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Talk:Internet Control Message Protocol

Is it true that ICMP is a transport layer protocol?
In CISCO CCNA Curriculum materials is correct answer for question "At which layer of the OSI model does ICMP operate?" is network layer —Preceding unsigned comment added by 85.70.144.73 (talk) 17:52, 17 March 2008 (UTC)

 * The lead section of the article recently accumulated some controversial statements on this subject, such as a rewrite of this old paragraph:

 * ICMP differs in purpose from TCP and UDP in that it is not used to send and receive data between end systems. It is usually not used directly by user network applications, with some notable exceptions being the ping tool and traceroute.

 * into this paragraph on 3 April 2008:

 * From a strictly technical perspective, ICMP functions at the transport layer of IP. However, it differs in purpose from other transport protocols such as TCP and UDP in that it is typically not used to ::send and receive data between end systems. It is usually not used directly by user network applications, with some notable exceptions being the ping tool and traceroute. As such, ICMP is often ::considered to be a "network" layer protocol.

 * and this additional final paragraph on 4 May 2008:

 * ICMP can "never" be considered a Network Layer protocol. If it were to be considered so, then, it will have to rely on another transport layer protocol to carry its data i.e. Its data will become the payload for a transport layer protocol, as in the case of IP. ICMP is a Transport layer protocol just like TCP and UDP.

 * A user deleted that contentious paragraph on 5 May 2008, promptly enough, but at the same time amplified the controversial conclusion:

 * As such, ICMP is commonly (but incorrectly) considered to be a "network" layer protocol.

 * Now it may be true that some analysts of how the Internet works after the fact have working definitions of "network layer" "Internet layer" and "transport layer" where ICMP fits in the "transport layer" and no other. However, ICMP was part of the Internet layer by definition, when it was built into the Internet. Understanding why it was in that layer would be part of understanding the historical development of the Internet. If what is commonly considered its "layer" has changed, that should be supported with some reference rather than argued originally, or worse, merely asserted.

 * The company Network Sorcery provides an online guide to Internet protocols that has a simple scheme for classifying protocols into layers that has apparently been favorably received by at least some technical writers and students. Network layer protocols have Ethertype numbers. Transport layer protocols have IP protocol numbers. Application layer protocols have port numbers. Unfortunately, that puts some protocols that have conventionally been considered in the network layer into the transport layer, including ICMP.

 * According to information, the OSI model has seven layers, then a conventional explanation of the TCP/IP model in terms of five layers developed. Meanwhile, the article Internet protocol suite currently has a chart that provides a nuanced view of only four layers, and historical references to support that view. It puts ICMP in the top of three sublayers in the Internet layer.

 * The difficulty that some have with this may be that "Internet layer" and "network layer" seem to be synonymous, yet what's in the "Internet layer" may be a matter of history and specific technical implementation, while what's in the "network layer" vs. in the "transport layer" may be a matter of classification according to information systems theory.
 * --Sonny Moonie (talk) 09:58, 17 May 2008 (UTC)

 * I think the important point is that the CCNA referes to the OSI modle, but here we refere to the TCP/IP-5-Layer Model. -- AssetBurned (talk) 16:29, 20 May 2008 (UTC)

 * ICMP is one of the layer 3 Protocol Network layer. Not a transport layer protocol Goodtiming1788 (talk) 04:42, 14 September 2018 (UTC)

Transport layer control protocol
ICMP is part of the transport layer, but the Internet protocol suite sidebar lists it as being in the network layer.

ICMP above IP
I thought so as well, so why didn't anybody fix it before? fixed now.

Is this still fixed??? Just checked and ICMP is listed at the internet layer. Very confusing!!!

Bad packet structure
how come the source address and destination address in the packet structure table are only 16 bits long ? ips are 32 bits long. see also IP packet format

title: Talk:Internet Control Message Protocol


text:
Coronation crown

A coronation crown is a crown used by a monarch when being crowned. In some monarchies, monarchs have or had a number of crowns for different occasions, such as a coronation crown for the moment of coronation and a state crown for general usage in state ceremonial.

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

title: Coronation crown


text:
WorldWide Access

WorldWide Access, also known as WWA, was an Internet Service Provider based in Chicago, Illinois. WorldWide Access was the service name of the company, which was called Computing Engineers, Inc.

WorldWide Access operated from 1993 until 1998, when it was acquired by Verio. At that time, WWA was located on the nineteenth floor of the Civic Opera Building at 20 N. Wacker Dr., where it had moved from the seventh floor six months earlier.

Services
WorldWide Access offered typical ISP accounts of the era, including terminal dial-up into BSD/OS UNIX shell systems, SLIP, and PPP; web hosting; UUCP and mail hosting; DNS registration and hosting; and leased-line circuits. The company also offered tech support for Macintosh computers, which was somewhat of a rarity at the time. WorldWide Access focused its sales efforts on signup up corporate clients but the company also served thousands of residential customers. The company focused heavily on customer service excellence and was considered to be one of the better ISP operations in the Chicago area.

MagicServer
WWA was one of the first ISPs in the Chicago area to capitalize on virtual web hosting, by custom-coding virtual hosting into the NCSA httpd webserver before it was a core part of the product. This service was called MagicServer (another service mark of the corporation). The MagicServer version of httpd worked around some of the problems that plagued other implementations, such as the number of open file descriptors on the system, but had issues of its own which led to its eventual abandonment in favor of the standard built-in Apache virtual hosting.

MagicServer hosts originally also ran on the BSD/OS shell servers, but were relocated to Sun SPARC hosts running Solaris in 1996. These were tako and anago, and later gari and soba were added.

Acquisition and the local competitors
WorldWide Access was ultimately only one of several Chicago-based small Internet providers, which, in the end, were nearly all swallowed up by larger providers. WWA was the first to be sold, to Verio, in April 1998.

 * EnterAct was acquired in 1998 by 21st Century, which was in turn later acquired by RCN Communications
 * American Information Systems ("AISNet") was acquired in 1999 by Exodus Communications
 * MCSNet was acquired in August 1998 by Winstar Communications
 * Tezcatlipoca ("Tezcat") was acquired in 2000 by Ripco
 * InterAccess was acquired in 2000 by Allegiance Telecom

Of the major local providers, only Ripco remained unsold, and it still operates independently as of 2017.

title: WorldWide Access


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Willis Buell

Willis (or Wyllys) Buell (c. 1790 – November 1851) was a native of Connecticut and third mayor of Atlanta.

Biography
Willis Buell was born in Connecticut in 1790. He is reportedly related to the famed Connecticut cartographer Abel Buell.

Buell's 1833 map of Muskingum County was among the first printed maps of any of Ohio's counties.

In the mid to late 1830s, he became the first Justice of the Peace of the 1026th militia district. He was a prosecuting attorney for the Supreme Court held in Muskingum from 1837 to April 1839.

In 1839, he was appointed by the City Council to serve on Zanesville's first board of examiners for its education system.

He lived in Georgia during the mid-1840s. Buell was among the original members of Atlanta's first Masonic lodge. He was known for his skill in portrait painting, establishing a studio within Atlanta's first Masonic Hall in 1847.

As a member of the Free and Rowdy Party, also known as the Rowdies, he served a single term as the third Mayor of Atlanta from January 1850 to January 1851, as stipulated by the city charter. Jonathan Norcross succeeded him as mayor.

Death
Willis Buell died in Atlanta, Georgia in November 1851.

title: Willis Buell


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Horatio P. Van Cleve

Horatio Phillips Van Cleve (November 23, 1809 – April 24, 1891) was a general in the Union Army during the American Civil War.

Early life
Van Cleve was born in Princeton, New Jersey. He studied for two years at Princeton University, and then entered the United States Military Academy. He graduated in 1831 and served at frontier posts in the Michigan Territory. He was commissioned as a second lieutenant of infantry on December 31, 1831. He resigned from the Army on September 11, 1836, and settled in Michigan. He taught in Cincinnati, Ohio, in 1840–41, and then engaged in farming near Ann Arbor, Michigan. Van Cleve was an engineer in the service of the state of Michigan in 1855, and then United States Surveyor of Public Lands in Minnesota. In 1856, he engaged in stock-raising.

Civil War
After the start of the Civil War, he was commissioned as colonel of the 2nd Minnesota Volunteer Infantry Regiment on July 22, 1861. He met wife Charlotte Ouisconsin Clark Van Cleve, at Fort Winnebago, while both her father and Horatio were stationed there. She would write the book Three Score Years and Ten, Life-Long Memories of Fort Snelling, Minnesota, and Other Parts of the West, about the early days of Fort Snelling and her travels through the pioneer midwest. She was the first white woman born in the Wisconsin Territory, in the settlement of Prairie du Chien.

Van Cleve served under Maj. Gen. George H. Thomas at Mill Springs, and was later promoted to brigadier general of volunteers on March 21, 1862, in recognition for his services at that battle. He commanded a brigade at the Siege of Corinth and a division at Perryville. He was disabled by a wound at Stones River, but returned to his division upon recovery. He fought at Chickamauga, and was in command of the post and forces at Murfreesboro, Tennessee, after the battle. He was in command of the defenses of the Nashville and Chattanooga Railroad until he was mustered out in 1865. In the omnibus promotions in 1866 following the war, he was brevetted major general, dating from March 13, 1865.

Postbellum life
He was adjutant general of Minnesota in 1866–70 and 1876–82.

Van Cleve died in Minneapolis, Minnesota on April 24, 1891, and is buried there in Lakewood Cemetery. His home in that city was added to the National Register of Historic Places in 1976. He had his favorite horse buried in the front yard of that house before he died.

A park in Minneapolis is named in his honor. (44°59'10"N 93°13'50"W)

title: Horatio P. Van Cleve


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Benjamin Bomar

Benjamin Franklin Bomar (August 9, 1816 – February 1, 1868) was the second mayor of Atlanta, Georgia.

Bomar was born in Spartanburg, South Carolina, to Reverend Thomas Bomar and Elizabeth Carlton High and studied medicine in Charleston. He practiced medicine in America's first gold rush town of Dahlonega, Georgia, for a number of years until he tired of the winters in the Appalachian Mountains. He heard good things about Texas from his brother, Gen. Alexander Carlton Bomar who was serving in the Mexican–American War, and decided to move his family there. En route to Texas with his wife Sarah Elizabeth Lumpkin Haynes of Cumming, Georgia, and two children, Bomar arrived in Atlanta on April 30, 1847, fell in love with the bustling young town and settled there, running a general merchandise business on Whitehall Street.

