Wikipedia - Benutzerbeiträge [de]

Miura-Faltung

2013-06-26T22:05:18Z

Robinh: angle of intersection

[[File:Miura-Ori CP.svg|thumb|250px|[[Crease pattern]] for an example Miura-ori. The crease lines intersect at 84 /96 degrees]]

The {{nihongo|'''Miura fold'''|ミウラ折り|Miura-ori}} is a rigid fold that has been used to simulate large [[solar panel]] arrays for space satellites in the [[Japanese space program|Japanese]] 1995 [[Space Flight Unit]].<ref>[http://www.origami-resource-center.com/origami-science.html Origami science]</ref> It was invented by [[Japan]]ese [[astrophysics|astrophysicist]] [[Koryo Miura]]. It is an example of the practical importance of ''[[rigid origami]]'', or treating hinges and rigid surfaces like the paper and creases in [[paper folding]] problems.

A folded Miura fold can be packed into a very compact area, its [[thickness]] restricted only by the thickness of the folded material. The fold can also be unpacked in just one motion by pulling on opposite ends of the folded material, and likewise folded again by pushing the two ends back together. This was beneficial to the aforementioned solar array as it reduced the number of [[Electric motor|motor]]s required to unfold it, reducing the overall weight and complexity of the mechanism.

[[File:Miura-ori.gif|thumb|300px|Miura-ori]]

== References ==
<references/>

== External links ==
* [http://www.miura-ori.com/English/e-index.html Miura-ori corporate site]
* {{Cite web|url=http://www.britishorigami.info/academic/miura.php|
title=The Miura-Ori map|
author=Ian Bain|postscript=}}
*Peter Forbes, ''The Gecko's Foot: How Scientists are Taking a Leaf from Nature's Book'', Harper Perennial, 2006, pp. 181–195.
* [[Yutaka Nishiyama]], [http://www.ijpam.eu/contents/2012-79-2/8/8.pdf Miura Folding: Applying Origami to Space Exploration, International Journal of Pure and Applied Mathematics, Vol.79, No.2, 269-279, 2012.]

[[Category:Paper folding]]

{{space-stub}}

No-go-Theorem

2011-06-28T20:21:10Z

Robinh: /* Examples of no-go theorems */ wikify antidynamo theorem

{{Unreferenced stub|auto=yes|date=December 2009}}
In [[theoretical physics]], a '''no-go theorem''' is a [[theorem]] that states that a particular situation is not physically possible.

==Examples of no-go theorems==
* [[Bell's theorem]]
* [[Coleman–Mandula theorem]]
* [[Haag-Lopuszanski-Sohnius theorem]]
* [[Earnshaw's theorem]]
* [[Uncertainty principle|Heisenberg uncertainty principle]]
* [[Weinberg-Witten theorem]]
* [[Antidynamo theorem]]s (e.g. Cowling's Theorem)
* [[No-communication theorem]]
* [[No teleportation theorem]]
* [[No cloning theorem]]
* [[No-broadcast theorem]]

{{DEFAULTSORT:No-Go Theorem}}
[[Category:Quantum field theory]]
[[Category:Supersymmetry]]

{{Physics-stub}}

[[es:Teorema de imposibilidad]]
[[pt:Teorema de impossibilidade]]
[[sq:Teoremë pamundësie]]
[[zh:不可行定理]]

Projektionsmatrix (Statistik)

2009-03-18T10:50:45Z

Robinh: correlated residuals

In [[statistics]], the '''hat matrix''', '''H''', relates the fitted values to the observed values. It describes the influence each observed value has on each fitted value<ref name="Hoaglin1977">
{{Citation| title = The Hat Matrix in Regression and ANOVA
| first1= David C. | last1= Hoaglin |first2= Roy E. | last2=Welsch
|journal= [[The American Statistician]] | volume=32 |number=1 | month=February| year= 1978| pages=17-22
|url= http://www.jstor.org/stable/2683469}}
</ref>.
The diagonal elements of the hat matrix are the [[leverage (statistics)|leverage]]s, which describe the influence each observed value has on the fitted value for that same observation.

If the vector of observed values is denoted by '''y''' and the vector of fitted values by <math>\hat{\mathbf{y}}</math>,
:<math>\hat{\mathbf{y}} = \mathbf{H y}.</math>
As <math>\hat{\mathbf{y}}</math> is usually pronounced "y-hat", the hat matrix is so named as it "puts a hat on '''y'''".

Suppose that we wish to solve a [[linear model]] using [[linear least squares]]. The model can be written as
:<math>\mathbf{y} = \mathbf{X \beta} + \mathbf{ \varepsilon},</math>
where '''X''' is a matrix of explanatory variables (the [[design matrix]]), '''β''' is a vector of unknown parameters to be estimated, and '''ε''' is the error vector.
The estimated parameters are
:<math>\mathbf{\hat{\beta}} = \left(\mathbf{X}^\top \mathbf{X} \right)^{-1} \mathbf{X}^\top \mathbf{y},</math>
so the fitted values are
:<math>\hat{\mathbf{y}} = \mathbf{X \hat{\beta}} = \mathbf{X} \left(\mathbf{X}^\top \mathbf{X} \right)^{-1} \mathbf{X}^\top \mathbf{y}.</math>
Therefore the hat matrix is given by
:<math>\mathbf{H} = \mathbf{X} \left(\mathbf{X}^\top \mathbf{X} \right)^{-1} \mathbf{X}^\top.</math>
In the language of [[linear algebra]], the hat matrix is the [[orthogonal projection]] onto the [[column space]] of the design matrix '''X'''.

The hat matrix corresponding to a [[linear model]] is [[symmetric matrix|symmetric]] and [[idempotent]], that is, '''H'''2 = '''H'''. However, this is not always the case; in [[local regression|locally weighted scatterplot smoothing (LOESS)]], for example, the hat matrix is in general neither symmetric nor idempotent.

The formula for the vector of residuals '''r''' can be expressed compactly using the hat matrix:
:<math>\mathbf{r} = \mathbf{y} - \mathbf{\hat{y}} = \mathbf{y} - \mathbf{H y} = (\mathbf{I} - \mathbf{H}) \mathbf{y}.</math>
The [[variance-covariance matrix]] of the residuals is therefore, by [[error propagation]], equal to <math>\mathbf{\left(I-H \right)^\top V\left(I-H \right) }</math>, where '''V''' is the variance-covariance matrix of the errors (and by extension, the observations as well).
For the case of linear models with [[independent and identically distributed]] errors in which '''V''' = σ2'''I''', this reduces to ('''I''' - '''H''')σ2<ref name="Hoaglin1977"/>.

For [[linear models]], the [[trace (linear algebra)|trace]] of the hat matrix is equal to the rank of '''X''', which is the number of independent parameters of the linear model.
For other models such as LOESS that are still linear in the observations '''y''',
the hat matrix can be used to define the [[degrees of freedom (statistics)#Effective degrees of freedom|effective degrees of freedom]] of the model.

Some other properties of the hat matrix are summarized in <ref>P. Gans, ''Data Fitting in the Chemical Sciences,'', Wiley, 1992.</ref>.

==Correlated residuals==

The above may be generalized to the case of correlated residuals. Suppose that the [[covariance matrix]] of the residuals is <math>\mathbf{A}</math>. Then <math>\hat{\mathbf{\beta}}=\mathbf{X}\left(\mathbf{X}^\top\mathbf{A}^{-1}\mathbf{X}\right)^{-1}\mathbf{X}^\top\mathbf{A}^{-1}\mathbf{y}</math> and the hat matrix is

:<math>\mathbf{H}=
\mathbf{X}\left(\mathbf{X}^\top\mathbf{A}^{-1}\mathbf{X}\right)^{-1}\mathbf{X}^\top\mathbf{A}^{-1}</math>

and again it may be seen that <math>\mathbf{H}^2=\mathbf{H}</math>.

== See also ==
*[[Moore-Penrose pseudoinverse]]
*[[Studentized residuals]]

== References ==
<references />

[[Category:Statistical terminology]]
[[Category:Regression analysis]]

Ynys Enlli

2007-10-06T20:11:02Z

Robinh: /* Bardsey Island Apple */ afal enlli

{{Infobox Mountain
| Name = Ynys Enlli
| Photo = Bardsey-island.jpg
| Caption = Bardsey Island seen from [[Mynydd Mawr]]
| Elevation = 167 m (548 ft)
| Location = [[Llŷn Peninsula]], [[Wales]]
| Prominence = 167 m
| Coordinates =
| Topographic map = [[Ordnance Survey|OS]] ''Landranger'' 123
| Type =
| First ascent =
| Easiest route =
| Grid_ref_UK = SH122218
| Listing = [[Marilyn (hill)|Marilyn]]
| Translation = Bardsey island
| Language = [[Welsh language|Welsh]]
| Pronunciation = 'mɐnɪð 'ɛnɬi
}}

'''Bardsey Island''' ([[Welsh language|Welsh]]: ''Ynys Enlli'') lies off the [[Llŷn peninsula]], in north [[Wales]]. The island is the site of a [[monastery]] founded by [[Saint Cadfan]] in the [[6th century|sixth century]], and of [[Bardsey Bird and Field Observatory]]. Its highest point is the summit of ''Mynydd Enlli''.

It supports a small 'all the year' round population of fewer than 10 people which is swollen during summer months by visitors staying in other houses on the island. Only one of the original 'crogloft' cottages survives as all the other cottages/houses were rebuilt during the 1870's with substantial detached & semi-detached farmhouses. They all have a set of farm buildings surrounded by high walls to keep out the weather. All the buildings are listed by [[Cadw]]—the Welsh Historic & Ancient Monuments organisation. Little has changed on the island since then—the last building to be put up was the chapel in 1875. There is no permanent electricity supply, most houses relying on candles and small gas lamps. A telephone link to the rest of the public network was established in 2001 but the telephone system on the island still uses 'wind the handle' telephones with the (permanently occupied) houses all being on the same [[party line (telephony)|party line]].

The Welsh colloquial term for toilet—''tŷ bach'' ("little house") still refers to a 'little house' at the bottom of the garden on Bardsey.

The Island is owned and managed by the Bardsey Island Trust (see external link below) who acquired it in 1979 after raising the money by public subscription. For many years previously, it had formed part of the estates of the Newborough Family of Glynllifon near Caernarfon. At its maximum, it supported a population of 92 at the time of the 1851 census. It was tradition for the oldest male on the island to called Brenin Enlli (King of Bardsey), crowned by Lord Newborough or his representaive. The actual crown is kept at the Maritime Museum in Liverpool, although calls have been made for it to return to the island.
By 1935 the population had dropped to 33. As the population dropped, the small school on the island, run by the Council, closed circa 1950.

==Pilgrimage==
The island became a place of [[pilgrimage]], especially popular with pilgrims who would come to die and be buried on the isle, hence giving rise to the tradition that twenty thousand saints are buried on the island. Three pilgrimages to Bardsey were rated as equivalent to one pilgrimage to [[Rome]]. [[Saint Deiniol]] and Saint [[Dubricius]] were buried in the old abbey before being translated to [[Bangor Cathedral|Bangor]] and [[Llandaff Cathedral]] respectively. [[Merlin (wizard)|Merlin]] the Magician is said to still be imprisoned on the island.

==Attractions==
Attractions on the island include a [[thirteenth century]] [[bell tower]], several [[Celtic cross]]es, and a wealth of [[bird]]s. Bardsey is a [[National Nature Reserve]] and a [[Site of Special Scientific Interest]]. The tallest square lighthouse in Britain built in 1821.

Occasional boats for day visitors sail to the island from [[Pwllheli]] and [[Aberdaron]].

==Bardsey Island Apple==
Bardsey is also home to the Bardsey Island [[Apple]], an apple originally unique to the island, although saplings can now be purchased. It was originally described by the media as "The World's Rarest Apple". The apple tree is believed to have been grown there since the [[1300s]], when the Island was inhabited by monks. However, due to the island's isolated location, it was not officially identified and classified until [[Ian Sturrock]] sent a sample to the [[National Fruit Collection]], in [[Brogdale]], [[Kent]] in [[1998]]. The variety is now known as '''Afal Enlli'''.

