text:
Talk:Spectral theorem

I think the "Fundamental theorem of Linear Algebra" is normally taken to be the statement that connects kernel, row and column spaces of a matrix. AxelBoldt 02:25 Jan 24, 2003 (UTC)

Added a statement of the spectral theorem for bounded self-adjoint operators. Hopefully this should leave this article in a more-or-less definitive state.CSTAR 21:09, 13 May 2004 (UTC)

Request: The section on the Spectral theorem for unbounded operators is very vague - it more or less just mentions its existence. Since for many applications it is precisely unbounded (differential) operators that are of interest, it would be very useful to at the very least state the Spectral theorem for unbounded self-adjoint operators.

examples
The section "functional analysis" takes some pains to point out the shift operator, and a scaling operator on L^2[0,1] have no eigenvalues, and then immediately states a theorem that none-the-less, these are unitarily equivalent to some multiplication operator on some measure space. It sure would be nice to have a detailed example for these. linas 05:48, 19 March 2006 (UTC)
 * A good example would be kinda hard to come by. In the proofs I've seen for this theorem, the multiplication operator and the unitary equivalence are defined quite abstractly, so the constructions in the proofs don't lend themselves to practical calculations. I'm not aware of any method for finding "nice" multiplication operators and unitary equivalences that works in any generality.

 * However, for the scaling operator you mention (I presume you mean the operator A from the article, with $$[A \varphi ](t) = t \varphi (t)$$), the multiplication and unitary operators are quite simple: The multiplication operator is just the scaling operator itself, and the unitary operator is just the identity operator. This operator has a spectrum, but no eigenvalues. The spectrum is just $$[0,\ 1]$$, the range of f(t)=t. However, none of these spectral values are eigenvalues, as the eigenvectors they'd lead to would have to be functions that were zero except at one point (for an eigenvalue $$\lambda$$, that point would be $$f^{-1}(\lambda ) = \lambda$$). However, such functions would be zero almost everywhere, so are equivalent to the zero function, so can't be eigenvalues.

 * I hope this explains it. James pic 10:02, 3 July 2007 (UTC)

Recent edit
The point is that the sentence

 * Then—using the fact that $$A x = \lambda x$$ iff $$\overline{A} \overline{x} = \overline{\lambda} \overline{x}$$

is completely irrelevant. Please remove it.--CSTAR 21:12, 25 April 2006 (UTC)

the following was written immediately prior to the appearance of the above comment:

To CSTAR and any others who are interested: Archelon does not wish to argue about the notation for adjointness of linear operators (or complex|Hermitian conjugation, more accurately) (the notation was changed for the sake of the appearance when rendered, but this[*] is a notoriously volatile issue), but has returned the other things CSTAR removed from the proof that the eigenvalues are real (only some of which were originally added by Archelon, incidentally). Archelon 21:19, 25 April 2006 (UTC)

the following was written immediately thereafter:

The sentence is not irrelevant; it is explanatory. Also, a perusal of the page history will reveal that Archelon is not responsible for it (merely in favour of its retention). Archelon's advice to CSTAR: If you find the sentence intolerable, remove it yourself.

[*] (i.e., the latter) Archelon 21:25, 25 April 2006 (UTC)

 * Message to archelon (who seems to refer to her/himself in the third person). I did. --CSTAR 21:41, 25 April 2006 (UTC)

 * Message from Archelon (which does indeed refer to itself in the third person). As you like.  Archelon 22:55, 25 April 2006 (UTC)

Proof
Can anyone explain this line, it wasn't entirely clear for me:

This is finite-dimensional, and A has the property that it maps every vector w in K into K

How do we know that anything in K is mapped into K? Why can't it be mapped into Span(e)? Can anyone clarify, please? 216.7.201.43 13:47, 10 August 2006 (UTC)

 * Is that paragraph clearer now? --CSTAR 14:59, 10 August 2006 (UTC)

 * Perfect, that makes sense now. It was hard to follow before. 216.7.201.43 15:32, 10 August 2006 (UTC)

Target audience
This article is not easy to read for someone who's just interested in ordinary real or complex matrices and has never heard of bra-ket notation (why use it here, this article is not about quantum physics?) or Hilbert spaces. While generality is a good thing, wouldn't it be good to also give something comprehensible to the layperson? Even the singular value decomposition article is more readable, and it deals with a generalization, at least if you're only interested in real or complex matrices. -- Coffee2theorems 00:15, 18 July 2007 (UTC)

I agree. The bra-ket notation makes this page unnecessarily difficult to understand.

 * Certainly, the statement of the theorem should be possible without bracket notation (and incidentally, I'm not sure that the $$\langle \cdot \vert \cdot \rangle$$ notation from physics is appropriate in a maths article - in maths literature $$\langle \cdot, \cdot \rangle$$ is more common), so I've given an alternative characterisation of the theorem in more elementary terms.

 * However, the proof really does need bracket notation - bracket notation is the best means we have of working with orthonormal bases. It would be possible to rewrite the proof substituting $$\langle x \vert y \rangle$$ for x*y, but that would make the proof messier, and most likely make the article less comprehensible to more experienced mathematicians

 * I guess you could put a note at the beginning of the proof for the mathematical layman explaining that this is all the bracket notation means, but the proof is somewhat of a detour from the article as it is - it might make sense to move the proof to Spectral theorem/Proofs, as per WikiProject_Mathematics/Proofs. This also has the added benefit of moving the more technical aspects of the article out of the way - so people don't have to see them if they don't want to. James pic 09:54, 17 August 2007 (UTC)

James said: "and most likely make the article less comprehensible to more experienced mathematicians"

Ummm, is that who the article is for?

At least give the example from basic linear algebra with real matrices. I just took linear algebra and this page was useless when we covered the spectral decomposition. I don't have time now to change it but just for future reference: this page needs heavy work. —Preceding unsigned comment added by 152.16.225.228 (talk) 15:54, 20 February 2008 (UTC)

Generalization to non-symmetric matrices
I'm looking at this section and it seems to have some shortcomings. For one, it talks about non-symmetric matrices, when non-Hermitian or non-normal matrices would be more relevant. It also talks about orthonormal systems of eigenvectors, which would only possible for normal matrices, such as Hermitian or real-symmetric matrices - the fact that this doesn't hold for non-normal matrices is what makes this theory interesting, and differentiates it from the more general operator valued theory. It also makes much of this section wrong.

I noticed a recently created article called Eigendecomposition (matrix), which seems to address these issues in greater detail, and with fewer of these fairly elementary mistakes. I'm tempted to replace this section with a See:Eigendecomposition (matrix), or at least replace the section with a condensed version of the article, and a See main article. Thoughts? James pic 09:58, 11 October 2007 (UTC)

 * i agree that that section has problems, so does the article Eigendecomposition (matrix). it's not clear what the section is saying. for instance, i don't see where it talks about orthonormal systems of eigenvectors, as you do. seems to me it states that eigenvectors of a matrix and its transpose are orthogonal in general (which is not true). i suggest it be removed altogether.

 * in any case, it's not really a generalization of the spectral theorem, which should be concerned with decomposing an operator or matrix into parts. Mct mht 13:44, 11 October 2007 (UTC)

 * Ahh, yes. I should really have said orthonormal bases rather than orthonormal systems.

 * You're probably right about removing it altogether. If I'm reading the section right, it's trying to say roughly the same things the Eigendecomposition article says (although not succeeding). This is a generalisation of the matrix results discussed at the beginning of this article, but neither a special case nor a generalisation of the spectral theorem itself.