The young town soon thereafter received its first charter, and elections were held December 1847. Moses Formwalt was made mayor, Bomar its alderman, and five others were elected councilmen, all for one-year terms. The next year, Bomar was elected mayor at the age of 32, as a member of the Free and Rowdy Party. During his term he selected and purchased six acres (24,000 m2) at $75 per acre to serve as the new Oakland Cemetery.

In 1849, while serving as mayor, Bomar co-founded Atlanta's first successful newspaper, the Daily Intelligencer.

He never practiced medicine regularly again. When Fulton County was formed as Atlanta's new home in 1854, he became the first clerk of its Superior Court which he remained as late as 1859, when his residence was on the Marietta road a mile outside of town (roughly where Howell Mill Road splits off today).

Benjamin Bomar was 44 years old at the outbreak of the American Civil War. He volunteered and served as the paymaster of Georgia's 28th Infantry, at a rank of captain. At the evacuation of the city following the Battle of Atlanta, his family refugeed to Macon, Georgia. After Lee's surrender, he rejoined the family in Atlanta; but by then his health was broken and he died less than three years later.

He was buried at Oakland Cemetery.

title: Benjamin Bomar


text:
Talk:Catalan number

Untitled
Need to get page number, ISBN for reference to enumerative combinatorics vol 2, and perhaps write up some more examples from there. Dmharvey 19:07, 31 May 2005 (UTC)

The first formula accompanying the quadruple factorial discussion might be made more clear with some parentheses- i.e., (2n)!/n! rather than 2n!/n!. I know that with just a little thought it is obvious, but since factorial has precedence over multiplication it caught me for a moment. By the way, this is a very nice article. :)

To Do list for this article
D. Andre, Note: Calcul des probabilites. Solution directe du probleme resolu par M. Bertrand, Comptes Rendus de l’Academie des Sciences, Paris, vol 105(1887), p. 436., where the reflection principle was first used (I think?) Dmharvey 12:07, 1 Jun 2005 (UTC)
 * The generating function actually yields the formula for C_n pretty easily, using the binomial formula for the square root term. This should really be described somewhere as the "generating function proof of the formula"; then the "Proof of the formula" section should be relabelled "Bijective proofs of the formula".
 * Need to mention the Ballot problem somewhere, which is a generalisation of many of the ideas in this article.
 * What was Andre's first name? I can't seem to work this out.
 * Need to add this reference:
 * I recall reading a long time ago (can't remember where) that the first disucssion of "exceedance" was in a probability setting. Consider a coin tossing game between A and B. They toss a coin 2n times. Heads gives A a point, tails gives B a point. Now, given that they each win n tosses, what is the probability that A is not ahead of B at any point of the game? You could also ask, for any k between 0 and n inclusive, what is the probability that A is ahead of B for precisely k turns? (you need to be a bit careful about how exactly you define when A is ahead.) The point is that it was shown that the answer does not depend on k, and so must be equal to 1/(n+1), which a priori is quite a surprising result. Would be nice to mention this in the History section, but the details need to be found.
 * My explanations of the two bijective proofs are a little wordy. Someone please write them better. Thanks.
 * Give C_3 examples/pictures for some of the other combinatorial interpretations listed.
 * Add more combinatorial interpretations; there are plenty of interesting and accessible ones still left. I don't have a copy of EC vol 2 handy.

"prepositional groups"
I have deleted the following from the "history" section.

 * It has been shown that the number of possible interpretations of a sentence, function of the number of prepositional groups ("he saw a man on the hill with a telescope"), is the Catalan number series.

It doesn't belong under History. Perhaps it belongs in the list of combinatorial applications. But the text quality needs to be improved, and I don't really know what it's about. Dmharvey Talk 17:11, 6 Jun 2005 (UTC)

 * That's just the number of binary parse trees. Not particularly interesting, seeing as equiparseable sentences with distinct meanings are highly artificial anyway. EdC 10:41, 21 July 2006 (UTC)

History
Ming An-tu discovered them before but they were published in 1839. 24.203.251.69 03:27, 31 October 2005 (UTC)

3x3 grid image in SVG
I've created the 3x3 grid image in SVG for the article in the spanish wikipedia:

 * http://es.wikipedia.org/wiki/Imagen:Catalan_number_3x3_grid_example.svg

I don't know about licensing, but I want to release it on the public domain as a trivial work. I hope it will be useful. Thank you.

Graphical relation between Catalan numbers, stairs with slope<45°, triangulated polygons
As an architect I try to understand things with graphics. See: http://home.versateladsl.be/vt649464/TrapVeelhNummering.PDF If someone wants to use it I can give a version without text.--Bleuprint (talk) 05:12, 8 February 2008 (UTC)

Ballot problem
Dmharvey wrote in the TODO list above:
 * Need to mention the Ballot problem somewhere, which is a generalisation of many of the ideas in this article.

I've added Bertrand's ballot theorem to the See also section, of course, some more details are worth including. --Kompik 11:28, 11 March 2006 (UTC)

hankel matrix stuff
Does anyone have any references for this hankel matrices stuff? Thanks. Dmharvey 11:15, 31 May 2006 (UTC)

 * Yes. Firstly, let me say that I'll don't know anything about uniqueness of such a series, only that this series have an all ones Hankel-transform.  I'll only talk about why the Hankel-transform of this sequence is all ones.
 * I've read of this property in the OEIS entry of Catalan numbers. I became curious and started to look for a proof.  This entry refers to the article  J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.  That article also states that the Catalan sequence has this property, and while it doesn't give a full proof, it does give a valueable hint to find it.
 * I've given this property as a task on a course, so I had to derive the complete proof, but I've never written the proof down completely, so it took me a while to reconstruct the proof from my old notebook and memory. As I think this is a notable property and proof, I'm glad you've asked about it so I'll finally write the proof down.  Btw, the problem lists for that course are available on my homepage: this one is problem number 5 on series 7 of term 4 (automn term 2005/2006).
 * Now I'll draft the proof. The basic idea (from the article) is that we will find the LU decomposition of the Hankel matrix as it's easy to calculate the determinant from them.  If you do the decomposition with a computer for some matrices, it's easy to guess the general statement.
 * Let $$ \mathbf H $$ be the Hankel-matrix formed fromed by the Catalan-numbers: $$ h_{k,l} = C_{k+l} $$ (note that we are numbering rows and columns from 0 here). This matrix is this:

1    1     2     5    14    42   132             1     2     5    14    42   132   429             2     5    14    42   132   429  1430             5    14    42   132   429  1430  4862            14    42   132   429  1430  4862 16796            42   132   429  1430  4862 16796 58786           132   429  1430  4862 16796 58786 208012

 * Now let's define the Catalan triangle like this: $$ c_{k,l} $$ is the number of paths of $$ k $$ right and $$ l $$ upwards segments that always stay below the diagonal from the starting point (i.e. no prefix of the path has more upwards segments then right ones). Then, clearly, $$ C_n = c_{n,n} $$.  The Catalan triangle has some interesting properties, one of which I should write about later.  The triangle looks like this:

1    0     0     0     0     0     0     0     0     0             1     1     0     0     0     0     0     0     0     0             1     2     2     0     0     0     0     0     0     0             1     3     5     5     0     0     0     0     0     0             1     4     9    14    14     0     0     0     0     0             1     5    14    28    42    42     0     0     0     0             1     6    20    48    90   132   132     0     0     0             1     7    27    75   165   297   429   429     0     0             1     8    35   110   275   572  1001  1430  1430     0             1     9    44   154   429  1001  2002  3432  4862  4862
 * Now let $$ \mathbf S $$ be a matrix we get from half of the elements from the Catalan-triangle like this: $$ s_{u,w} = c_{u+w,u-w} $$. $$ \mathbf S $$ looks like this:

1    0     0     0     0     0     0             1     1     0     0     0     0     0             2     3     1     0     0     0     0             5     9     5     1     0     0     0            14    28    20     7     1     0     0            42    90    75    35     9     1     0           132   297   275   154    54    11     1
 * I state that $$ \mathbf S \mathbf S^{\textrm T} = \mathbf H $$. For this, we need to prove that $$ C_{u+v} = \sum_w s_{u,w} s_{v,w} = \sum_{0 \le w \le \max(u, v)} c_{u+w,u-w} c_{v+w,v-w} $$.  Now $$ C_{u+v} $$ is, by definition, the number of paths of $$ u+v $$ right and $$ u+v $$ upwards segments which are under the main diagonal, which means that none of its prefixes have more up then right segments, and also that none of its suffixes have more right than up segments.  Let's split this path to a first part that's $$ 2u $$ long and a second one that's $$ 2v $$ long.  Let $$ u + w $$ be the number of right segments in the first part of the path.  Then, clearly, $$ w $$ is positive because this part is a prefix, and this part has $$ u - w $$ up segments.  Also, the second part of the path has $$ v - w $$ right segments and $$ v + w $$ up segments, and all suffixes of this part has at most the same number of up segments then right pointing ones.  It's also easy to see that if the first part of the path has no more up segments than right in any of its prefixes, and the second part of the path has no more right than up segments in any of its suffixes, we can combine these two parts to a valid path which stays under the diagonal.  Thus, we can calculate $$ C_{u+v} $$ by multiplying the number of valid first parts and the number of valid second parts, and summing this product for every $$ w $$.  The number of valid first parts is, by definition $$ c_{u+w,u-w} $$.  To calculate the number of second parts, we have to mirror them, so reverse the order of paths in it and replace up paths with right ones and vice versa.  Then we have a path which has $$ v + w $$ right pointing segments and $$ v - w $$ upward pointing ones, and each of whose prefixes have no less right segments then up segments.  The number of such paths is $$ c_{v+w,v-w} $$ so the matrix equation is indeed true.
 * Now observe that $$ s_{u,v} = 0 $$ if $$ u < v $$ and $$ s_{u,u} = 1 $$, so $$ \mathbf S $$ is a triangular matrix with all ones in its diagonal. Thus, $$ \det(\mathbf S) = 1 $$, thus indeed $$ \det(\mathbf H) = \det(\mathbf S) \det(\mathbf S^{\textrm T}) = 1 $$ which is what we wanted to prove.
 * The proof of that the determinant of the Hankel matrix starting with $$ C_1 $$,

1    2     5    14    42             2     5    14    42   132             5    14    42   132   429            14    42   132   429  1430            42   132   429  1430  4862
 * is also one is almost the same as above. The difference is that instead of $$ \mathbf S $$ we use the matrix $$ \mathbf T $$ defined by $$ t_{u,w} = c_{u+w+1,u-w} $$ .  This matrix contains the other half of the elements of $$ \mathbf C $$ like this.

