Sea Shell Chalk

This is a piece i have been working on the last few weeks, in which i have been producing small balls of chalk from crushing sea shells. These balls are laid out along a chalk map of the Great Barrier Reef, and the viewer is invited to take them away and return them to the ocean in bags with information on them also acting as my business card.

Buy people removing the chalk, I am trying to make a statement about the disappearance of reef systems, with only a ghostly trace of the Barrier Reef left behind. At the same time the act of putting these balls of natural calcium carbonate back into the sea, has implications of a nullifying effect on the rising PH levels of of the ocean, one of the major threats of coral reef degradation.


These jars are also an idea i have been playing about with, where plaster casts of corals are held in overly acidic sea water, the result of which is the dissolving of the casts over a period of a couple of weeks, being left with a layer of sediment.

Natural History Museum

I recently payed a visit to the Natural History Museum London as part of my research, only to discover the newly constructed Darwin Centre, who's premises houses large numbers of marine specimens along with research facilities, catalogues, examples of plants, and land invertebrates. The centre is also home to an interactive wall, highlighting the dangers coral reefs face due to climate change, covering ocean acidification, changes in ocean currents and the transference of carbon between land and sea. The piece is highly colourful and extremely intriguing inviting the viewer to explore the reef whilst imposing the message that these Eco systems are in trouble.

Coral skeleton prints

Tubastraea aurea

Euphyllia ancora

Japanese Knotweed. www.news.bbc.co.uk

A tiny Japanese insect that could help the fight against an aggressive superweed has been given the go-ahead for a trial release in England.

Since Japanese knotweed was introduced to the UK it has rapidly spread, and the plant currently costs over £150m a year to control and clear.

But scientists say a natural predator in the weed's native home of Japan could also help to control it here.

The insect will initially be released in a handful of sites this spring.

This is the first time that biocontrol - the use of a "natural predator" to control a pest - has been used in the EU to fight a weed.

Wildlife Minister Huw Irranca-Davies said: "These tiny insects, which naturally prey on Japanese Knotweed, will help free local authorities and industry from the huge cost of treating and killing this devastating plant."

Alien invaders

Japanese knotweed was introduced to the UK by the Victorians as an ornamental plant, but it soon escaped from gardens and began its rampant spread throughout the UK.

It grows incredibly quickly - more than one metre a month - and rapidly swamps any other vegetation in its path.

It is so hardy that it can burst through tarmac and concrete, causing costly damage to pavements, roads and buildings.




Green Room: Hailing the arrival of alien predators
But removal is difficult and expensive; new estimates suggest it costs the UK economy £150m a year.

However, in Japan, the plant is common but does not rage out of control like it does in the UK, thanks to the natural predators that keep it in check.

Scientists at Cabi - a not-for-profit agricultural research organisation - used this as their starting point to track down a potential knotweed solution.

They looked at the superweed's natural predators - nearly 200 species of plant-eating insects and about 40 species of fungi - with the aim of finding one with an appetite for Japanese knotweed and little else.

After testing their candidates on 90 different UK plant species, including plants closely related to Japanese knotweed such as bindweeds and important crops and ornamental species, they discovered a psyllid called Aphalara itadori was the best control agent.

The little insect feeds on the sap of the superweed, stunting its growth.

Dr Dick Shaw, the lead researcher on the project from Cabi, told BBC News: "Safety is our top priority. We are lucky that we do have an extremely specific agent - it just eats invasive knotweeds."


This timelapse footage shows Japanese knotweed growing more than 1m-tall (3ft) in just three weeks

Following peer review by the Advisory Committee on Releases to the Environment and a public consultation, the UK government has now given the go-ahead for release of Aphalara itadori, under licence, in England.

The Welsh Assembly is expected to announce its decision on the psyllid soon.

The insects will initially be released on a handful of sites.


These will be isolated and, in addition to as having the superweed present, will also have UK species that are closely related to Japanese knotweed planted there to check that the psyllid only targets the invasive species.

Dr Shaw said: "In the early stages, a contingency plan is in place so that should, in the unlikely event, any unintended consequences be detected, we will be able to do something about it.

"Insecticide and herbicide treatment will be on standby for rapid response."

If this phase is successful, the insect will be released at further sites, where it will undergo an intensive monitoring programme over the next five years.

Dr Shaw said: "On the localised sites, I would expect to see damaged knotweed this season.

"However, biocontrol is a long-term strategy - it could take five to 10 years to have a real impact."

The government believes that if the plan is successful it will reduce the costs to the building and engineering industries of clearing the plant.

However, some critics say that it is impossible to be certain that the Japanese insect will only target the superweed and could attack other species once in the wild.