 * I feel I ought to stick up for the Eigendecomposition article here though. The article has some style and structure issues, certainly, but it seems to be fairly accurate for a newly created article, and it deals with a notable topic that's not covered elsewhere. James pic 15:22, 12 October 2007 (UTC)

Normal matrix - a detail I do not understand
Hi,

I am trying to understand the spectral theorem for normal matrices. I understand the thing about the Schur decomposition and that using that on the normality criterion implies that the upper triangular matrix in the Schur decomposed factorization of the normal matrix has to obey the relation $$\mathbf{TT}^* = \mathbf{T}^*\mathbf{T}$$, i.e., the upper triangular matrix has to be be normal as well. Then the article says: Therefore T must be diagonal (the whole point of the theorem). My problem is that I do not see very easily why that is so. I can easily understand that if it is diagonal the normality criterion is met, but I do not understand that it has to be diagonal. To try and understand it I then wrote down the expression for the diagonal elements of $$(\mathbf{TT}^*)_{i,i}$$ and found that this implies that
 * $$\sum_{k=1}^n\left|T_{i,k}\right|^2 = \sum_{k=1}^n\left|T_{k,i}\right|^2$$

where the span of the sums can be further reduced by taking advantage of the fact that T is upper triangular.

However, still, it is not evident for me why T has to be diagonal. Evidently, I am missing some (probably trivial) point in the line of argumentation here. Could this section be elaborated a bit in the article to make it more understandable? -- Slaunger (talk) 13:57, 12 February 2009 (UTC)

 * if you write down an arbitrary, say, 2 by 2 upper-triangular matrix T and impose the condition T*T = TT*, you will see immediately that the off-diagonal entry must be zero. Mct mht (talk) 04:50, 13 February 2009 (UTC)

 * Actually, I did just that as well prior to posting, and I do see that clearly for the n=2 case. I just find that somewhat primitive, and figured there should be a smarter argument valid for the general n-dimensional case. -- Slaunger (talk) 10:57, 13 February 2009 (UTC)

 * the same 2 by 2 argument, applied to an appropriate 2 by 2 operator matrix, yields the general case. Mct mht (talk) 10:48, 15 February 2009 (UTC)

 * which I think is becoming such a complicated argument that only a small fraction of readers would get that by themselves, which makes me think it could be a good thing to extend the explanation about this crucial point in the line of argumentation;-) I would rather not like to do it myself thaough, as I am not a native writer and my linear algebra is rusty... --Slaunger (talk) 20:10, 16 February 2009 (UTC)

Why the name?
The article doesn't say why it's called the spectral theorem. ᛭ LokiClock (talk) 02:17, 5 September 2011 (UTC)

"Principal axes of a Matrix"?
Principal axes of a Matrix redirects here from the principle axis disambiguation link. But principal axes aren't mentioned anywhere? Warrickball (talk) 09:04, 21 May 2012 (UTC)

Untidy notation
The notation is highly untidy:
 * (at least, before undid not only my try to unify the notation, but previous editors' work as well)
 * HTML-entities
 * Unicode-characters

both standalone and in diverse mixtures.
 * Wiki-formatting

I would like to unify this to, since the technology for appropriate display (via MathJax) is available for everyone: It is not 2004 anymore…

Anyone willing to join in? --*thing goes (talk) 22:37, 14 May 2015 (UTC)

 * Inline math is now uniform.

 * It is not as simple as saying it displays okay for you. YohanN7 (talk) 22:46, 14 May 2015 (UTC)
 * Who in the year 2015 cannot make use of MathJax?
 * Besides: The notation is _still_ not uniform, e.g. A* vs. A*, HTML-entities, Unicode-chars, …--*thing goes (talk) 23:02, 14 May 2015 (UTC)
 * I did put a notice at Wikipedia talk:WikiProject Mathematics. This is a recurring story. YohanN7 (talk) 23:12, 14 May 2015 (UTC)
 * I'm afraid that MathJax is unacceptable to some of us – I disabled it out of frustration because it was slowing the rendering many pages unacceptably, and at times failing to render at all. So until it is actually set as the default display, do not assume that "since the technology for appropriate display (via MathJax) is available for everyone".  —Quondum 00:11, 15 May 2015 (UTC)
 * This article is already a marvel of uniformity, only minor tweaks to be made (e.g. superscripted star). Aside from an integral sign, it is a candidate for the use of HTML everywhere (math). —Quondum 00:18, 15 May 2015 (UTC)

As well as the misplaced asterisks, we have mismatched fonts (the inline capital letters are more slanted than the display-math ones for me) and very bad spacing on the inline matrix products (much more spaced out than the displayed ones). It is only a "marvel of uniformity" if you're myopic. —David Eppstein (talk) 00:46, 15 May 2015 (UTC)
 * Well, conceded, uniformity of two styles: inline and standalone separately. The Template:math formatting does produce unduly strongly sloping italics, but maybe that is a separate issue? Until the inline/standalone norm is changed, this one is about as uniform as can be given that dichotomy, not so?  This article is not the place to fight that battle. —Quondum 03:07, 15 May 2015 (UTC)

 * I'd be happy to see Latex everywhere, including for ordinary text. But now we don't even have one version of TeX for mathematical formulas, we have three versions of PigTeX, none of which is satisfactory. MathJax, for instance, is unbearably slow, I refuse to use it. One would believe we were in 2004 1994, not 2015. How is it even possible to produce such crappy software with today's hardware technology? Besides, it is endowed with bugs that PNG rendering does not have. MathML is better and faster, but still buggy. People will make different choices (if they ever chose—if they don't they get PNG). As long as this is the case, inline LaTeX should be avoided because it totally $${\mathbf{RUINS}}$$ the appearance with PNG rendering, it is not merely a matter of something sloping a gazillionth of an inch too much or too little. YohanN7 (talk) 08:13, 15 May 2015 (UTC)

 * I think we ought to be forward-looking with this. People's ability to view MathJax or some future equivalent will improve over time, while the wiki text will stay the same or have to be tediously edited. More TeX is better in the long run. And by the way, I'm using MathML and find it perfectly pleasant. --Sammy1339 (talk) 00:20, 16 May 2015 (UTC)

 * I respectfully disagree with this argument. The vast majority of viewers are not logged in users, and they will be seeing the default PNG. We have been unable to move from that for many years, with no prospect of this changing in the next few years – essentially indefinitely. The Wikimedia Foundation has firmly indicated that no resources will be allocated to this change. The question of conversion (which already we will have to find a solution to once the default display changes) hardly counts as an argument at this stage; it is also a much smaller problem (mostly, bots could tackle this). —Quondum 01:18, 16 May 2015 (UTC)

 * Just out of curiosity, what resources would be needed to simply change the default option to MathML? --Sammy1339 (talk) 12:43, 16 May 2015 (UTC)

 * Neither of yours respective favorite options (MathJax, MathML) work universally, while PNG does to some extent. They are also both buggy (besides MathJax being unacceptably slow) and, like PNG, fail to align properly with surrounding text (this is unlike HTML) and fail to acquire the correct size. This "status quo" (sort of) has been maintained the last few years, and, as it looks, will be maintained the coming few years. It is pointless to debate this in the context of a single article. YohanN7 (talk) 13:48, 16 May 2015 (UTC)

 * Where would be the place? It's my understanding that MathML reverts to PNG in cases where it doesn't work, so there's no loss in setting it to the default. Unless I'm wrong about that it seems like a change worth considering - it would mostly end this recurring debate, and certainly improve the appearance of math article for most users. --Sammy1339 (talk) 14:28, 16 May 2015 (UTC)

 * The first place would be here. And no, MathML does not revert to PNG when it has bugs. It displays either incorrectly, like e.g. here, or an error message, like e.g here. Those are just examples from a single article. Your "most users" argument doesn't work, especially since you have to augment it with "most articles".
 * It is also an interesting exercise to display that same page (or any sizable article) using MathJax. Unless you have the computer power of Google, it takes forever to render. Face it, both the MathML and the MathJax implementations used are poopypants software that cannot be relied as a default. YohanN7 (talk) 14:59, 16 May 2015 (UTC)

Definition of "unitary operator"
This article refers to:
 * a unitary operator $U:H → L^{2}_{μ}(X)$

But the article titled unitary operator says a unitary operator is a certain kind of operator from a space into itself. Should another definition be used here instead? If so, it should be stated here. 160.94.28.231 (talk) 01:20, 30 April 2016 (UTC)

Hermitian condition and hermitian conjugate
The article claims the following: "An equivalent condition is that A∗ = A, where A∗ is the hermitian conjugate of A", refering to the conjugate of the operator A.

