven numbers of judges were predicated on eliminating the possibility of a tie, and the last to cast his vote was the head of the court.

Function and procedures
The Sanhedrin as a body claimed powers that lesser Jewish courts did not have. As such, they were the only ones who could try the king, extend the boundaries of the Temple and Jerusalem, and were the ones to whom all questions of law were finally put. Moreover, the lesser Sanhedrin of 23 judges was the only juridical body in Israel having the statutory and constitutional authority and power to render a verdict of capital punishment to would-be offenders, and the greater Sanhedrin of 71 judges was solely authorized to send forth the people to a battle waged of free choice.

Before 191 BCE the High Priest acted as the ex officio head of the Sanhedrin, but in 191 BCE, when the Sanhedrin lost confidence in the High Priest, the office of Nasi was created. After the time of Hillel the Elder (late 1st century BCE and early 1st century CE), the Nasi was almost invariably a descendant of Hillel. The second highest-ranking member of the Sanhedrin was called the Av Beit Din, or 'Head of the Court' (literally, Av Beit Din means 'father of the house of judgment'), who presided over the Sanhedrin when it sat as a criminal court.

During the Second Temple period, the Sanhedrin met in a building known as the Hall of Hewn Stones (Lishkat ha-Gazit), which has been placed by the Talmud and many scholars as built into the northern wall of the Temple Mount, half inside the sanctuary and half outside, with doors providing access variously to the Temple and to the outside. The name presumably arises to distinguish it from the buildings in the Temple complex used for ritual purposes, which could not be constructed of stones hewn by any iron implement.

In some cases, it was necessary only for a 23-member panel (functioning as a Lesser Sanhedrin) to convene. In general, the full panel of 71 judges was convened only on matters of national significance (e.g., a declaration of war) or when the 23-member panel failed to reach a conclusive verdict.

By the end of the Second Temple period, the Sanhedrin reached its pinnacle of importance, legislating all aspects of Jewish religious and political life within parameters laid down by Biblical and Rabbinic tradition.

Summary of Patriarchal powers
The following is a summary of the powers and responsibilities of the Patriarchate from the onset of the third century, based on rabbinic sources as understood by L.I. Levine:
 * 1) Representative to Imperial authorities;
 * 2) Focus of leadership in the Jewish community:
 * 3) Receiving daily visits from prominent families;
 * 4) Declaration of public fast days;
 * 5) Initiating or abrogating the ban (herem);
 * 6) Appointment of judges to Jewish courts in the Land of Israel;
 * 7) Regulation of the calendar;
 * 8) Issuing enactments and decrees with respect to the applicability or release from legal requirements, e.g.:
 * 9) Use of sabbatical year produce and applicability of sabbatical year injunctions;
 * 10) Repurchase or redemption of formerly Jewish land from gentile owners;
 * 11) Status of Hellenistic cities of the Land of Israel re: purity, tithing, sabbatical year;
 * 12) Exemptions from tithing;
 * 13) Conditions in divorce documents;
 * 14) Use of oil produced by gentiles;
 * 15) Dispatching emissaries to diaspora communities;
 * 16) Taxation: both the power to tax and the authority to rule/intervene on the disposition of taxes raised for local purposes by local councils.

Up to the middle of the fourth century, the Patriarchate retained the prerogative of determining the Hebrew calendar and guarded the intricacies of the needed calculations, in an effort to constrain interference by the Babylonian community. Christian persecution obliged Hillel II to fix the calendar in permanent form in 359 CE. This institution symbolized the passing of authority from the Patriarchate to the Babylonian Talmudic academies.

Archaeological findings
In 2004, excavations in Tiberias conducted by the Israel Antiquities Authority uncovered a structure dating to the 3rd century CE that may have been the seat of the Sanhedrin when it convened in that city. At the time it was called Beit Hava'ad.

Nasi (president)
Before 191 BCE the High Priest acted as the ex officio head of the Sanhedrin, but in 191 BCE, when the Sanhedrin lost confidence in the High Priest, the chair passed to the new office of the Nasi. The Sanhedrin was headed by the chief scholars of the great Talmudic Academies in the Land of Israel, and with the decline of the Sanhedrin, their spiritual and legal authority was generally accepted, the institution itself being supported by voluntary contributions by Jews throughout the ancient world.

Being a member of the house of Hillel and thus a descendant of King David, the Nasi (prince), who was the chairman of the assembly, enjoyed almost royal authority. His functions were political rather than religious, though the office’s influence was not limited to the secular realm. The Patriarchate attained its zenith under Judah ha-Nasi, who compiled the Mishnah.

Revival attempts
Since the dissolution of the Sanhedrin in or around 358 CE, there have been several attempts to re-establish it.

There are records of what may have been attempts to reform the Sanhedrin in Arabia, in Jerusalem under the Caliph Umar, and in Babylon (Iraq), but none of these attempts were given attention by later rabbinic authorities and little information is available about them.

Maimonides (1135–1204) proposed a rationalist solution for achieving the goal of re-establishing semikhah and the Sanhedrin. There have been several attempts to implement Maimonides' recommendations by Rabbi Jacob Berab in 1538, Rabbi Yisroel Shklover in 1830, Rabbi Aharon Mendel haCohen in 1901, Rabbi Zvi Kovsker in 1940, Rabbi Yehuda Leib Maimon in 1949, and a group of Israeli rabbis in 2004.

Napoleon Bonaparte's "Grand Sanhedrin"
The "Grand Sanhedrin" was a Jewish high court convened by Napoleon I to give legal sanction to the principles expressed by the Assembly of Notables in answer to the twelve questions submitted to it by the government. It did not follow the halakhic procedures of the traditional Sanhedrin.

On 6 October 1806, the Assembly of Notables issued a proclamation to all the Jewish communities of Europe, inviting them to send delegates to the Sanhedrin, to convene on 20 October. This proclamation, written in Hebrew, French, German, and Italian, speaks in extravagant terms of the importance of this revived institution and of the greatness of its imperial protector. While the action of Napoleon aroused in many Jews of Germany the hope that, influenced by it, their governments also would grant them the rights of citizenship, others looked upon it as a political contrivance. When in the war against Prussia (1806–07) the emperor invaded Poland and the Jews rendered great services to his army, he remarked, laughing, "The sanhedrin is at least useful to me." David Friedländer and his friends in Berlin described it as a spectacle that Napoleon offered to the Parisians.

title: Sanhedrin


text:
Talk:Nimber

I just can't
Pleas for the love of pete one of you super smart peole make a youtube video... some of us cant even read and there is literally nothing relevant that come up on yt when searching nimber. I'm sorry that my life has turned out the way it has but please somebody.... 68.13.124.209 (talk) —Preceding undated comment added 04:30, 2 August 2017 (UTC)

Standard value?
Nice article! I didn't understand this:
 * (2) The nimber square of a Fermat 2-power x is equal to the standard value of 3x/2.

What does "standard value of 3x/2" mean? AxelBoldt 01:50 Jan 5, 2003 (UTC)

Thanks. The part that you asked about has been edited. It means the value of 3x/2 under the ordinary multiplication of natural numbers, so that the nimber square of 2 is 3, the nimber square of 4 is 6, the nimber square of 16 is 24, the nimber square of 256 is 384, etc. David McAnally 21:22 Jul 1, 2004 (AEST)

Nested exponents
Other than the clumsy workaround 22^n or some sort of graphic (such as appears on the Fermat number page), is there any way to get Wikipedia to deal with nested exponents? I changed to the above workaround, as the previous format looked like 22n in my browser. MJSS 20:29, 3 Sep 2004 (UTC)

 * If worse comes to worst you could resort to TeX and write: $$2^{2^n}$$. Formerly, TeX looked good when "displayed" and often looked terrible when embedded in lines of text.  Now it may look less than beautiful, but usually is nowhere near as bad as it used to be.  Of course, if you're going to "display" it, thus

 * $$\int_0^\infty 1\,dx$$

 * then using TeX works well. Michael Hardy 22:17, 3 Sep 2004 (UTC)

 * Oh -- one more thing. The paragraph I wrote above was already indented, so I need to indent the "displayed" TeX twice. Michael Hardy 22:18, 3 Sep 2004 (UTC)

There is a similar problem with omega^omrga^omega at the point where it was pointed out that the set of nimbers less than omega^omega^omega is an algebraically closed field. Like 2^2^n, it does not look right, although it once did.

David McAnally 25 Septemeber, 2004

What does the following look like to you?

 * $$\omega^{\omega^\omega}\neq 2^{2^n}.$$

Specifically where in the article is the problem you're referring to?

Michael Hardy 00:14, 26 Sep 2004 (UTC)

i don't understand addition

 * α + β = mex{α ′ + β : α ′ < α, α + β ′ : β ′ < β},

This definition doesn't make any sense to me. There are too many colons and commas inside the set braces. Revolver 19:19, 27 July 2005 (UTC)

I have modified the definition to

 * α + β = mex({α ′ + β : α ′ < α} ∪ {α + β ′ : β ′ < β}).

This should make it more understandable. Figaro 3:01, 13 August, 2005 (EST)

Okay, I thought that may have been one intended meaning. I'm still not sure I understand addition, though. If α and β are finite ordinals, with α not zero, then it seems that

 * {α ′ + β : α ′ < α} = {β, ..., α + β − 1}

If α and β are both nonzero, then

({α ′ + β : α ′ < α} ∪ {α + β ′ : β ′ < β}) = {min{α, β}, ..., α + β − 1}

so that

mex({α ′ + β : α ′ < α} ∪ {α + β ′ : β ′ < β}) = 0

If α = β = 0, it's also = 0, since the argument of the mex function is the empty set.