==External links==
* [http://www.bardsey.org/english/bardsey/welcome.asp?pid=1 Barsdey Island official web site]
* [http://www.bbc.co.uk/wales/northwest/sites/bardsey/ BBC's Bardsey Island Webpages ]
* [http://www.bbfo.org.uk/ Bardsey Bird and Field Observatory]
* [http://www.bardseyapple.co.uk Bardsey Island Apple website]

[[Category:Caernarfonshire]]
[[Category:Tourism in Gwynedd]]
[[Category:Geography of Gwynedd]]
[[Category:History of Caernarfonshire]]
[[Category:Islands of Wales]]
[[Category:Marilyns of Wales]]
[[Category:Mountains and hills of north Wales]]
[[Category:National Nature Reserves in Wales]]
[[Category:Sites of Special Scientific Interest in West Gwynedd]]

[[ca:Ynys Enlli]]
[[cy:Ynys Enlli]]
[[de:Bardsey Island]]
[[es:Bardsey]]
[[gl:Bardsey]]

Ynys Enlli

2007-10-06T20:06:05Z

Robinh: wikify sturrock

{{Infobox Mountain
| Name = Ynys Enlli
| Photo = Bardsey-island.jpg
| Caption = Bardsey Island seen from [[Mynydd Mawr]]
| Elevation = 167 m (548 ft)
| Location = [[Llŷn Peninsula]], [[Wales]]
| Prominence = 167 m
| Coordinates =
| Topographic map = [[Ordnance Survey|OS]] ''Landranger'' 123
| Type =
| First ascent =
| Easiest route =
| Grid_ref_UK = SH122218
| Listing = [[Marilyn (hill)|Marilyn]]
| Translation = Bardsey island
| Language = [[Welsh language|Welsh]]
| Pronunciation = 'mɐnɪð 'ɛnɬi
}}

'''Bardsey Island''' ([[Welsh language|Welsh]]: ''Ynys Enlli'') lies off the [[Llŷn peninsula]], in north [[Wales]]. The island is the site of a [[monastery]] founded by [[Saint Cadfan]] in the [[6th century|sixth century]], and of [[Bardsey Bird and Field Observatory]]. Its highest point is the summit of ''Mynydd Enlli''.

It supports a small 'all the year' round population of fewer than 10 people which is swollen during summer months by visitors staying in other houses on the island. Only one of the original 'crogloft' cottages survives as all the other cottages/houses were rebuilt during the 1870's with substantial detached & semi-detached farmhouses. They all have a set of farm buildings surrounded by high walls to keep out the weather. All the buildings are listed by [[Cadw]]—the Welsh Historic & Ancient Monuments organisation. Little has changed on the island since then—the last building to be put up was the chapel in 1875. There is no permanent electricity supply, most houses relying on candles and small gas lamps. A telephone link to the rest of the public network was established in 2001 but the telephone system on the island still uses 'wind the handle' telephones with the (permanently occupied) houses all being on the same [[party line (telephony)|party line]].

The Welsh colloquial term for toilet—''tŷ bach'' ("little house") still refers to a 'little house' at the bottom of the garden on Bardsey.

The Island is owned and managed by the Bardsey Island Trust (see external link below) who acquired it in 1979 after raising the money by public subscription. For many years previously, it had formed part of the estates of the Newborough Family of Glynllifon near Caernarfon. At its maximum, it supported a population of 92 at the time of the 1851 census. It was tradition for the oldest male on the island to called Brenin Enlli (King of Bardsey), crowned by Lord Newborough or his representaive. The actual crown is kept at the Maritime Museum in Liverpool, although calls have been made for it to return to the island.
By 1935 the population had dropped to 33. As the population dropped, the small school on the island, run by the Council, closed circa 1950.

==Pilgrimage==
The island became a place of [[pilgrimage]], especially popular with pilgrims who would come to die and be buried on the isle, hence giving rise to the tradition that twenty thousand saints are buried on the island. Three pilgrimages to Bardsey were rated as equivalent to one pilgrimage to [[Rome]]. [[Saint Deiniol]] and Saint [[Dubricius]] were buried in the old abbey before being translated to [[Bangor Cathedral|Bangor]] and [[Llandaff Cathedral]] respectively. [[Merlin (wizard)|Merlin]] the Magician is said to still be imprisoned on the island.

==Attractions==
Attractions on the island include a [[thirteenth century]] [[bell tower]], several [[Celtic cross]]es, and a wealth of [[bird]]s. Bardsey is a [[National Nature Reserve]] and a [[Site of Special Scientific Interest]]. The tallest square lighthouse in Britain built in 1821.

Occasional boats for day visitors sail to the island from [[Pwllheli]] and [[Aberdaron]].

==Bardsey Island Apple==
Bardsey is also home to the Bardsey Island [[Apple]], an apple originally unique to the island, although saplings can now be purchased. It was originally described by the media as "The World's Rarest Apple". The apple tree is believed to have been grown there since the [[1300s]], when the Island was inhabited by monks. However, due to the island's isolated location, it was not officially identified and classified until [[Ian Sturrock]] sent a sample to the [[National Fruit Collection]], in [[Brogdale]], [[Kent]] in [[1998]].

==External links==
* [http://www.bardsey.org/english/bardsey/welcome.asp?pid=1 Barsdey Island official web site]
* [http://www.bbc.co.uk/wales/northwest/sites/bardsey/ BBC's Bardsey Island Webpages ]
* [http://www.bbfo.org.uk/ Bardsey Bird and Field Observatory]
* [http://www.bardseyapple.co.uk Bardsey Island Apple website]

[[Category:Caernarfonshire]]
[[Category:Tourism in Gwynedd]]
[[Category:Geography of Gwynedd]]
[[Category:History of Caernarfonshire]]
[[Category:Islands of Wales]]
[[Category:Marilyns of Wales]]
[[Category:Mountains and hills of north Wales]]
[[Category:National Nature Reserves in Wales]]
[[Category:Sites of Special Scientific Interest in West Gwynedd]]

[[ca:Ynys Enlli]]
[[cy:Ynys Enlli]]
[[de:Bardsey Island]]
[[es:Bardsey]]
[[gl:Bardsey]]

Blockmatrix

2007-02-19T13:06:34Z

Robinh: /* Direct sum */ arbitrary dimensioned arrays

In the [[mathematics|mathematical]] discipline of [[matrix theory]], a '''block matrix''' or a '''partitioned matrix''' is a partition of a [[Matrix (mathematics)|matrix]] into rectangular smaller matrices called '''blocks'''. Looking at it another way, the matrix is written in terms of smaller matrices written side-by-side. A block matrix must conform to a consistent way of splitting up the rows, and the columns: we group the rows into some adjacent 'bunches', and the columns likewise. The partition is into the rectangles described by one bunch of adjacent rows crossing one bunch of adjacent columns. In other words, the matrix is split up by some horizontal and vertical lines that go all the way across.

== Example ==

The matrix

:<math>P = \begin{bmatrix}
1 & 1 & 2 & 2\\
1 & 1 & 2 & 2\\
3 & 3 & 4 & 4\\
3 & 3 & 4 & 4\end{bmatrix}</math>

can be partitioned into 4 2×2 blocks

:<math>P_{11} = \begin{bmatrix}
1 & 1 \\
1 & 1 \end{bmatrix}, P_{12} = \begin{bmatrix}
2 & 2\\
2 & 2\end{bmatrix}, P_{21} = \begin{bmatrix}
3 & 3 \\
3 & 3 \end{bmatrix}, P_{22} = \begin{bmatrix}
4 & 4\\
4 & 4\end{bmatrix}.</math>

The partitioned matrix can then be written as

:<math>P_{\mathrm{partitioned}} = \begin{bmatrix}
P_{11} & P_{12}\\
P_{21} & P_{22}\end{bmatrix}.</math>

==Block diagonal matrices==

A '''block diagonal matrix''' is a block matrix which is a [[square matrix]], and having [[main diagonal]] blocks square matrices, such that the off-diagonal blocks are zero matrices. A block diagonal matrix '''A''' has the form

:<math>
\mathbf{A} = \begin{bmatrix}
A_{1} & 0 & \cdots & 0 \\ 0 & A_{2} & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & A_{n}
\end{bmatrix}
</math>

where ''A''''k'' is a square matrix; in other words, it is the [[Matrix addition#Direct sum|direct sum]] of ''A''1, …, ''A''''n''. It can also be indicated as <math>A_1\oplus A_2\oplus\ldots\oplus A_n</math> or <math>\mbox{diag}\left(A_1, A_2,\ldots, A_n\right)</math> (the latter being the same formalism used for a [[diagonal matrix]]).
Any square matrix can trivially be considered a block diagonal matrix with only one block.

For the [[determinant]] and [[trace (linear algebra)|trace]], the following properties hold
:<math> \operatorname{det} \mathbf{A} = \operatorname{det} A_1 \cdots \operatorname{det} A_n</math>,
:<math> \operatorname{trace} \mathbf{A} = \operatorname{trace} A_1 +\cdots +\operatorname{trace} A_n</math>.

==Block tridiagonal matrices==

A '''block tridiagonal matrix''' is another special block matrix, which is just like the block diagonal matrix a [[square matrix]], having square matrices (blocks) in the lower diagonal, [[main diagonal]] and upper diagonal, with all other blocks being zero matrices.
It is essentially a [[tridiagonal matrix]] but has submatrices in places of scalars. A block tridiagonal matrix '''A''' has the form

:<math>
\mathbf{A} = \begin{bmatrix}
B_{1} & C_{1} & & & \cdots & & 0 \\
A_{2} & B_{2} & C_{2} & & & & \\
& \ddots & \ddots & \ddots & & & \vdots \\
& & A_{k} & B_{k} & C_{k} & & \\
\vdots & & & \ddots & \ddots & \ddots & \\
& & & & A_{n-1} & B_{n-1} & C_{n-1} \\
0 & & \cdots & & & A_{n} & B_{n}
\end{bmatrix}
</math>

where ''A''''k'', ''B''''k'' and ''C''''k'' are square sub-matrices of the lower, main and upper diagonal respectively.

Block tridiagonal matrices are often encountered in numerical solutions of engineering problems (e.g. [[computational fluid dynamics]]). Optimized numerical methods for [[LU factorization]] are available and hence efficient solution algorithms for equation systems with a block tridiagonal matrix as coefficient matrix. The [[Thomas algorithm]], used for efficient solution of equation systems involving a [[tridiagonal matrix]] can also be applied using matrix operations to block tridiagonal matrices (see also [[Block LU decomposition]]).

==Direct sum==
For any arbitrary matrices ''A'' (of size ''m'' × ''n'') and ''B'' (of size ''p'' × ''q''), we have the '''direct sum''' of ''A'' and ''B'', denoted by <math>A \oplus B</math> and defined as

:<math>
A \oplus B =
\begin{bmatrix}
a_{11} & \cdots & a_{1n} & 0 & \cdots & 0 \\
\vdots & \cdots & \vdots & \vdots & \cdots & \vdots \\
a_{m 1} & \cdots & a_{mn} & 0 & \cdots & 0 \\
0 & \cdots & 0 & b_{11} & \cdots & b_{1q} \\
\vdots & \cdots & \vdots & \vdots & \cdots & \vdots \\
0 & \cdots & 0 & b_{p1} & \cdots & b_{pq}
\end{bmatrix}
</math>

For instance,

:<math>
\begin{bmatrix}
1 & 3 & 2 \\
2 & 3 & 1
\end{bmatrix}
\oplus
\begin{bmatrix}
1 & 6 \\
0 & 1
\end{bmatrix}
=
\begin{bmatrix}
1 & 3 & 2 & 0 & 0 \\
2 & 3 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 6 \\
0 & 0 & 0 & 0 & 1
\end{bmatrix}
</math>

This operation generalizes naturally to arbitrary dimensioned arrays (provided that A and B have the same number of dimensions).