1    0     0     0     0     0     0             2     1     0     0     0     0     0             5     4     1     0     0     0     0            14    14     6     1     0     0     0            42    48    27     8     1     0     0           132   165   110    44    10     1     0           429   572   429   208    65    12     1
 * Finally, let me ask you or anyone else reading this to feel free correcting errors or anything you don't like in this proof inline (unlike normal posts on talk pages). Thanks.  – b_jonas 23:03, 31 July 2006 (UTC)

 * I'm reacting to this sentence: "The Catalan numbers form the unique sequence with this property." This cannot be true, as the Hankel transform is invariant under the binomial transform (see the article on the binomial transform). —Preceding unsigned comment added by 84.215.177.45 (talk) 15:46, 26 January 2011 (UTC)

RE: Catalan Recurrence
The Catalan Recurrence

C(x)=SIGMA C(i) C(n-1)

has not been solved properly. A Quadratic eqn. appears out of nowhere. Can someone explain where it came from?

 * It's not "out of nowhere", although the explanation is not very explicit. It comes from realizing that the sum defines a Cauchy product.  I'll see if I can add something on this. Michael Hardy 20:43, 20 August 2006 (UTC)

 * OK, I've expanded that section, adding a more leisurely derivation of the quadratic equation. Michael Hardy 21:07, 20 August 2006 (UTC)

Is it possible to explain why a particular root of the Quadratic equation is used instead of the another one? In the expanded presentation that is no justification on that. —Preceding unsigned comment added by 207.46.55.31 (talk • contribs)

 * I've added an explicit explanation of that. Michael Hardy 02:07, 22 June 2007 (UTC)

Acortis (talk) 18:45, 30 May 2021 (UTC) The recurrence relation :$$C_0 = 1 \quad \text{and} \quad C_{n+1}=\frac{2(2n+1)}{n+2}C_n.$$ does not appear ro be correct!!

# python C = {} C[0] = 1 for n in range(5): C[n+1] = 2*(2*n+1)//(n+2)*C[n] print(C)

{0: 1, 1: 1, 2: 2, 3: 4, 4: 8, 5: 24}

Darcourse (talk) 06:45, 20 June 2021 (UTC) $$C_{n+1}=\frac{1}{n+2}\binom{2n+2}{n+1}=\frac{(2n+2)(2n+1)}{(n+2)(n+1)^2}\binom{2n}{n}=\frac{2(2n+1)}{(n+2)(n+1)}\binom{2n}{n}=\frac{2(2n+1)}{n+2}C_n$$

Two more Catalan problems
Perhaps these two problems with Catalan solutions are already in the harder stuff in the article. If not, do they belong?

1. How many ways can 2n ordered objects be arranged in a 2 x n matrix so that the elements are strictly increasing left to right and top down? (sometimes posed as a photographer arranging 2n people in 2 rows so that the heights increase left to right and front to back)

2. How many ways can n non-intersecting diagonals be drawn in a 2n-gon? (How many ways can 2n people seated at a circular table shake hands with no one's arms crossing) Jd2718 18:00, 5 November 2006 (UTC)

 * These have been added.--RDBury (talk) 17:53, 8 February 2009 (UTC)

Catalan numbers

 * $$ a\,$$
 * $$ a(a+b)=\,$$
 * $$ a(a+b)(a+b+c)=\,$$
 * $$ a(a+b)(a+b+c)(a+b+c+d)=\,$$
 * $$a\,$$
 * $$ab+a^2\,$$
 * $$abc+ab^2+ca^2+2ba^2+a^3\,$$
 * $$a^2c^2+abcd+abc^2+adb^2+cda^2+ab^3+da^3+2acb^2+2bda^2+4bca^2+3a^2b^2+2ca^3+3ba^3+a^4\,$$

The sum of the entries of every row is $$ n! \,$$ Twentythreethousand (talk) 16:36, 31 May 2008 (UTC)
 * More relevantly, the number of terms is Cn. Similarly, the number of terms in the expansion of (a1+a2+...+ak)n is $${n+k-1 \choose n}$$. Both of these can be proven by mapping the terms to lattice paths.--RDBury (talk) 18:28, 8 February 2009 (UTC)

Other kind of Catalan numbers?
Where should we send the reader who typed "Catalan numbers" into the search box, looking for how to count to ten in Catalan? --Damian Yerrick (talk | stalk) 21:31, 23 August 2008 (UTC)
 * That would probably be Catalan language but it doesn't exist yet.--RDBury (talk) 06:25, 4 January 2012 (UTC)
 * This is actually a joke exercise in Stanley's book, asking the student to "Explain the significance of the following sequence: un, dos, tres, quatre, cinc, sis, set, vuit, nou, deu..." Miclugo (talk) 20:21, 23 September 2022 (UTC)

Ballot problem/second proof
The reflection method is described both here and in Bertrand's ballot theorem. I added a more obvious link in the article; should there be an attempt to merge? Also, it's not entirely incorrect to call it André's reflection method, he had the basic idea but without the reflection part. The reflections are essentially only a way of giving a one-one proof that $${2n\choose n-1} = {2n\choose n+1}$$.--RDBury (talk) 17:11, 8 February 2009 (UTC)

Is the definition of Dyck's word correct?
The article says that "A Dyck word is a string .. such that no initial segment of the string has more Y's than X's" then it lists several examples including XXXYYY. But: X, XX, XXX, XXXY are all initial segments of XXXYYY and each of them has more X's than Y's.--Jirka6 (talk) 00:25, 10 April 2009 (UTC)

 * My fault, sorry. Of course it is correct. I switched X and Y.--Jirka6 (talk) 22:18, 13 April 2009 (UTC)

Trees and catalan numbers
The nice picture with green trees is correct, the description was not. There is an infinite number of binary trees (not necessarily full) with n leaves. Also, "ordered" is already implied by "binary". The picture actually belongs to (what used to be) the next item, I fixed that. --Ikska (talk)

As a binomial coefficent
What do you think? Is it worthy of inclusion in the article that a Catalan number can be written in terms of a generalized binomial coefficient?:
 * $$\begin{align}C_n

&= \frac{2n!}{n! (n+1)!} = \frac{(1 \cdot 3 \cdot \ldots \cdot (2n-1))(2 \cdot 4 \cdot \ldots \cdot 2n)}{n! (n+1)!} = 2^{2n} \frac{(\frac 12 \cdot \frac 32 \cdot \ldots \cdot \frac{2n-1}2)(\frac 22 \cdot \frac 42 \cdot \ldots \cdot \frac{2n}2)}{n! (n+1)!} \\ &= 2^{2n} \frac{\left(\frac{\Gamma(n+1/2)}{\Gamma(1/2)}\right)(n!)}{n! (n+1)!} = 2^{2n} \frac{\left(\frac{\Gamma(n+1/2)}{(-1/2)\Gamma(-1/2)}\right)}{(n+1)!} = -2^{2n+1} \frac{\left(\frac{\Gamma(n+1/2)}{\Gamma(-1/2)}\right)}{(n+1)!} = -2^{2n+1} \binom{n-\frac 12}{-\frac 32} \,,\end{align}$$ using the Gamma function. Thanks -- Quantling (talk) 17:01, 21 April 2010 (UTC)

New non-geometric bijective proof
I have added a new bijective proof aimed to directly derive the fascinating $$\tfrac{1}{n+1}$$ factor in the formula. I think it makes a nice complement to the existing bijective proofs as it is not based on a geometric interpretation but instead uses Dyke words and calculates the factor algebraically by comparing coefficients.

I tried several approaches and found this to be the most economical. I made this proof up myself as I could not find a similar one with the same features on the web. Still it should be simple and straightforward enough to be immediately obvious and verifiable by anyone with basic math skills in order to justify its inclusion into wikipedia. If it has been done before (which seems likely), please feel free to add a reference.

Bernhard Oemer (talk) 16:02, 10 January 2011 (UTC)

Section "quadruple factorial"
What the heck is this section refering to? Where does the name "quadruple factorial" come from? Is it notable at all? Right now I'm inclined to delete it because I can't figure out what it's about, but if someone can tell me what it means, then I'd be happy to reverse my position. (Maybe it would be better as a subsection somewhere?) --JBL (talk) 13:32, 17 September 2012 (UTC)

 * Hearing nothing after one year, I've removed mentions of the "quadruple factorial". --JBL (talk) 03:10, 16 September 2013 (UTC)

Second proof
I have just finished some copyediting of the second proof to improve the English and flow of the proof. I tried to preserve as much of the section as I could, but it did require some significant changes to increase clarity and deal with some of the harder parts of the proof. I did not, at this time, put back the historical sentence concerning Andre's reflection method, since there is an editor who objects to that, and so, it should be discussed here. My feeling is that it should be returned since it has encyclopedic value and we are writing an encyclopedia, not a textbook. The statement is of interest and I should point out a comment concerning it made above on this talk page. Bill Cherowitzo (talk) 06:41, 8 January 2015 (UTC)
 * I would accept one sentence about the author if it provided some new information in addition to the reflection article. The point to discuss the authorship of reflection method, whenever you apply it is stupid verbosity and as any verbosity it was confusing: I could not even understand who is author of what. `Encyclopedia` does not mean that you copy-paste referred material under every reference. Which encyclopedic standard tells you that you must copy only the historic sections but not the whole referenced articles every time you use/refer them? Finally, sane people can distinguish Andreas reflection from Schwarz reflection without notice. Only dumb ones will follow the hyperlink and confuse it with Schwarz reflection. For them, you should notice that Andre's reflection principle is different from both electricity, economics, computer manufactoring, psychology and everything we have in the world (there are 20 reflection principles that you had to enumerate in your article at least). It seems that your purpose was to draw the proof into the stupid verbosity. I do not understand which fluence you are talking about. --Javalenok (talk) 13:09, 11 January 2015 (UTC)

Incorrect Equation
The last formula in the first equation of the page:

$$C_n = \prod\limits_{k=2}^{n}\frac{n+k}{k} \qquad\mbox{ for }n\ge 0.$$

Is incorrect (or at least gives inconsistent answers with the other formulas), for example for

n = 0, 1, 2, 3, 4, 5

this gives:

1, 1, 2, 4, 14, 36

but should be:

1, 1, 2, 5, 14, 42

— Preceding unsigned comment added by Agold1982 (talk • contribs)