If one of them is zero, the other not, say α not zero, but β = 0, then it should be = α

This seems to agree with your exclusive-or definition, except for the case where each is nonzero. Where am I making a mistake? Revolver 20:51, 13 August 2005 (UTC)

The definition of addition is recursive, so that, in the definition

 * α + β = mex({α ′ + β : α ′ < α} ∪ {α + β ′ : β ′ < β}),

the addition on the right hand side is not ordinal addition, but nimber addition. Your suggestions above use ordinal addition. It is possible to prove by induction that α + 0 = α for all nimbers α. Similarly, 0 + α = α for all nimbers α. It follows that

 * 1 + 1 = mex{{0 + 1, 1 + 0}) = mex({1, 1}) = 0,

 * 1 + 2 = mex(0 + 2, 1 + 0, 1 + 1}) = mex({2, 1, 0}) = 3,

 * 2 + 1`= mex({0 + 1, 1 + 1, 2 + 0}) = mex({1, 0, 2}) = 3,

 * 1 + 3 = mex({0 + 3, 1 + 0, 1 + 1, 1 + 2}) = mex({3, 1, 0, 3}) = 2,

 * 3 + 1 = mex({0 + 1, 1 + 1, 2 + 1, 3 + 0}) = mex({1, 0, 3, 3}) = 2,

 * 2 + 2 = mex({0 + 2, 1 + 2, 2 + 0, 2 + 1}) = mex({2, 3, 2, 3}) = 0,

and so on. The exclusive-or evaluation of the sum of two finite nimbers is provable by induction on the rwo nimbers. Figaro 19:23 17 August, 2005 (AEST)

 * Yup. My fault for missing the word "recursively"! Revolver 03:52, 18 August 2005 (UTC)

Tables?
I think it would be good to include addition and multiplication tables for the range 0-15. I've done the computation but I'm not sure how to format it. (I'm also not sure whether decimal, hex, or binary would be most illustrative. Thoughts?)  75.36.182.157 00:56, 15 April 2007 (UTC) Never mind. I looked up the formatting info for myself, decided on decimal as most appropriate, and boldly went ahead with the new section. 75.36.182.157 10:18, 21 April 2007 (UTC)

Size of the nimbers and revert
The sources cited and those I have read are set up so that nimbers are not a countable set, but rather are a proper class, larger than any set. Various subclasses of nimbers are interesting, including both a very small subclass which happens to be a set and happens not to be algebraically closed, and also another subclass which happens to be a set and an algebraically closed field. The former was presumably intended by 195.69.84.154, but they also deleted the latter.

It is important to cite sources for wikipedia. Note that the material challenged by 195.69.84.154 is taken fairly directly from the sources, but the edits by 195.69.84.154 are unsourced and contradict the given sources.

It would not be a problem to include a new source that defines the nimbers to be one of these tiny sets that 195.69.84.154 is probably talking about, and discuss its properties, but this should not interfere with talking about the larger sets and classes of nimbers already discussed in the article and the current sources. JackSchmidt (talk) 17:24, 5 December 2007 (UTC)

 * Rereading the online source, it appears that perhaps only a sentence or two is dedicated to the nimbers. Almost everything else is background or explanation of the surreal numbers.  Someone might want to check if the reference should be included there, but there are already nice references.  At any rate, despite nimbers only getting a quick mention in the online reference, it definitely indicates that they form a proper class. JackSchmidt (talk) 17:53, 7 December 2007 (UTC)

On algebraically closedness
I have some doubts about algebraically closedness of the nimbers. Of course, they have all roots of irreducible polynomials of degree $$2^k$$... But, by the way, what is the root of $$x^3+x+1$$??? 195.69.84.154 (talk) 13:18, 26 February 2008 (UTC)

 * Well, it's more than ω and less than $$\omega^{\omega^\omega}$$. There's no reason the nim-product of two infinite ordinals can't be finite.  But if you want to understand how to solve equations like this in general I'm afraid you have to read On Numbers And Games.  18.21.0.86 (talk) 22:53, 3 May 2008 (UTC)

I also have my doubts on algebraically closedness. I will now prove that the field of nimbers does not contain the field of order 8.

It is pretty straightforward to prove that $$2^a - 1 $$ divides $$ 2^b - 1 $$ iff a divides b.

Take any positive integers x,y, using geometric series we have: $$ 2^x - 1 = 1 + 2 + 2^2 + ... + 2^(x-1) $$ This, times the sum $$ 1 + 2^x + 2^(2x) + ... + 2^((y-1) x) $$ gives $$ 1 + 2 + 2^2 + ... +2^(x - 1 + xy -x ) = 1 + 2 + ... + 2^(xy - 1) = 2^(xy) - 1 $$ thus we have $$ 2^x - 1 $$ divides $$ 2^(xy) - 1 $$ Thus a divides b implies $$ 2^a - 1 $$ divides $$ 2^b - 1 $$.

For the reverse direction, suppose $$ 2^a - 1 $$ divides $$ 2^b - 1 $$.

Since $$ 2^a - 1 $$ divides itself, it divides the difference $$ (2^b - 1) - (2^a - 1) $$. Taking the difference of the powerseries gives

2^a + 2^(a+1) + ... + 2^(b-1)

= 2^a ( 1 + 2 + ... + 2^(b-a-1))

Clearly, 2^a - 1 is relatively prime to 2^a, so this implies that 2^a-1 divides

1 + 2 + ... 2^(b-a-1) = 2^(b-a) - 1

Repeating this, we have that 2^a - 1 divides 2^c - 1 for all c congruent to b mod a.

Suppose we have c s.t. 0 < c < a, b congruent to c mod a. Then $$ 2^c - 1 < 2^a - 1 $$, but $$ 2^c - 1 $$ is not 0 since c is not 0. Contradiction. Hence b is congruent to 0 mod a, implying a divides b.

In particular, this proves that the multiplicative group of GF(2^(2^n)), which has order 2^(2^n) - 1, is not divisible by 2^(3) - 1, and thus cannot contain a subgroup of order 2^(3) - 1. Since the multiplicative group of GF(2^3) has order 2^3 - 1, this implies that GF(2^3) is not contained in ANY field GF(2^(2^n)). Taking the claim in the article at face value that the nimbers from 0 to 2^(2^n) - 1 are isomorphic to GF(2^(2^n)), this implies that no finite subfield of the nimbers contains GF(2^3) (or GF(2^x) for any x not a power of 2). Since GF(2^3) is finite, any embedding of it embeds it into a finite subset of the nimbers, we conclude that the field of nimbers does not contain a copy of GF(2^3).

Going back to the previous writer's irreducible polynomial x^3 + x + 1, we can now actually PROVE that there can be no root of this polynomial in the nimbers. If there were an x satisfying this, then x generates a multiplicative subgroup of the nimbers:

x

x^2

x+1

x^2 + x

x^2 + x + 1

x^2 + 1

1

of order 7. If any earlier power of x is 1, then that power is relatively prime to 7, impyling that x is 1, which is false when we substitute the value x=1 into the polynomial. Hence this is definitely a subgroup of order 7. And since for any nimber value x could take, there is a 2^(2^n) above it, this would imply some order 7 subgroup in a 2^(2^n) - 1 group, which we proved is impossible by divisibility considerations.

Thus the nimbers are NOT algebraically closed, as claimed in the article. (Assuming the claim that GF(2^(2^n)) is isomorphic to the first 2^(2^n) nimbers).

Render787 (talk) 22:40, 27 October 2008 (UTC)

Also, I think you can prove the claim that GF(2^(2^n)) is isomorphic to the first 2^(2^n)) nimbers by showing that that set is closed under multiplication (almost certainly is by a similar argument to showing that it is closed under addition) and under inverses. It certainly appears to be true. Someone should cite a proof of that, though, or else my reasoning above and my deletion of the algebraicaly closed claim would be in error. In either case, either the GF(2^(2^n)) claim or the algebraically closed claim has to go.

Render787 (talk) 23:05, 27 October 2008 (UTC)

I also just realized on re-reading the article that the claim was only made when infinite nimbers were used... So my proof may not stand... Someone who knows how ordinal arithmetic works with polynomials should point out what these roots are for polynomials like x^3 + x + 1, because that would substantially improve the article and make it much more informative.

My proof above actually shows that the set of finite nimbers is not algebraically closed. I will revert the change.

Render787 (talk) 23:14, 27 October 2008 (UTC)

 * I once calculated that $$\omega^2 + 3 \omega$$ is a root of the polynomial $$x^3+x+1$$. I just checked, and it seems right.  However, I  don't have a source to justify addition to the article.  Perhaps, it's insignificant enough not to require a source.  As hint to the verification, use the fact that $$\omega^3 = 2$$. DRLB (talk) 16:01, 28 October 2008 (UTC)

Actually three roots \omega^2+3\omega, 2\omega^2+3\omega,3\omega^2+\omega. All have the form x=y+(1/y) which, if you plug thus into the original equation, gives x^3=2 or x^3=3. Different number cube roots of 2 or 3 give the different x roots given above. Olthe3rd1 (talk) 01:53, 29 June 2019 (UTC)

Need the right syntax, can my response be edited accordingly? Olthe3rd1 (talk) 01:54, 29 June 2019 (UTC)

Terminology
131.215.167.232 changed "nim-addition" (resp. "nim-multiplication") to "nim-dition" (resp. "nim-tiplication"). I've reverted that, as the former spellings have some Google hits including the original books by Conway et al, while the latter spellings seem to have no Web presence other than this page itself. Joule36e5 (talk) 04:45, 17 November 2008 (UTC)

Nimber multiplication vs Game Thoery
Does anyone know if there exists a game-theoretic interpretation of nimber multiplication? I've been scouring the net for some time now, and there are a few pages that mention that some such interpretation exists, but none of them actually demonstrate it. —Preceding unsigned comment added by 83.10.99.117 (talk) 23:59, 13 March 2009 (UTC)

 * I was wondering that myself. There must be some reason that nimber multiplication is defined as it is, whether related to nim or to game theory more generally.  I know the significance of addition to nim – under "normal play", a position is winning for the player who has just moved iff the nim-sum of heap sizes is zero.  The article ought to state this, but I'm not sure how best to fit it into the section as it stands.  But in any case, what about multiplication? — Smjg (talk) 00:11, 5 January 2014 (UTC)

Why 2^2^n?
To quote "This subset is closed under both operations, since 16 is of the form 2^2^n."