Is this in general true? With the usual inner product it indeed is, but for any? Is the definition of a scalar product so tight that really ANY inner product has the hermitian conjugate as the conjugate operator? — Preceding unsigned comment added by 77.0.166.225 (talk) 02:13, 27 January 2019 (UTC)

What about the spectral theorem for normal operators
I thought that perhaps the most compehensive spectral theorem was the one that applies to normal operators, at least on a Hilbert space. But that particular version of the spectral theorem seems to be missing from the article (except in the finite-dimensional case).50.205.142.50 (talk) 20:30, 13 March 2020 (UTC)

Normal operators
I hope someone knowledgeable about the subject can extend this excellent article to specifically include bounded normal operators on an infinite-dimensional Hilbert space.

title: Talk:Spectral theorem


text:
Languages of Iran

Iran's ethnic diversity means that the languages of Iran come from a number of linguistic origins, although the primary language spoken and used is Persian. The Constitution of the Islamic Republic of Iran asserts that the Persian language alone must be used for schooling and for all official government communications. The constitution also recognizes Arabic as the language of Islam, and assigns it formal status as the language of religion. Although multilingualism is not encouraged, the use of minority languages is permitted in the course of teaching minority-language literature. Different publications have reported different statistics for the languages of Iran; however, the top three languages spoken are consistently reported as Persian, Azeri and Kurdish.

Language policy and planning of Iran
The current language policy of Iran is addressed in Chapter Two of the Constitution of the Islamic Republic of Iran (Articles 15 & 16). It asserts that the Persian language is the lingua franca of the Iranian nation and as such, required for the school system and for all official government communications. In addition, the constitution recognizes the Arabic language as the language of Islam, giving it formal status as the language of religion and regulating its spread within the Iranian national curriculum.

Due to the nation's social and ethnic diversity, the constitution also acknowledges and permits the use of minority languages in the mass media as well as within the schools, in order to teach minority-language literature. The minority languages of Iran do not receive formal status and are not officially regulated by the authorities.

The first legislation which granted the Persian language its status was initiated by Qajar dynasty in 1906, as part of an electoral law that positioned it as the official language of the state of Iran, its government, its political institutions and its legal system. Over time, this enactment was followed by others, which eventually led to a monolingual policy by the Iranian regime.

Perceiving multilingualism as a threat to the nation's unity and territorial integrity, and seeing the need to restrict minority languages’ use and to advance the Persian language's hegemony, Iran's language policy consists of a non-translation outline as well: all government, administration and educational settings are obliged to use only Persian for any written communication. This applies to political institutions (i.e. the Iranian Parliament), official bureaucratic communication (forms, signage etc.) and schooling (all children from the age of six are exposed only to Persian as the language of teaching and learning and of textbooks within the public school system). In other words, the Iranian authorities hold that minorities need to learn the Iranian vernacular to an extent that will allow them to communicate with state institutions.

Among the institutions accountable for advancing Iranian Language Planning (e.g. Ministry of Education and Ministry of Science, Research and Technology) is the Academy of Persian Language and Literature, which was established on 1935, under Reza Shah Pahlavi. Constantly seeking to revise and elaborate the nation's official language, this institute focuses on the linguistics of the Persian language and on the internal aspects of Language Planning, rather than on the use of minority languages within Iranian society. Other Language Planning aspects (e.g. sociolinguistic or functional literacy) have not been assigned to a formal institute and are currently handled free of any official master plan by the educational ministries.

Languages of Iran
Different publications have reported different statistics for the languages of Iran. There have been some limited censuses taken in Iran in 2001, 1991, 1986 and 1949–1954. The following are the languages with the greatest number of speakers (data from the CIA World Factbook):

Classification categories of the spoken languages:
 * Indo-European (Iranic mainly, smaller amounts of other branches represented mainly by Armenian, amongst others)
 * Turkic (mainly Azerbaijani, with smaller amounts of Turkmen, Qashqai, and Afshar)
 * Semitic (mainly Arabic, but also Neo-Aramaic, Hebrew, and Mandean)
 * Kartvelian (such as Georgian)
 * North Caucasian (Circassian)

Census in the 1990s
A census was taken in the Iranian month of Mordad (July 21 – August 21) in 1991. In this census, all 49,588 mothers who gave birth in the country were issued birth certificates and asked about their mother-tongue. They reported: 46.2% Persian, 20.6% Azerbaijani, 10% Kurdish, 8.9% Luri, 7.2% Gilaki and Mazandarani, 3.5% Arabic, 2.7% Baluchi, 0.6% Turkmen, 0.1% Armenian, and 0.2% Others (e.g. Circassian, Georgian, etc.). The local dialect of Arabic spoken in Iran is Khuzestani Arabic, but the varieties of Arabic taught across Iran to students in secondary schools, regardless of their ethnic or linguistic background, are Modern Standard Arabic and Classical Arabic, the latter a liturgical language of Islam.

Other estimations
In 1986, a nationwide census was undertaken to determine the percentage of Iranians that know Persian, those who do not know, and those who know it fluently.

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

title: Languages of Iran


text:
An Wang

An Wang (February 7, 1920 – March 24, 1990) was a Chinese–American computer engineer and inventor, and cofounder of computer company Wang Laboratories, which was known primarily for its dedicated word processing machines. An Wang was an important contributor to the development of magnetic-core memory.

Early life and career
A native of Kunshan County in Suzhou (Soochow) Prefecture, he was born in Shanghai, China. His father taught English at an elementary school outside Shanghai, while his mother Zen Wan (Chien) Wang was a homemaker. He graduated from Shanghai Jiao Tong University with a degree in electrical engineering in 1940. He immigrated to the United States in June 1945 to attend Harvard University for graduate school, earning a PhD in applied physics in 1948. After graduation, he worked at Harvard with Howard Aiken on the design of the Mark IV, Aiken's first fully electronic computer. Wang coinvented the pulse transfer controlling device with Way-Dong Woo, a schoolmate from China who fell ill before their patent was issued. The new device implemented write-after-read which made magnetic core memory possible. Harvard reduced its commitment to computer research in 1951, prompting Wang to start his own engineering business.

Wang Laboratories
Wang founded Wang Laboratories in June 1951 as a sole proprietorship. The first years were lean and Wang raised US$50000 working capital by selling one third of the company to a machine tools manufacturer Warner & Swasey Company.

In 1955, when the core memory patent was issued, Wang sold it to IBM for US$500000 and incorporated Wang Laboratories with Ge-Yao Chu, a schoolmate. The company grew slowly and in 1964 sales reached US$1000000. Wang began making desktop electronic calculators with digital displays, including a centralised calculator with remote terminals for group use.

By 1970, the company had sales of US$27 million and 1,400 employees. They began manufacturing word processors in 1974, copying the already popular Xerox Redactron word processor, a single-user, cassette-based product.

In 1976, they started marketing a multi-user, display-based product, based on the Zilog Z80 processor. Typical installations had a master unit (supplying disk storage) connected to intelligent diskless slaves which the operators used. Connections were via dual coax using differential signaling in an 11-bit asynchronous ASCII format clocked at 4.275 MHz. This product became the market leader in the word processing industry. In addition to calculators and word processors, Wang's company diversified into minicomputers in the early 1970s. The Wang 2200 was one of the first desktop computers with a large CRT display and ran a fast hardwired BASIC interpreter. The Wang VS system was a multiuser minicomputer whose instruction set was very close to the design of IBM's System/370. It was not binary-compatible because register usage conventions and system call interfaces were different. The Wang VS serial terminals could be used in data processing mode and word processing mode. They were user-programmable in data-processing mode and used the same word processing software as the earlier dedicated word processing systems.