Note that any element in the [[direct sum]] of two [[vector space]]s of matrices could be represented as a direct sum of two matrices.

==Application==

In [[linear algebra]] terms, the use of a block matrix corresponds to having a [[linear mapping]] thought of in terms of corresponding 'bunches' of [[basis vector]]s. That again matches the idea of having distinguished [[direct sum]] decompositions of the [[domain (mathematics)|domain]] and [[range (mathematics)|range]]. It is always particularly significant if a block is the zero matrix; that carries the information that a summand maps into a sub-sum.

Given the interpretation ''via'' linear mappings and direct sums, there is a special type of block matrix that occurs for square matrices (the case ''m'' = ''n''). For those we can assume an interpretation as an [[endomorphism]] of an ''n''-dimensional space ''V''; the block structure in which the bunching of rows and columns is the same is of importance because it corresponds to having a single direct sum decomposition on ''V'' (rather than two). In that case, for example, the [[diagonal]] blocks in the obvious sense are all square. This type of structure is required to describe the [[Jordan normal form]].

This technique is used to cut down calculations of matrices, column-row expansions, and many [[computer science]] applications, including [[VLSI]] chip design. An example is the [[Strassen algorithm]] for fast [[matrix multiplication]].

[[Category:Matrices]]

Graue Schmiere

2006-08-25T07:44:55Z

Robinh: rvv

'''''Grey goo''''' refers to a hypothetical [[End of civilization|end-of-the-world]] event involving [[molecular nanotechnology]] in which out-of-control [[self replication|self-replicating]] robots consume all living matter on [[Earth]] while building more of themselves (a scenario known as [[ecophagy]]).

The term is usually used in a [[science fiction]] context. In a worst-case scenario, all of the matter in the [[universe]] could be turned into goo (with "goo" meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear [[goo]]-like), killing the universe's inhabitants. The disaster is posited to result from an accidental [[mutation]] in a self-replicating nanomachine used for other purposes, or possibly from a deliberate [[doomsday device]].

==Definition of grey goo==
The term was first used by molecular nanotechnology pioneer [[Eric Drexler]] in his book ''[[Engines of Creation (book)|Engines of Creation]]'' (1986). In Chapter 4, ''Engines Of Abundance'', Drexler explores a scary scenario of [[exponential growth]] with such [[assembler (nanotechnology)|assemblers]]:

:"Thus the first replicator assembles a copy in one thousand seconds, the two replicators then build two more in the next thousand seconds, the four build another four, and the eight build another eight. At the end of ten hours, there are not thirty-six new replicators, but over 68 billion. In less than a day, they would weigh a ton; in less than two days, they would outweigh the Earth; in another four hours, they would exceed the mass of the Sun and all the planets combined - if the bottle of chemicals hadn't run dry long before."

Drexler describes grey goo in Chapter 11 ''Engines Of Destruction'':

:"...early assembler-based replicators could beat the most advanced modern organisms. "Plants" with "leaves" no more efficient than today's solar cells could out-compete real plants, crowding the biosphere with an inedible foliage. Tough, omnivorous "bacteria" could out-compete real bacteria: they could spread like blowing pollen, replicate swiftly, and reduce the biosphere to dust in a matter of days. Dangerous replicators could easily be too tough, small, and rapidly spreading to stop - at least if we made no preparation. We have trouble enough controlling viruses and fruit flies."

It is thus worth noting that grey goo need not be grey or gooey. They could be like, for all purposes, a [[plant]] or [[bacteria]]. It is only the result of their ecophagy that would resemble grey goo.

==Other varieties==

Grey goo has several whimsical cousins, differentiated by their colors and raisons d'être. Most of these are not as commonly referred to as grey goo, however, and the definitions are informal:
* ''Golden Goo'' is the backfiring of a get-rich-quick scheme to assemble gold or other economically valuable substance.
* ''Black Goo'' is goo that has been designed to carry a plague and intentionally unleashed into a populated area.
* ''Red Goo'' is goo unleashed intentionally by [[terrorism|terrorists]], a doomsday weapon, or a private individual who wishes to commit [[suicide]] with a bang.
* ''Khaki Goo'' is goo intended by the military to wipe out somebody else's continent, planet, etc.
* ''Blue Goo'' is goo deliberately released in order to stop some other type of grey goo. It might well be the only solution to such a disaster, and would hopefully be better controlled than the original goo.
* ''Pink Goo'' is mankind. It replicates relatively slowly, but some people think it will nevertheless fill any amount of space given enough time. In the pink goo worldview the spread of humanity is a catastrophe and space exploration opens up the possibility of the entire galaxy or the universe getting filled up with Pink Goo - the ultimate crime, something to be stopped at any cost.
* ''Green Goo'' is goo deliberately released, for example by [[ecoterrorist]]s, in order to stop the spread of Pink Goo, either by sterilization or simply by digesting the pink goo. Some form of this, along with an antidote available to the selected few, has been suggested as a strategy for achieving [[zero population growth]]. The term originates from the science fiction classic, <cite>[[Soylent Green]]</cite>.

==Living goo==
One convenient analogy for the grey goo problem is to consider bacteria as the most perfect example of biological nanotechnology. As they have not reduced the world to '''living goo''', some consider it unlikely that some artificial construct will manage to do so with grey goo.

Even so, some people argue that living goo, or even a combination of [[nanotechnology]] and [[biotechnology]] to create organic [[replicators]], is a more realistic threat than grey goo. Arguing that bacteria are [[ubiquitous]] and extraordinarily powerful, [[Bill Bryson]] (2003) says that the Earth is "their planet" and that we're only allowed to exist on it because "they allow us to". Margulis and Sagan (1995) go further, arguing that all organisms, having descended from bacteria, ''are'' in a sense bacteria. Many kinds of bacteria are in fact essential for human life and are found in large quantities in the human digestive tract, in a [[symbiotic relationship]].

Thus a living goo could be a [[multicellular organism]] that obtains its raw materials to grow through ecophagy, and then grows through a process of [[exponential assembly]] such as [[cell division]].

==Risks and precautions==
It is unclear whether the molecular nanotechnology would be capable of creating grey goo at all. Among other common refutations, theorists suggest that the very size of [[nanoparticles]] inhibits them from moving very quickly. While the biological matter that composes life releases significant amounts of [[energy]] when [[oxidisation|oxidised]], and other sources of energy such as sunlight are available, this energy might not be sufficient for the putative nanorobots to out-compete existing organic [[life]] that already uses those resources, especially considering how much energy nanorobots would use for locomotion. If the nanomachine was itself composed of [[organic molecule]]s, then it might even find itself being preyed upon by preexisting bacteria and other natural life forms.

If nanorobots were built of [[inorganic]] compounds or made much use of elements that are not generally found in living matter, then they would need to use much of their metabolic output for fighting [[entropy]] as they purified (reduce sand to silicon, for instance) and synthesized the necessary building blocks. There would be little chemical energy available from inorganic matter such as rocks because, aside from a few exceptions ([[coal]], for example) it is mostly well-oxidized and sitting in a [[Free energy|free-energy]] minimum.

Assuming a molecular nanotechnological [[replicator]] were capable of causing a grey goo disaster, safety precautions might include programming them to stop reproducing after a certain number of [[generation]]s (but see [[cancer]]), designing them to require a rare material that would be sprayed on the construction site before their release, or requiring constant direct control from an external computer. Another possibility is to [[encrypt]] the memory of the replicators in such a way that any changed copy is overwhelmingly likely to [[decrypt]] to non-functioning static.

In [[Britain]], the [[Charles, Prince of Wales|Prince of Wales]] called upon the [[Royal Society]] to investigate the "enormous environmental and social risks" of nanotechnology in a planned report, leading to much delighted media commentary on grey goo. The Royal Society's report on nanoscience was released on [[29 July]] [[2004]].

Recently, new analysis has shown that the danger of grey goo is far less likely than originally thought.<ref>{{cite press release| url=http://www.crnano.org/PR-IOP.htm| date=June 9, 2004| title=Leading nanotech experts put 'grey goo' in perspective| publisher=Center for Responsible Nanotechnology| accessdate=2006-06-17}}</ref> However, other long-term major risks to society and the environment from nanotechnology have been identified.<ref>{{cite web
| url=http://www.crnano.org/dangers.htm| title= Current Results of Our Research| publisher=Center for Responsible Nanotechnology| accessdate=2006-06-17}}</ref> Drexler has made a somewhat public effort to retract his grey goo hypothesis, in an effort to focus the debate on more realistic threats associated with knowledge-enabled nanoterrorism and other misuses.

==Famous quotes==
* "We cannot afford certain types of accidents", Eric Drexler, [[Engines of creation]], [[1986]]
* "I wish I had never used the term 'grey goo'", Eric Drexler, [[Nature (journal)|Nature]] [[10 June]] [[2004]]
* "Yes... Yes, I feel that there's no chance for me to exist, if they do... no chance, no room, no world I can cope with... I don't want to feel it, I keep pushing it back, but it's coming closer and I know I have no place to run... I can't explain what it feels like, I can't catch hold of it — and that's part of the terror, that you ''can't'' catch hold of anything — it's as if the whole world were suddenly destroyed, but not by an explosion — an explosion is something hard and solid — but destroyed by... by some horrible kind of softening... poke your finger through stone and the stone would give, like jelly, and mountains would slither, and buildings would switch their shapes like clouds — and that would be the end of the world, not like fire and brimstone, but ''goo''." Cherryl Taggart in [[Ayn Rand]]'s [[Atlas Shrugged]], [[1957]]

==Fictional depictions==
{{spoiler}}
===In books===
"[[Autofac]]" is a 1955 science fiction short story by [[Philip K. Dick]] that features one of the earliest treatments of self-replicating machines.

In [[Stanisław Lem]]'s ''Ciemność i Plesń'' (''Darkness and Mildew''), 1959, spores of an engineered lifeform that can use nuclear energy escape the lab. In order for the spores to activate, they need to be in the dark and near a rare species of mildew (hence the title), after which they grow exponentially.

In [[Michael Crichton]]'s ''[[The Andromeda Strain]]'', (1969) also made into a movie, a rapidly evolving virus/prion-like chemical consumes many types of organic molecules with catastrophic results. This story overlaps both the grey goo and the out-of-control virus scenarios. The same author's ''[[Prey (novel)|Prey]]'', (2002) presents a somewhat less limited scenario where a company in Nevada accidentally/purposely releases self-assembling nanobots into the desert, which quickly replicate and evolve and threaten all of the human protagonists.

The plot of [[John Sladek]]'s 1968 novel ''The Reproductive System'' (British title ''Mechasm'') is based on small (but not nano-scale) machines who scour the world for material to make more of themselves. The phrase "grey goo" is not used but the idea is the same.

In the [[Adam Warren]]-penned ''[[Dirty Pair]]'' [[manga]], (1979-) mankind has ventured out into the stars as a result of the '''Nodachi Nanoclysm''' (often referred to as just "the Nanoclysm"), where nano absorbed the majority of the solar system before gaining sentience and annihilating itself to save its creators. As a result, with rare exceptions, nanotechnology is universally banned in human civilizations.

[[Greg Bear]]'s novel ''[[Blood Music]]'' (1983) is a classic of the field, depicting a form of grey goo originally derived from human [[lymphocyte]]s.

[[Frank Miller (comics)|Frank Miller]]'s graphic novel, ''Ronin'', (1983-84) is set in a future New York which is being overtaken by a post-[[Technological singularity|singularity]] computer complex capable of physically replicating itself.

[[Alan Moore]]'s comic book, ''[[Promethea]]'', takes place in a technologically-futuristic modern world, where the synthetic "Elastagel" is ubiquitous. In one issue, a [[Y2K]] malfunction causes all the Elastagel to melt and run together, essentially creating a [[The Blob|Blob]]-like creature that causes havoc before being destroyed by the protagonist.