 * (3+2)/2 * (3+3)/3 = 5. (5+2)/2 * (5+3)/3 * (5+4)/4 * (5+5)/5 = 42.  It is also easy to check that this formula agrees with the factorial formula. --JBL (talk) 14:55, 27 November 2015 (UTC)

 * You are completely right, this was my mistake. (Agold1982)

Name: Mingantu, Minggatu?
https://en.wikipedia.org/wiki/Minggatu "Mingantu" felt bogus to me, so I Googled it, and found the more plausible entry, "Minggatu," above. My feeling is that this "Mingantu" thingie, and the related renaming of his hometown as "Ming Antu," apparently, by some Chinese bureaucrat, are the work of perhaps well-intentioned but semi-literate functionaries. The Han government in Beijing is faced with all sorts of ethnic frictions, and they're scurrying around trying to solve them, but clearly some of the people involved are acting without really understanding what they're doing. (We have the same sort of thing in the West, with all the halfwits who pronounce the Chinese capital a Frenchified "bay-zhhing." It's furrin, but if I make it sound French that will show people how cosmopolitan and sophisticated I am, right? Feh!) Imho, we ought to go with the way the guy pronounced it himself, and in Roman letters that would be "Minggatu," to the minimum possible distortion. Fixing this will involve inserting the Wikipedia reference as #14, and renumbering the higher footnote numbers, which I'm afraid is beyond my Wiki skills. Could somebody else maybe do that? David Lloyd-Jones (talk) 12:31, 6 November 2017 (UTC)

 * Um, your feelings about this are irrelevant. None of the listed sources use this spelling, and if anything, the biography article should be moved to reflect the spellings we have in sources.  --Deacon Vorbis (talk) 13:10, 6 November 2017 (UTC)

Should there be a mention of inversion of power series?
Should there be a mention of inversion of power series? One way to define the Catalan numbers is to say that they are the coefficients in the inverse series of x(1-x), regarded as a power series in x. In other words, if you set y=x(1-x) and solve for x as a series in y, you get them as coefficients. Maybe this follows pretty readily from one of the other descriptions given here. I don't feel confident enough to wade in and make a change to the article. Ishboyfay (talk) 23:22, 16 November 2017 (UTC)
 * , there seems to already be a blurb about it at Lagrange inversion theorem. You could always just write a sentence or two that mentions something about it and link to there.  --Deacon Vorbis (talk) 00:25, 17 November 2017 (UTC)
 * On further thought, it's so similar to what appears in Proof 1 that it's not a useful addition. Ishboyfay (talk) 03:50, 18 November 2017 (UTC)

Which Catalan number for counting triangulations of a polygon
Knowing that some Catalan number counts the number of triangulations of a polygon is part of the excitement of what mathematics is all about. Knowing Catalan number it is, through the mnemonic that "the n-th Catalan number counts the case of n triangles" is intended to be the frosting on the cake. I'd like to put in the count of triangles without it getting reverted. Thank you, 64.132.59.226 (talk) 13:32, 30 January 2018 (UTC)
 * The flowery language about the excitement of mathematics really isn't needed. My concern when I reverted was that the new wording makes it sound like triangulations into other numbers of triangulations are possible, but those just aren't being counted here, which isn't the case.  –Deacon Vorbis (carbon • videos) 13:51, 30 January 2018 (UTC)
 * Thank you Deacon Vorbis for the detailed feedback. Yes, I agree that triangulations formed "by connecting vertices with non-crossing line segments" will always have exactly n triangles and that simply inserting "n" into the article text could instead be interpreted as specified by Deacon Vorbis.  In contrast,  triangulations of a convex (n+2)-gon could have more than n triangles, e.g. because triangles themselves can be further triangulated.  What edits would you make to the following proposed language?:
 * Cn is the number of different ways a convex polygon with n + 2 sides can be triangulated into exactly n triangles. The following hexagons illustrate the case n = 4:
 * 64.132.59.226 (talk) 14:54, 30 January 2018 (UTC)
 * I like the following better. What edits would you make to the following proposed language?  Please speak up yea or nay lest your silence be considered acquiescence.
 * A convex polygon with n + 2 sides can be cut into triangles by connecting vertices with non-crossing line segments (a form of polygon triangulation). The number of triangles formed is n and the number of different ways that this can be achieved is Cn. The following hexagons illustrate the case n = 4:
 * 64.132.59.226 (talk) 12:57, 31 January 2018 (UTC)

The discussion has ground to a halt so let's try the BOLD, revert, discuss cycle. Because the edit I am making attempts to address the prior criticism, if you find yourself compelled to revert the edit then also comment here as to your reasons. Make your comments constructive; "it would be better if we ..." helps much more than "that is worse because ..." because the former helps to find the right direction to go, but the latter lists only one of many possible directions that should be avoided. 64.132.59.226 (talk) 13:36, 2 February 2018 (UTC)
 * This version seems fine to me. --JBL (talk) 13:56, 2 February 2018 (UTC)

Redundancy in Applications in combinatorics
In the list of applications, applications 2, 3, and 13 are stating the same thing. Also, applications 4 and 12 are redundant. I am going to remove applications 3, 12, and 13 upon consensus.

Plaba123 (talk) 16:23, 15 October 2018 (UTC)

 * First of all, a lot of these are going to be fairly similar, and I think a little redundancy for listing what's counted is actually okay. That being said, I think 12 (rooted binary trees) is definitely just a repeat of 4 (same thing), so it's safe to remove.  I think #13 (mountain ranges) is probably okay to remove too, but more so because it's really the same as #6 (lattice paths), although this one isn't quite as clear-cut.  But 2 and 3 are probably different enough that they should have their own entries.  If anything, #2 is too similar to #1, but the connection to #3 isn't quite so immediately obvious.  –Deacon Vorbis (carbon • videos) 17:22, 15 October 2018 (UTC)

 * Thanks for your input. I'll start off by removing #12 (rooted binary trees). Plaba123 (talk) 01:25, 16 October 2018 (UTC)

Second recursive formula
The second recursive formula was shifted one to the right, it returned 1 for C_0, 2 for C_1, 5 for C_2 and so on. OEIS gives the same recursive definition (https://oeis.org/A000108):

2*(2*n-1)*a(n-1) = (n+1)*a(n)

I see that my change was reverted, could it be incorporated? Pranomostro (talk) 21:06, 18 February 2019 (UTC) comment added by Pranomostro (talk • contribs) 20:51, 18 February 2019 (UTC)

 * Side note first: there's certainly nothing wrong with notifying someone on their talk page of a discussion on an article's talk page, but if you want to get someone's attention on an article talk page post directly, you can just WP:PING them (I'll generally use either the or  template, depending).  Anyway, about the recurrence relation, you might want to double check that you're using the right value for $n$.  The formula that's already here is correct and agrees with what's listed at the OEIS.  –Deacon Vorbis (carbon • videos) 02:11, 19 February 2019 (UTC)

I'm sorry if I violated some wikiquette by notifying you on your talk page, thanks for the pointers :D

Now, about the recurrence relation, the following was my thought process:

When plugging in the indices [0;13]:

The given values for the catalan numbers were:

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012

S1: $$C_n = \frac{1}{n+1}{2n\choose n}$$ gives the following values for C_0, C_1, C_2 etc.:

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012

OEIS lists the catalan numbers the same way:

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012

S2: $$C_0 = 1 \quad \text{and} \quad C_{n+1}=\frac{2(2n+1)}{n+2}C_n$$ gives the following numbers (and is used in the current article):

1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900

Note that one $$1$$ is missing.

S3: $$C_0 = 1 \quad \text{and} \quad C_{n+1}=\frac{2(2n-1)}{n+1}C_n$$. This is equivalent to 2*(2*n-1)*a(n-1) = (n+1)*a(n) from OEIS and returns the following sequence:

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012

Here is the code I used, in python3:

There might still be good reasons to keep the current version. First of all, there is a proof for it in this article, and secondly, it is a lot more common. On the other hand, it may be misleading (it misled me at first as well). I hope I made my case clear here, and will stop pestering you now.

Have a nice day.

Pranomostro (talk) 21:16, 19 February 2019 (UTC)
 * You are mistaken, and the version in the article is correct. Your error comes from replacing n+1 and n with n and n-1 in the subscripts, but not also making the same substitution for the other copies of n.  The simplest way to verify that you are mistaken is to plug in n=0 in the version in the article.—JBL (talk) 23:42, 19 February 2019 (UTC)

via Wolfram Alpha rising factorial
Using WA, one can use the following query: (5*4^(n-3) * (Pochhammer 7/2,n-3)) / (Pochhammer 5,n-3) for n=3,10
 * alternately, Table[ CatalanNumber@ n, {n, 0, 100}]    --Billymac00 (talk) 18:44, 3 September 2020 (UTC)

 * And? --JBL (talk) 19:34, 3 September 2020 (UTC)

Relation to matrix chain multiplication
Thank you @JayBeeEll for your recent concern about my edit to this article. Would you please give more information about your comment "this is not an example of what is being discussed"? The paragraph is about the number of associative ways to multiply an ordered set of n+1 objects. For the matrix chain multiplication problem, the n+1 objects are matrices. To me, it is the premier example where people care about the association order for the multiplications. Thank you — Q uantling (talk | contribs) 17:38, 8 February 2021 (UTC)
 * The paragraph is about the number of ways to associate, whereas mcm is the context in which people care about different associations. The latter is not an example of the former.  In fact, the connection between the Catalan numbers (the topic of this article, and the common thread that binds all the different examples in that section together) and the mcm problem is rather weak: one does not need to know a priori how many parenthesizations there are in order to solve mcm, and there's nothing about mcm that is more Catalan-y than the generic observation about possible associations of any binary operation.  I did not remove the link from the article -- it's now in the see also section -- but if you really think it would be better in the bullet point, we could talk about other phrasing.  One possibility might be to extend the parenthetical in the previous sentence: "(or the number of ways of associating n applications of a binary operator, as in the matrix chain multiplication problem)". --JBL (talk) 17:54, 8 February 2021 (UTC)

That parenthetical works for me. Thank you — Q uantling (talk | contribs) 19:53, 8 February 2021 (UTC)

Taking this to GA and maybe, beyond
If any talk-page watcher has any interest in taking this to a GA or improve the overall quality, I will appreciate their collaboration. Will start drafting at User:TrangaBellam/Catalan Number. Thanks, TrangaBellam (talk) 18:00, 21 April 2022 (UTC)

 * It needs a lot of work, but I am definitely interested. End-of-semester busyness may be an issue for me for the next few weeks, though. --JBL (talk) 18:02, 21 April 2022 (UTC)

We
I think using "we" in the proofs is kinda weird and should be removed — Preceding unsigned comment added by 2604:3D09:1580:9600:C884:4058:E2C4:3F13 (talk) 03:19, 17 May 2022 (UTC)

Method of images
@Darcourse et al. There is use of the method of images in the second proof of the Catalan numbers formula. While the method of images is used for continuous cases, such as energy potentials in the presence of boundary conditions, it is also used for discrete cases. A random walk that starts at the origin on the real line, that takes steps of ±1, and that is prohibited from going to −1 — in our case the number of '(' minus the number of ')' cannot be −1 — can be modeled by adding the random walk to a "negative" of the random walk that starts at −2. For any given number of steps, both the random walk from the origin and the one from −2 have equal chance of ending up at −1, and thus adding that "negative" "image" that starts at −2 to the original random walk from the origin ends up zeroing all values at −1, which is exactly what we need when we are enumerating Catalan numbers.