In 1984, Wang and his family owned about 55 percent of the company stock, and Forbes magazine, estimating his worth at US$1.6 billion, ranked him as the fifth richest American.

Wang Laboratories, which in 1989 once employed over 30,000 people, was headquartered in Tewksbury, Massachusetts and later Lowell, Massachusetts. When Wang looked to retire from actively running his company in 1986, he insisted upon handing over the corporate reins to his son Fred Wang. Hard times ensued for the company and the elder Wang was eventually forced to remove his son in 1989.

Later years
An Wang also founded the Wang Institute of Graduate Studies in Tyngsborough, Massachusetts, which offered a graduate program in software engineering. He made substantial donations to this organization, including the proceeds of his autobiography, Lessons. However, enrollment remained low, and in 1987, after nearly a decade of operation, Wang decided to discontinue funding the institution and transferred ownership of the campus to Boston University.

An Wang also made a substantial contribution for the restoration of a Boston landmark, which was then called the Metropolitan Theatre. The "Met" was renamed in 1983 as The Wang Theatre, and the Metropolitan Center became known as the Wang Center for the Performing Arts. Wang donated $4 million to Massachusetts General Hospital's ambulatory care center, which was renamed to the Wang Building.

Wang was one of twelve recipients of the Medal of Liberty in 1986. He was inducted into the National Inventors Hall of Fame in 1988. The An Wang Middle School in Lowell, Massachusetts, is named in his honor, as is the An Wang Professorship of Computer Science and Electrical Engineering at Harvard University, held by Roger W. Brockett and Hanspeter Pfister, the An Wang Professorship of Computer Science at Brown University, held by John E. Savage, and the Wang Professorship of Cognitive and Neural Systems at Boston University, held by Stephen Grossberg; see sites.bu.edu/steveg.

An Wang died of cancer in 1990. He and his wife, Lorraine (Chiu) Wang, lived in Lincoln, Massachusetts. Lorraine Wang died on March 1, 2016, at Emerson Hospital in Concord, Massachusetts. They had three children.

Aphorisms
An Wang is known for a number of pithy aphorisms summing up principles based on his experience in business and life. Examples include:

 * "Success is more a function of consistent common sense than of genius."

Patents

 * "Pulse transfer controlling device", filed October 21, 1949, issued May 17, 1955
 * "Calculating Apparatus" (using logarithms for calculation), filed September 22, 1964, issued September 17, 1968
 * "Distributed data processing system", filed June 20, 1977, issued March 20, 1979.
 * Ideographic typewriter. October 13, 1981
 * Helical print head mechanism. October 27, 1981
 * Selective paper insertion and feeding means for individual sheet printing apparatus. June 7, 1983
 * Data communication system. December 18, 1984
 * High density dot matrix printer. April 2, 1985
 * Scanner document positioning device. April 30, 1985
 * Management communication terminal system. May 6, 1986
 * Method of polling to ascertain service needs. June 17, 1986
 * Writing pad. January 20, 1987
 * Game racket. December 15, 1987
 * Composite document accessing and processing terminal with graphic and text data buffers. July 7, 1992
 * Keyboard with finger-actuable and stylus-actuable keys. August 2, 1994

title: An Wang


text:
The Urantia Book

The Urantia Book (sometimes called The Urantia Papers or The Fifth Epochal Revelation) is a spiritual, philosophical, and religious book that originated in Chicago, Illinois, United States sometime between 1924 and 1955. When first published, it claimed to have been written by celestial beings. The actual authorship remains a matter of debate, though it has been noted that it appears to have plagiarized multiple sources, without attribution. It received various degrees of interest ranging from praise to criticism for its religious and science-related content, its unusual length, and the unusual names and origins of the authors named within the book.

The text introduces the word "Urantia" as the name of the planet Earth and states that its intent is to "present enlarged concepts and advanced truth." The book aims to unite religion, science, and philosophy. Its large amount of content on topics of interest to science is unique among documents said to have been received from celestial beings. Among other topics, the book discusses the origin and meaning of life, mankind's place in the universe, the history of the planet, the relationship between God and people, and the life of Jesus.

The Urantia Foundation, a U.S.-based non-profit group, first published The Urantia Book in 1955. In 2001, a jury found that the English-language book's copyright was no longer valid in the United States after 1983. Therefore, the English text of the book became a public domain work in the United States, and in 2006 the international copyright expired.

Authorship
The exact circumstances of the origin of The Urantia Book are unknown. The book and its publishers do not name a human author. Instead, it is written as if directly presented by numerous celestial beings appointed to the task of providing an "epochal" religious revelation.

As early as 1911, William S. Sadler and his wife Lena Sadler, physicians in Chicago and well known in the community, are said to have been approached by a neighbor who was concerned because she would occasionally find her husband in a deep sleep and breathing abnormally. She reported that she was unable to wake him at these times. The Sadlers came to observe the episodes, and over time, the individual produced verbal communications that claimed to be from "student visitor" spiritual beings. This changed sometime in early 1925 with a "voluminous handwritten document," which from then on became the regular method of purported communication. The individual was never identified publicly but has been described as "a hard-boiled business man, member of the board of trade and stock exchange."

The Sadlers were both respected physicians, and William Sadler was a sometime debunker of paranormal claims. In 1929, he published a book called The Mind at Mischief, in which he explained the fraudulent methods of mediums and how self-deception leads to psychic claims. He wrote in an appendix that there were two cases that he had not explained to his satisfaction:

"The other exception has to do with a rather peculiar case of psychic phenomena, one which I find myself unable to classify. ... I was brought in contact with it, in the summer of 1911, and I have had it under my observation more or less ever since, having been present at probably 250 of the night sessions, many of which have been attended by a stenographer who made voluminous notes. A thorough study of this case has convinced me that it is not one of ordinary trance. ... This man is utterly unconscious, wholly oblivious to what takes place, and, unless told about it subsequently, never knows that he has been used as a sort of clearing house for the coming and going of alleged extra-planetary personalities. ... Psychoanalysis, hypnotism, intensive comparison, fail to show that the written or spoken messages of this individual have origin in his own mind. Much of the material secured through this subject is quite contrary to his habits of thought, to the way in which he has been taught, and to his entire philosophy. In fact, of much that we have secured, we have failed to find anything of its nature in existence."

In 1923, a group of Sadler's friends, former patients, and colleagues began meeting for Sunday philosophical and religious discussions, but became interested in the strange communications when Sadler mentioned the case at their fourth meeting and read samples at their request. Shortly afterwards, a communication reportedly was received about which this group would be allowed to devise questions and that answers would be given by celestial beings through the "contact personality."

Sadler presented this development to the group, and they generated hundreds of questions without full seriousness, but their claim is that it resulted in the appearance of answers in the form of fully written papers. They became more impressed with the quality of the answers and continued to ask questions, until all papers now collected together as The Urantia Book were obtained. The group was known as the Forum, and was formalized as a closed group of 30 members in 1925 who pledged not to discuss the material with others. Over time, some participants left and others joined, leading to a total membership of 486 people over the years from diverse backgrounds and a mix of interest levels. A smaller group of five individuals called the Contact Commission, including the Sadlers, was responsible for gathering the questions from the Forum, acting as the custodians of the handwritten manuscripts that were presented as answers, and arranging for proofreading and typing of the material. Bill Sadler, Jr. is noted to have composed the table of contents that is published with the book.