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Is there Japanese Knotweed growing in your area? Has it caused damage? Should we use insects to control it? Send us your comments and your pictures of Japanese knotweed.

Aquarium Corals, Eric H. Borneman 2001, T.F.H publications, Inc, ISBN 1-890087-47-5

Borneman is an aquarist and researcher and has written periodicals, books, and speaks frequently at aquarist and scientific conferences. Aquarium Corals is seen to be one of the definitive guides to coral husbandry amongst peers, scientists and hobbyists alike.

Although entitled “Aquarium” the book is far from just a guide to keeping corals in the home. It includes taxonomic identification (scientific and general) of pretty much every coral in known existence, with each species natural and captive requirements. It informs the reader on water chemistry around the world, history, conservation, diseases, breeding and propagation, feeding, light waves, how to set up a captive system from start to finish, and is full of detailed scientific information on coral make up from polyp structure to the microscopic level of zooxanthellae. If you need to know anything about corals I can pretty much guarantee the information you require will be in this book. To coincide with all this information are hundreds of high quality images capturing the essence of the reef and its individual inhabitants.

Aquarium Corals has been one of my main sources of information on corals and reef systems. Throughout my coral keeping period this book proved to be invaluable. As far as relating to my practice, it has provided me with the insight to just how complex and fragile our reefs are. It seems to me plainly obvious the huge effects climate change will have, this book points out that even the smallest fluctuations in aquarium stability will have fairly disastrous effects, let alone on a whole ocean. However the conservation chapter in this book is sparse, and doesn’t contain the information I would like to see on the effects of climate change on the reef. It does go into diseases, but doesn’t directly relate the two like other sources have, perhaps due to the date of publication and reluctance to acknowledge global warming in America.

Artful Ecologies, Art Nature and Environment Conference 2006, RANE research cluster and University College Falmouth, Edited Daro Montag, 2008

Susan Boafo "Speaking With The Sun"

Artful Ecologies is a publication to coincide with the RANE (research in art, nature and environment) conference Artful Ecologies held in Falmouth, Cornwall 2006 led by Daro Montag. The conference was held to look at the global crisis we face as a result of climate change, and the role of the artist within the subject. The book includes a collection of papers submitted by speakers, and accounts of work produced by artists, largely in the local environment.

Speakers included Tim Collins, Reiko Goto, John K. Grande, Stacy Levy, F. David Peat, Alan Sonfist, George Steinmann and Suzi Gablik who was unable to attend but provided a paper for the conference. Each of the speakers contributed views on art into today’s society, focusing on our environment, and delving into the subjects of spirituality, symbolism and the world of the transdiscipinary.

Artists include Stephen Turner, Jane Atkinson, Susan Boafo, Georg Dietzler, Martin Prothero, Dave Pritchard, Stacy Righton, Andy Webster, Jon Bird and Kerry Morrison. Similarly the work produced comes from the transdicsiplinarity and multidisciplinary of art, science and nature. Processes vary from data collection of geology and water properties, through to natural phenomenon and electro chemistry, each producing visual interpritations from the information gathered.

My own practice is currently residing in the transdisciplinary of art nature and science. This book is of particular interest to me, giving an insight into practises and processes used by artists working within my field. It also provides a range of areas for further research and artists to look at.

Hyperbolic geometry
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Lines through a given point P and asymptotic to line R.
A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines.In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid.

Because there is no precise hyperbolic analogue to Euclidean parallel lines, the hyperbolic use of parallel and related terms varies among writers. In this article, the two limiting lines are called asymptotic and lines sharing a common perpendicular are called ultraparallel; the simple word parallel may apply to both.

A characteristic property of hyperbolic geometry is that the angles of a triangle add to less than a straight angle (half circle). In the limit as the vertices go to infinity, there are even ideal hyperbolic triangles in which all three angles are 0°.

Contents [hide]
1 Non-intersecting lines
2 Triangles
3 Circles, Spheres, and Balls
4 History
5 Models of the hyperbolic plane
6 Visualizing hyperbolic geometry
7 Gyrovector spaces
8 See also
9 Notes
10 References
11 External links


[edit] Non-intersecting lines
An interesting property of hyperbolic geometry follows from the occurrence of more than one parallel line through a point P: there are two classes of non-intersecting lines. Let B be the point on l such that the line PB is perpendicular to l. Consider the line x through P such that x does not intersect l, and the angle θ between PB and x counterclockwise from PB is as small as possible; i.e., any smaller angle will force the line to intersect l. This is called an asymptotic line in hyperbolic geometry. Symmetrically, the line y that forms the same angle θ between PB and itself but clockwise from PB will also be asymptotic. x and y are the only two lines asymptotic to l through P. All other lines through P not intersecting l, with angles greater than θ with PB, are called ultraparallel (or disjointly parallel) to l. Notice that since there are an infinite number of possible angles between θ and 90 degrees, and each one will determine two lines through P and disjointly parallel to l, there exist an infinite number of ultraparallel lines.