In [[Jeffrey Carver]]'s 1989 novel, ''From a Changeling Star'', medical NAGs (nano-agents) capable of healing a human body from severe trauma run dangerously amok, causing amnesia and bizarre behavior. Competing NAGs, known collectively as an intelligence named Dax, help to reconstruct the memories and reveal a conspiracy regarding an attempt to cause Betelgeuse to go supernova.

[[Walter Jon Williams]]'s novel ''[[Aristoi (novel)|Aristoi]]'' (1993) featured a future wherein Earth was consumed and destroyed by runaway nano, referred to as "mataglap", from an [[Indonesian]] expression, "Mata Gelap," meaning "cloudy eye," "dark eye," or "dilated eye." Mata Gelap is considered to be an indication that one is blind to reason, and possibly about to [[run amok]].

In [[Ken Macleod]]'s ''[[The Stone Canal]]'', (1996) blue goo is a generic anti-nanomachine antiseptic.

In [[Iain M. Banks]]'s "Culture" series, specifically in ''[[Excession]]'', (1996) the major possible threat to the Culture is considered to be something called an "Aggressive Hegemonizing Swarm", selfish self-replicating devices intent on turning all matter in the Universe into copies of themselves.

In [[Stephen Baxter]]'s ''[[Moonseed]]'', (1998) Venus and the entire earth are engulfed by grey goo forcing the inhabitants of Earth to flee to the Moon, which is immune to the goo because of an alien presence.

[[Wil McCarthy]]'s science fiction novel ''[[Bloom (novel)|Bloom]]'' (1999) is set in a future in which a grey goo has overwhelmed the entire inner solar system, with the only remaining colonies of humans surviving in the asteroid belt and on Jupiter's moons.

In [[Yukito Kishiro]]'s ''[[Battle Angel Alita]]: Last Order'' (2000-), gray goo is mentioned by a Venusian councilor during a LADDER meeting. Apparently the result of bored teenagers messing with common nanotechnology, it is the reason LADDER has made very strict laws concerning the use of nanotech in the solar system.

[[James Alan Gardner]] includes a grey goo incident in his sci-fi novel ''[[Ascending]]'' (2001). A spy on a starship intentionally causes the incident using a computer-sabotaging nano agent.

In [[Jasper Fforde]]'s Thursday Next novel ''[[Lost in a Good Book]]'' (2002), the entire world is (and later is not) turned into a sweet-tasting pink goo by nanomachines designed to manufacture strawberry Dream Topping.

Patrick Larkin's contribution to the [[Robert Ludlum]] Covert-One series, called ''[[The Lazarus Vendetta]]'' (2003), is about nanotechnology initially derived for benevolent purposes but intentionally set loose by terrorists on the public using biological signals. Victims are turned into "organic soup" as the book states; piles of goo and bone fragments.

[[Alastair Reynolds]]' book ''[[Century Rain]]'' (2004) describes an Earth decimated by an eruption of nanotechnology (an event referred to as the "Nanocaust"). Although not a strictly traditional "grey-goo" scenario, it is still an outline of an apocalypse arising from uncontrolled nanomachinery.

[[Kurt Vonnegut]]'s [[Ice-nine]] from the novel ''[[Cat's Cradle]]'' has similar properties to grey goo and is capable of "freezing" liquid water instantly if it touches it. It was accidentally dropped into the ocean and caused all the world's water to crystallize. It was in essence, a [[Doomsday device]].

===In television===
In the science fiction television series ''[[Lexx]]'', self-replicating robot arms called ''[[Mantrid]] drones'' wind up consuming the mass of an entire universe. Mantrid drones were macroscopic machines, but they apparently used nanotechnology as part of their means of manufacturing new parts for themselves.

''[[Stargate SG-1]]'' also fought a form of macroscopic self replicating machines. This enemy was known as the "[[Replicators]]". The basic building block of the Replicators is a 1cm trapezoidal block containing its own power supply and computing/memory capacity. These blocks could be then organized into structures as simple as six-legged arachnoid scout bot to [[FTL|faster-than-light]] capable star ships of unlimited size. The first replicators were built by a defective [[android]], but due to their immense computing power and [[hive mind]], they quickly became sentient and began executing their own agenda of converting the entire universe into replicators. The initial replicators were macroscopic, but more advanced nanoscopic versions appeared that could mimic humanoid lifeforms.

''[[Star Trek: Enterprise]]'' has an episode entitled "[[Vox Sola (Enterprise episode)|Vox Sola]]" in which the Enterprise is being overtaken by a biological entity. A strange, symbiotic alien creature boards Enterprise and captures several crew members and Hoshi has to decipher the creature's complex language. On the entity's planet, T'Pol, Reed, Phlox and Hoshi land in a shuttlepod and release the entity at the coordinates given earlier. Phlox also releases the tendril severed in the Cargo Bay, which is reabsorbed. As the shuttlepod returns to the Enterprise, dawn breaks and the area is revealed to be covered with one huge grey organism. Granted this "organism" would be labeled "green goo" due to being biological and not a nanotechnological (mechanical) entity, but the entity is related to grey goo due to appearance and hyper-assimilation actions.

In ''[[Babylon 5]]'' 's spin-off ''[[Crusade]]'', a race called the Drakh have released a nanovirus plague on Earth, which will destroy all life on Earth within five years if it is not stopped.

An episode of [[Cartoon Network]]'s series ''[[Justice League Unlimited]]'' entitled "Heart of Darkness" pitted the comic book heroes of the [[DC comics]] universe against a nanotechnological [[weapon of mass destruction]] created by an ancient alien race designed to defeat its enemy by literally devouring the planet from under them. It is stopped when [[The Atom]] is sent inside the central mass to examine and attack it at the source.

One fanciful depiction of a grey goo crisis was in an episode of the ''[[Gargoyles (animated series)|Gargoyles]]'' [[animated series]] where the protagonists face an advanced form of nanotechnology. They eventually manage to convince it to stop its spread.

The [[computer-animated]] cartoon series ''[[ReBoot]]'' featured a [[computer virus]] called 'Medusa' that was stolen by Megabyte from Hexadecimal and accidentally unleashed, speading in a manner similar to grey goo, turning everyone and everything in mainframe save for Bob and Hexadecimal to stone. Bob then confronts Hexadecimal and convinces her to release the antivirus, returning mainframe and its inhabitants to normal.

Another cartoon version of "grey goo" is seen in an episode of ''[[G.I. Joe: A Real American Hero|G.I.Joe]]'' titled ''The Germ'', in which an experimental pathogen dubbed "Bacteria X" is stolen by Crimson Guard agents who double-cross [[Destro]]. In typical Cobra fashion, the vial is clumsily dropped along with a growth formula that Destro was developing, and the combination transforms into a giant blob that consumes everything in its path. The Joes throw everything at it from missiles to insecticide — to little effect — and even send Airtight into the blob with an explosive dose of antibiotics, but the attack only prompts the blob to divide into two. When one blob is weakened after devouring a path through an apple orchard, the Joes figure its disagreeable reaction is caused by traces of poison, actually [[cyanide]], in the apple seeds, so they bombard the blob with apples to destroy it.<ref>{{cite web| url=http://www.joeheadquarters.com/eps1x.shtml| title=GI Joe Season 1 Episode Summaries| accessdate=2006-03-16}}</ref>

===In other media===
In the virtual world ''[[Second Life]]'', it is a popular term referring to player-coded objects that self-replicate out of control and thus (intentionally or otherwise) consume server resources and end up as a [[Denial of Service]] attack.

[[Sierra Entertainment]]'s computer game ''[[Outpost 2]]'' was a ''[[Civilization (computer game)|Civilization]]''-like game which theme was based on a space colony where a lab exploded, creating a plague that consumed everything in its path, called 'the Blight'. As a side effect, the entire planet was transformed into a huge computer.

''[[Sid Meier's Alpha Centauri]]'' the unofficial sequel to ''[[Civilization 2]]'' had one "Secret project" called the Nano-factory. When built, units can be repaired in the field, even in enemy territory. The premise was of a nanomachine fluid that can absorb and reprocess any items to which it is exposed and use that raw material to produce weapons and equipment.
"Industrial Grade Nano-Paste, Planet's most valuable commodity, can also be one of its most dangerous. Simply pour out several canisters, slide in a programming transponder, and step well away while the stuff cooks. In under an hour the nano will use available materials to assemble a small factory, a hovertank, or enough impact rifles to equip a regiment. -Col. Corazon Santiago, 'Planet: A Survivalist's Guide'"

Also seen in ''Alpha Centauri'' was a colony upgrade called a Nanoreplicator, which ostensibly used nanomachines to perfectly replicate any item down to the atomic level.

In the introduction sequence of [[Ion Storm Inc.|Ion Storm]]'s futuristic PC and Xbox game ''[[Deus Ex: Invisible War]]'', a nanotechnology bomb called a nanite detonator is detonated by a terrorist cell to destroy the city of [[Chicago, Illinois|Chicago]]. The result of the bomb being detonated is a wave of grey goo that consumes and destroys the entire city.

[[Activision]]'s computer strategy game ''[[Civilization: Call to Power]]'' contained a military unit called the 'Eco Ranger', which could be used under an 'Ecotopian' government to completely destroy a city and its surroundings, almost like a nuclear weapon. Unlike a nuclear weapon, which halved a city population, destroyed all military units and tile improvements around the city as well as polluting several adjacent tiles, this unit was supposed to use nanomachines, 'grey goo', to completely destroy the city and its surroundings, converting the area into pristine wilderness.

The [[Zerg]] in [[Blizzard Entertainment]]'s ''[[StarCraft]]'' series have a structure called a Creep Colony, it is a building sized organ that produces "Creep". Creep is a layer of [[purple]] tissue that all Zerg buildings are built on. It functions as connective, circulatory and nervous tissue tying all the structures into one organism.

On [[Mr. Bungle]]'s 1999 album ''California'' the song "None of Them Knew They Were Robots" contains the lyrics, "I feel the Grey Goo boiling in my blood."

The Konami game ''Nanobreaker'' has an opening sequence in which nanomachines reduce all the living organisms on an island to grey goo.

==References==
<references/>
*[[Lynn Margulis]] and [[Doris Sagan]] - ''What is Life?'' (1995). Simon & Schuster. ISBN 0-684-81087-5
*Bill Bryson ''[[A Short History of Nearly Everything]]'' (2003)
*[http://www.etcgroup.org/article.asp?newsid=373 Green Goo: Nanotechnology Comes Alive!]
*[http://www.wired.com/news/medtech/0,1286,64235,00.html?tw=wn_tophead_5 Green Goo: The New Nanothreat] from Wired

== See also ==
* [[Bootstrapped-Brain]]
* [[Clanking replicator]] (often called [[John von Neumann|von Neumann]] machine)
* [[Technology assessment]]
* [[Ice-9]]
* [[The Blob]] - a movie example of living goo

== External links ==

* [http://www.nanotechweb.org/articles/society/3/6/1/1 Drexler dubs "grey goo" fears obsolete]
* [http://www.iop.org/EJ/news/-topic=763/journal/0957-4484 Nanotechnology pioneer slays "grey goo" myths]
* [http://www.nanotec.org.uk/finalReport.htm Online edition of the Royal Society's report ''Nanoscience and nanotechnologies: opportunities and uncertainties'']
* [http://news.bbc.co.uk/1/hi/sci/tech/3788673.stm Nanotech guru turns back on 'goo']
* [http://news.bbc.co.uk/2/hi/science/nature/4538547.stm U.S. robot builds copies of itself]
* [http://www.exitmundi.nl/graygoo.htm Exit Mundi article on the grey goo doomsday theory]
* [http://www.greygoo.org/ The First Church of the Grey Goo - humorous new apocalyptic religion]
* [http://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2003/07/10/ecfnano09.xml Could nanobots destroy us? - The Telegraph (UK newspaper) on Grey Goo]
* [http://members.optusnet.com.au/exponentialist/GreyGoo.htm A look at the exponential nature of grey goo population growth]

[[Category:Nanotechnology]]
[[Category:Artificial life]]
[[Category:Environmental disasters]]
[[Category:Armageddon]]

[[es:Goo gris]]
[[sv:Grey goo]]

Loch Ryan

2005-07-15T13:04:42Z

Robinh: lighthouse

'''Loch Ryan''' is a [[Scottish]] sea loch that furnishes a natural sheltered anchorage for ships. It is situated between [[Rhinns of Galloway]], and South [[Ayrshire]]; it is bound by [[Milleur Point]] and [[Finnarts Point]].