The Sadlers and others involved, now all deceased, claimed that the papers of the book were physically materialized from 1925 until 1935 in a way that was not understood even by them, with the first two parts being completed in 1934 and the third and fourth in 1935. The last Forum gathering was in 1942.

After the last of Part IV was obtained in 1935, an additional period of time supposedly took place where requests for clarifications resulted in revisions. Sadler and his son William (Bill) Sadler, Jr. at one point wrote a draft introduction and were told that they could not add their introduction. The Foreword was then "received."

The communications purportedly continued for another two decades while members of the Forum studied the book in depth, and according to Sadler and others, permission to publish it was given to them in 1955. The Urantia Foundation was formed in 1950 as a tax-exempt educational society in Illinois, and through privately raised funds, the book was published on October 12, 1955.

Only the members of the Contact Commission witnessed the activities of the "sleeping subject", and only they knew his identity. The individual is claimed to have been kept anonymous in order to prevent undesirable future veneration or reverence for him. Martin Gardner claims that an explanation concerning the origin of the book more plausible than celestial beings is that the Contact Commission, particularly William Sadler, was responsible. Gardner's conclusion is that a man named Wilfred Kellogg was the sleeping subject and authored the work from his subconscious mind, with William Sadler subsequently editing and authoring parts. Brad Gooch believes Sadler wrote the book, possibly with help from others on the Contact Commission. A statistical analysis, using the Mosteller and Wallace methods of stylometry, indicates at least nine authors were involved in the Urantia documents. Comparing Sadler's The Mind at Mischief to the Urantia documents does not indicate authorship or extensive editing of the latter by Sadler, without ruling out the possibility Sadler made limited edits or contributions.

Copyright status
In 1991, after having compiled an index of The Urantia Book and distributed free copies via computer disk and printouts, Kristen Maaherra was sued by the Urantia Foundation for violating their copyright on the book. In 1995, Maaherra won a Summary Judgment declaring the Urantia Foundation's copyright renewal invalid. Upon appeal, the judgment was reversed and awarded to the Urantia Foundation.

Four years later, in 1999, Harry McMullan III and the Michael Foundation published a book, Jesus–A New Revelation, which included verbatim 76 of the 196 papers included in The Urantia Book. McMullan and the Michael Foundation subsequently sought a legal declaration that the Urantia Foundation's US copyright in The Urantia Book was either invalid or, alternatively, that the copyright had not been infringed upon. Urantia Foundation's copyright was held to have expired in 1983 because the book was deemed to have been neither a composite work nor a commissioned work for hire. These two arguments having been rejected, a U.S. court held that, since the "sleeping subject" (whom the court referred to as "the Conduit") had died prior to 1983, only the Conduit's heirs would have been eligible to renew the copyright in 1983 and, since they had not done so, the Urantia Foundation's copyright on the book had expired and the book had therefore passed into the public domain. This decision was upheld on appeal. In 2006, the international copyright on the English text expired.

Overview
The Urantia Book is approximately 2,000 pages long, and consists of a body of 196 "papers" divided in four parts, and an introductory foreword:
 * Part I, titled "The Central and Superuniverses," addresses what the authors consider the highest levels of creation, including the eternal and infinite "Universal Father," his Trinity associates, and the "Isle of Paradise."
 * Part II, "The Local Universe," describes the origin, administration, and personalities of the local universe of "Nebadon" the part of the cosmos where Earth resides. It presents narratives on the inhabitants of local universes and their work as it is coordinated with a scheme of spiritual ascension and progression of different orders of beings, including humans, angels, and others.
 * Part III, "The History of Urantia," compiles a broad history of the Earth, presenting a purported explanation of the origin, evolution, and destiny of the world and its inhabitants. Topics include Adam and Eve, Melchizedek, essays on the concept of the Thought Adjuster, "Religion in Human Experience," and "Personality Survival."
 * Part IV, "The Life and Teachings of Jesus," is the largest part at 775 pages, and is often noted as the most accessible and most impressive, narrating a detailed biography of Jesus that includes his childhood, teenage years, family life, and public ministry, as well as the events that led to his crucifixion, death, and resurrection. Its papers continue about appearances after he rose, Pentecost and, finally, "The Faith of Jesus."

Nature of God
According to The Urantia Book, God is the creator and upholder of all reality—an omniscient, omnipresent, omnipotent, infinite, and eternal spirit personality. The most fundamental teaching about God in the book is that the human concept that most closely approximates the nature of God is that of a Father. Specifically, "the Father idea is [still] the highest human concept of God." It is also said that, "The face which the Infinite turns toward all universe personalities is the face of a Father, the Universal Father of love."

God, according to the book, is one Deity who functions on a range of different levels of reality, both personal and impersonal. God is taught to exist in a Trinity of three perfectly individualized persons who are co-equal: God the Father, God the Son, and God the Spirit. These persons are referred to by additional titles in the book, primarily as the "Universal Father," "Eternal Son," and "Infinite Spirit." While stating that the concept of one God in three persons is difficult to fully understand, the book says that the idea: "...in no manner violates the truth of the divine unity. The three personalities of Paradise Deity are, in all universe reality reactions and in all creature relations, as one."

The Father, Son, and Spirit are considered "existential" persons of Deity, those in existence from the eternal past to the eternal future. In addition, three persons of Deity are described who are "experiential," or incomplete and in the process of actualizing: God the Supreme; God the Ultimate; and God the Absolute. Of these three, God the Supreme, or "the Supreme Being," is given the most explanation, as the person of Deity evolving in time and space to unify finite reality and the infinite. The persons of God the Ultimate and God the Absolute are considered to be remote from the possibility of comprehension and are covered on a limited basis.

Many types of celestial beings are enumerated in the book, and one of particular note is a joint "offspring" of the Universal Father and Eternal Son called a "Creator Son." A divine Creator Son is considered the highest personification of the Universal Father and Eternal Son that is possible for people to know and: "...is, to all practical intents and purposes, God." Jesus of Nazareth is identified as a Creator Son who incarnated on Earth, and the central theme of the book's section recounting his life and teachings is that the religion he preached is the highest known to the world.

The final paper states:

"To "follow Jesus" means to personally share his religious faith and to enter into the spirit of the Master's life of unselfish service for man. One of the most important things in human living is to find out what Jesus believed, to discover his ideals, and to strive for the achievement of his exalted life purpose. Of all human knowledge, that which is of greatest value is to know the religious life of Jesus and how he lived it."

God and the individual
God is described as the Father of each individual, and through the direct gift of a fragment of his eternal spirit, called a Thought Adjuster, is said to be able to guide the individual toward an increased understanding of him. The Thought Adjuster is a central teaching of the book and is also referred to as a "Mystery Monitor" and "indwelling presence," as well as a "divine spark." The idea is compared within the book to the Hindu atman and the ancient Egyptian ka. In relation to biblical traditions, the Thought Adjuster is said to be the meaning behind the phrases "being made in God's image" and the "kingdom of God is within you":

"The Adjuster is the mark of divinity, the presence of God. The "image of God" does not refer to physical likeness nor to the circumscribed limitations of material creature endowment but rather to the gift of the spirit presence of the Universal Father in the supernal bestowal of the Thought Adjusters upon the humble creatures of the universes."

Each person is said to receive one such fragment at the time of his or her first independent moral decision, on average around the age of five years and 10 months. The Adjuster then serves noncoercively as a divine partner in the mind of the individual for the rest of life, and to the extent that a person consents with their free will to want to find God, it leads the person toward more mature, spiritualized thinking. A person's Thought Adjuster is described as distinct from either the soul or the conscience. In The Urantia Book ' s teachings, the degree to which a human mind chooses to accept its Adjuster's guidance becomes the degree to which a person's soul "grows" and becomes a reality that can then survive death. The soul is in essence an embryonic spiritual development, one parental factor being the divine Adjuster and the other being the human will.