If addition of two nimbers is indeed just XOR, then 16 being of the form 2^n is entirely sufficient. This can also be seen in the table for n=0,1,2,3,4 ie. 2^n = 1,2,4,8,16. Of course, that is not true for multiplication. MaZe Pallas (talk) 05:46, 7 March 2010 (UTC)

 * I think you answered your own question. The quote says both operations, and nimber multiplication is only closed within ordinals taking the form 2^2^n (as mentioned in article). TricksterWolf (talk) 19:15, 7 July 2013 (UTC)

Formal (non-prose) definition of nimber please?
The non prose starts of with the recursive definition of nim addition, but I as a reader have no clue what a nimber is, or how to represent it. Also the recursive definition assumes the reader knows what the primes (') mean applied to nimbers... — Preceding unsigned comment added by 83.134.138.194 (talk) 21:53, 3 May 2012 (UTC)

 * A nimber is an ordinal number with two new operations defined on it (nimber addition and nimber multiplication). Nimber addition on two nimbers is the bitwise XOR of the nimbers; multiplication is more complex to define.  Finite nimbers are simply the natural numbers (0, 1, 2, 3, etc.).  See ordinal number for more detail on transfinite ordinals.  TricksterWolf (talk) 18:56, 7 July 2013 (UTC)

Explaining nimbers with simpler English?
Nimbers are a really neat mathematical concept and there's a lot of fun things you can do with them from a recreational-math standpoint. But the article doesn't convey any of the wonder of nimbers and the useful bits are hidden under deep mathematical symbiology which most people might not even be equipped to unpack, which is a shame, because nimbers are really easy to understand if you explain them in plain English. For crying out loud, the article doesn't even link to the article on Nim!

I wrote this to explain nimbers to friends and think it might be useful to integrate into this article, perhaps rewritten in a more encyclopedic fashion:

There's a game called Nim. In Nim, you have a certain number of piles of objects, and a turn consists of removing some number of objects from a pile. You win if you remove the last object. So you might have a Nim game where you have a pile of 2 objects and a pile of 3 objects. Player A takes an object from the second pile; now you have two piles of 2 objects. Player B takes two objects from the first pile, and then player A wins the game by taking both objects from the second pile.

Nim is of mathematical interest because a wide variety of simple games with specific traits are mathematically equivalent to games of Nim. These games are called impartial games because each player's available moves are identical, and the only difference is whose turn it is to play.

What makes Nim particularly interesting from an analytical standpoint is that you can "add" games of Nim. For instance, let's take the game described above with a pile of 2 and a pile of 3. This is, in itself, two games of Nim - it's a game of Nim with a single pile of 2 added to a game of Nim with a single pile of 3. If we add the "nimbers" for 2 and 3, we should get the nimber for the combined game.

Let's say we're looking at piles of 2, 5, and 11 and want to find the nimber for the combined game. Here's how we do that. First, we turn the numbers into binary numbers: 0010 0101 1011 Then, we count the number of 1s in each column. If it's odd, that column's value is a 1 in the resulting nimber. If it's even, that column's value is a 0. There's one 1 in the leftmost column, one 1 in the next columnm two 1s in the next column, and two in the last column. So the nimber we get is 1100 (the binary number), which is equivalent to 12. Note that if you add two games with the same nimber, you get a value of 0, because each column will either have two 1s or zero 1s.

You can use nimbers to identify whether the first or second player can force a win in a game. If the nimber of a game is 0, then the first player loses given optimal play; if it's any other value, then the first player wins, and their optimal play is to change the game state to make the nimber 0. 24.136.1.234 (talk) 14:37, 8 December 2015 (UTC)

Infinite nimbers
It would be nice to give some examples for the addition and multiplication of infinite nimbers. For example, what is $$\omega\oplus 1$$? I tried to calculate it using the formula given, getting 0; however I somehow suspect that is not the right result. --93.134.38.51 (talk) 15:27, 17 August 2016 (UTC) The addition formula is

Replacing $α ⊕ β = mex(\{α′ ⊕ β : α′ < α\} ∪ \{α ⊕ β′ : β′ < β\})$ with $α$ and $ω$ with $β$ gives

Now, $1$ means that $ω ⊕ 1 = mex(\{α′ ⊕ 1 : α′ < ω\} ∪ \{ω ⊕ β′ : β′ < 1\})$ is any finite nimber. Its bitwise exclusive OR with $α′ < ω$ swaps 0 with 1, swaps 2 with 3, etc. In particular, every possible finite nimber can be achieved. Also, $α′$ means that $1$ can only be $β′ < 1$ and $β′$. So the minimum excluded nimber is $0$. 𝕃eegrc (talk) 15:49, 17 August 2016 (UTC) Ah, thank you, I now see where I went wrong: I mistakenly used the normal ordinal addition inside the sets. Anyway, I still think the article should give a few infinite examples. --93.134.38.51 (talk) 16:29, 17 August 2016 (UTC)
 * Please do. 𝕃eegrc (talk) 16:54, 17 August 2016 (UTC)

same notation for both XOR and nim-sum?
why is it that the text uses the same symbol for both XOR and nim-sum? don't your think that's confusing?
 * Because, as the article explains, they are more or less the same operation. —David Eppstein (talk) 16:53, 11 May 2019 (UTC)

Calculation of reciprocal
What is meant by the subtraction operation in the expression (1+( '- )) -1? Why is this not rendered as an addition since nimbers are additive self-inverse? Olthe3rd1 (talk) 23:14, 28 June 2019 (UTC)

nimbers form a set???
the article says nimbers are a proper class and not a set, but since nimbers are equinumerous with ordinal numbers, and ordinal numbers form a set, I think this is wrong? AltoStev ( talk ) 16:25, 21 February 2023 (UTC)

 * The ordinals also form a proper class not a set. There is no set of all ordinal numbers, at least not in standard forms of set theory (see universal set). As our ordinal number article states: "The class of all ordinals is not a set." —David Eppstein (talk) 17:02, 21 February 2023 (UTC)
 * That seems unusual since natural numbers form a set... but apparently ordinals can have omegas so I was mistaken....
 * This implies there are infinite nimbers a la infinite ordinals, but it's unclear how they work tbh.  AltoStev  ( talk ) 23:05, 25 February 2023 (UTC)
 * Omega-notation only gives you some of the countable ordinals. The ordinals get far bigger than that. —David Eppstein (talk) 23:15, 25 February 2023 (UTC)

Nimbers as surreals?
I came to this article from one on game theory and surreals, where the motivating construction is {?|?} where we fill in the blanks. This article doesn't seem to have any of this context. It isn't clear from this article exactly what inductively defined games correspond to the nimbers. It seems to jump directly to assuming all nimbers can be talked about by proxy using a corresponding ordinal. Matthew Pocock (talk) 12:38, 27 August 2023 (UTC)

 * Nimbers are not surreal numbers. They both come from the inductive construction of an arithmetic on infinite games, but they are a different subset of the games. The only value they have in common is zero. —David Eppstein (talk) 15:06, 27 August 2023 (UTC)

Online version of Northcott's game
Over ten years ago based on what my physics teacher showed us between lessons, we created "Pawn Duel" as an online game as simple illustration for counting moves in chess. It turned out to be a human-comprehensible version of Northcott's game, practical to set up if you have a chess board. Over the course of these years somebody else even got inspired and created a small flash game called "Spartans vs Goblins", which is a graphic version for kids.

I have tried creating a page describing this example as comprehensible, even for kids. It was deleted as too specific. I am not an active wiki contributor and don't know all the practices. Hence, could somebody support me, or point to a place where this practical example of Northcott's game (https://nim.ai1.co/pawnduel/) is appreciated by community? — Preceding unsigned comment added by Okkay (talk • contribs) 23:12, 9 September 2023 (UTC)

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

title: Talk:Nimber


text:
Robots in literature

Artificial humans and autonomous artificial servants have a long history in human culture, though the term Robot and its modern literary conception as a mobile machine equipped with an advanced artificial intelligence are more fairly recent. The literary role of artificial life has evolved over time: early myths present animated objects as instruments of divine will, later stories treat their attempted creation as a blasphemy with inevitable consequences, and modern tales range from apocalyptic warnings against blind technological progress to explorations of the ethical questions raised by the possibility of sentient machines.

Recently, a popular overview of the history of androids, robots, cyborgs and replicants from antiquity to the present has been published. Treated fields of knowledge are: history of technology, history of medicine, philosophy, literature, film and art history, the range of topics discussed is worldwide.

Early uses
The earliest examples were all presented as the results of divine intervention and include: The dry bones that came to life in the Book of Ezekiel (Chapter 37); three-legged self-navigating tables created by the god Hephaestus (Iliad xviii); and the statue Galatea, brought to life by the prayers of her creator Pygmalion.