I propose to mention this in the section on the second proof, via something like

but I am open to alternatives. Thanks — Q uantling (talk | contribs) 14:57, 16 October 2023 (UTC)

 * The MoI article is way too technical for the level the Catalan number article is aimed at, and the connection is no way obvious. You could add it to 'see also', but I can't see how it is related at all. Darcourse (talk) 03:55, 17 October 2023 (UTC)
 * The Method of images article is lacking an example that is a discrete case. I plan to make edits there and then revisit the present discussion. — Q uantling (talk | contribs) 12:58, 17 October 2023 (UTC)

Connection to Mandelbrot set
If you take the variable c and run it through the function for the Mandelbrot set, $$f(z)=z^2+c$$, an infinite number of times, you get an infinite series denoted by:

$$\sum_{n=1}^\infty C_n c^n$$

where $$C_n$$ is the nth Catalan number. And the curve in the complex plane for which this infinite series equals two is precisely the boundary of the Mandelbrot set. Denelson83  02:17, 19 January 2024 (UTC)

 * With the notation of this article, the formula is off by one, yes? I believe that the limiting value of $f(f(... f(f(0)) ...)) = f(f(... f(f(c)) ...))$ is $$\sum_{n=0}^{\infty} C_n c^{n+1}$$.  One gets absolute convergence of the series for $|c| < 1/4$, so we'd have to explain what we mean by "you get an infinite series" for other values of $c$.
 * I cannot verify in a few minutes that the Mandelbrot set boundary is when the series value $$\sum_{n=0}^{\infty} C_n c^{n+1} = 2$$, especially if it is to be meaningful when we don't have absolute convergence. If this is to go into the article, we'd need a quick proof (WP:CALC) or a citation.  Thank you — Q uantling (talk | contribs) 14:13, 19 January 2024 (UTC)
 * It is minimally cited in the OEIS entry for the Catalan Numbers, A000108, by Donald D. Cross. It is not a proof, but it does give you a brief idea as to the connection.  Cross goes into this in a bit more detail here, illustrating a slow rate of convergence. --  Denelson83  20:05, 19 January 2024 (UTC)
 * This is cute but I would want to see a much better source (from the point of view of WP:RS) before adding anything about this to either article. --JBL (talk) 20:38, 19 January 2024 (UTC)
 * I have attempted to contact Donald Cross to see if he has been able to come up with a proof for this connection. It is just too bad we cannot note this as an unsolved conjecture, despite the fact that cursory observations provide support to it.

 * And I should have said "absolute value", as in $$\left\vert\sum_{n=0}^{\infty} C_n c^{n+1}\right\vert = 2$$. --  Denelson83  19:45, 2 February 2024 (UTC)
 * Wikipedia is not part of the research literature, it is a tertiary source. If other people writing reliable, secondary sources comment on this as an usolved problem, then we can follow them.  --JBL (talk) 20:28, 2 February 2024 (UTC)
 * Putting on my WP:CALC hat, let's define the "convergence" here. Let's write $f0(c) = 0$ and, for positive integer $n$, let's write $fn(c) = (fn−1(c))2 + c$.  For any particular value of $n$, the value of $fn(c)$ is a polynomial function of $c$ with integer coefficients.  We'll write $[cm]fn(c)$ for the integer coefficient of $cm$ in the polynomial $fn(c)$.  For positive integer $m$, we have the convergence that
 * $$\lim_{n\rightarrow\infty}[c^m]f_n(c) = C_{m-1}\,,$$
 * the $(m−1)$-th Catalan number.
 * This convergence is not the same as
 * $$\lim_{n\rightarrow\infty}f_n(c)\,,$$
 * which converges only for those elements of the Mandelbrot set that converge to a point under the $z2 + c$ iteration, rather than either cycling around inside the Mandelbrot set or running off to infinity.
 * This convergence is also not the same as that for the infinite series
 * $$\sum_{m=1}^\infty C_{m-1}c^m\,,$$
 * which converges absolutely only for $|c| < 1/4$. (Well, maybe for $|c| ≤ 1/4$.)
 * I don't know which of these forms of convergence, if any, is the one that is being used in the comparison to 2.
 * Even if we iron out all these mathematical details, we still need a reliable source that this result has notability.
 * That's my 2¢. — Q uantling (talk | contribs) 20:32, 2 February 2024 (UTC)
 * And such a reliable source is something I hope to one day find. --  Denelson83  21:42, 2 February 2024 (UTC)

title: Talk:Catalan number


text: File:TopekaCityCrest.png

title: File:TopekaCityCrest.png


text:
Moses Formwalt

Moses W. Formwalt (1820 – May 26, 1852 ) was the first mayor of the city of Atlanta, which was then in DeKalb County, Georgia. Atlanta was chartered in December 1847 (the name had been changed from Marthasville in December 1845), and the first election of officers took place on January 29, 1848. Formwalt drew a larger share of the 215 votes than Jonathan Norcross and was elected mayor, representing the Free and Rowdy Party. First meeting of the city council followed on February 2 at the Jonas Smith grocery (site of the Howard Johnson hotel near Five Points). Things proceeded pretty normally throughout his one-year term: roads were cut, wells dug, law and order somewhat maintained (a jail was built); and on January 17, 1849, Dr. Benjamin F. Bomar succeeded him as mayor.

Born in Tennessee, Formwalt came to Decatur in 1836 and established a tin shop on Decatur St. in Atlanta in 1846 where one of his most popular products were stills. He became mayor at age 28. Two years after leaving office, he began serving as deputy sheriff of DeKalb County; a short time later he was stabbed to death by a prisoner while escorting him from the council chamber. He was buried at Oakland Cemetery and is honored by Formwalt Street just southwest of downtown.

title: Moses Formwalt


text:
Beguines and Beghards

The Beguines and the Beghards  were Christian lay religious orders that were active in Western Europe, particularly in the Low Countries, in the 13th–16th centuries. Their members lived in semi-monastic communities but did not take formal religious vows; although they promised not to marry "as long as they lived as Beguines", to quote an early Rule of Life, they were free to leave at any time. Beguines were part of a larger spiritual revival movement of the 13th century that stressed imitation of Jesus' life through voluntary poverty, care of the poor and sick, and religious devotion.

Etymology
The term "Beguine" (beguinas; begijn) is of uncertain origin and may have been pejorative. Scholars no longer credit the theory expounded in the Encyclopædia Britannica Eleventh Edition (1911) that the name derived from Lambert le Bègue, a priest of Liège. Other theories, such as derivation from the name of St. Begga and from the purported, reconstructed Old Saxon word *beggen, "to beg" or "to pray", have also been discredited. The origin of the movement's name continues to be uncertain, as are the dates for the beginning of the movement itself.

There is likewise no evidence that Beguines ever formed part of the Cathar heretical groups. Encyclopedias, when they mention this latter explanation at all, tend to dismiss it.

Communities and status

At the beginning of the 12th century, some women in the Low Countries lived alone and devoted themselves to prayer and good works without taking vows. At first there were only a few, but in the course of the century, their numbers increased. In the Middle Ages there were more women than men due to the structure of urban demographics and marriage patterns in the Low Countries. These women lived in towns, where they attended to the poor. During the 13th century, some of them bought homes that neighbored each other. These small communities of women soon attracted the attention of secular and clerical authorities. Moved or inspired by the women's commitment to prayer, the sacraments, and charitable service in the world, local clergy sought to channel and deploy the women's spiritual fame in response to contemporary problems, especially the institutional church's war on heresy. Several clerics sought to promote these mulieres religiosae (or religious women) as saints after their deaths. Probably the most famous instance of this was the relationship between James of Vitry and Marie d'Oignies, who is sometimes referred to as the prototypical Beguine, in the early 13th century. Marie d'Oignies inspired James. She encouraged and improved his preaching and many of her miracles served to promote the sacramental program of Lateran IV. After Marie's death, James traveled to Rome on behalf of the "religious women" in the Diocese of Liège, seeking papal permission for the women to live in common and incite one another to live good Christian lives.

Beguines were not nuns, but they are sometimes conflated with them. Beguines took personal, informal vows of chastity. Animated by the ideals of the vita apostolica—the same ideals that led to the formation of the mendicant orders—Beguines pursued a life of contemplative prayer and active service in the world. As women, Beguines were forbidden to preach and teach, yet they actively exhorted their fellow Christians to live lives of penance, service, and prayer.

Beguines were never recognized as an official, papally approved religious order. They did not follow an approved rule, they did not live in convents, and they did not give up their personal property. In fact, Beguines were free to abandon their religious vocation at any time since it was not enforced by any binding monastic vow. In many cases, the term "Beguine" referred to a woman who wore humble garb and stood apart as living a religious life above and beyond the practice of ordinary laypeople.

In cities such as Cambrai, Valenciennes, and Liège, local officials established formal communities for these women that became known as beguinages. Beguinages (Begijnhoven in Dutch-speaking areas) tended to be located near or within town centers and were often close to the rivers that provided water for their work in the cloth industry.

While some women joined communities of like-minded lay religious women, adopting the label "Beguine" by virtue of entering a beguinage, many women lived alone or with one or two other like-minded women. Beguines engaged in a range of occupations to support themselves. Women in the Low Countries tended to work in the cities' lucrative wool industry. Parisian Beguines were important contributors to the city's burgeoning silk industry.