The loch is about 13 km from north to south, and about 5km wide at its widest point. Nearby roads include the [[A77]] and [[A718]]; the settlements of [[Cairnryan]], [[Kirkcolm]], and [[Stranraer]] stand on its banks.

There is a sandbank, [[The Scar]], running down the west side of the loch near Kirkcolm. The loch has a headland, Cairn Point on which the small village of Cairnryan stands. A [[lighthouse]] was built here in [[1847]].

Loch Ryan

2005-07-15T13:03:46Z

Robinh: copyvio

Graue Schmiere

2005-06-13T07:10:28Z

Robinh: revert vandalism

'''Grey goo''', a term coined by nanotechnology pioneer [[Eric Drexler]], refers to a hypothetical [[End of the world (religion)|end-of-the-world]] event involving [[nanotechnology]] in which out-of-control [[self replication|self-replicating]] robots consume all life on [[Earth]] while building more of themselves (a scenario known as [[ecophagy]]). It is usually used in a [[science fiction]]al context. In a worst-case scenario, all of the matter in the [[universe]] could be turned into goo (with "goo" meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear goo-like), killing the universe's residents. The disaster could result from an accidental [[mutation]] in a self-replicating nanomachine used for other purposes, or possibly from a deliberate [[doomsday device]].

It is unclear whether nanotechnology is capable of creating grey goo at all. While the biological matter that composes life releases significant amounts of [[energy]] when [[oxidisation|oxidised]], and other sources of energy such as sunlight are available, this energy might not be sufficient for the robots to out-compete existing organic life that already uses those resources. If the nanomachine is itself composed of organic molecules, then it might even find itself being preyed upon by preexisting bacteria and other natural life forms. One way to think about the grey goo problem is to consider [[virus|viruses]] as the most perfect example of nanotechnology; as they have not reduced the world to grey goo in 4 billion years of evolution, it is unlikely that some artifical construct will manage to do so.

If they are built of [[inorganic]] compounds or make much use of elements that are not generally found in living matter, then they will need to use much of their metabolic output for fighting [[entropy]] as they purify (reduce sand to silicon, for instance) and synthesize the necessary building blocks. There would be little chemical energy available from inorganic matter such as rocks because, aside from a few exceptions ([[coal]], for example) it's mostly well-oxidized and sitting in a [[Free energy|free-energy]] minimum.

Because of these limitations grey goo may only be possible in an environment which lacks indigenous life to compete with it for resources. However, some proponents of nanotechnology argue that artificial nanomachines might be able to outcompete natural life because they could have [[irreducible complexity|irreducibly complex]] designs that life could not have developed via natural evolution.

Some also consider it unlikely that an artificial self-replicator could spontaneously evolve in a manner that could present an immediate threat.

==Precautions==

Assuming a nanotechnological replicator is capable of causing a grey goo disaster, safety precautions might include programming them to stop reproducing after a certain number of generations (but see [[cancer]]), designing them to require a rare material that would be sprayed on the construction site before their release, or requiring constant direct control from an external computer. Another possibility is to encrypt the memory of the replicators in such a way that any changed copy is overwhelmingly likely to decrypt to nonfunctioning static.

==Other varieties==bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Grey goo has several whimsical cousins, differentiated by their colors and raisons d'être. Most of these are not as commonly referred to as grey goo, however, and the definitions are informal:
* ''Golden Goo'' is the backfiring of a get-rich-quick scheme to assemble gold or other economically valuable substance.
* ''Black Goo'' (or ''Red Goo'') is goo unleashed intentionally by [[terrorism|terrorists]], a doomsday weapon, or a private individual who wishes to commit [[suicide]] with a bang.
* ''Khaki Goo'' is goo intended by the military to wipe out somebody else's continent, planet, etc.
* ''Blue Goo'' is goo deliberately released in order to stop some other type of grey goo. It might well be the only solution to such a disaster, and would hopefully be better controlled than the original goo.
* ''Pink Goo'' is mankind. It replicates relatively slowly, but some people think it will nevertheless fill any amount of space given enough time. In the pink goo worldview the spread of humanity is a catastrophe and space exploration opens up the possibility of the entire galaxy or the universe getting filled up with Pink Goo - the ultimate crime, something to be stopped at any cost.
* ''Green Goo'' is goo deliberately released, for example by [[ecoterrorist]]s, in order to stop the spread of Pink Goo, either by sterilization or simply by digesting the pink goo. Some form of this, along with an antidote available to the selected few, has been suggested as a strategy for achieving [[zero population growth]]. The term originates from the science fiction classic, <cite>[[Soylent Green]]</cite>.

==Famous quotes==

* "We cannot afford certain types of accidents", [[Eric Drexler]], [[Engines of creation]], 1986
* "I wish I had never used the term 'grey goo' " Drexler, [[Nature (journal)|Nature]] [[10 June]] [[2004]]

==Fictional depictions==

===In books===

[[Wil McCarthy]]'s science fiction novel ''[[Bloom (novel)|Bloom]]'' is set in a future in which a grey goo has overwhelmed the entire inner solar system, with the only remaining colonies of humans surviving in the asteroid belt and on Jupiter's moons.

[[Greg Bear]]'s novel ''[[Blood Music]]'' is a classic of the field, depicting a form of grey goo originally derived from human [[lymphocyte]]s.

[[Walter Jon Williams]]'s novel [[Aristoi_(novel)|Aristoi]] featured a future wherein Earth was consumed and destroyed by runaway nano, referred to as "mataglap", from an [[Indonesian]] word meaning "dilated eye" (referring to the look on one's face when they go berserk).

In the [[Adam Warren]]-penned ''[[Dirty Pair]]'' [[manga]], mankind has ventured out into the stars as a result of the '''Nodachi Nanoclysm''' (often referred to as just "the Nanoclysm"), where nano absorbed the majority of the solar system before gaining sentience and annihilating itself to save its creators. As a result, with rare exceptions, nanotechnology is universally banned in human civilizations.

In [[Ken Macleod]]'s ''[[The Stone Canal]]'', blue goo is a generic anti-nanomachine antiseptic. In [[Iain M. Banks]]'s "Culture" series, specifically in ''[[Excession]]'', the major possible threat to the Culture is considered to be something called an "Agressive Hegemonizing Swarm".

===In television===

In the science fiction television series ''[[Lexx]]'', self-replicating robot arms called [[Mantrid]] drones wind up consuming the mass of an entire universe. Mantrid drones were macroscopic machines, but they apparently used nanotechnology as part of their means of manufacturing new parts for themselves.

''[[Stargate SG-1]]'' also fought a form of macroscopic self replicating machines. This enemy was known as the ''[[Replicators]]''. The basic building block of the Replicators is a 1cm trapezoidal block containing its own power supply and computing/memory capacity. However, these blocks could be organized into units as small as 6 legged scout bot to [[FTL]] capable star ships of unlimited size. Initially the creation of a synthetic life, due to their immense computing power and [[hive mind]], they quickly became sentient and began executing their agenda of converting the entire universe into replicators. Initally macroscopic, more advanced nanoscopic versions appeared that could mimic humanoid lifeforms.

An episode of [[Cartoon Network]]'s series [[Justice League Unlimited]] entitled "Heart of Darkness" pitted the comic book heroes of the [[DC comics]] universe against a nanotechnological [[weapon of mass destruction]] created by an ancient alien race designed to defeat its enemy by literally devouring the planet from under them.

One fanciful depiction of a grey goo crisis was in an episode of the ''[[Gargoyles (animated series)|Gargoyles]]'' [[animated series]] where the protagonists face an advanced form of nanotechnology. They eventually manage to convince it to stop its spread.

Another cartoon version of "grey goo" is The Germ, an episode of ''[[GI Joe]]'' written by Roger Slifer. Psyudomondo U Bacteria, better known as Bacteria X, is stolen by the Crimson Guard, when they double cross Destro. In usual Cobra form, the Crimson Guard drops the Germ and a growth formula that Destro was working on, and it forms a giant blob that's eating everything in its path. The Joes throw everything at it from missiles to insecticide, and even send Airtight into the blob with explosive antibiotics. The blob separates in two after the Joes' attack, and one blob is weakened after going through an apple orchard. The Joes figure it's because of the poison in the apple seeds, so they bombard the blob with apples, which destroys the Germ.
[http://www.joeheadquarters.com/eps1x.shtml synopsis]

===In other media===

[[Sierra Entertainment]]'s computer game ''[[Outpost 2]]'' was a [[Civilization]]-like game which theme was based on a space colony where a lab exploded, creating a plague that consumed everything in its path, called 'the Blight'. The game was a [[real-time strategy]] game that failed terribly, as review sites rated it as one of the most boring games ever. The game came with a small novel counting the happenings of each level on both sides.

==See also==
* [[clanking replicator]]
* [[technology assessment]]
* [[Ice-9 Type Transition]]

==Bibliography==

* [[Greg Bear]], <cite>[[Blood Music]]</cite>, the classic sci-fi novel about ecophagy. Arguably it is a Green or Golden Goo-type.
* [[Kurt Vonnegut]], <cite>[[Cat's Cradle]]</cite>, centering around a grey-goo-like [[polywater]], "'''ice-nine'''," converting every drop of [[water]] on [[Earth]] into a [[solid]]. It should be noted that Vonnegut's ice-nine is an alternate form of water, not a life form or nanomachine.

==External links==
* [http://www.nanotechweb.org/articles/society/3/6/1/1 Drexler dubs "grey goo" fears obsolete]
* [http://www.iop.org/EJ/news/-topic=763/journal/0957-4484 Nanotechnology pioneer slays "grey goo" myths]
* [http://news.bbc.co.uk/1/hi/sci/tech/3788673.stm Nanotech guru turns back on 'goo']
* [http://news.bbc.co.uk/2/hi/science/nature/4538547.stm U.S. robot builds copies of itself]
* [http://www.greygoo.org/ The First Church of the Grey Goo - humorous new apocalyptic religion]

[[Category:Nanotechnology]]
[[Category:Artificial life]]
[[Category:Man-made disasters]]

[[sv:Grey goo]]

Graue Schmiere

2005-06-09T12:15:22Z

Robinh: grey goo and viruses

'''Grey goo''', a term coined by nanotechnology pioneer [[Eric Drexler]], refers to a hypothetical [[End of the world (religion)|end-of-the-world]] event involving [[nanotechnology]] in which out-of-control [[self replication|self-replicating]] robots consume all life on [[Earth]] while building more of themselves (a scenario known as [[ecophagy]]). It is usually used in a [[science fiction]]al context. In a worst-case scenario, all of the matter in the [[universe]] could be turned into goo (with "goo" meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear goo-like), killing the universe's residents. The disaster could result from an accidental [[mutation]] in a self-replicating nanomachine used for other purposes, or possibly from a deliberate [[doomsday device]].

It is unclear whether nanotechnology is capable of creating grey goo at all. While the biological matter that composes life releases significant amounts of [[energy]] when [[oxidisation|oxidised]], and other sources of energy such as sunlight are available, this energy might not be sufficient for the robots to out-compete existing organic life that already uses those resources. If the nanomachine is itself composed of organic molecules, then it might even find itself being preyed upon by preexisting bacteria and other natural life forms. One way to think about the grey goo problem is to consider [[virus|viruses]] as the most perfect example of nanotechnology; as they have not reduced the world to grey goo in 4 billion years of evolution, it is unlikely that some artifical construct will manage to do so.