More recent humaniform examples include the brooms from the legend of the sorcerer's apprentice derived from a tale by Lucian of Samosata in the 1st century AD, the Jewish legend of the golem created like Adam from clay, and Mary Shelley's Frankenstein. These tales include an indictment of human folly at presuming to take on the role of creator.

Notable mechanical representations of humans include the life-sized singing puppet Olimpia in the short story "The Sandman" by E. T. A. Hoffmann in 1816 and a bipedal anthropomorphic mechanism in The Steam Man of the Prairies by Edward S. Ellis in 1868. These examples are stories about human-controlled mechanisms without autonomy or self-awareness.

In Lyman Frank Baum's children's novel Ozma of Oz, the first-ever introduction of a humanoid-appearance mechanical man that would satisfy the later "humanoid robot" definition occurred in 1907 - some fifteen years before the word "robot" was coined - with Tik-Tok, powered with a trio of clockwork movements for his thinking, movement and speech, none of which he could wind up himself.

In 1912, Selma Lagerlöf published the poem Slåtterkarlarna på Ekolsund which was published in the first part of Troll och människor. In the poem Christopher Polhem is hired to create mechanical mowers for a farmer.

The modern "robot"
The first use of the word "robot" was in Karel Čapek's play R.U.R. (Rossum's Universal Robots) written in 1920 and first performed in Czechoslovakia in 1921, in New York City in 1922 and an English edition published in 1923. Čapek's Robots are artificially manufactured from organic materials to labor for humans, and as the play progresses they revolt and overthrow their human creators. However, the play ends on an optimistic note: Robots' artificial biology causes a male and female Robot to fall in love, preserving the spirit of humanity as a result. R. U. R. and its Robots reflect contemporary anxieties about dehumanization amid the mass industrialization and militarism of the early twentieth century.

While Karel Čapek's play introduced the word "robot" into languages around the globe, he later wrote a letter to the Oxford English Dictionary of etymology in which he named his brother, painter and writer Josef Čapek, as its true inventor. In an article in the Czech Lidové noviny in 1933 he also explains that he originally wanted to call the creatures "laboři" from the Latin word labor. Karel found the word too bookish and sought advice from Josef who suggested to call them "robots". The word, which is always capitalized in Čapek's play, derives from robota which means "drudgery" in Czech and means "work" in Slovak.)

The theme of robots has been picked up by science fiction writers and many volumes are focused on robots and their interaction with the human species. Of particular note is the work of Isaac Asimov as a large part of his work centers on robots. Asimov is particularly known for his creation of the Three laws of robotics which that author uses in stories as both to define his robots and how these interact within the worlds he creates.

title: Robots in literature


text:
Talk:List of fictional computers

Red Dwarf and Queeg 500
I quote: "Holly, and Queeg 500, the on-board computer and back-up computer (respectively) for the space ship Red Dwarf in the BBC television series of the same name. (1988)". Queeg 500 wasnt the backup computer - wasnt it Holly all along? If think this should be reworded. SIGURD42 15:57, 17 June 2006 (UTC)
 * "Queeg" states this to make the practical joke work, and all characters (and audience) believe it and act as if this were the case. I vote to leave this as-is by taking the view that Queeg is a fictional computer by the standards of the Red Dwarf universe, and a doubly fictional computer by ours. AleatoricConsonance 10:04, 19 June 2006 (UTC)
 * It's only the basis for one episode. By that logic, we should have the talking toaster in here :)  It should be removed. Dave420 16:01, 30 November 2006 (UTC)
 * There are many computers that only appear in one single episode of a given television series, such as "Gambit" from Blakes 7, or "Laandru" from Star Trek. Why do you feel that Queeg -- a rather unique example of a metafictional computer -- should be excluded from the list, where the others are not? (And Talkie Toaster appeared in more than one episode of Red Dwarf). AleatoricConsonance 12:15, 18 December 2006 (UTC)

Another Question
I was looking at the discussion Talk:List_of_fictional_computers and it made me question the addition of The Matrix. I breifly browsed The Matrix article, and it commented that the actual Matrix is a artificial reality to pacify humans. In this sense, wouldn't it be a program (though of large scale) rather than an actual computer system. The article as well as the movie itself gives the impression that The Matrix was a huge program, but not a name of an actual and physical system. Pertaining to the movie, the actual system is probally the mass of machine technology, the humans containment centers, and etc. Its a minor problem however, I'm just questioning it. --Deadcore 23:27, 7 January 2006 (UTC)
 * The movies did not define the underlying technology or indeed the exact nature of the Matrix, but it's clearly a computer system of some kind. The List of Fictional Computers is quite broad in its current definition of a 'computer' and includes sophisticated programs that are in some ways indistinguishable from the hardware ... most of these are artificial intelligences, usually with some kind of personality. It's the same with human beings: what is, after all, the difference between your mind and your brain? In a horribly simplistic way, we could argue that one is hardware, one is software, but both are so strongly coupled and interdependant it makes no sense to separate them. It's a good question, but I believe the Matrix should be remain as-is AleatoricConsonance 01:49, 8 January 2006 (UTC)

Euclid?
Would it be valid to add the "personal" computer named of Maximillian Cohen, the main character in the movie Pi? In the movie, the computer named Euclid is used to test and power Max's theories in mathematics. Judging from the use in the movie, I would say the computer is intended to be powerful. And I can find no reference that there was actually a computer named Euclid. At least not specifically for the fictional story of Pi. The technology of this computer is furthered, when persons from a Wall Street firm present Max with advanced cutting-edge components to intergrated into Euclid. --Deadcore

 * I have not seen the movie Pi, but Euclid seems worthy of inclusion to me. AleatoricConsonance 01:41, 7 January 2006 (UTC)

 * Euclid has been added here --Deadcore 23:27, 7 January 2006 (UTC)

 * Should we add Euclid? It contains a Ming Mecca chip, and they haven't even been declassified yet ;-) Msaunier (talk) 18:21, 26 August 2011 (UTC)

Incorporating external list
Re the list of fictional computers: I think we should incorporate this information rather than link to it (yeah, I know, credit etc., but we're talking about a list here). --Eloquence

Real computers in fiction
Note that "computers in fiction" need not feature fictional computers. For example, a fictional story could use entirely credible real-world computers as a plot element. See Rob Slade's huge list of reviews, linked on the page. -- Anon.

Mycroft (Holmes?)
Is the computer in The Moon is a Harsh Mistress called "Mycroft Holmes", or just "Mycroft"? —Paul A 06:24, 27 Oct 2003 (UTC)
 * The computer's actual name is only Mycroft, but it is named after Mycroft Holmes. The name is then shortened to Mike for the majority of the story. I'll fix the entry on the list. McGravin 20:20, 10 May 2006 (UTC)

Theoretical computers
I wonder if this list should include theoretical computers like Donald Knuth's MIX. Or maybe there should be an article about that category. ;Bear 15:33, 2004 Apr 7 (UTC)

 * I guess the Turing Machine would also be relevant in that regard. --Wernher 16:27, 7 Apr 2004 (UTC)

Tron
I don't remember enough about the movie "Tron" to be able to write about it except that it was chock full of patent absurdities. But somebody could add it to this list. ;Bear 21:44, 2004 May 10 (UTC)

Computers and AIs
That article is a list of fictional computers, so why there are AIs listed there as well, like Wintermute? There is a difference. Two things can be done about this. Those AIs can be removed (or moved to another page), or a disclaimer could be added in the beginning of the article. – Mackeriv 04:58, 28 Jun 2004 (UTC)
 * I think AIs should be included in this list, with a statement/disclaimer added if desired. After all, this list reflects more the personality (if a machine can be said to have one; but this is sci-fi, so they do) than the hardware. Rossumcapek 23:20, 30 Jun 2004 (UTC)

Slight link correction
In the Helpful / benevolent fictional computers, there's an entry for The ship, hub and planetary Minds in Iain M. Banks' "Culture" novels and stories.

It incorrectly links to Minds, where it should actually link to Mind_(The_Culture)

Non-Intelligent Computers
This is just my opinion, but it seems to me non-intelligent computers, which includes the LCARS as far as I know, should really be considered "neutral", even if they are mostly beneficial. After all, they could be turned to malevolent uses, and they wouldn't question it (except in a "Please confirm password" sort of way). What does everyone else think? [User:Daibhid C|Daibhid C]] 23:00 9 Sept 2004 (UTC)
 * I agree. A computer that can't "think" is simply a tool, like a hammer. And, like a hammer, it can be used for both helpful and harmful means. Chronolegion 17:33, 4 April 2007 (UTC)

LCARS is just the name of the end user display interface, as that many computer operations are voice activated in Star Trek. May not even be a computer program, let alone a computer system. A look at the Next Generation Technical Manual has a definition, to be sure.

The article should Include TCARS, ST Voyager, Season 5, Episode "Relativity". TCARS is the 29th Century advancement/equivalent of the LCARS system, TCARS stands for (Touch) or (Temporal) Computer Access and Retrieval System. There must be an article somewhere in an Encyclopedia for Star Trek, other reference here http://memory-alpha.org/wiki/Tcars An article on the USS Relativity can be found in Star Trek Magazine volume 1 issue #20. 160.149.1.36 (talk) 17:35, 29 December 2010 (UTC) Darren Hensley,

Mature literature
Making computers in fiction either good/bad or helpful/harmful/neutral etc. is okay for children's stories and really banal shallow stories but in mature writing there are two problems with this: firstly that hardly anybody is really good or bad, so the anthropomorphic characterisation of the computer is giving the machine a personality which isn't very realistic even in fiction; secondly, in a well crafted mature novel the intentions of a sentient AI computer may well be whole point of the story around which everything revolves and may not necessarily be revealed even at the end of the story.