Beguinages were not convents. There was no overarching structure such as a mother-house. Each beguinage adopted its own rule. The Bishop of Liège created a rule for Beguines in his diocese. However, every community was complete in itself and fixed its own order of living. Later, many adopted the rule of the Third Order of Saint Francis.

Beguine communities varied in terms of the social status of their members; some of them only admitted ladies of high degree; others were reserved exclusively for persons in humble circumstances; others still welcomed women of every condition, and these were the most popular. Several, like the great beguinage of Ghent, had thousands of inhabitants. The Beguinage of Paris, founded before 1264, housed as many as 400 women. Douceline of Digne (c. 1215-1274) founded the Beguine movement in Marseille; her hagiography, which was composed by a member of her community, sheds light on the movement in general.

This semi-monastic institution was adapted to its age and spread rapidly throughout the land. Some Beguines became known as "holy women" (mulieres sanctae), and their devotions influenced religious life within the region. Beguine religious life was part of the mysticism of that age. There was a beguinage at Mechelen as early as 1207, at Brussels in 1245, at Leuven before 1232, at Antwerp in 1234, and at Bruges in 1244. By the close of the century, most communes in the Low Countries had a beguinage; several of the great cities had two or more.

Some influential Beguinages were Begijnhof (Amsterdam), Begijnhof (Breda), and Begijnhof (Utrecht).

Criticism and social response
As the 13th century progressed, some Beguines came under criticism as a result of their ambiguous social and legal status. As a conscious choice to live in the world but in a way that effectively surpassed (at least in piety) or stood out from most laypeople, Beguines attracted disapprobation as much as admiration. In some regions, the term Beguine itself denoted an ostentatiously, even obnoxiously religious woman; an image that quickly led to accusations of hypocrisy (consider the Beguine known as "Constrained Abstinence" in the Roman de la Rose). Some professed religious were offended by the assuming of "religious" status without the commitment to a rule, while the laity resented the implicit disapproval of marriage and other markers of secular life. The women's legal standing in relation to ecclesiastical and lay authorities was unclear. Beguines seemed to enjoy the best of both worlds: holding on to their property and living in the world as laypeople while claiming the privileges and protections of the professed religious.

On the other hand, admirers such as the secular cleric Robert de Sorbon (died 1274) noted that Beguines exhibited far more devotion to God than even the cloistered, since they voluntarily pursued a religious life without vows and walls, surrounded by the world's temptations.

The power of the Beguine label is evident in the "watershed" moments of Beguine history, from its first appearance in the sermons of James of Vitry (the Beguine movement's earliest and perhaps most famous promoter), to its reference in the trial of the doomed mystic Marguerite Porete (who was burned at the stake in Paris on charges of heresy in 1310), to its centrality in the condemnation of lay religious women at the Council of Vienne in 1311–1312.

Marguerite Porete
Sometime during the early to mid-1290s, Marguerite Porete wrote a mystical book known as The Mirror of Simple Souls. Written in Old French, the book describes the annihilation of the soul, specifically its descent into a state of nothingness—of union with God without distinction. While clearly popular throughout the Middle Ages and beyond (perhaps dozens of copies circulated throughout late-medieval western Europe) the book provoked controversy, likely because of statements such as "A soul annihilated in the love of the creator can, and should, grant to nature all it desires", which was viewed as meaning some kind of immorality the Church, its sacraments, or its canons. Porete taught that souls in such a state desired only good and would not be able to sin.

Also at issue was the manner in which Porete disseminated her teachings, which was evocative of actions and behaviors some clerics were finding increasingly problematic among lay religious women in that era. Indeed, Porete was eventually tried by the Dominican inquisitor of France and burned at the stake as a relapsed heretic in 1310. In 1311—the year after Porete's death—ecclesiastical officials made several specific connections between Porete's ideas and deeds and the Beguine status in general at the Council of Vienne. One of the council's decrees, Cum de Quibusdam, claimed that Beguines "dispute and preach about the highest Trinity and the divine essence and introduce opinions contrary to the Catholic faith concerning the articles of the faith and the sacraments of the church".

Post-1312 decline
After the Council of Vienne in 1312, the Beguines declined. By the 14th century, some communities were absorbed by monastic and mendicant orders. Many, however, survived the aftermath of the Vienne decrees.

Most of these institutions were suppressed during the Reformation of the 16th century or during the stormy years of revolutions and social unrest of the French Revolution. A few béguinages persisted until the early 20th century in parts of Belgium, including those of Bruges, Lier, Mechelen, Leuven and Ghent, which last numbered nearly a thousand members in 1905.

Surviving Beguines

The community of Begijnhof, Amsterdam, credited with having considerably influenced the development of what was the city's southern edge in the late Middle Ages, survived the Protestant Reformation staunchly Catholic. Their parish church was confiscated and given over to exiled English Puritans. The last Amsterdam Beguine died in 1971, but the Begijnhof remains one of the city's best-known landmarks.

Marcella Pattyn, the last traditional Beguine, died on 14 April 2013 in Kortrijk at the age of 92. Born in the Belgian Congo in 1920, she was accepted into the Holy Corner of Elizabeth of Hungary at Sint-Amandsberg, Ghent, in 1941 and moved to the Béguinage of St Elisabeth at Kortrijk in 1960, where she became one of a community of nine.

Second and third waves
Writer Jean Hughes Raber, a student of medieval women's movements, posited a second wave of the Beguine movement, which occurred in the 17th century, when it was supported by Archbishop Mathias Hovius. His involvement included helping improve the Great Beguines at Mechelen. Raber says there was no clear end to the Second Movement. She suggests that Catholic lay movements, such as those of Dorothy Day in the United States, the Company of St. Ursula and communities of women initiated by Francisca Hernandez, can be seen as extensions of the Beguines into the 20th century.

Raber suggests the Beguines' response to social and economic forces in the 12th century offers a model that can meet current conditions: economic uncertainty or worse, single women comprising a larger section of the population, and loss of wealth in the form of deflated values of housing. She cites a California-based group, the American Beguines, as an example of the revival of the Beguine Movement, with notable but not necessarily problematic differences. In recent decades, a new Beguine movement has arisen in Germany.

Recently, the Beguines of Mercy were founded in Vancouver, British Columbia, Canada. It is a contemplative third order of educated Catholic women whose roots are in spiritual community. Their affiliations are good works, quiet contemplation, and living out their spiritual values.

Notable Beguines
Among Beguines who have become well-known representatives of the movement in contemporary literature are: Christina von Stommeln, Douceline of Digne, Hadewijch, Marguerite Porete, Marie d'Oignies, and Mechthild of Magdeburg. Modern Beguines include Marcella Pattyn, and perhaps Dorothy Day.

Beghards (laymen)
A widespread religious revival inspired several societies for men which were kindred to the Beguines. Of these, the Beghards were the most numerous and the most important.

Membership
The Beghards were all laymen and, like the Beguines, they were not bound by vows, the rule of life which they observed was not uniform, and the members of each community were subject only to their own local superiors. They held no private property; the brethren of each cloister had a common purse, dwelt together under one roof and ate at the same board. They were for the most part men of humble origin—like weavers, dyers, and fullers—who were closely connected with the city craft-guilds. For example, no man could be admitted to the Beghards' community at Brussels unless he were a member of the Weavers' Company. The Beghards were often men to whom fortune had not been kind—men who had outlived their friends, or whose family ties had been broken by some untoward event and who, by reason of failing health or advancing years, or perhaps on account of some accident, were unable to stand alone. If "the medieval towns of the Netherlands found in the Beguinage a solution of their feminine question", the growth of the Beghard communities provided a place for the worn-out working man.

The men had banded together in the first place to build up the inner man. While working out their own salvation, they remained mindful of their neighbors and, thanks to their connection with the craft-guilds, they influenced the religious life. They are credited with shaping the religious opinion of the cities and towns of the Netherlands for more than 200 years, especially for the peasant.

Relation to the Church
Religious authorities believed the Beguines had heretical tendencies and sometimes tried to bring disciplinary measures against them. The Synods of Fritzlar (1259), Mainz (1261), and Eichstätt (1282) brought measures against them and they were forbidden as "having no approbation" by the Synod of Béziers (1299). They were condemned by the Council of Vienne (1312), but this sentence was mitigated by Pope John XXII (1321), who permitted the Beguines to resume their mode of life after reform.

The Beghards were more obstinate; during the 14th century, they were repeatedly condemned by the Holy See, the bishops (notably in Germany) and the Inquisition. Ernest Gilliat-Smith, writing in the Catholic Encyclopedia said that men of faith and piety were found among the Beghards. In their behalf, Pope Gregory XI (1374–77) and Pope Boniface IX (1394) addressed Bulls to the bishops of Germany and the Netherlands. The doctrine of Quietism is believed to resemble the stance of these community members.

Modern decline
Before the close of the Middle Ages, Beghard communities were in decline. Their numbers diminished with the waning of the textile trade and, when that industry died, gradually dwindled away. The highest number of such medieval foundations in Flanders and Wallonia was 94, but in 1734 they had been reduced to just 34. Pope Gregory XVI referred to them critically in his 1832 encyclical letter Mirari vos. There were 20 remaining foundations in 1856.

Literary references

 * Joyce Hollyday's 2020 novel Pillar of Fire offers a fictionalized account of Beguines based in part on the writing of Marguerite Porete.
 * In his multi-volume novel The Life and Opinions of Tristram Shandy, Gentleman (1759–1767), Laurence Sterne has his character Corporal Trim describe a Beguine.
 * In Charlotte Brontë's 1853 novel Villette, Beguines and a beguinage are mentioned in Chapter 17, "La Terrasse".
 * Françoise Mallet-Joris's first novel was Le rempart des Béguines (1952; published in 2006 in a new English translation as The Illusionist). The title is the name of the street where Tamara, a courtesan, lives apart from the bourgeois society of Gers, a fictional Flemish town.
 * The 2012 novel Ink & Honey (revised and reissued 2022) by Sibyl Dana Reynolds, tells the fictional story and journey of a group of beguines, the sisters of Belle Coeur, set in medieval France.
 * In Umberto Eco's 1980 novel The Name of the Rose (1983 in English), the Beghards are frequently mentioned among the heretical movements which the Inquisition is persecuting.
 * Bernard Cornwell in his 2003 novel Heretic has a character, Genevieve, who is a condemned Beguine heretic rescued by the main character, Thomas of Hookton.
 * Karen Maitland in her 2009 novel The Owl Killers portrays a group of Beguines in the fictional early 14th-century English village of Ulewic.
 * Ken Follett in his 2012 novel World Without End mentions the life of Beguines in the Netherlands.
 * Helga Gielen in her 2019 virtual tour in the Grand Beguinage of Leuven explains the difference between Beguines and nuns.
 * In chapter 53 of Jean de Meun's 13th classic of Old French literature, Roman de la Rose, the Beguines are described by the allegorical antagonist False-Seeming are described as "to which vermin are no strangers, for in truth from far they're odorous" who wear "foul crumpled hose" and "ugly sandalled shoes".