If they are built of [[inorganic]] compounds or make much use of elements that are not generally found in living matter, then they will need to use much of their metabolic output for fighting [[entropy]] as they purify (reduce sand to silicon, for instance) and synthesize the necessary building blocks. There would be little chemical energy available from inorganic matter such as rocks because, aside from a few exceptions ([[coal]], for example) it's mostly well-oxidized and sitting in a [[Free energy|free-energy]] minimum.

Because of these limitations grey goo may only be possible in an environment which lacks indigenous life to compete with it for resources. However, some proponents of nanotechnology argue that artificial nanomachines might be able to outcompete natural life because they could have [[irreducible complexity|irreducibly complex]] designs that life could not have developed via natural evolution.

Some also consider it unlikely that an artificial self-replicator could spontaneously evolve in a manner that could present an immediate threat.

==Precautions==

Assuming a nanotechnological replicator is capable of causing a grey goo disaster, safety precautions might include programming them to stop reproducing after a certain number of generations (but see [[cancer]]), designing them to require a rare material that would be sprayed on the construction site before their release, or requiring constant direct control from an external computer. Another possibility is to encrypt the memory of the replicators in such a way that any changed copy is overwhelmingly likely to decrypt to nonfunctioning static.

==Other varieties==

Grey goo has several whimsical cousins, differentiated by their colors and raisons d'être. Most of these are not as commonly referred to as grey goo, however, and the definitions are informal:
* ''Golden Goo'' is the backfiring of a get-rich-quick scheme to assemble gold or other economically valuable substance.
* ''Black Goo'' (or ''Red Goo'') is goo unleashed intentionally by [[terrorism|terrorists]], a doomsday weapon, or a private individual who wishes to commit [[suicide]] with a bang.
* ''Khaki Goo'' is goo intended by the military to wipe out somebody else's continent, planet, etc.
* ''Blue Goo'' is goo deliberately released in order to stop some other type of grey goo. It might well be the only solution to such a disaster, and would hopefully be better controlled than the original goo.
* ''Pink Goo'' is mankind. It replicates relatively slowly, but some people think it will nevertheless fill any amount of space given enough time. In the pink goo worldview the spread of humanity is a catastrophe and space exploration opens up the possibility of the entire galaxy or the universe getting filled up with Pink Goo - the ultimate crime, something to be stopped at any cost.
* ''Green Goo'' is goo deliberately released, for example by [[ecoterrorist]]s, in order to stop the spread of Pink Goo, either by sterilization or simply by digesting the pink goo. Some form of this, along with an antidote available to the selected few, has been suggested as a strategy for achieving [[zero population growth]]. The term originates from the science fiction classic, <cite>[[Soylent Green]]</cite>.

==Famous quotes==

* "We cannot afford certain types of accidents", [[Eric Drexler]], [[Engines of creation]], 1986
* "I wish I had never used the term 'grey goo' " Drexler, [[Nature (journal)|Nature]] [[10 June]] [[2004]]

==Fictional depictions==

===In books===

[[Wil McCarthy]]'s science fiction novel ''[[Bloom (novel)|Bloom]]'' is set in a future in which a grey goo has overwhelmed the entire inner solar system, with the only remaining colonies of humans surviving in the asteroid belt and on Jupiter's moons.

[[Greg Bear]]'s novel ''[[Blood Music]]'' is a classic of the field, depicting a form of grey goo originally derived from human [[lymphocyte]]s.

[[Walter Jon Williams]]'s novel [[Aristoi_(novel)|Aristoi]] featured a future wherein Earth was consumed and destroyed by runaway nano, referred to as "mataglap", from an [[Indonesian]] word meaning "dilated eye" (referring to the look on one's face when they go berserk).

In the [[Adam Warren]]-penned ''[[Dirty Pair]]'' [[manga]], mankind has ventured out into the stars as a result of the '''Nodachi Nanoclysm''' (often referred to as just "the Nanoclysm"), where nano absorbed the majority of the solar system before gaining sentience and annihilating itself to save its creators. As a result, with rare exceptions, nanotechnology is universally banned in human civilizations.

In [[Ken Macleod]]'s ''[[The Stone Canal]]'', blue goo is a generic anti-nanomachine antiseptic. In [[Iain M. Banks]]'s "Culture" series, specifically in ''[[Excession]]'', the major possible threat to the Culture is considered to be something called an "Agressive Hegemonizing Swarm".

===In television===

In the science fiction television series ''[[Lexx]]'', self-replicating robot arms called [[Mantrid]] drones wind up consuming the mass of an entire universe. Mantrid drones were macroscopic machines, but they apparently used nanotechnology as part of their means of manufacturing new parts for themselves.

''[[Stargate SG-1]]'' also fought a form of macroscopic self replicating machines. This enemy was known as the ''[[Replicators]]''. The basic building block of the Replicators is a 1cm trapezoidal block containing its own power supply and computing/memory capacity. However, these blocks could be organized into units as small as 6 legged scout bot to [[FTL]] capable star ships of unlimited size. Initially the creation of a synthetic life, due to their immense computing power and [[hive mind]], they quickly became sentient and began executing their agenda of converting the entire universe into replicators. Initally macroscopic, more advanced nanoscopic versions appeared that could mimic humanoid lifeforms.

An episode of [[Cartoon Network]]'s series [[Justice League Unlimited]] entitled "Heart of Darkness" pitted the comic book heroes of the [[DC comics]] universe against a nanotechnological [[weapon of mass destruction]] created by an ancient alien race designed to defeat its enemy by literally devouring the planet from under them.

One fanciful depiction of a grey goo crisis was in an episode of the ''[[Gargoyles (animated series)|Gargoyles]]'' [[animated series]] where the protagonists face an advanced form of nanotechnology. They eventually manage to convince it to stop its spread.

Another cartoon version of "grey goo" is The Germ, an episode of ''[[GI Joe]]'' written by Roger Slifer. Psyudomondo U Bacteria, better known as Bacteria X, is stolen by the Crimson Guard, when they double cross Destro. In usual Cobra form, the Crimson Guard drops the Germ and a growth formula that Destro was working on, and it forms a giant blob that's eating everything in its path. The Joes throw everything at it from missiles to insecticide, and even send Airtight into the blob with explosive antibiotics. The blob separates in two after the Joes' attack, and one blob is weakened after going through an apple orchard. The Joes figure it's because of the poison in the apple seeds, so they bombard the blob with apples, which destroys the Germ.
[http://www.joeheadquarters.com/eps1x.shtml synopsis]

===In other media===

[[Sierra Entertainment]]'s computer game ''[[Outpost 2]]'' was a [[Civilization]]-like game which theme was based on a space colony where a lab exploded, creating a plague that consumed everything in its path, called 'the Blight'. The game was a [[real-time strategy]] game that failed terribly, as review sites rated it as one of the most boring games ever. The game came with a small novel counting the happenings of each level on both sides.

==See also==
* [[clanking replicator]]
* [[technology assessment]]
* [[Ice-9 Type Transition]]

==Bibliography==

* [[Greg Bear]], <cite>[[Blood Music]]</cite>, the classic sci-fi novel about ecophagy. Arguably it is a Green or Golden Goo-type.
* [[Kurt Vonnegut]], <cite>[[Cat's Cradle]]</cite>, centering around a grey-goo-like [[polywater]], "'''ice-nine'''," converting every drop of [[water]] on [[Earth]] into a [[solid]]. It should be noted that Vonnegut's ice-nine is an alternate form of water, not a life form or nanomachine.

==External links==
* [http://www.nanotechweb.org/articles/society/3/6/1/1 Drexler dubs "grey goo" fears obsolete]
* [http://www.iop.org/EJ/news/-topic=763/journal/0957-4484 Nanotechnology pioneer slays "grey goo" myths]
* [http://news.bbc.co.uk/1/hi/sci/tech/3788673.stm Nanotech guru turns back on 'goo']
* [http://news.bbc.co.uk/2/hi/science/nature/4538547.stm U.S. robot builds copies of itself]
* [http://www.greygoo.org/ The First Church of the Grey Goo - humorous new apocalyptic religion]

[[Category:Nanotechnology]]
[[Category:Artificial life]]
[[Category:Man-made disasters]]

[[sv:Grey goo]]

Hotellingsche T-Quadrat-Verteilung

2005-02-26T22:01:56Z

Robinh: see talkpage

In [[statistics]], '''Hotelling's T-square statistic''', named for [[Harold Hotelling]],
is a generalization of [[Student's t distribution|Student's t statistic]] that is used in multivariate hypothesis testing.

Hotelling's T-square statistic is defined as follows. Suppose

:<math>{\mathbf x}_1,\dots,{\mathbf x}_n</math>

are ''p''×1 [[column vector]]s whose entries are [[real number]]s. Let

:<math>\overline{\mathbf x}=(\mathbf{x}_1+\cdots+\mathbf{x}_n)/n</math>

be their [[mean]]. Let the ''p''×''p'' [[positive-definite matrix|nonnegative-definite matrix]]

:<math>{\mathbf W}=\sum_{i=1}^n (\mathbf{x}_i-\overline{\mathbf x})(\mathbf{x}_i-\overline{\mathbf x})'/(n-1)</math>

be their "[[sample variance]]". (The transpose of any matrix ''M'' is denoted above by ''M''′). Let μ be some known ''p''×1 column vector (in applications a hypothesized value of a population mean). Then Hotelling's T-square statistic is

:<math>
T^2=n(\overline{\mathbf x}-{\mathbf\mu})'{\mathbf W}^{-1}(\overline{\mathbf x}-{\mathbf\mu}).
</math>

Note that <math>T^2</math> may be determined for any matrix of [[rank (linear algebra)|rank]] at least ''p''.

The reason that this is interesting is that if <math>\mathbf{x}\sim N_p(\mu,{\mathbf V})</math> is a [[random variable]] with a [[multivariate normal distribution]] and <math>{\mathbf W}\sim W_p(n,{\mathbf V})</math> has a [[Wishart distribution]], and <math>{\mathbf x}</math> and <math>{\mathbf W}</math> are [[statistical independence|independent]], then the [[probability distribution]] of <math>T^2</math> is '''Hotelling's T-square distribution'''.

The assumptions above are frequently met in practice: it can be shown that if <math>{\mathbf x}_1,\dots,{\mathbf x}_n\sim N_p(\mu,{\mathbf V})</math>, are independent, and <math>\overline{\mathbf x}</math> and <math>{\mathbf W}</math> are as defined above then <math>{\mathbf W}</math> has a Wishart distribution with ''m'' = ''n'' − 1 degrees of freedom and is independent of <math>\overline{\mathbf x}</math>, and

:<math>\overline{\mathbf x}\sim N_p(\mu,V/n).</math>

If, moreover, both distributions are nonsingular, it can be shown that

:<math>
\frac{m-p+1}{pm}
T^2\sim F_{p,m-p+1}
</math>
where <math>F</math> is the [[F-distribution]].

[[it:Variabile casuale T-quadrato di Hotelling]]
[[Category:Statistics]]

Hotellingsche T-Quadrat-Verteilung

2005-02-25T09:04:41Z

Robinh: I thought the symbol Q was confusing... and I think m should be n.

In [[statistics]], '''Hotelling's T-square statistic''', named for [[Harold Hotelling]],
is a generalization of [[Student's t distribution|Student's t statistic]] that is used in multivariate hypothesis testing.