I think the good/bad classification should be removed and the list replaced with an article which cites these computers as examples of computers in fiction.

--wayland 09:43, 9 Nov 2004 (UTC)

 * I agree with this. Look at the List of fictional robots and androids article which sorts by medium and date of publication / production. This makes the article into a timeline of the concept and how it has developed over time . Which is much more interesting.Lumos3 21:37, 9 Nov 2004 (UTC)

 * Thirded. It seems to me that fictional computers in most serious stories tend to be either no more "intelligent" than today's machines (and so incapable of moral decisions) or have an almost completely alien viewpoint (as with HAL). The current "good/bad" division doesn't allow for either of those.

 * I recategorised the whole list by Media as per the List of fictional robots and androids article. Works in "Unsorted" weren't apparent to me on superficial glance what media they belonged to. The works are now in rough alphabetical order for the interim (I used a script so it's imperfect), but I think that sorting by chronology as per the List of Robots is the best way to go. I simply don't have time to do that right now. Dig in everyone! AleatoricConsonance 14:51, September 2, 2005 (UTC)

 * Nice work Lumos3 17:01, 2 September 2005 (UTC)

 * Thank you. Just wondering, even though Anne McCaffreys dragon books date from the late 60's, the character of AIVAS wasn't introduced until the late 80's IIRC. Should it be date of appearance, or date of series? I think date of appearance makes more sense. AleatoricConsonance 06:55, September 3, 2005 (UTC)

 * I use date of first appearance, or alternatively a range from first appearance to last one. Lumos3 09:44, 23 November 2005 (UTC)

The addition of dates is going well and we could contemplate sorting into chronological order soon. Lumos3 09:44, 23 November 2005 (UTC)

Value judgements
Who came up with the idea to divide this list among value judgements, and who is making the determination?

For example, VIKI is listed under "harmful" computers, while HAL 9000 is listed under "neutral" computers. Both machines arrive at their damaging conclusions in similar ways, and both were built as benevolent.

So many science fiction stories deal with the philosophical question of pure or conflicted logic resulting in computer decisions that are done based on benevolent precepts leading to malevolent results. So does this division purport to indicate the intent of computers (most of which would be benevolent) or the acts of computers (most of which would in truth be neutral)?

It's a mess of a question that can only be determined based on POV, and I think the distinctions should be eliminated.

- Keith D. Tyler  [ flame ]  21:26, Jan 12, 2005 (UTC)

Computers vs. computer programs
The following are not computers, but computer programs:
 * Max Headroom
 * Master Control Program
 * Joshua

--KeithTyler

 * You're right. Perhaps marking the pertinent items with "(note: computer program)" might be a suitable solution? After all, people are probably going to end up at this article when searching for this class of 'AI-beings', and I don't think having a separate article on 'Fictional computer programs' is quite the way to go. Or? --Wernher 19:55, 13 Jan 2005 (UTC)

 * Joshua IS a computer program like you said, even though it states it is a subprogram of WOPR the fictional computer listed above it. But as I said, you are correct, it is a fictional computer program, not a computer itself. Unless there is a similar article about fictional computer programs to add Joshua to, maybe add it as a worthy mention (note) beside the WORP entry. --Deadcore 23:09, 7 January 2006 (UTC)

Earliest fictional computer
If golems and mythic golden statues qualify for the list of fictional robots, then would the Brazen Heads supposedly constructed by Francis Bacon, Albertus Magnus and the Knights Templar to answer any question qualify as fictional computers? Daibhid C 15:43, 13 January 2006 (UTC)
 * I find it difficult to think of any justification for their inclusion AleatoricConsonance 02:02, 14 January 2006 (UTC)

Sentient computers
I created the above page for a discussion of sentient computers in general discussion. Contributions welcome (some computers now appear to have developed already developed the contrariness demonstrated by their fictional counterparts ;).) Jackiespeel 17:29, 11 May 2006 (UTC)

Femputer?
Should femputer from Futurama be included on this list? (It wasn't actually a computer, but a fembot pretending to be a femputer...but since robot brains are esentially computers could it/she still be considered a computer? Ace-o-aces 15:40, 23 July 2006 (UTC)
 * I think we can justify its inclusion on the same basis as Holly/Queeg above. That's consistant. This list, at this time, does not include robots on the basis of their computer-brains (although the distinction can get blurry). There exists a separate list for robots. AleatoricConsonance 13:15, 24 July 2006 (UTC)

Nature of Interociter?
I wouldn't call the Interociter from This Island Earth a computer. To me it seems more like a thought amplifier and transceiver. The same goes for the Krell machine in Forbidden Planet. ChrisWinter 23:36, 11 August 2006 (UTC)

CABAL
I'm sure I read at tha CABAL is Computer Assisted Biologically Argumented Life-form, not what the article reads.

Jurassic Park film
The film of Jurassic Park includes a remarkable computer which surely fits into this list, but I don’t have enough detail to add it myself. It plays a crucial part in the plot and at one point is identified as "Unix" by the character of the grand-daugher of the creator of the Park, though it seems to be an exotic form of Unix. Coconino 17:24, 4 April 2007 (UTC)
 * It was a real computer - see SGI Crimson

Missing in action
Asimov hypothesized large, stationary positronic computers before his various "ACs".

His positronic robots should appear.

P1, from The Adolescence of P1.

Bishop from the Aliens series.

Atlant 23:15, 22 May 2007 (UTC)

Deep Thought and Earth should be in same category
Deep thought and Earth are currently listed under Literature and Radio respectively, but should be in the same category since they come from the same work. While the Radio play came first (Hitchhikers guide ...) the book is now more familiar. Thoughts? I'll put in a cross ref. Chris

S1m0ne
I think this one should be included, is the one from the Al Pacino Film (Same name)

66.183.108.19 (talk) 06:13, 27 November 2007 (UTC)Müller

What about Muddlehead from Poul Anderson's The Trouble Twisters?
Poul Anderson wrote many stories about David Falkyn and the crew of the Muddlin' Through, which included the computer Muddlehead. Start with the Trouble Twisters from 1967. Definitely a computer. —Preceding unsigned comment added by 64.26.147.43 (talk) 11:28, 19 July 2008 (UTC)

CABAL and EVA
"CABAL (Computer Assisted Biologically Augmented Lifeform) the computer of Nod in Westwood's Command & Conquer: Tiberian Sun, Command and Conquer: Renegade, and, by implication, Command and Conquer: Tiberian Dawn (1995)" It is actually common knowledge that in Tiberium Dawn, the bortherhood of NOD use a pirate version of EVA.. so the 'and, by implication, command and conquer: tiberian dawn' part is incorrect. I should probably change it. —Preceding unsigned comment added by 203.51.169.36 (talk) 14:26, 7 April 2009 (UTC)

Logarithmically Engineered Governing Intelligence of Nod (LEGION)
The idea that this is what the acronym, "LEGION", means is entirely spurious. Nobody is going to believe this, but its origin is an April fools prank I played on the EA C&C forums well over a year ago. I don't expect anybody to believe me as I can't produce the original thread, but consider these two points: 1. "Logarithmically engineered" makes no sense and 2. Nobody is going to find "Logarithmically Engineered Governing Intelligence of Nod" anywhere in Command & Conquer canon material. If you can, go ahead and present the source; I will be both amazed and maybe slightly miffed that they actually stole my idea. Especially since, again, it doesn't make sense and only sounds impressive to people who don't know what a Logarithm is. Incidentally, I've removed the reference to this acronym on the article, as it is not confirmed in C&C canon what LEGION actually stands for, if anything.Cranec (talk) 13:27, 9 September 2009 (UTC)

The Invisible Boy
The name of the movie that is now called "The Invisible Boy" was origionally named "The Giant Computer" but at the time the ramifications on the growing company I.B.M., caused Hollywood to change the name. Why was not this machine mentioned? —Preceding unsigned comment added by 72.251.44.60 (talk) 02:26, 30 September 2009 (UTC)

Membership criteria and survival of AFD
Since I !voted for deletion, I'm going to throw some really tight membership criteria up at the wall and in the finest Wikipedia tradition, we can work toward a usable set. I was hoping that List of fictional vehicles had criteria that I could rip off, but it looks like that list is in trouble too. If this list is to justify the human effort and material resources required to maintain and distribute it, it needs to have a purpose.

I think if the list is to be useful, somehow the computer must be significant to the story, not just background "furniture". The Batmobile, for example, is a significant element of "Batman" universe, and has had extensive discussion and third party literature. The subcompact that Harry and Sally rode in to New York is probably too dull and trivial a plot element to be notable. Similarly, the mechanical voice of the Enterprise that runs the self-destruct sequence is notable, but the desktop PC that Horatio Caine uses to get the suspect's photo and current whereabouts from the DNA in an eyelash is not notable.

So far as we know, computers are not self-aware; any fiction that has a Wikipedia article, or in principle that is notable enough to have a Wikipedia article, contains a computer that should be listed.