Thus we have this modified form of the parallel postulate: In hyperbolic geometry, given any line l, and point P not on l, there are exactly two lines through P which are asymptotic to l, and infinitely many lines through P ultraparallel to l.

The differences between these types of lines can also be looked at in the following way: the distance between asymptotic lines shrinks toward zero in one direction and grows without bound in the other; the distance between ultraparallel lines (eventually) increases in both directions. The ultraparallel theorem states that there is a unique line in the hyperbolic plane that is perpendicular to each of a given pair of ultraparallel lines.

In Euclidean geometry, the angle of parallelism is a constant; that is, any distance between parallel lines yields an angle of parallelism equal to 90°. In hyperbolic geometry, the angle of parallelism varies with the Π(p) function. This function, described by Nikolai Ivanovich Lobachevsky, produces a unique angle of parallelism for each distance . As the distance gets shorter, Π(p) approaches 90°, whereas with increasing distance Π(p) approaches 0°. Thus, as distances get smaller, the hyperbolic plane behaves more and more like Euclidean geometry. Indeed, on small scales compared to , where is the (constant) Gaussian curvature of the plane, an observer would have a hard time determining whether he is in the Euclidean or the hyperbolic plane.

[edit] Triangles
Distances in the hyperbolic plane can be measured in terms of a unit of length , analogous to the radius of the sphere in spherical geometry. Using this unit of length a theorem in hyperbolic geometry can be stated which is analogous to the Pythagorean theorem. If are the legs and is the hypotenuse of a right triangle all measured in this unit then:


The cosh function is a hyperbolic function which is an analog of the standard cosine function. All six of the standard trigonometric functions have hyperbolic analogs. In trigonometric relations involving the sides and angles of a hyperbolic triangle the hyperbolic functions are applied to the sides and the standard trigonometric functions are applied to the angles. For example the law of sines for hyperbolic triangles is:



For more of these trigonometric relationships see hyperbolic triangles.

Unlike Euclidean triangles whose angles always add up to 180 degrees or π radians the sum of the angles of a hyperbolic triangle is always strictly less than 180 degrees. The difference is sometimes referred to as the defect. The area of a hyperbolic triangle is given by its defect multiplied by R2 where . As a consequence all hyperbolic triangles have an area which is less than πR2. The area of an ideal hyperbolic triangle is equal to this maximum.

As in spherical geometry the only similar triangles are congruent triangles.

[edit] Circles, Spheres, and Balls
In hyperbolic geometry the circumference of a circle is greater than times the diameter. It is in fact equal to


where is the radius of the circle. Its area is


The volume of a sphere is


where again is the radius and its surface area is

.
For the the surface of a sphere in n dimensional space the corresponding expression is


where is full the n dimensional solid angle:

.
The denominator uses the gamma function.

The volume of the ball in n dimensional space is:

.
[edit] History
A number of geometers made attempts to prove the parallel postulate by assuming its negation and trying to derive a contradiction, including Proclus, Ibn al-Haytham (Alhacen), Omar Khayyám,[1] Nasir al-Din al-Tusi, Witelo, Gersonides, Alfonso, and later Giovanni Gerolamo Saccheri, John Wallis, Johann Heinrich Lambert, and Legendre.[2] Their attempts failed, but their efforts gave birth to hyperbolic geometry.

The theorems of Alhacen, Khayyam and al-Tusi on quadrilaterals, including the Ibn al-Haytham–Lambert quadrilateral and Khayyam–Saccheri quadrilateral, were the first theorems on hyperbolic geometry. Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo, Gersonides, Alfonso, John Wallis and Saccheri.[3]

In the 18th century, Johann Heinrich Lambert introduced the hyperbolic functions and computed the area of a hyperbolic triangle.

In the nineteenth century, hyperbolic geometry was extensively explored by János Bolyai and Nikolai Ivanovich Lobachevsky, after whom it sometimes is named. Lobachevsky published in 1830, while Bolyai independently discovered it and published in 1832. Carl Friedrich Gauss also studied hyperbolic geometry, describing in a 1824 letter to Taurinus that he had constructed it, but did not publish his work. In 1868, Eugenio Beltrami provided models of it, and used this to prove that hyperbolic geometry was consistent if Euclidean geometry was.