Hotelling's T-square statistic is defined as follows. Suppose

:<math>{\mathbf x}_1,\dots,{\mathbf x}_n</math>

are ''p''×1 [[column vector]]s whose entries are [[real number]]s. Let

:<math>\overline{\mathbf x}=(\mathbf{x}_1+\cdots+\mathbf{x}_n)/n</math>

be their [[mean]]. Let the ''p''×''p'' [[positive-definite matrix|nonnegative-definite matrix]]

:<math>{\mathbf W}=\sum_{i=1}^n (\mathbf{x}_i-\overline{\mathbf x})(\mathbf{x}_i-\overline{\mathbf x})'/(n-1)</math>

be their "[[sample variance]]". (The transpose of any matrix ''M'' is denoted above by ''M''′.) Let μ be some known ''p''×1 column vector (in applications a hypothesized value of a population mean). Then Hotelling's T-square statistic is

:<math>
T^2=n(\overline{\mathbf x}-{\mathbf\mu})'{\mathbf W}^{-1}(\overline{\mathbf x}-{\mathbf\mu}).
</math>

Note that <math>T^2</math> may be determined for any matrix of observations.

The reason that this is interesting is that if <math>\mathbf{x}\sim N_p(\mu,{\mathbf V})</math> is a [[random variable]] with a [[multivariate normal distribution]] and <math>{\mathbf W}\sim W_p(n,{\mathbf V})</math> has a [[Wishart distribution]], and <math>{\mathbf x}</math> and <math>{\mathbf W}</math> are [[statistical independence|independent]], then the [[probability distribution]] of <math>T^2</math> is '''Hotelling's T-square distribution'''.

The assumptions above are frequently met in practice: it can be shown that if <math>{\mathbf x}_1,\dots,{\mathbf x}_n\sim N_p(\mu,{\mathbf V})</math>, are independent, and <math>\overline{\mathbf x}</math> and <math>{\mathbf W}</math> are as defined above then <math>{\mathbf W}</math> has a Wishart distribution with ''m'' = ''n'' − 1 degrees of freedom and is independent of <math>\overline{\mathbf x}</math>, and

:<math>\overline{\mathbf x}\sim N_p(\mu,V/n).</math>

If, moreover, both distributions are nonsingular, it can be shown that

:<math>
\frac{m-p+1}{pm}
T^2\sim F_{p,m-p+1}
</math>
where <math>F</math> is the [[F-distribution]].

[[it:Variabile casuale T-quadrato di Hotelling]]
[[Category:Statistics]]

GWR-Klasse 4073

2004-12-28T11:54:58Z

Robinh: /typo*/

The '''Castle class locomotives''' were a group of [[4-6-2]] steam locomotive of the [[Great Western Railway]]. They were originally designed by the railway's Chief Mechanical Engineer, [[Charles Collett| C B Collett]], for working the company's express passenger trains.

==History==
A development of the earlier [[GWR 4000 Class|Star Class]], one hundred and sixty-five (165) were built, over a 25 year span from August [[1923]] to August [[1950]]. They were numbered 4073–4099; 5000–5099; 7000–7037.

In addition, six more were added to the class by rebuilding older locomotives—five [[GWR 4000 Class|Star Class]] locomotives; and the [[Great Western Railway]]'s sole [[4-6-2]] locomotive, number 111 [[GWR 111 The Great Bear|The Great Bear]].

The Castle class was noted for superb performance on The Cheltenham Flyer during the 1930s: on June 6th [[1932]], pulled by [[GWR 5006 Treganna Castle|Treganna Castle]], the train covered 77 miles (124 km) from [[Swindon]] to [[Paddington]] at an average speed of 81.68 miles per hour (131.45 km/h). This world record for steam traction was widely regarded as an astonishing feat.

In 1926, number 5000 [[GWR 5000 Launceston Castle|Launceston Castle]] was loaned to the [[London, Midland and Scottish Railway]] where it ran trials between London to [[Carlisle, England|Carlisle]].
It was rumoured that LMS tried to persuade GWR to build a batch of Castles for use on the West Coast Main Line.

[[Withdrawal]] started in the 1950s; the last to be withdrawn was Clun Castle.

A few survive in preservation as either working examples or static exhibits, including [[GWR 5073 Caerphilly Castle|Caerphilly Castle]], [[GWR 7029 Clun Castle|Clun Castle]], [[GWR 4079 Pendennis Castle|Pendennis Castle]], [[5029 Nunney Castle|Nunney Castle]], and [[GWR 5080 Defiant|Defiant]].

{{msg:stub}}

==Specifications==

Cylinders: 4; 16" diameter, 26" stroke 
Valve gear: inside cylinders – [[Walschaert]]'s; outside cylinders – derived from inside cylinders via rocking bars. 
Valves: Piston Valves 
Boiler Presure: 225 lbf/in² 
Driving wheel diameter: 6' 8.5" 
Tractive Effort: 31,625 lbf 
Engine Weight: 79 tons 17 cwt 
Tender Weight: 46 tons 14 cwt 

==List of engines==
===Engines rebuilt from earlier locomotives===
<table border=1 cellspacing=0 cellpadding=4>
<tr>
<td rowspan=2>Number</td>
<td colspan=2>Name</td>
<td colspan=2>Date</td>
<td rowspan=2>Notes</td>
</tr>
<tr>
<td>First</td>
<td>Second</td>
<td>Rebuilt</td>
<td>Withdrawn</td>
</tr>
<tr>
<td> 111</td>
<td>''[[Viscount Churchill]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>rebuilt from ''[[111 The Great Bear|The Great Bear]]''</td>
</tr>
<tr>
<td>4000</td>
<td>''North Star''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>rebuilt from [[GWR Star class|Star Class]] 4000 ''North Star''</td>
</tr>
<tr>
<td>4009</td>
<td>Shooting Star</td>
<td>100 A1 ''[[Lloyd's of London|Lloyds]]''</td>
<td>?</td>
<td>?</td>
<td>rebuilt from [[GWR Star class|Star Class]] 4009 ''Shooting Star''</td>
</tr>
<tr>
<td>4016</td>
<td>Knight of the Golden Fleece</td>
<td>[[Prince Albert's Light Infantry (Somerset Regiment)|The Somerset Light Infantry (Prince Albert's)]]</td>
<td>?</td>
<td>?</td>
<td>rebuilt from [[GWR Star class|Star Class]] 4016 ''Knight of the Golden Fleece''</td>
</tr>
<tr>
<td>4032</td>
<td>''Queen Alexandra''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>rebuilt from [[GWR Star class|Star Class]] 4032 ''Queen Alexandra''</td>
</tr>
<tr>
<td>4037</td>
<td>''Queen Phillipa''</td>
<td>''[[The South Wales Borderers]]''</td>
<td>?</td>
<td>?</td>
<td>rebuilt from [[GWR Star class|Star Class]] 4037 ''Queen Phillipa''</td>
</tr>
</table>