The book says: "But you yourself are mostly unconscious of this inner ministry. You are quite incapable of distinguishing the product of your own material intellect from that of the conjoint activities of your soul and the Adjuster." The book is strongly fideistic and teaches that neither science nor logic will ever be able to prove or disprove the existence of God, arguing that faith is necessary to become conscious of God's presence in human experience, the Thought Adjuster.

Persistently embracing sin is considered the same as rejecting the leadings of the Adjuster, rejecting the will of God. Constant selfishness and sinful choosing lead eventually to iniquity and full identification with unrighteousness, and since unrighteousness is unreal, it results in the eventual annihilation of the individual's identity. Personalities like this become "as if they never were." The book says that: "...in the last analysis, such sin-identified individuals have destroyed themselves by becoming wholly unreal through their embrace of iniquity." The concepts of Hell and reincarnation are not taught.

The book says that a person ultimately is destined to fuse with his or her divine fragment and become one inseparable entity with it as the final goal of faith. Uniting with the Adjuster fragment is the "reward of the ages," the moment when a human personality has successfully and unalterably won eternal life, described as typically taking place in the afterlife, but also a possibility during earthly life. The result during human life is a "fusion flash," with the material body consumed in a fiery light and the soul "translated" to the afterlife. The Hebrew prophet Elijah being taken to heaven without death in "chariots of fire" is said to be a rare example in recorded history of a person who translated instead of experiencing death.

After a person fuses with his or her fragment of God, "then will begin your real life, the ascending life, to which your present mortal state is but the vestibule." A person continues as an ascending citizen in the universe and travels through numerous worlds on a long pilgrimage of growth and learning that eventually leads to God and residence on Paradise. Mortals who reach this stage are called "finaliters." The book goes on to discuss the potential destinies of these "glorified mortals."

The book regards human life on earth as a "short and intense test," and the afterlife as a continuation of training that begins in material life. The "religion of Jesus" is considered to be practiced by way of loving God the Father, thereby learning to love each person the way Jesus loves people; that is, recognizing the "fatherhood of God and its correlated truth, the brotherhood of man," resulting in unselfish service to others.

Cosmology
The book describes that at the center of the cosmos is the stationary Isle of Paradise—the dwelling place of God—with Paradise being surrounded by "Havona," an eternal universe containing a billion perfect worlds, around which seven incomplete and evolutionary "superuniverses" circle.

The word "universe" in the book is used to denote a number of different scales of organization. A "superuniverse" is roughly the size of a galaxy or group of galaxies, and the seven superuniverses along with Paradise-Havona are together designated as the "grand universe." A "local universe" is a portion of a superuniverse, with 100,000 local universes being in each superuniverse. Beyond the seven superuniverses, uninhabited "outer space levels" are described. The term "master universe" refers to what in modern usage would be the total universe—all existing matter and space taken as a whole.

Urantia is said to be located in a remote local universe named "Nebadon," which itself is part of superuniverse number seven, "Orvonton." The physical size of a local universe is not directly stated, but each is said to have up to 10 million inhabited worlds.

History and future of the world
The book's extensive teachings about the history of the world include its physical development about 4.5 billion years ago, the gradual changes in conditions that allowed life to develop, and long ages of organic evolution that started with microscopic marine life and led to plant and animal life in the oceans, later on land. The emergence of humans is presented as having occurred about a million years ago from a branch of superior primates originating from a lemur ancestor. The first humans are said to have been male and female twins called Andon and Fonta, born "993,419 years prior to 1934."

The Urantia Book teaches not only biological evolution, but that human society and spiritual understandings evolve by slow progression, subject both to periods of rapid improvement and the possibility of retrogression. Progress is said to follow a divine plan that includes periodic gifts of revelation and ministry by heavenly teachers, which eventually will lead to an ideal world status of "light and life" in the far distant future.

Although there is the ideal and divine plan of progression, it is said to be fostered and administered by various orders of celestial beings who are not always perfect. Urantia is said to be a markedly "confused and disordered" planet that is "greatly retarded in all phases of intellectual progress and spiritual attainment" compared to more typical inhabited worlds, due to an unusually severe history of rebellion and default by its spiritual supervisors.

Comparison to Christianity
More than one third of the content of The Urantia Book is devoted to a narrative of the life and teachings of Jesus, and the Judeo-Christian tradition is given an importance exceeding any other. The book's teachings claim to be a clarification and expansion of Christian belief. However, numerous differences are noted between its teachings and commonly accepted Christian doctrines.

Jesus is held in high regard by The Urantia Book, as he is in the New Testament of the Bible. The following are attributed to him in both texts:
 * He was both human and divine, the Son of God incarnate who was born to Mary, whose husband was Joseph.
 * He performed many of the miracles described in the Bible, such as the resurrection of Lazarus, the turning of water into wine, the feeding of the five thousand, and numerous healings of the blind, diseased, and infirm.
 * He taught twelve apostles, [they were disciples or students. Paul was an apostle] most of whom went on to spread his teachings.
 * He was crucified, and on the third day after his death, rose from the dead.
 * He will return to the world again some day.

Some differences with Christianity include:
 * Jesus' crucifixion is not considered an atonement for the sins of humanity. The crucifixion is taught to be an outcome of the fears of religious leaders of the day, who regarded his teachings as a threat to their positions of authority.
 * Jesus is considered the human incarnation of "Michael of Nebadon," one of more than 700,000 "Paradise Sons" of God, or "Creator Sons." Jesus is not considered the second person of the Trinity as he is in Christianity. The book refers to the Eternal Son as the second person of the Trinity.
 * Jesus was born on Earth through natural means of conception instead of a virgin birth.
 * Jesus did not walk on water or perform some of the miracles that are attributed to him in the Bible.

Comparison to Seventh-day Adventism
Gardner notes similarities between Seventh-day Adventism and the teachings of The Urantia Book, and sees this as evidence that William Sadler and Wilfred Kellogg had a role in editing or writing the book, since they both were one-time believers in Adventism. For instance, two basic Adventist beliefs that distinguish it from mainline Christianity are the doctrines of soul sleeping and annihilationism, both of which The Urantia Book also supports. Lewis notes that from the perspective of the book being a "revelation," it could be claimed the "celestial beings" simply found areas of Adventist belief to be accurate and therefore presented and expanded on them. While the book supports aspects of Adventism, it also is mixed with teachings that are heresies to Adventists.

Other comparisons
The book can be seen as belonging in the genre of spiritual literature that includes A Course in Miracles and Conversations with God. Gardner compares it with Oahspe, noting that though Oahspe is "vastly inferior to the UB both in ideas and style of writing," they are similar in claiming to have been written by celestial beings channelled through a human conduit, teaching that there is "one ultimate God who oversees a vast bureaucracy of lesser deities" while both outline an elaborate cosmology. The book's claimed supernatural origin has been compared to similar claims of the Book of Mormon, Science and Health, the Quran, and the Bible, with belief in it not being seen as necessarily a greater leap in reason.

Comparisons with facets of various world religions are incorporated in the book, including Buddhism, Islam, Taoism, Judaism, Hinduism, Shinto, and Confucianism. For example, Paper 131, "The World's Religions" discusses the aspects of these religions that are in common with what the book claims is the "religion of Jesus." The stance of the book is that there "is not a Urantia religion that could not profitably study and assimilate the best of the truths contained in every other faith."

Consideration as literature
The Urantia Book has been enjoyed by some as a form of science fiction, historical fiction, or fantasy. The Urantia Book is noted for its high level of internal consistency and an advanced writing style. Skeptic Martin Gardner, in a book otherwise highly critical of The Urantia Book, writes that it is "highly imaginative" and that the "cosmology outrivals in fantasy the cosmology of any science-fiction work known to me." Gooch says that for nonbelievers, the book is a mixture of being "fascinating, inspiring, compelling, haunting, entertaining, annoying, incomprehensible, and always wordy."