The term "hyperbolic geometry" was introduced by Felix Klein in 1871.[4]

For more history, see article on non-Euclidean geometry, and the references Coxeter and Milnor.

[edit] Models of the hyperbolic plane
There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disc model, the Poincaré half-plane model, and the Lorentz model, or hyperboloid model. These models define a real hyperbolic space which satisfies the axioms of a hyperbolic geometry. Despite the naming, the two disc models and the half-plane model were introduced as models of hyperbolic space by Beltrami, not by Poincaré or Klein.


Poincaré disc model of great rhombitruncated {3,7} tiling
Lines through a given point and asymptotic to a given line, illustrated in the Poincaré disc modelThe Klein model, also known as the projective disc model and Beltrami-Klein model, uses the interior of a circle for the hyperbolic plane, and chords of the circle as lines.
This model has the advantage of simplicity, but the disadvantage that angles in the hyperbolic plane are distorted.
The distance in this model is the cross-ratio, which was introduced by Arthur Cayley in projective geometry.
The Poincaré disc model, also known as the conformal disc model, also employs the interior of a circle, but lines are represented by arcs of circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.
The Poincaré half-plane model takes one-half of the Euclidean plane, as determined by a Euclidean line B, to be the hyperbolic plane (B itself is not included).
Hyperbolic lines are then either half-circles orthogonal to B or rays perpendicular to B.
Both Poincaré models preserve hyperbolic angles, and are thereby conformal. All isometries within these models are therefore Möbius transformations.
The half-plane model is identical (at the limit) to the Poincaré disc model at the edge of the disc
The Lorentz model or hyperboloid model employs a 2-dimensional hyperboloid of revolution (of two sheets, but using one) embedded in 3-dimensional Minkowski space. This model is generally credited to Poincaré, but Reynolds (see below) says that Wilhelm Killing and Karl Weierstrass used this model from 1872.
This model has direct application to special relativity, as Minkowski 3-space is a model for spacetime, suppressing one spatial dimension. One can take the hyperboloid to represent the events that various moving observers, radiating outward in a spatial plane from a single point, will reach in a fixed proper time. The hyperbolic distance between two points on the hyperboloid can then be identified with the relative rapidity between the two corresponding observers.
[edit] Visualizing hyperbolic geometry

A collection of crocheted hyperbolic planes, in imitation of a coral reef, by the Institute For FiguringM. C. Escher's famous prints Circle Limit III and Circle Limit IV illustrate the conformal disc model quite well. In both one can see the geodesics. (In III the white lines are not geodesics, but hypercycles, which run alongside them.) It is also possible to see quite plainly the negative curvature of the hyperbolic plane, through its effect on the sum of angles in triangles and squares.

For example, in Circle Limit III every vertex belongs to three triangles and three squares. In the Euclidean plane, their angles would sum to 450°; i.e., a circle and a quarter. From this we see that the sum of angles of a triangle in the hyperbolic plane must be smaller than 180°. Another visible property is exponential growth. In Circle Limit IV, for example, one can see that the number of demons within a distance of n from the center rises exponentially. The demons have equal hyperbolic area, so the area of a ball of radius n must rise exponentially in n.

There are several ways to physically realize a hyperbolic plane (or approximation thereof). A particularly well-known paper model based on the pseudosphere is due to William Thurston. The art of crochet has been used to demonstrate hyperbolic planes with the first being made by Daina Taimina.[5] In 2000, Keith Henderson demonstrated a quick-to-make paper model dubbed the "hyperbolic soccerball".

[edit] Gyrovector spaces
Main article: Gyrovector space
Gyrovector spaces are a generalization of vector spaces. Gyrovectors can be used to unify the study of Euclidean and hyperbolic geometry. Soon after special relativity was developed in 1905 it was realized that Einstein's velocity addition law could be interpreted in terms of hyperbolic geometry. The set of admissible velocities forms a hyperbolic space. In general relativistic velocity addition is non-associative. The gyrovector approach tackles the issue by introducing the concepts of gyroassociativity and gyrocommutativity. The use of the prefix gyro comes from Thomas gyration which is the mathematical abstraction of Thomas precession into an operator called a gyrator and denoted gyr.

The Bloch vector of quantum computation is not really a vector but can be seen as an example of a gyrovector and the geometry of quantum computation is really hyperbolic geometry and its algebra is the algebra of gyrovector spaces.

Different models of hyperbolic geometry are regulated by different gyrovector spaces. The Beltrami-Klein model is regulated by gyrovector spaces based on relativistic velocity addition.[6] The Poincaré ball model is regulated by gyrovector spaces based on Möbius transformations.[7]

[edit] See also