===New engines built===
<table border=1 cellspacing=0 cellpadding=4>
<tr>
<td rowspan=2>Number</td>
<td colspan=2>Name</td>
<td colspan=2>Date</td>
<td rowspan=2>Notes</td>
</tr>
<tr>
<td>First</td>
<td>Second</td>
<td>Built</td>
<td>Withdrawn</td>
</tr>
<tr>
<td>[[GWR 4073 Caerphilly Castle|4073]]</td>
<td>''[[Caerphilly Castle]]''</td>
<td>—</td>
<td>[[1923]]</td>
<td>?</td>
<td>Preserved</td>
</tr>
<tr>
<td>4074</td>
<td>''Caldicott Castle''</td>
<td>''[[Caldicot Castle]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4075</td>
<td>''[[Cardiff Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4076</td>
<td>''[[Carmarthen Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4077</td>
<td>''[[Chepstow Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4078</td>
<td>''[[Pembroke Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>[[GWR 4079 Pendennis Castle|4079]]</td>
<td>''[[Pendennis Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>Preserved</td>
</tr>
<tr>
<td>4080</td>
<td>''[[Powderham Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4081</td>
<td>''[[Warwick Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4082</td>
<td>''[[Windsor Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4083</td>
<td>''[[Abbotsbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4084</td>
<td>''[[Aberystwyth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4085</td>
<td>''[[Berkeley Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4086</td>
<td>''[[Builth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4087</td>
<td>''[[Cardigan Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4088</td>
<td>''[[Dartmouth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4089</td>
<td>''[[Donnington Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4090</td>
<td>''[[Dorchester Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4091</td>
<td>''[[Dudley Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4092</td>
<td>''[[Dunraven Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4093</td>
<td>''[[Dunster Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4094</td>
<td>''[[Dynevor Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4095</td>
<td>''[[Harlech Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4096</td>
<td>''[[Highclere Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4097</td>
<td>''[[Kenilworth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4098</td>
<td>''[[Kidwelly Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>4099</td>
<td>''[[Kilgerran Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5000</td>
<td>''[[Launceston Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5001</td>
<td>''[[Llandovery Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5002</td>
<td>''[[Ludlow Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5003</td>
<td>''[[Lulworth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5004</td>
<td>''[[Llanstephan Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5005</td>
<td>''[[Manorbier Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5006</td>
<td>''[[Tregenna Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5007</td>
<td>''[[Rougemont Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5008</td>
<td>''[[Raglan Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5009</td>
<td>''[[Shrewsbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5010</td>
<td>''[[Restormal Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5011</td>
<td>''[[Tintagel Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5012</td>
<td>''[[Berry Pomeroy Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5013</td>
<td>''[[Abergavenny Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5014</td>
<td>''[[Goodrich Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5015</td>
<td>''[[Kingswear Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5016</td>
<td>''[[Montgomery Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5017</td>
<td>''[[St Donat's Castle|St Donats Castle]]''</td>
<td>''[[The Gloucestershire Regiment]] [[28th Regiment of Foot|28th]] [[61st Regiment of Foot|61st]]''</td>
<td>?</td>
<td>?</td>
<td>Renamed [[1954]]</td>
</tr>
<tr>
<td>5018</td>
<td>''[[St Mawes Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5019</td>
<td>''[[Treago Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5020</td>
<td>''[[Trematon Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5021</td>
<td>''[[Whittington Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5022</td>
<td>''[[Wigmore Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5023</td>
<td>''[[Brecon Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5024</td>
<td>''[[Carew Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5025</td>
<td>''[[Chirk Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5026</td>
<td>''[[Criccieth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5027</td>
<td>''[[Farleigh Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5028</td>
<td>''[[Llantilio Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>[[GWR 5029 Nunney Castle|5029]]</td>
<td>''[[Nunney Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>Preserved</td>
</tr>
<tr>
<td>5030</td>
<td>''[[Shirburn Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5031</td>
<td>''[[Totnes Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5032</td>
<td>''[[Usk Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5033</td>
<td>''[[Broughton Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5034</td>
<td>''[[Corfe Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5035</td>
<td>''[[Coity Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5036</td>
<td>''[[Lyonshall Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5037</td>
<td>''[[Monmouth Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5038</td>
<td>''[[Morlais Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5039</td>
<td>''[[Rhuddlan Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5040</td>
<td>''[[Stokesay Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5041</td>
<td>''[[Tiverton Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5042</td>
<td>''[[Winchester Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5043</td>
<td>''[[Barbury Castle]]''</td>
<td>''[[Earl of Mount Edgcumbe]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5044</td>
<td>''[[Beverstone Castle]]''</td>
<td>''[[Earl of Dunraven and Mount-Earl|Earl of Dunraven]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5045</td>
<td>''[[Bridgwater Castle]]''</td>
<td>''[[Earl of Dudley]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5046</td>
<td>''[[Clifford Castle]]''</td>
<td>''[[Earl Cawdor]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5047</td>
<td>''[[Compton Castle]]''</td>
<td>''[[Earl of Dartmouth]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5048</td>
<td>''[[Cranbrook Castle]]''</td>
<td>''[[Earl of Devon]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5049</td>
<td>''[[Denbigh Castle]]''</td>
<td>''[[Earl of Plymouth]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5050</td>
<td>''[[Devizes Castle]]''</td>
<td>''[[Earl of St Germans]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>[[GWR 5051 Drysllwyn Castle|5051]]</td>
<td>''[[Drysllwyn Castle]]''</td>
<td>''[[Earl Bathurst]]''</td>
<td>?</td>
<td>?</td>
<td>Preserved. Carries both names (one each side)</td>
</tr>
<tr>
<td>5052</td>
<td>''[[Eastnor Castle]]''</td>
<td>''[[Earl of Radnor]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5053</td>
<td>''[[Bishop's Castle]]''</td>
<td>''[[Earl Cains]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5054</td>
<td>''[[Lamphey Castle]]''</td>
<td>''[[Earl of Ducie]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5055</td>
<td>''[[Lydford Castle]]''</td>
<td>''[[Earl of Eldon]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5056</td>
<td>''[[Ogmore Castle]]''</td>
<td>''[[Earl of Powis]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5057</td>
<td>''[[Penrice Castle]]''</td>
<td>''[[Earl Waldergrave]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5058</td>
<td>''[[Newport Castle]]''</td>
<td>''[[Earl of Clancarty]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5059</td>
<td>''[[Powis Castle]]''</td>
<td>''[[Earl St Aldwyn]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5060</td>
<td>''[[Sarum Castle]]''</td>
<td>''[[Earl of Berkeley]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5061</td>
<td>''[[Sudelery Castle]]''</td>
<td>''[[Earl of Birkenhead]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5062</td>
<td>''[[Tenby Castle]]''</td>
<td>''[[Earl of Shaftesbury]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5063</td>
<td>''[[Thornbury Castle]]''</td>
<td>''[[Earl Baldwin of Bewdley|Earl Baldwin]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5064</td>
<td>''[[Tretower Castle]]''</td>
<td>''[[Bishop's Castle]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5065</td>
<td>''[[Upton Castle]]''</td>
<td>''[[Newport Castle]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5066</td>
<td>''[[Wardour Castle]]''</td>
<td>''[[Sir Felix Pole]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5067</td>
<td>''[[St Fagans Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5068</td>
<td>''[[Beverston Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5069</td>
<td>''[[Isambard Kingdom Brunel]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5070</td>
<td>''[[Daniel Gooch|Sir Daniel Gooch]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5071</td>
<td>''[[Clifford Castle]]''</td>
<td>''[[Supermarine Spitfire|Spitfire]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5072</td>
<td>''[[Compton Castle]]''</td>
<td>''[[Hawker Hurricane|Hurricane]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5073</td>
<td>''[[Cranbrook Castle]]''</td>
<td>''[[Bristol Blenheim|Blenheim]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5074</td>
<td>''[[Denbigh Castle]]''</td>
<td>''[[Handley Page Hampden|Hampden]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5075</td>
<td>''[[Devizes Castle]]''</td>
<td>''[[Vickers Wellington|Wellington]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5076</td>
<td>''[[Drysllwyn Castle]]''</td>
<td>''[[Gloster Gladiator|Gladiator]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5077</td>
<td>''[[Eastnor Castle]]''</td>
<td>''[[Fairey Battle]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5078</td>
<td>''[[Lamphey Castle]]''</td>
<td>''[[Bristol Beaufort|Beaufort]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5079</td>
<td>''[[Lydford Castle]]''</td>
<td>''[[Westland Lysander|Lysander]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>[[GWR 5080 Defiant|5080]]</td>
<td>''[[Ogmore Castle]]''</td>
<td>''[[Boulton Paul Defiant|Defiant]]''</td>
<td>?</td>
<td>?</td>
<td>Preserved</td>
</tr>
<tr>
<td>5081</td>
<td>''[[Penrice Castle]]''</td>
<td>''[[Lockheed Hudson]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5082</td>
<td>''[[Powis Castle]]''</td>
<td>''[[Fairey Swordfish|Swordfish]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5083</td>
<td>''[[Bath Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5084</td>
<td>''[[Reading Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5085</td>
<td>''[[Evesham Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5086</td>
<td>''[[Viscount Horne]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5087</td>
<td>''[[Tintern Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5088</td>
<td>''[[Llantony Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5089</td>
<td>''[[Westminster Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5090</td>
<td>''[[Neath Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5091</td>
<td>''[[Cleve Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5092</td>
<td>''[[Tresco Abbey]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>?rebuilt from [[GWR Star class|Star Class]]?</td>
</tr>
<tr>
<td>5093</td>
<td>''[[Upton Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5094</td>
<td>''[[Tretower Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5095</td>
<td>''[[Barbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5096</td>
<td>''[[Bridgwater Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5097</td>
<td>''[[Sarum Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5098</td>
<td>''[[Clifford Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>5099</td>
<td>''[[Compton Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7000</td>
<td>''[[Viscount Portal]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7001</td>
<td>''[[Denbigh Castle]]''</td>
<td>''[[Sir James Milne]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7002</td>
<td>''[[Devizes Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7003</td>
<td>''[[Elmley Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7004</td>
<td>''[[Eastnor Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7005</td>
<td>''[[Lamphey Castle]]''</td>
<td>''[[Sir Edward Elgar]]''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7006</td>
<td>''[[Lydford Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7007</td>
<td>''[[Ogmore Castle]]''</td>
<td>''Great Western''</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7008</td>
<td>''[[Swansea Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7009</td>
<td>''[[Althelney Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7010</td>
<td>''[[Avondale Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7011</td>
<td>''[[Banbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7012</td>
<td>''[[Barry Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7013</td>
<td>''[[Bristol Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7014</td>
<td>''[[Caerhays Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7015</td>
<td>''[[Carn Brea Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7016</td>
<td>''[[Chester Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7017</td>
<td>''[[George Jackson Churchward|G. J. Churchward]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7018</td>
<td>''[[Drysllwyn Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7019</td>
<td>''[[Fowey Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7020</td>
<td>''[[Gloucester Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7021</td>
<td>''[[Haverfordwest Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7022</td>
<td>''[[Hereford Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7023</td>
<td>''[[Penrice Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7024</td>
<td>''[[Powis Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7025</td>
<td>''[[Sudeley Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7026</td>
<td>''[[Tenby Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7027</td>
<td>''[[Thornbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7028</td>
<td>''[[Cadbury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7029</td>
<td>''[[Clun Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td>Last ''Castle'' to be [[withdrawn]]. Preserved</td>
</tr>
<tr>
<td>7030</td>
<td>''[[Cranbrook Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7031</td>
<td>''[[Cromwell's Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7032</td>
<td>''[[Denbigh Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7033</td>
<td>''[[Hartlebury Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7034</td>
<td>''[[Ince Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7035</td>
<td>''[[Ogmore Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7036</td>
<td>''[[Taunton Castle]]''</td>
<td>—</td>
<td>?</td>
<td>?</td>
<td></td>
</tr>
<tr>
<td>7037</td>
<td>''[[Swindon]]''</td>
<td>—</td>
<td>[[1950]]</td>
<td>?</td>
<td></td>
</tr>
</table>

[[Category:Locomotives]]
[[Category:4-6-0 locomotives]]

Clun Castle

2004-11-16T08:28:20Z

Robinh: disamb

'''Clun Castle''', is a now ruined [[castle]] in the small town of [[Clun]], [[Shropshire]].
{{substub}}

"Clun Castle" may also refer to [[7029 Clun Castle]], a [[GWR Castle class|Castle Class locomotive]].


[[Category:Shropshire]]
[[Category:Castles in England]]
[[Category:English Heritage]]

Hotellingsche T-Quadrat-Verteilung

2004-08-27T13:18:58Z

Robinh:

Hotellingsche T-Quadrat-Verteilung

2004-08-27T13:14:20Z

Robinh:

In [[statistics]], '''Hotelling's T-square distribution''', named for [[Harold Hotelling]],
is a generalization of [[Student's t distribution]] that is used in multivariate hypothesis testing.

If
:<math>
T^2=m({\mathbf x}-{\mathbf\mu})'{\mathbf W}^{-1}({\mathbf x}-{\mathbf\mu})
</math>
where <math>x\sim N_p(\mu,{\mathbf V})</math> is a random variable with a [[multivariate Gaussian distribution]] and <math>{\mathbf W}\sim W_p(m,{\mathbf V})</math> has a [[Wishart distribution]],
then <math>T^2</math> is called '''Hotelling's T-square statistic'''.

If <math>x</math> is independent of <math>{\mathbf W}</math>, and both distributions are nonsingular, it can be shown that

:<math>
\frac{m-p+1}{pm}
T^2\sim F_{p,m-p+1}
</math>
where <math>F</math> is the [[F-distribution]].

Graue Schmiere

2004-06-10T11:54:07Z

Robinh: famous goo quotes

'''Grey goo''' refers, usually in a [[science fiction]]al context, to a hypothetical human [[extinction]] event involving [[nanotechnology]], in which out-of-control self-replicating robots ([[Von Neumann machine|Von Neumann machines]]) consume all life on [[Earth]] while building more of themselves (a scenario known as [[ecophagy]]). In a worst-case scenario, all of the matter in the [[Milky Way|Galaxy]] could be turned into goo (with "goo" meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear goo-like), killing the Galaxy's residents. The disaster could result from an accidental [[mutation]] in a self-replicating nanomachine used for other purposes, or possibly from a deliberate [[doomsday device]].

==Precautions==

Assuming a nanotechnological replicator is capable of causing a grey goo disaster, safety precautions might include programming them to stop reproducing after a certain number of generations, or designing them to require a rare material that would be sprayed on the construction site before their release. However, it should be noted that there are reasons to believe that nanotechnology might not be capable of creating grey goo at all.

==Limitations on grey goo activity==

The primary limitation on even arbitrarily sophisticated nanotechnology which could prevent a runaway grey goo reaction is the lack of a sufficient source of energy. A nanomachine wouldn't be able to get much energy out of eating inorganic matter such as rocks because, aside from a few exceptions ([[coal]], for example) it's mostly well-oxidized and sitting in a free-energy minimum.

This means that the nanobots would be competing with natural life forms for organic matter or sunlight, life forms which have been evolving for over four billion years to optimize their ability to compete for these resources. If the nanomachine is itself composed of organic molecules, then it might even find itself being preyed upon by preexisting [[bacteria]] and other natural life forms. If they are built of inorganic compounds or make much use of elements that are not generally found in living matter, then they will need to use much of their metabolic output to fighting [[entropy]] as they purify (reduce sand to silicon, for instance) and synthesize the necessary building blocks. Grey goo may only be possible in an environment which lacks indigenous life to compete with it for indigenous resources. However, some proponents of nanotechnology argue that it is possible nanomachines could be developed that are able to outcompete natural life through the use of novel chemical processes that life would be unable to develop via natural evolution due to [[irreducible complexity]].

Some also consider it highly unlikely that an artificial self-replicator could spontaneously evolve in a manner that could present an immediate threat. A traditional response to the grey goo scenario in nanotechnology discussions: "How likely is it that your car could spontaneously mutate into a wild car, run off road and live in the forest off of tree sap?"

==Other varieties==

Grey goo has several cousins, differentiated by their colors and raisons d'être. Most of these are not as commonly referred to as grey goo, however, and the definitions are informal:
* ''Red Goo'' is goo unleashed intentionally by [[terrorism|terrorists]], a doomsday weapon, or a private individual who wishes to commit [[suicide]] with a bang.
* ''Khaki Goo'' is goo intended by the military to wipe out somebody else's continent, planet, etc.
* ''Golden Goo'' is the backfiring of a get-rich-quick scheme to assemble gold or other economically valuable substance. The details are left to the imagination.
* ''Blue Goo'' is goo deliberately released in order to stop some other type of grey goo. It might well be the only solution to such a disaster, and would hopefully be better controlled than the original goo.
* ''Pink Goo'' is humanity. It replicates relatively slowly, but will nevertheless fill any amount of space given enough time. Some people think that allowing the entire Galaxy to get filled with Pink Goo would be the ultimate crime, to be stopped at any cost.
* ''Green Goo'' is goo deliberately released, for example by ecoterrorists, in order to stop the spread of Pink Goo, either by sterilization or simply by digesting the pink goo. Some form of this, along with an antidote available to the selected few, has been suggested as a strategy for achieving zero population growth.

==Famous quotes==

* "We cannot afford certain types of accidents", [[Eric Drexler]], [[Engines of creation]]
* "I wish I had never used the term 'grey goo' " Drexler, [[Nature (journal)|Nature]] 10 June 2004

==Bibliography==

* Greg Bear, <cite>Blood Music</cite>, the classic sci-fi novel about ecophagy. Arguably it is a Green Goo-type.