Parts I, II, and III are chiefly written in expository language. The papers are informational, matter-of-fact, and instructional. Part IV of the book is written as a biography of Jesus' life, and some feel it is a rich narrative with well-developed characters, high attention to detail, woven sub-plots, and realistic dialogue. Considered as literature, Part IV is favorably compared to retellings of Jesus' life, such as The Gospel According to Jesus Christ by José Saramago and Behold the Man by Michael Moorcock. Martin Gardner considers Part IV to be an especially "well-written, impressive work," and says, "Either it is accurate in its history, coming directly from higher beings in position to know, or it is a work of fertile imagination by someone who knew the New Testament by heart and who was also steeped in knowledge of the times when Jesus lived."

Criticisms of claims as a revelation
The authors refer to the book as the fifth revelation of "epochal significance" to humankind, the fourth epochal revelation having been the life of Jesus. The assertion in The Urantia Book that it constitutes "the most recent presentation of truth to the mortals of Urantia" has been criticized as a product of "human efforts." Because the book asserts certain tenets of Christianity, such as the atonement doctrine, are of human origin, while presenting a great deal more of Jesus' life not recorded in any versions of the Bible, others with a Christian viewpoint have argued it cannot be genuine. Gooch notes that while its "somewhat dated, elegant" prose could be read as fiction, due to its claim of divine revelation "the book invites reactions far more scathing than [it] ... might otherwise merit."

Criticism of its science
In Paper 101, "The Real Nature of Religion," the authors write: "We full well know that, while the historic facts and religious truths of this series of revelatory presentations will stand on the records of the ages to come, within a few short years many of our statements regarding the physical sciences will stand in need of revision in consequence of additional scientific developments and new discoveries. These new developments we even now foresee, but we are forbidden to include such humanly undiscovered facts in the revelatory records. Let it be made clear that revelations are not necessarily inspired. The cosmology of these revelations is not inspired."

As pointed out by skeptic Martin Gardner, the science in The Urantia Book reflects some views that prevailed at the time the book originated. The claim by the authors that no unknown scientific discoveries could be imparted can function as a ruse to allow mistakes to be dismissed later. The appeal to consequence that post-1955 scientific knowledge is not being presented is consistent with a book written by humans in the 1950s instead of celestial beings with superior knowledge.

Examples of criticisms regarding the science in The Urantia Book include:
 * The described formation of the Solar System is consistent with the Chamberlin-Moulton planetesimal hypothesis, which though popular in the early part of the 20th century, was discarded by the 1940s after major flaws were noted. The currently accepted scientific explanation for the origin of the Solar System is based on the nebular hypothesis.
 * According to the book's descriptions, the universe is hundreds of billions of years old and periodically expands and contracts — "respires" — at 2-billion-year intervals. Recent observations measure the true age of the universe to be 13.8 billion years. The book does not support the Big Bang theory.
 * A fundamental particle called an "ultimaton" is proposed, with an electron being composed of 100 ultimatons. The particle is not known to be described anywhere else and the concept is at odds with modern particle physics.
 * The Andromeda Galaxy is claimed to be "almost one million" light years away, repeating a systematic mistake in the measurements of the distance to galaxies made in the 1920s. The galaxy is now known to be 2.5 million light years away.
 * The book repeats the mistaken idea that planets close to a sun will gradually spin slower until one hemisphere is left always turned to the sun due to tidal locking, citing Mercury as an example. Scientists at the time of the book's origin thought one side of Mercury always faced the Sun, just as one side of the Moon always faces the Earth. In 1965, radio astronomers discovered however that Mercury rotates fast enough for all sides to see exposure to the Sun. Scientists further established that Mercury is locked in this spin rate in a stable resonance of 3 spins for every 2 orbits, and it is not slowing and so will never have one side left always turned to the Sun.
 * Some species are said to have evolved suddenly from single mutations without transitional species. The theory originated with Dutch botanist Hugo De Vries but was short-lived and is not now supported.
 * The book erroneously says that a solar eclipse was predicted in 1808 by the Native American prophet Tenskwatawa. The eclipse actually was predicted in late April 1806 and occurred on June 16, 1806. In 2009, the Urantia Foundation acknowledged the error and revised the book.
 * Controversial statements about human races can be found in the book. Gardner recounts that William S. Sadler also wrote eugenicist works that contain similar arguments to some ideas presented in The Urantia Book.

While some adherents of the book believe that all of the information in The Urantia Book including its science is literally true, others believe the science is not fully accurate. For example, Meredith Sprunger, a believer in The Urantia Book and retired minister of the United Church of Christ, wrote that research "has revealed that virtually all of the scientific material found in the UB was the accepted scientific knowledge of the period in which the book was written, was held by some scientists of that time, or was about to be discovered or recognized." He further argued against its literal infallibility and said that fundamentalism over the book is "just as untenable as Biblical fundamentalism."

Other believers maintain that the book has prophetically anticipated scientific advances. They believe more of its science — if not all of it — will be proven correct in the future. Gardner evaluated many of these claims as of 1995 and argued that they were fairly unconvincing. Because the book is said to have been written by the revelators by 1935 but not published until 1955, discoveries from science during the two intervening decades are often declared to be prophetic by believers, while skeptics point out that edits could have been made to the book up to its 1955 publication. For instance, the catalytic role that carbon plays in the sun's nuclear reactions is described in the book, and Hans Bethe's announcement of the discovery was made in 1938.

The only apparent anticipation of science the book has made, in Gardner's opinion, is that it says the magnetic sense that homing pigeons possess is "not wholly wanting as a conscious possession by mankind." In 1980, a British zoologist, Robin Baker, published evidence that humans have a limited magnetic sense.

Mark McMenamin, a professor of geology, quotes a section of the book describing a billion-year-old supercontinent that subsequently split apart, forming ocean basins where early marine life developed. He says, "This amazing passage, written in the 1930s, anticipates scientific results that did not actually appear in the scientific literature until many decades later." McMenamin also states, "Of course I am being selective here in my choice of quotations, and there are reams of scientifically untenable material in The Urantia Book."

Use of other published material without attribution
The Urantia Book states in its Foreword that more than one thousand "human concepts representing the highest and most advanced planetary knowledge of spiritual values and universe meanings" were selected in preparing the papers. The authors say that they were required to "give preference to the highest existing human concepts pertaining to the subjects to be presented" and would "resort to pure revelation only when the concept of presentation has had no adequate previous expression by the human mind." One of the authors wrote in Part IV: "I well know that those concepts which have had origin in the human mind will prove more acceptable and helpful to all other human minds."

In recent years, students of the papers have found that the free use of other sources appears to be true. None of the material allegedly used from other sources is directly cited or referenced within the book.

In 1992, a reader of The Urantia Book, Matthew Block, self-published a paper that showed The Urantia Book utilized material from 15 other books. All of the source authors identified in Block's paper were published in English between 1905 and 1943 by U.S. publishers and are typically scholarly or academic works that contain concepts and wording similar to what is found in The Urantia Book. Block has since claimed to have discovered over 125 source texts that were incorporated into the papers.

The use of outside source materials was studied separately by Gardner, and Gooch, and they concluded, consistent with their respective conclusion that the book's author(s) must have been human, that the book therefore plagiarized many of the sources noted by Block.

For instance, Gardner and Block note that Paper 85 appears to have been taken from the first eight chapters of Origin and Evolution of Religion by Edward Washburn Hopkins, published by Yale University Press in 1923. Each section of the paper corresponds to a chapter in the book, with several passages possibly used as direct material and further material used in Papers 86-90 and 92. (In addition to the book's "heavy indebtedness to Hopkins," Gardner discovered that Hopkins was a major reference in an earlier book authored by Sadler, adding to Gardner's view that it is more likely Sadler had a hand in writing or editing The Urantia Book than that celestial beings wrote it.) Likewise, much of The Urantia Book material relating to the evolution of mankind appears to have been directly taken from Henry Fairfield Osborn, Man Rises to Parnassus: Critical Epochs in the Prehistory of Man published by Princeton University Press in 1928.