To be eligable for this list, a candidate must be: A listable computer may be self-aware, but need not be.
 * An artificial construct (not talking about mentats or idiots-savant)
 * Not primarily humanoid-shaped (that's a robot) (already a criterion)
 * Specifically identifiable ( not just "Un-named machine in a video game", etc.)
 * Mentioned in notable fiction (that is, something that already has a Wikipedia article).
 * or supply references in the increasingly unlikely case that the notable fiction doesn't yet have an article.
 * Critical to the story, not just background.
 * Distinctly different from capabilities of real-world computers at the time the story was written. (Sometimes fiction has computers that are dumber than real life... Slipstick Libby spent a lot of his duty time translating to and from binary for a computer that was too dumb to manage that itself. )

If an entity is notable enough to have its own Wikipedia article linked to its entry in a list, then I don't think it's needful to also provide a citation within the list. That would make the list article bulky. If we're just asserting that the entity exists and is a suitable member of the list class, surely the pointer within Wikipedia is sufficent. It's an index. If it doesn't already have an article, it must have a source that satisfies notabilty.

I think the list should continue to be organized chronologicaly in the categories of literature, film, etc. as we have now. --Wtshymanski (talk) 16:39, 1 February 2010 (UTC)
 * Distinctly different from capabilities of real-world computers at the time the story was written. What about the computer from Terminator, Skynet[Skynet (Terminator)]?  It did manage to wipe out billions of people, and although you never saw it, it was key in that series, controlling all the terminators, and talked about as a major plot element.  Real life computers could do what it does, running an AI program, one that copies itself all over the internet to preserve itself, and has access codes to the military computers, or is able to hack them.  We've seen in the real world military computers getting hacked by foreign governments, and also a lone hacker acting on their own.  The Bat Computer is just a very fast computer, it originally having large tape drives, but being updated as new computers did exist.  Nothing in it now that a real computer couldn't do.   D r e a m Focus  18:36, 1 February 2010 (UTC)
 * There are still no AI's hacking into other computers as of 2010, and certainly weren't in the 1980's when the Terminator stores were written. The Bat Computer is novel becuase it's a privately-owned computer in an era when this was unusual, and also doing a type of work that was unfamiliar at the time. That's why the Batcomputer makes the list and Horatio Caine's PDA doesn't. --Wtshymanski (talk) 19:12, 2 February 2010 (UTC)

Support This list certainly needs some kind of filter otherwise as computers become part of everyday life then every film, novel and TV programme will be eligible for entry. I largly support Wtshymanski's proposal. Not sure about Distinctly different from capabilities of real-world computers at the time the story was written. Its possible for a computer of completely normal capability to feature significantly in the plot of a story. Cant think of an example right now. I would also exclude fictional software such as viruses and computer components such as disk drives and memory cards. Lumos3 (talk) 11:03, 22 February 2011 (UTC)
 * As User: Coconino pointed out (4 April 2007 above),  the computer in the film Jurassic Park could be considered central to the plot yet it has no capabilities beyond those available at the time the film was made. If a computer is central to a plot then its in if its just used as part of everyday life, like lifting a phone or driving a car then its not. Thats  my opinion. Lumos3 (talk) 22:44, 23 February 2011 (UTC)

As a old SF fan, I think we need to realize fictional should be in capabilities when compared to computers of the era in which the fiction was published. P1 running on a network of IBM360s would make the list, but a fictionalize Watson playing a game show would not make it. This list should contain the list of computers that envision the future in one way or another. Skynet, Dora, GENIE, MCP and their siblings told stories of possibilities, not realities. --D. Norris 11:55, 22 February 2011 (UTC)

Lucy from Hackers was only kinda fictional
Not sure how to integrate this into the article, but Lucy is a real Macintosh. In the "effects" scenes, you can't see the computer itself, but it's clearly shown to be running Macintosh System 7, and the monitor is a Radius Mac monitor (identifiable by it's "clipped" corner) appropriate to the time period. The floppy drive is a Macintosh external 3.5" drive (Apple drives were quite similar, but did not have the embossed logo on top). However, when the secret service guys are confiscating Lucy, she's an Apple //GS and an AppleColor RGB monitor. Msaunier (talk) 18:22, 26 August 2011 (UTC)

OREC and Zen
These appear under "Literature", even though they are attributed to the BBC serial Blake's 7'. Shouldn't they more properly be under "Television"? — Preceding unsigned comment added by 71.182.224.206 (talk) 00:38, 1 September 2013 (UTC)

Star Trek
Under the guidelines, I recommend Nomad be moved to the Robot/Android list. Yes, there is a computer inside it, but principally, Nomad is a space probe. Otherwise, V'ger qualifies to be on this list. Meanwhile, not having Weebo from the film Flubber is correctly not on this list.

What about M5 from the episode "The Ultimate Computer?" What about Landru in the episode "The Return of the Archons?" There's also the alien computer in the episode "Assignment: Earth." The Guardian of Forever in the episode "The City on the Edge of Forever." There's also the Oracle in the episode "For the World Is Hollow and I Have Touched the Sky." Less so, there's the anonymous, apparently intelligent, computer in the episode "That Which Survives," and the non-verbal Vaal in the epsidode "The Apple." Just saying that Star Trek in the 60's had a lot of "intelligent" computers. And that doesn't count the Enterprise's own "computer." — Preceding unsigned comment added by 162.251.236.4 (talk) 19:48, 14 December 2019 (UTC)

WOMAC, from "Answer Affirmative or Negative" by Barbara Paul
WOMAC is a computer in a university library that answers technical questions with quotes from poetry. First appearance April 1972 issue of "Analog Science Fiction/Science Fact". Short story by Barbara PaulAye Robot (talk) 01:04, 29 March 2016 (UTC)

asdf
Never ending list, should be deleted or made explicit that it will never be complete and is a hopeless page. 104.228.101.152 (talk) 05:58, 18 December 2016 (UTC)
 * I don't think the fact that it can never be complete renders the page "hopeless". Nonetheless I've added a note to make explicit that the list is a dynamic list and is never likely to be fully complete. —me_and 09:37, 30 October 2020 (UTC)

Starchild Trilogy - Plan of Man
Needs an entry for the dictatorial computer "The Plan of Man" in the [| Starchild Trilogy] by [| Frederik Pohl] and [| Jack Williamson]. I'll do this when I get time if nobody else does. Jlodman (talk) 23:27, 7 February 2022 (UTC)

A comment on the name of the computer in "The Moon is a Harsh Mistress", and a question about a minor computer in a comic
In the copy of "The Moon is a Harsh Mistress" that I have, the computer "Mycroft Holmes" was nick-named "mycroft" by the computer repair technician because it was a "HOLMES mark IV, mod L". "HOLMES" stood for "High-Optional, Logical, Multi-Evaluating Supervisor".

The comments about the name are in the first couple of pages of the story. I don't know if this is regarded as the "official" version, or is a later edited version.

I also have a question about whether or not a specifc computer in an old Disney comic would count in this discussion.

There was a Carl Barks - Disney "Scrooge McDuck" story I remember from long ago, and I think it was "The Money Well", published in around 1958, where Scrooge is trying to use a computer to work out how to hide his money from the Beagle Boys. It was enormous, expensive to run, and used a lot of electricity. It was used partly as part of a running joke and the first time he tried to use it in the story it printed an answer that told him he needed new glasses, because he'd pressed the wrong buttons twice. (Clearly it was intelligent enough to realise what the problem was.)

Eventually, it was largely responsible for him being able to create a usable plan to hide his money. (Which he fouled up, because he was too cheap to buy new glasses.) It did however, seem to do most of the planning for him.

I admit my memory of the story may be imperfect or incorrect. I read it many (many) years ago. The computer may have been described as an "electronic calculating machine", or something similar, but from what I remember it was clearly what would be classed as an early computer. From what I remember, it didn't have any specified name or type.

If my memory is correct, would that computer qualify for inclusion in the list?

A.J.E. 101.188.25.89 (talk) 14:15, 28 July 2023 (UTC)

Merger proposal 18 March 2024
It is proposed that List of fictional artificial intelligences be merged into this list. There is no clear criterion for determining that a particular fictional computing device should be described as a computer or as an artificial intelligence that appears to be being used here. Many of the computers on this list are described, in the list, as AI--so the distinction seems blurry at best and nonexistent at worst. As this list is more substantial, I propose a merger to this list rather than the reverse. Dash77 (talk) 22:42, 18 March 2024 (UTC)

title: Talk:List of fictional computers


text:
Administrative divisions of Taiwan

Taiwan (Republic of China) is divided into multi-layered statutory subdivisions. Due to the complex political status of Taiwan, there is a significant difference in the de jure system set out in the original constitution and the de facto system in use today.

The ROC defines the Taiwan Area (Free Area) as its actual controlled territories, which is constitutionally divided into two provinces and six special municipalities, with each province subdivided into cities and counties. After a constitutional amendment in 1997, the provinces became non-self-governing bodies and remained as nominal divisions under the constitution, with no governing powers. The provincial governments were abolished in 2018. Provincial borders remained for statistical purposes.

With provinces non-functional in practice, Taiwan is divided into 22 subnational divisions (6 special municipalities, 3 cities, and 13 counties), each with a local government led by an elected head and a local council. Special municipalities and cities are further divided into districts for local administration. Counties are further divided into townships and county-administered cities, these divisions have a degree of autonomy with elected leaders and local councils, which share responsibilities with the county governments. Matters for which local governments are responsible or partially responsible include social services, education, urban planning, public construction, water management, environmental protection, transport and public safety.

When the ROC retreated to Taiwan in 1949, its claimed territory consisted of 35 provinces, 12 special municipalities, 1 special administrative region (Hainan) and 2 autonomous regions (Tibet and Outer Mongolia). However, since its retreat, the ROC has controlled only Taiwan Province and some islands of Fujian Province. The ROC also controls the Pratas Island and Taiping Island in the Spratly Islands, which are part of the disputed South China Sea Islands. They were placed under Kaohsiung administration after the retreat to Taiwan.