General and cited references

 * Burnham, Louisa A., So Great a Light, So Great a Smoke: The Beguin Heretics of Languedoc, Cornell University Press, 2008.
 * De Cant, Geneviève, Majérus Pascal & Verougstraete Christiane, A World of Independent Women: From the 12th Century to the Present Day: The Flemish Beguinages, Riverside: Hervé van Caloen Foundation, 2003.
 * Deane, Jennifer Kolpacoff, Beguines' Reconsidered: Historiographical Problems and New Directions, Monastic Matrix, 2008.
 * McDonnell, Ernest W., The Beguines and Beghards in Medieval Culture: With Special Emphasis on the Belgian Scene, New York: Octagon Books, 1969 (1954 edition online at HathiTrust).
 * Miller, Tanya Stabler, The Beguines of Medieval Paris: Gender, Patronage, and Spiritual Authority, Philadelphia, University of Pennsylvania Press, 2014
 * Murk-Jansen, Saskia, Brides in the Desert: The Spirituality of the Beguine, Maryknoll, NY: Orbis Books, 1998
 * Neel, Carol, The Origins of the Beguines, Signs, 1989.
 * Petroff, Elizabeth Alvilda, Body and Soul: Essays on Medieval Women and Mysticism, Oxford: Oxford University Press, 1994
 * Philippen, L. J. M., De Begijnhoven: Oorsprong, Geschiedenis, Inrichting. Antwerp: Ch. and H. Courtin, 1918.
 * Reichstein, Frank-Michael, Das Beginenwesen in Deutschland, 2nd edition, Berlin, 2017.
 * Simons, Walter, Cities of Ladies: Beguine Communities in the Medieval Low Countries, 1200–1565, Philadelphia: University of Philadelphia Press, 2001.
 * Simons, Walter, "Staining the Speech of Things Divine: The Uses of Literacy in Medieval Beguine Communities", Thérèse De Hemptinne & Maria Eugenia Gongora (eds.), The Voice of Silence: Women's Literacy in a Men's Church, Turnhout, Brepols, 2004.
 * Swan, Laura, The Wisdom of the Beguines: The Forgotten Story of a Medieval Women's Movement, BlueBridge, 2014.
 * Van Aerschot Suzanne & Heirman Michiel, Les béguinages de Flandre. Un patrimoine mondial, Brussels: éditions Racine, 2001.
 * Von Der Osten-Sacken, Vera, Jakob von Vitrys Vita Mariae Oigniacensis. Zu Herkunft und Eigenart der ersten Beginen, Göttingen: Vandenhoeck & Ruprecht, 2010 (=VIEG 223).

 * Attribution

title: Beguines and Beghards


text:
The Transcendentalist

The Transcendentalist is a lecture and essay by American writer and thinker Ralph Waldo Emerson. It is one of the essays he wrote while establishing the doctrine of American Transcendentalism. The lecture was read at the Masonic Temple in Boston, Massachusetts in January 1842.

The work begins by contrasting materialists and idealists. Emerson laments the absence of "old idealists." He goes on to outline the fundamental beliefs and characteristics of the New England Transcendentalists. He discusses the nature of epistemology and the debate between Locke and Kant on Imperative forms and Transcendental forms, and discusses perception and reality in a blatantly Platonic sense. He says that solitude is a state of being that should be encouraged, for it allows humanity to achieve a higher level of alignment with nature and prevents the contamination that one encounters within a society.

Henry David Thoreau embodied the majority of these characteristics, except for neglecting to take action against the government. Thoreau was a staunch abolitionist; his home was a stop on the Underground Railroad. He was actively subverting the government, but Emerson admitted that there was no perfect Transcendentalist. Emerson created a perfect, ideal archetype for the Transcendentalist, but also realized that it would be adapted to fit imperfect humans in an imperfect world.

title: The Transcendentalist


text:
Tranexamic acid

Tranexamic acid is a medication used to treat or prevent excessive blood loss from major trauma, postpartum bleeding, surgery, tooth removal, nosebleeds, and heavy menstruation. It is also used for hereditary angioedema. It is taken either by mouth or by injection into a vein.

Tranexamic acid is a synthetic analog of the amino acid lysine. It serves as an antifibrinolytic by reversibly binding four to five lysine receptor sites on plasminogen. This decreases the conversion of plasminogen to plasmin, preventing fibrin degradation and preserving the framework of fibrin's matrix structure. Tranexamic acid has roughly eight times the antifibrinolytic activity of an older analogue, ε-aminocaproic acid. Tranexamic acid also directly inhibits the activity of plasmin with weak potency (IC50 = 87 mM), and it can block the active-site of urokinase plasminogen activator (uPA) with high specificity (Ki = 2 mM), one of the highest among all the serine proteases.

Side effects are rare. Some include changes in color vision, seizures, blood clots, and allergic reactions. Tranexamic acid appears to be safe for use during pregnancy and breastfeeding. Tranexamic acid is an antifibrinolytic medication.

Tranexamic acid was first made in 1962 by Japanese researchers Shosuke and Utako Okamoto. It is on the World Health Organization's List of Essential Medicines. Tranexamic acid is available as a generic drug.

Medical uses
Tranexamic acid is frequently used following major trauma. Tranexamic acid is used to prevent and treat blood loss in a variety of situations, such as dental procedures, heavy menstrual bleeding, and surgeries with high risk of blood loss.

Trauma
Tranexamic acid has been found to decrease the risk of death due to any cause in people who have significant bleeding due to trauma. It is most effective if taken within the first three hours following major trauma. It also decreases the risk of death if given within the first three hours of brain injury.

Menstrual bleeding
Tranexamic acid is sometimes used to treat heavy menstrual bleeding. When taken by mouth it both safely and effectively treats regularly occurring heavy menstrual bleeding and improves quality of life. Another study demonstrated that the dose does not need to be adjusted in females who are between ages 12 and 16. In a 10-year study, tranexamic acid and other oral medicines (mefenamic acid) were found to be as effective as the levonorgestrel intrauterine coil; the same proportion of women had not had surgery for heavy bleeding and had similar improvements in their quality of life.

Childbirth
Tranexamic acid is sometimes used (often in conjunction with oxytocin) to reduce bleeding after childbirth. Death due to postpartum bleeding is reduced in women receiving tranexamic acid.

Surgery

 * Tranexamic acid is sometimes used in orthopedic surgery to reduce blood loss, to the extent of reducing or altogether abolishing the need for perioperative blood transfusion. It is of proven value in clearing the field of surgery and reducing blood loss when given before or after surgery. Drain and number of transfusions are reduced.
 * In surgical corrections of craniosynostosis in children it reduces the need for blood transfusions.
 * In spinal surgery (e.g., scoliosis), correction with posterior spinal fusion using instrumentation, to prevent excessive blood loss.
 * In cardiac surgery, both with and without cardiopulmonary bypass (e.g., coronary artery bypass surgery), it is used to prevent excessive blood loss.

Dentistry
In the United States, tranexamic acid is FDA approved for short-term use in people with severe bleeding disorders who are about to have dental surgery. Tranexamic acid is used for a short period of time before and after the surgery to prevent major blood loss and decrease the need for blood transfusions.

Tranexamic acid is used in dentistry in the form of a 5% mouth rinse after extractions or surgery in patients with prolonged bleeding time; e.g., from acquired or inherited disorders.

In China, tranexamic acid is allowed in over-the-counter toothpastes, with six products using the drug. , there are no limits on dosage, nor requirements for labeling the concentration. 0.05% TXA in toothpaste is allowed OTC in Hong Kong. <5% TXA in over-the-counter toothpaste is first patented and marketed by Lion Corporation in Japan, where it is still sold. Presence of unauthorized TXA has led to the Canadian recall of a Yunnan Baiyao toothpaste in 2019.

Hematology
There is not enough evidence to support the routine use of tranexamic acid to prevent bleeding in people with blood cancers. However, there are several trials that are currently assessing this use of tranexamic acid. For people with inherited bleeding disorders (e.g. von Willebrand's disease), tranexamic acid is often given. It has also been recommended for people with acquired bleeding disorders (e.g., directly acting oral anticoagulants (DOACs)) to treat serious bleeding.

Nosebleeds
The use of tranexamic acid, applied directly to the area that is bleeding or taken by mouth, appears useful to treat nose bleeding compared to packing the nose with cotton pledgets alone. It decreases the risk of rebleeding within 10 days.

Cosmetic Uses
Tranexamic acid can be used in skincare products as a cosmetic active to reduce the appearance of inflammation and hyperpigmentation. Tranexamic acid is a zwitterion amino acid, and has a low permeability coefficient in the stratum corneum. Tranexamic acid can be combined with penetration enhancers and microneedling to overcome this limitation. Cosmetic uses may also employ lipophilic derivatives of tranexamic acid (ester prodrugs like Cetyl tranexamate mesylate) that are not zwitterionic and thus have improved skin permeability.

Contraindications

 * Allergic to tranexamic acid
 * History of seizures
 * History of venous or arterial thromboembolism or active thromboembolic disease
 * Severe kidney impairment due to accumulation of the medication, dose adjustment is required in mild or moderate kidney impairment

Adverse effects
Side effects are rare. Some reported adverse events include seizures, changes in color vision, blood clots, and allergic reactions such as anaphylaxis. Whether the risk of venous thromboembolism (blood clots) is actually increased is a matter of debate. The risk is mentioned in the product literature, and they were reported in post marketing experience. Despite this, and the inhibitory effect of tranexamic acid on blood clot breakdown, large studies of the use of tranexamic acid have not shown an increase in the risk of venous or arterial thrombosis, even in people who had previously experienced thrombosis under other circumstances.

Special populations

 * For pregnancy, no harm has been found in animal studies.
 * Small amounts appear in breast milk if taken during lactation.

Society and culture
Tranexamic acid was first synthesized in 1962 by Japanese researchers Shosuke and Utako Okamoto. It is on the World Health Organization's List of Essential Medicines.