In one example cited by Block and confirmed by Gardner and Gooch, the original author discusses the periodicity of the chemical elements and concludes that the harmony in the construction of the atom suggests some unspecified plan of organization. The authors of The Urantia Book assert that this harmony is evidence of the intelligent design of the universe. W. F. G. Swann writes on page 64 of The Architecture of the Universe (italics indicate edits as compared to The Urantia Book, bolding indicates deletions): "Starting from any one of them [i.e., chemical elements], and noting some property such as the melting point, for example, the property would change as we went along the row, but as we continued it would gradually come back to the condition very similar to that which we started ... The eighth element was in many respects like the first, the ninth like the second, the tenth like the third, and so on. Such a slate of affairs point[s] not only to a varied internal structure, but also to a certain harmony in that variation suggestive of some organized plan in building the atom."

Contrast with The Urantia Book ' s version: "Starting from any one element, after noting some one property, such a quality will exchange for six consecutive elements, but on reaching the eighth, it tends to reappear, that is, the eighth chemically active element resembles the first, the ninth the second, and so on. Such a fact of the physical world unmistakably points to the sevenfold constitution of ancestral energy and is indicative of the fundamental reality of the sevenfold diversity of the creations of time and space."

Block and other believers do not see the use of the source materials as plagiarism, but express a view instead that the quality of the way the material was borrowed is consistent with authorship by celestial beings and that study of the sources leads to an even deeper understanding of The Urantia Book. Gooch, a professor of English, assessed that the use of the sources "does reveal to us an author with a busy genius for metaphysical invention and poetic turns of phrase whose scam was at worst benign and at most visionary." Asked by Gardner what he thought of these plagiarisms, Sprunger responded in a letter by saying that if humans wrote the book the plagiarisms would indeed be disturbing but not if it was written by supermortals.

Adherents
It is difficult to gauge how many adherents there may be as there are multiple organizations to census. Informal study groups "tend to sprout, ripen, then vanish or splinter" and have not been counted reliably. Readers sometimes join study groups after reading on their own for years or decades, others join them soon after developing an interest in the book, while "for most, worship remains as individual as the act of reading." Disagreements over the legal ownership of the book, its interpretation, and the reception of new revelations have led to some splintering, though these disagreements appear to have been settled to the satisfaction of most adherents. The movement generally incorporates a nonsectarian view, contending that individuals with different religious backgrounds can receive the book's teachings as an enrichment rather than as a contradiction of their faiths.

The movement inspired by The Urantia Book has not developed clergy or institutions such as churches, or temples.

Sarah Lewis notes that, "The Urantia Revelation is not securing legitimacy through historically known and accepted means to any great degree, nor is it even using common language that would increase the likelihood of understanding and therefore acceptance. It introduces new concepts and a new language, and this does not make acceptance any easier." She assesses that the movement is uncontroversial compared to other ones, "lacking the zealous proselytizing found within many other groups," and that it is therefore likely to remain small and unaffected by opposing views.

Urantia Foundation advocated a "slow growth" policy in the past and had not significantly marketed the book. Sales by Urantia Foundation went from 7,000 in 1990 to 24,700 in 1997, and steadily increased to nearly 38,000 in 2000, an "upturn that seems to represent a genuine trend rather than just some spike on a sales chart," but in 2011 Urantia Foundation reported worldwide annual sales of 16,000 copies and over 60,000 downloads from various sites. Since the book was determined to be in the public domain in 2001, other organizations, such as The Urantia Book Fellowship under the publishing name Uversa Press, have also published the book. Copies of The Urantia Book are on the Internet in various formats and it has been adapted to more recent platforms such as the Kindle and the iOS App Store. Several audio books of the text are also on the Internet.

The International Urantia Association had twenty-six reader associations worldwide as of 2002, and The Urantia Book Fellowship (formerly the Urantia Brotherhood, founded in 1955 with Urantia Foundation as the original social fraternal organization of believers) claimed roughly twelve hundred official members, with the highest concentrations in the West of the United States and the Sun Belt, especially California, Colorado, Florida, and Texas. It appears an increasing number of people are forming study groups, participating in Internet discussion groups, and hosting or visiting websites about it.

Independent channelers
The Teaching Mission is a group of Urantia channellers. According to Richard Landes, "The foundation considers them self-deluded, but they have created a schism that continues to disrupt the movement."

Vern Grimsley was a preacher who founded a Urantian outreach organization called Family of God in the 1970s, which was initially supported by others in the movement, including the Urantia Foundation. Beginning in the early 1980s, Grimsley claimed he heard voices that were from the same higher beings who wrote The Urantia Book, and that the voices warned of an impending world war followed by a nuclear holocaust. While some in the movement believed him, others including the Urantia Foundation concluded Grimsley's messages were spurious, former friends eventually began to shun him, and in later years he is said to have lived in obscurity.

In popular culture

 * In 1975, the band Spirit included the song "Urantia" on their Spirit of '76 album. The piece was co-written by guitarist Randy California, who had been "immersed in the Urantia Foundation" for a few years at that point.
 * The jazz fusion band Weather Report have a song entitled 'Havona' on their 1977 studio album Heavy Weather. 'Havona' is the last track on the respective studio album on side two and was composed by bassist Jaco Pastorius (1951–1987) as a reference to a term (i.e. The Paradise-Havona System) which appears in The Urantia Book.
 * Karlheinz Stockhausen (1928–2007) based his seven-opera cycle Licht on the cosmology of The Urantia Book.
 * Stevie Ray Vaughan (1954–1990), American blues rock guitarist: "Stevie often brought along the book of Urantia and read Lindi passages from the strange publication."
 * Jimi Hendrix (1942–1970): "Jimi also had with him the Book of Urantia, an alternative Bible... Jimi carried this book with him everywhere--along with his Bob Dylan songbook--and told friends he had learned much from its pages."
 * Jerry Garcia (1942–1995) of Grateful Dead was a reader of The Urantia Book and claimed it was "one of his favorite esoteric works"
 * Kerry Livgren (1949–present) of Kansas is quoted as saying, "In 1977, I discovered a book that convinced me I had reached the end of my quest. It was called The Urantia Book ...."
 * American guitarist Steve Vai (1960–present) composed and released a song entitled 'Midway Creatures' (from his seventh studio album Real Illusions: Reflections) which is a term that also appears in The Urantia Book, more specifically in Paper 77.
 * American alternative metal band Deftones' ninth album, Ohms (album), features a track named Urantia.
 * American synth-metal band Deadsy's song "The Mansion World" from their 2002 album Commencement (album) has many references to themes in The Urantia Book.

Symbols

An important symbol described in The Urantia Book as "the banner of Michael" and the "material emblem of the Trinity government of all creation," consists of three azure blue concentric circles on a white background. The circles are said to be "emblematic of the infinity, eternity, and universality of the Paradise Trinity".

The incarnated priest and contemporary of Abraham, Machiventa Melchizedek, wore on his breast an emblem of three concentric circles representative of the Paradise Trinity. During a system-wide rebellion instigated by Lucifer, the so-called "war in heaven," Lucifer's emblem was a banner of white with one red circle, in the center of which a black solid circle appeared.

title: The Urantia Book


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Talk:Madame X (film)

There is a French movie "L’étrange Madame X", it seems to be a different plot. see http://frenchfilms.topcities.com/nf_L_etrange_Madame_X_rev.html Ericd

title: Talk:Madame X (film)


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Competitive analysis

Competitive analysis may refer to:

 * Competitor analysis
 * Competitive analysis (online algorithm)

title: Competitive analysis