Since 1949, the government has made some changes in the area under its control. Taipei became a special municipality in 1967 and Kaohsiung in 1979. The two provincial governments were "streamlined", with their functions transferred to the central government (Fujian in 1956 and Taiwan in 1998). In 2010, New Taipei, Taichung, and Tainan were upgraded to special municipalities. And in 2014, Taoyuan County was also upgraded to Taoyuan special municipality. This brought the top-level divisions to their current state:

According to Article 4 of the Local Government Act, laws pertaining to special municipalities also apply to counties with a population exceeding 2 million. This provision does not currently apply to any county, although it previously applied to Taipei County (now New Taipei City) and Taoyuan County (now Taoyuan City).

Territory
After the World War II in 1945, the Republic of China (1912–1949) acquired Taiwan (Formosa) and Penghu (the Pescadores) from the Empire of Japan. After the Chinese Civil War in 1949, the ROC was reduced to mainly the island of Taiwan and some offshore islands, with the People's Republic of China (PRC) controlling the mainland. However, it continued to formally claim all 35 provinces (including those that no longer form part of the area of the People's Republic of China) in official maps by the ROC government and ignored the changes imposed by the PRC. By 1967 and 1979, the ROC set up Taipei and Kaohsiung as its special municipalities, with three more added in 2010 and one in 2014. As of 2024, the ROC has not officially renounced claims in mainland China aside from Outer Mongolia under the Chen Shui-bian administration in 2002, though the ROC has also not recently published official maps depicting mainland China as part of its territory.

This history gives two different sources of the current Taiwanese administrative divisions on the free area of the Republic of China or Taiwan Area. These provinces were streamlined in 1998 and their governments became non-functional in 2019.
 * Taiwan Province: The island of Taiwan (Formosa) and Penghu (the Pescadores): inherited from the divisions of Taiwan under the Empire of Japan.
 * Fuchien Province: Kinmen (Quemoy) and the Matsu Islands – offshore islands inherited from the ROC's Fuchien divisions. The original province was partitioned between the PRC and the ROC following the Battle of Guningtou in 1949. In addition, the ROC still controls over Pratas Island and part of the Spratly Islands in the South China Sea.   These were originally part of the Hainan Special Administrative Region, but were transferred to the special municipality of Kaohsiung in 1996.

Changes to divisions
Since 1949, the government has made some changes in the area under its control. The two provincial governments were downscaled and much of their functions transferred to the central or county governments. Six special municipalities have been created.

Since 1949, the most controversial part of the political division system has been the existence of Taiwan Province, as its existence was part of a larger controversy over the political status of Taiwan. Since 1998, most of the duties and powers of Taiwan Provincial Government have been transferred to the central government, through amendments to the constitution. The much smaller Fukien province, Fujian Provincial Government has been downsized since 1956.

There has been some criticism of the current administrative scheme as being inefficient and not conducive to regional planning. In particular, most of the administrative cities are much smaller than the actual metropolitan areas, and there are no formal means for coordinating policy between an administrative city and its surrounding areas.

Before 2008, the likelihood of consolidation was low. Many of the cities had political demographics which were very different from their surrounding counties, making the prospect of consolidation highly politically charged. For example, while the Kuomintang argued that combining Taipei City, Taipei County, and Keelung City into a metropolitan Taipei region would allow for better regional planning, the Democratic Progressive Party argued that this was merely an excuse to eliminate the government of Taipei County, which it had at times controlled, by swamping it with votes from Taipei City and Keelung City, which tended to vote Kuomintang.

On 1 October 2007, Taipei County was upgraded to a quasi-municipality (準直轄市) on the same level as Kaohsiung City and Taipei City. This allowed the county to have the organizational and budgetary framework of a de jure municipality, but it was still formally styled as a county. Taichung County and Tainan City lobbied the central government for similar status. Taoyuan County was also upgraded to a quasi-municipality on 1 January 2011, as its population was above 2 million on the date of elevation.

Under President Ma Ying-jeou's administration, the central government has reorganized more counties and cities. Four mergers and promotions were approved in 2009 and became effective on 25 December 2010 and one more became effective on 25 December 2014.

The summary of changes on administrative divisions are shown below.

This brought the top-level divisions of Taiwan (ROC) to its current state: 2 nominal provinces without administrative function and 6 special municipalities; and under the provinces, 13 counties and three cities.

Special municipalities, counties, and cities
Currently there are three types and in total 22 administrative divisions are directly governed by the central government (Executive Yuan). According to the Local Government Act of Taiwan, a place with population more than 1.25 million may become a special municipality, a place with population between 0.5 and 1.25 million may become a city. Counties with population more than 2 million may grant some extra privileges in local autonomy that was designed for special municipalities.

These 22 divisions are also regulated by the Local Government Act as local self-governance bodies. Each division has its own executive called "city/county government" and own legislature called "city/county council". The city mayors, county magistrates and all legislators are elected by the people under its jurisdiction every four years. Geographically,
 * Six special municipalities, three provincial cities, and ten counties are on the main island of Taiwan

 * {|class=wikitable

!Special municipalities!!colspan=2|Counties!!Cities
 * valign=top|Kaohsiung City New Taipei City Taichung City Tainan City Taipei City Taoyuan City
 * valign=top|Changhua County Chiayi County Hsinchu County Hualien County Miaoli County
 * valign=top|Nantou County Pingtung County Taitung County Yilan County Yunlin County
 * valign=top|Chiayi City Hsinchu City Keelung City
 * }
 * }

 * Penghu County administers the Penghu Islands.
 * Kinmen County administers the Kinmen Islands and the Wuqiu Islands.
 * Lienchiang County administers the Matsu Islands.
 * Kaohsiung also administers Pratas Island (Tungsha Island or Dongsha Island) and Taiping Island of the South China Sea Islands.

Townships, county-administered cities and districts
The 22 main divisions in the country are further divided into 368 subdivisions. These 368 divisions can be categorized as the following.

According to the Local Government Act, a county is divided into townships and county-administered cities. The county seat or place with population between 100,000 and 500,000 may become a county-administered city. A special municipality or a city is divided into districts.

The townships, county-administered cities in counties, and mountain indigenous district in special municipalities are also local self-governance bodies. Each division has its own executive called "township/city/district office" and own legislature called "township/city/district council". The city mayors, township/district chiefs and all legislators are elected by the people under its jurisdiction every four years. The normal districts in special municipalities and cities are governed as branches of the municipality/city government and do not hold any local self-governance power.

The mountain indigenous township and districts are created for its significant population of Taiwanese indigenous peoples, in these divisions, only Taiwanese indigenous peoples may be elected to be the township/district chiefs.

Lower-level administrative divisions
The 368 divisions are further divided into villages and neighborhoods.

The village chiefs are elected by the people under its jurisdiction every four years. The neighborhood chiefs are appointed by the village chief.

Joint Service Centers of Executive Yuan
The central government operates five regional Joint Service Centers (JSC, 區域聯合服務中心) outside Taipei as outposts of the government ministries in the Executive Yuan, similar to the cross-departmental mode of working in the former Government Offices in England. These regions, laid out the Comprehensive National Spatial Development Plan for Taiwan (臺灣地區國土綜合開發計劃), can be considered a de facto level of government, perhaps equivalent to the English regions or the federal districts of Russia.

The divisions of northern Taiwan are not covered by any JSC, including Hsinchu (city and county), Keelung, New Taipei, Taipei, Taoyuan and Yilan. They are served directly by the headquarter of Executive Yuan in Taipei.

Romanization
The romanization used for Taiwanese placenames above the county level is a modified form of Wade–Giles, ignoring the apostrophes and hyphens of the original, thus yielding "Taipei" instead of "T'ai-pei" and "Yilan" instead of "I-lan", for example. Some postal romanizations also exist, like "Keelung" and "Kinmen". In 2002, the ROC adopted Tongyong Pinyin as its national standard for romanization. Most townships and county-administered cities changed their romanization to Tongyong Pinyin at that time. However, some local administrations, like Taipei and Taichung, decided to use Hanyu Pinyin. In 2009, Tongyong Pinyin was replaced by Hanyu Pinyin as the ROC government standard. Currently, most of the divisions are romanized by Hanyu Pinyin system, but some local governments still use Tongyong Pinyin, like Kaohsiung. In 2011, the ROC Ministry of the Interior restored historical romanizations for two towns, Lukang and Tamsui.

title: Administrative divisions of Taiwan


text:
Cha-cha-cha

Cha cha cha may refer to:
 * Cha-cha-chá (music), a style of Cuban dance music
 * Cha-cha-cha (dance), a Latin American dance accompanying the music

Film and television

 * Cha Cha Cha (film), a 2013 Italian crime film
 * Cha Cha Cha (1964 film), a 1964 Indian film
 * Cha Cha Cha (TV series), a TV show from Argentina
 * Cha Cha Cha Films, a film production company

Music

 * Cha Cha Cha (album), a 1995 album by EMF
 * Cha Cha Cha, 1955 album by Monchito and the Mambo Royals
 * Cha Cha Cha, 1982 album by Anne Linnet Band
 * Cha Cha Cha, 1977 album by Irwin Goodman
 * Cha Cha Cha, 2014 album by Abelardo Barroso
 * "Cha Cha Cha" (MC Lyte song), 1989
 * "Cha Cha Cha" (Käärijä song), 2023, the Finnish entry in the Eurovision Song Contest 2023
 * "The Bear Cha Cha Cha", a song from Bear in the Big Blue House
 * "The Cha-Cha-Cha", a 1962 song by Bobby Rydell
 * "Cha Cha Cha", by The Little Ones, 2006

Other

 * Cha Cha Cha (restaurant), a restaurant chain in Portland, Oregon, United States
 * Cha Cha Cha Township, a shopping centre in rural Zimbabwe
 * ChaChaCha, a team playing format in golf

title: Cha-cha-cha


text:
Talk:Local coordinate system

I redirected to Manifold, where the concept is explained and exclusively used. The old text didn't make any sense to me:
 * A commensurate relation between any one particular member P (or point) of any one particular set S, and sufficiently many other members of this same S; local coordinate system lcs( P, S ).