Brand names
Tranexamic acid is marketed in the US and Australia in tablet form as Lysteda and in Australia, Sweden and Jordan it is marketed in an IV form and tablet form as Cyklokapron, in the UK and Sweden as Cyclo-F. In the UK it is also marketed as Femstrual, in Asia as Transcam, in Bangladesh as Intrax & Tracid, in India as Pause, in Pakistan as Transamin, in South America as Espercil, in Japan as Nicolda, in France, Poland, Belgium and Romania as Exacyl and in Egypt as Kapron. In the Philippines, its capsule form is marketed as Hemostan and in Israel as Hexakapron.

Legal status
The US Food and Drug Administration (FDA) approved tranexamic acid oral tablets (brand name Lysteda) for treatment of heavy menstrual bleeding in November 2009.

In March 2011, the status of tranexamic acid for the treatment of heavy menstrual bleeding was changed in the UK, from POM (Prescription only Medicines) to P (Pharmacy Medicines) and became available over the counter in UK pharmacies under the brand names of Cyklo-F and Femstrual.

Research
Tranexamic acid might alleviate neuroinflammation in some experimental settings.

Tranexamic acid can be used in case of postpartum hemorrhage; it can decrease the risk of death due to bleeding by one third according to the WHO.

Tentative evidence supports the use of tranexamic acid in hemoptysis.

In hereditary angioedema

In hereditary hemorrhagic telangiectasia: tranexamic acid has been shown to reduce frequency of epistaxis in patients with severe and frequent nosebleed episodes from hereditary hemorrhagic telangiectasia.

In melasma: tranexamic acid is sometimes used in skin whitening as a topical agent, injected into a lesion, or taken by mouth, both alone and as an adjunct to laser therapy; as of 2017 its safety seemed reasonable but its efficacy for this purpose was uncertain because there had been no large scale randomized controlled studies nor long term follow-up studies. It is allowed as a quasi-drug for skin whitening in Japan.

In hyphema: tranexamic acid has been shown to be effective in reducing risk of secondary hemorrhage outcomes in people with traumatic hyphema.

title: Tranexamic acid


text:
Talk:Ultima I: The First Age of Darkness

Town names
Most of the "town" characters in Ultima I were named after friends of Richard Garriott (though he used their pseudonyms from the Society for Creative Anachronism in most cases). —The preceding unsigned comment was added by 65.33.164.224 (talk • contribs).

Fair use rationale for Image:Ultima1.gif
Image:Ultima1.gif is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in Wikipedia articles constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

Please go to the image description page and edit it to include a fair use rationale. Using one of the templates at Fair use rationale guideline is an easy way to insure that your image is in compliance with Wikipedia policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.

If there is other other fair use media, consider checking that you have specified the fair use rationale on the other images used on this page. Note that any fair use images uploaded after 4 May, 2006, and lacking such an explanation will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have any questions please ask them at the Media copyright questions page. Thank you.BetacommandBot 16:25, 4 June 2007 (UTC)

My recent edit

 * Explaining a few things about my recent edit. The most reliable source is of course from the man himself, in his official book, The Official Book of Ultima, which I referenced at a few more places.  It says he sold 50,000 copies of this game.  This is from the original version, not any of the many times it was included in various collections.   D r e a m Focus  10:53, 18 September 2011 (UTC)

By June 1982 it sold 20,000 copies and by 1990 it had sold 50,000 copies. The second part seems a bit misleading. The reference doesn't show what year the sales figures were from. I doubt it continued to sell equally well for 8 years. Perhaps "went on to sell" 50,000 copies.  D r e a m Focus  12:32, 29 January 2012 (UTC)

External links modified (January 2018)
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Lead-in: "Exclusively" for the Apple II
"Exclusively" indicates other options were actively excluded. Maybe "solely" is a better word in this case? Scottman 01 (talk) 13:01, 27 April 2018 (UTC)
 * Yeah, seems like "originally released for the Apple II" should be sufficient. Sneftel (talk) 14:21, 27 April 2018 (UTC)


text:
User:209.181.211.69

Got a Wikipedia Account? Vandals Got Your Password (Score:5, Interesting)

http://yro.slashdot.org/comments.pl?cid=12669970&sid=151065&tid=158

As an on-again, off-again Wikipedian [wikipedia.org] responsible for countless edits as well as several full articles, I used to be happy to leave administrative matters there to others. Such was my bliss, anyway, until I stumbled upon something extremely troubling--something that forced upon me an awareness of the project's astonishingly careless attitude toward privacy and security. This is the product, apparently, of an obsession with countering vandalism so all-consuming that administrators are even willing to expose unlucky bystanders to identity theft.

This is what I discovered.

A Wikipedia developer, intending to catch sockpuppet accounts (multiple accounts created by the same individual), queried the user database for a list of accounts whose passwords matched passwords belonging to known vandals and trolls. Hoping the results would be useful to others, he published his findings [wikipedia.org] on his user page. Of course, such a list necessarily included anyone who happened to be using, merely by coincidence, the same passwords as the targeted individuals. As a matter of fact, it seems likely that the dragnet caught at least some people by chance alone. But only the people on the list could know for sure.

That in itself sounds unfortunate, but none too dangerous. The horrifying punchline is this: in publishing the results of his query, the developer had effectively given these vandals and trolls a list of usernames with whom they shared a password. And once so equipped, the vitals of each compromised account--including the email address--were just a login away.

Leaking people's passwords, usernames, and email addresses to anyone is damaging enough, let alone to established miscreants.

Anywhere else, a mistake like this would be acknowledged, the offending information removed, and the potential victims notified. Not so on Wikipedia, where the list spawned nothing but a protracted debate [wikipedia.org] and then a vote to remove the page [wikipedia.org]. In a second blow to Wikipedia's reputability--the first being the mistake itself--the vote finally succumbed to addled logic and shortsightedness, as did a motion to restrict its visibility to site administrators. And so the page has remained linked and visible now for almost a full year, a threat to any innocents listed therein and an affront to anyone with an interest in their privacy and personal security.

Imagine if you were on that list. (In fact, maybe you are.) Wouldn't you wonder how it was possible for Wikipedia to expose your password to malicious users for the better part of a year? Wouldn't you marvel that no one had alerted you?

I don't mean to single anyone out here, which is why I've refrained from mentioning the name of the careless developer. The real indictment, in my view, is of the process that:

1. Allowed such an egregious breach of privacy; 2. Failed to correct it, even after it came to attention; 3. Failed to notify those whose passwords had been leaked.

It is my opinion that this incident is only symptomatic of a larger problem: Wikipedia's tradition of policymaking by ad hoc polling. It is also, perhaps, a harbinger of disasters to come. A draft privacy policy [wikimedia.org] offers some hope, but interest in its adoption appears to have stagnated.

For the foreseeable future, then, it would be unwise for anyone to entrust their privacy to the Wikipedia site, when the project's developers and administrators have so clearly demonstrated a severe unfitness to guard it, to say nothing of a callous contempt for the real-world safety of contributors.

title: User:209.181.211.69


text:
Seaton Schroeder

Seaton Schroeder (August 17, 1849 – October 19, 1922) was an admiral of the United States Navy. He contributed to the development of the Driggs-Schroeder rapid-fire gun.

Biography
Schroeder was born in Washington, D.C., the son of Francis Schroeder, the Resident Minister to Sweden. His mother was the daughter of William Winston Seaton, who, with his brother-in-law, Joseph Gales, owned and edited the National Intelligencer. Seaton served as the Mayor of Washington, D.C., from 1840 to 1850.

He entered the United States Naval Academy in 1864, which, because of the American Civil War, was in Newport, Rhode Island. After graduating in June 1868 he served with the Pacific Fleet in 186869 under Admiral John Rodgers in screw sloop, USS Benicia (1868), and fought in the Salt River near Seoul, Korea. His sea tours took him to Alaska, Japan, and the Philippines in USS Saginaw (1859), to the West Indies in USS Canandaigua (1862), and on a world cruise on USS Swatara (1873).

Marriage and family
Schroeder married Maria Campbell Bache Wainwright on January 16, 1879. The couple had five children.

Maria Wainwright (born March 14, 1856, Washington, D.C.), came from a family of several American statesmen. She was the great-great-granddaughter of Benjamin Franklin, the great-granddaughter of Treasury Secretary Alexander J. Dallas, the granddaughter of Texas legislator Richard Bache, Jr., a niece of Vice President George Mifflin Dallas, the daughter of naval officer Richard Wainwright, and the sister of Admiral Richard Wainwright.

She died on July 12, 1926, aged 70 in Jamestown, Rhode Island.

Career
After specializing in hydrographic duties for 11 years, he spent two years in the Office of Naval Intelligence (ONI) where he helped develop the Driggs-Schroeder rapid-fire gun in partnership with Navy Commander William H. Driggs. He returned to sea in 1890 as the Commanding Officer of USS Vesuvius (1888). In 1893, he began a three-year tour as an ordnance officer for the Naval Gun Factory at the Washington Navy Yard and as the recorder of the Board of Inspection and Survey, joining the Board as a member in 1894.

Following his appointment as executive officer of the battleship USS Massachusetts (BB-2), he participated in the American blockade of Santiago, Cuba, during the Spanish–American War and was advanced three numbers in rank "for eminent and conspicuous conduct in battle" during five engagements between May 31 and July 4, 1898.

He was appointed Naval governor of Guam on 19 July 1900, and there commanded USS Yosemite (1892) and later, USS Brutus (AC-15). On May 1, 1903, Schroeder became Chief Intelligence Officer of the Navy. He assumed command of USS Virginia (BB-13) upon her first commissioning on May 7, 1906 and afterwards commanded various divisions in the Atlantic Fleet.

Promoted to rear admiral in 1908, he hoisted his flag on USS Connecticut (BB-18) when he took command of the Atlantic Fleet on March 8, 1909. Two months later, Schroeder was assigned to the Navy General Board. Schroeder was placed on the retired list on August 17, 1911, and retired to his home in Jamestown, Rhode Island.

Rear Admiral Schroeder was recalled to active duty in 1912 to prepare a new signal book, and again in World War I to serve as Chief Hydrographer and the Navy representative on the United States Geographic Board. He died at the Naval Hospital, Washington, D.C., on October 19, 1922.

Legacy

 * In 1942, the destroyer USS Schroeder (DD-501) was named in his honor.
 * Seaton Blvd. in the capitol city of Guam, Hagåtña, was named after him.
 * One of the 10 Southern Mountains of Guam was renamed from Finacresta to Mt. Schroeder (288m).

title: Seaton Schroeder