 * Collectively, all local coordinate systems which have been determined for all members of all subsets of a particular set T allow to evaluate which of all subsets of this T constitute neighbourhoods, thereby to characterize the topology pertaining to this T, and to evaluate whether or not this same T constitutes amanifold.

 * (Synonym: chart.)

I don't know what a commensurate relation is; it's not a mathematical concept. In any even, a local coordinate system is most certainly not a relation between one point of a set and "sufficiently many" other points. The abbreviation lcs is non-standard. The second sentence is near incomprehensible. Local coordinate systems certainly do not "allow to evaluate" whether T is a manifold; a manifold is a topological spaces together with local coordinate systems.

It doesn't help that the same text can also be found at chart.

Is this a troll? AxelBoldt 02:25 Jan 5, 2003 (UTC)

As for I don't know what a commensurate relation is; it's not a mathematical concept.
 * I don't know which mathematical concepts you're considering; but should We not require articles, e.g. about what is and what isn't a neighbourhood, which instruct Physics as well as Mathematics?

As for Local coordinate systems certainly do not "allow to evaluate" whether T is a manifold
 * The reference was to

 * Collectively, all local coordinate systems which have been determined for all members of all subsets of a particular set [...]

 * The question how to evaluate whether or not a given Set is a manifold may be considered if and where manifold appears in an article.

As for In any [event], a local coordinate system is most certainly not a relation between one point of a set and "sufficiently many" other points.
 * As far as the notion of a relation between one point of a set and "sufficiently many" other points appears therefore comprehensible to Us, it may still prove useful. Alternative views on its name may be discussed where the notion itself appears in an article.

As for The abbreviation lcs is non-standard.
 * Can you please provide the Wikipedia Reference how to evaluate whether or not the abbreviation of local coordinate system to lcs conforms to standards We ought to observe. (Please consider abbreviations such as used in Talk:EPR_paradox as well.)

As for The second sentence is near incomprehensible.
 * Thanks for reproducing what you did comprehend nevertheless.

As for ''Is this a troll? AxelBoldt 02:25 Jan 5, 2003 (UTC)''

 * Regards, Frank W ~@) R,			Jan. 5, 23:33 PST.

title: Talk:Local coordinate system


text:
Talk:Cha-cha-cha

Correct spelling
Is it Cha-Cha or Cha Cha? -- Zoe

 * It is neither. In Spanish, it is  either chachachá or cha-cha-chá after the rhythm of the dance, which is one-two cha cha cha.  So, in English cha-cha-cha is the best. Thed two-cha versions are erroneous.  Thus, the title of the article is wrong.  I will try a Move command, although the last time I did it Brion Vibber yelled at me because I said it was confusing.  Ortolan88

 * First, it is two-three-cha cha cha that came from Rumba and Mambo, rather than one-two-whatever, which was bastardized in USA ballroom chain studios and seems to be ethernalized in Country/western Cha-cha-cha and trickled back into Latin nightclub dancing.
 * Second, I would't call 'Cha-cha' erroneous today; this is how English language evolves: economy. Hint: TV, limo, pram(preambulator, huh?),...
 * Third, I'd gladly distinguish "authentic" (tongue in cheek) Cuban Cha-cha-chá and "strictly balroom" Chacha, just as some still can tell Rhumba from Rumba.
 * Fourth, it is Cha-cha-chá, not cha-cha-chá.

 * mikkalai

 * Ha, Move worked! Looks like my good buddy Brion reworded the instructions so they are now clear.

 * I do wonder now if the dance is called Cha-cha in the competitive dance world, but if so, it is a misnomer because those three cha's are the key to the whole dance, which I once knew how to do back in the Perez Prado regime. Ortolan88

 * FWIW, my dictionary has "cha-cha" only, no "cha-cha-cha". Neither one made the OED. -- Someone else 05:10 Jan 5, 2003 (UTC) (who is visualizing the can-can-can).

 * I'm working from Clave Diccionario de Uso Español Actual, which is pretty much the standard for the Americas. Ortolan88

 * I can vouch for the fact that it's "Cha Cha" is US collegiate competions. (To be honest, I didn't even know "Cha-cha-cha" was ever correct, although of course one has to count it that way.) USABDA  calls it "Cha Cha" or "Cha-Cha" as well, so it goes up through the amateur level under that name, and probably higher since I'm sure they want to follow what the professionals do. -Salli 15:38, 25 Sep 2004 (UTC)

 * It's also "cha cha" on the British university circuit and among British professionals, so I've put it back in the lede. Samsara (talk • contribs) 00:23, 9 December 2006 (UTC)
 * And I remoioved it. It is ballroom dance that is called chacha see Cha-cha-cha (dance). Music style correct name is is cha-cha-cha. `'mikkanarxi 02:59, 9 December 2006 (UTC)

Since this page has now coalesced into a page about cha-cha-chá (music), I suppose we can erase the cha-cha disambiguation stuff at the top of the page.Ricardovacilon 00:57, 17 January 2007 (UTC)

Origin
I removed the following because it seems to contradict the origins of chachacha according to just about everything I've read (not on a Wikipedia clone), which attributes invention to Enrique Jorrin. Tuf-Kat 16:28, Sep 2, 2004 (UTC)
 * The English dance teacher Pierre Lavelle visited Cuba in 1952 and found a form of rumba being performed with extra steps: the slow step of the basic pattern is replaced with the triple step (cha-cha-cha chasse). He taught these steps as a separate dance which came to be known as Cha-cha-cha, or the Cha-Cha.

Is the music called "cha-cha"?
Hi, I've just cut out the Cha-cha-cha (dance) article. Here is the question: is this music genre referred to as "Cha-cha"? If not, then the corresponding redirect(s) must be re-redirected to the dance article. Mikkalai 22:01, 4 Feb 2005 (UTC)

Likewise, this simplification has caused some amount of feedback into the way that people refer to the genre. Thus, if you talk to someone who dances, they might refer to the music as cha cha, while someone who just plays the music might refer to it as cha cha cha. However, there is no clearcut line. This is just speculation, but I would bet that the naming convention varies depending on the region. This is probably not a question that can be easily answered. For reference purposes, I am a local of the San Diego area, and I have found that most people use two or sometimes just one 'cha' in the name. If anyone from another local has any insight into this matter, please follow up with this post. 128.54.52.97 19:30, 22 February 2007 (UTC)
 * Alright, here it is: The dance and music were properly named with 3 chas, however in many dance contemporary studios, they teach the rhythm with only two chas in order to avoid confusion. When beginning students count the dance in their head with cha cha cha, they tend to sub-divide the beats between the 3 and 6 (or 7 and 2) into three equal parts as opposed to sub dividing beat 4 and 8 in half and then giving the a full beat to the final step of the sashay. Also, if you listen closely to most cha cha(cha?) songs, you will notice an emphasis on the first beat of the measure and a synchopation on the fourth beat. This 2, 3, 4 and 1 beat is often counted as 2, 3, cha, cha, 1 to help clarify it in students minds. Now, since many students today have learned this dance and never once danced it to the 2, 3, cha cha cha count, they have taken to simply calling it the "Cha Cha".

Split article
American Latin Ballroom Cha cha and Cuban cha-cha-chá are too different to be covered in the same article.

I noticed that there's a page called Cha-cha-cha (dance) with info on American Latin Ballroom chacha...

If no one minds, I'll remove the material about dance, since this is a music pageRicardovacilon 18:44, 14 January 2007 (UTC)

byto.de external link
InvDev (talk), the author of the edit, asked me to explain why I removed this external link from the article, and why I didn't consider a database of Cha-Cha-Cha music to be useful: I removed the link because the site does not appear to be of particular value. It seems to be under early construction and without much information. The first time I viewed the site, I saw that it was mostly written in the German language, with many PHP errors making the site unusable. (I viewed the page again from a different computer and browser (Firefox) and saw that the errors were gone. I viewed the page again just now with my original browser (Safari), and again I see that the PHP errors and the German have returned.) I also saw that the song entries seem to have a lot of random comments (see "My Sharona"), making me wonder whether the site is legitimate. --Ben James Ben 03:22, 12 October 2007 (UTC)
 * Cha-cha-cha music and videos

Ok, thanks, I try to reach the programmer of the site, I use the page for myself in germanand thought it would be useful. --InvDev 10:40, 12 October 2007 (UTC)

Ok, found my mistakte, I wrote a wrong link: Would you please recheck? Thx in fwd. --InvDev 10:57, 12 October 2007 (UTC)
 * Cha-cha-cha music and videos

Clave
As far as I know, Cha Cha Chá has no clave. The bell does not play as the bongo bell does in son, it is the same pattern over all bars, and claves are not used as an instrument. Wasn't the "removal" of clave done on purpose to simplify it for non-Cuban dancers who are not used to the concept of clave? Happily ever after 10:58, 18 October 2007 (UTC)

Focus on the music
Here the main focus is on the dance but this cannot be seen from the title. There is a separate article on the music: cha-cha-cha (music). Happily ever after 19:01, 21 October 2007 (UTC)

title: Talk:Cha-cha-cha