Wikipedia articles of interest
For anybody who does not know, there’s a simple version of wikipedia available, which tries to keep things as simple as possible so as many people as possible can understand what’s going on in those articles. The article I link to here is not from the simple wikipedia, but it is an in some sense ‘corresponding’ attempt by the wikipedia community to make general relativity more accessible to ‘the masses’. It’s a featured article, and there are lots of links. I read the main article on the subject matter (also featured) first, which is probably the wrong reading order if you plan on reading both.
“In mathematics, a transcendental number is a (possibly complex) number that is not algebraic—that is, it is not a root of a non-zero polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e. Though only a few classes of transcendental numbers are known (in part because it can be extremely difficult to show that a given number is transcendental), transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers are countable while the sets of real and complex numbers are both uncountable. All real transcendental numbers are irrational, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental; e.g., the square root of 2 is irrational but not a transcendental number, since it is a solution of the polynomial equation x2 − 2 = 0. […]
The set of transcendental numbers is uncountably infinite. […] Any non-constant algebraic function of a single variable yields a transcendental value when applied to a transcendental argument. […] The non-computable numbers are a strict subset of the transcendental numbers.
All Liouville numbers are transcendental, but not vice versa.”
The article has more. Here’s a (very technical!) related article about the Lindemann-Weierstrass theorem.
iii. Diamond (featured).
“In mineralogy, diamond (from the ancient Greek αδάμας – adámas “unbreakable”) is a metastable allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions. Diamond is renowned as a material with superlative physical qualities, most of which originate from the strong covalent bonding between its atoms. In particular, diamond has the highest hardness and thermal conductivity of any bulk material. Those properties determine the major industrial application of diamond in cutting and polishing tools and the scientific applications in diamond knives and diamond anvil cells.
Diamond has remarkable optical characteristics. Because of its extremely rigid lattice, it can be contaminated by very few types of impurities, such as boron and nitrogen. Combined with wide transparency, this results in the clear, colorless appearance of most natural diamonds. Small amounts of defects or impurities (about one per million of lattice atoms) color diamond blue (boron), yellow (nitrogen), brown (lattice defects), green (radiation exposure), purple, pink, orange or red. Diamond also has relatively high optical dispersion (ability to disperse light of different colors), which results in its characteristic luster. Excellent optical and mechanical properties, notably unparalleled hardness and durability, make diamond the most popular gemstone.
Most natural diamonds are formed at high temperature and pressure at depths of 140 to 190 kilometers (87 to 120 mi) in the Earth’s mantle. Carbon-containing minerals provide the carbon source, and the growth occurs over periods from 1 billion to 3.3 billion years (25% to 75% of the age of the Earth). Diamonds are brought close to the Earth′s surface through deep volcanic eruptions by a magma, which cools into igneous rocks known as kimberlites and lamproites. Diamonds can also be produced synthetically in a high-pressure high-temperature process which approximately simulates the conditions in the Earth mantle. […] The rate at which temperature changes with increasing depth into the Earth varies greatly in different parts of the Earth. In particular, under oceanic plates the temperature rises more quickly with depth, beyond the range required for diamond formation at the depth required. The correct combination of temperature and pressure is only found in the thick, ancient, and stable parts of continental plates where regions of lithosphere known as cratons exist. Long residence in the cratonic lithosphere allows diamond crystals to grow larger. […]
Diamond-bearing rock is carried from the mantle to the Earth’s surface by deep-origin volcanic eruptions. The magma for such a volcano must originate at a depth where diamonds can be formed […] (three times or more the depth of source magma for most volcanoes). This is a relatively rare occurrence. These typically small surface volcanic craters extend downward in formations known as volcanic pipes. […] The magma in volcanic pipes is usually one of two characteristic types, which cool into igneous rock known as either kimberlite or lamproite. The magma itself does not contain diamond; instead, it acts as an elevator that carries deep-formed rocks (xenoliths), minerals (xenocrysts), and fluids upward. […]
Diamond is the hardest known natural material on the Mohs scale of mineral hardness, where hardness is defined as resistance to scratching and is graded between 1 (softest) and 10 (hardest). Diamond has a hardness of 10 (hardest) on this scale. Diamond’s hardness has been known since antiquity, and is the source of its name.
Diamond hardness depends on its purity, crystalline perfection and orientation: hardness is higher for flawless, pure crystals oriented to the <111> direction (along the longest diagonal of the cubic diamond lattice). [….] Somewhat related to hardness is another mechanical property toughness, which is a material’s ability to resist breakage from forceful impact. The toughness of natural diamond has been measured as 7.5–10 MPa·m1/2. This value is good compared to other gemstones, but poor compared to most engineering materials. […]
The production and distribution of diamonds is largely consolidated in the hands of a few key players, and concentrated in traditional diamond trading centers, the most important being Antwerp, where 80% of all rough diamonds, 50% of all cut diamonds and more than 50% of all rough, cut and industrial diamonds combined are handled. This makes Antwerp a de facto “world diamond capital”. Another important diamond center is New York City, where almost 80% of the world’s diamonds are sold, including auction sales. […]
De Beers and its subsidiaries own mines that produce some 40% of annual world diamond production. For most of the 20th century over 80% of the world’s rough diamonds passed through De Beers, but in the period 2001–2009 the figure has decreased to around 45%. De Beers sold off the vast majority of its diamond stockpile in the late 1990s – early 2000s and the remainder largely represents working stock (diamonds that are being sorted before sale). […]
80% of mined diamonds (equal to about 135,000,000 carats (27,000 kg) annually), unsuitable for use as gemstones, are destined for industrial use. In addition to mined diamonds, synthetic diamonds found industrial applications almost immediately after their invention in the 1950s; another 570,000,000 carats (110,000 kg) of synthetic diamond is produced annually for industrial use. Approximately 90% of diamond grinding grit is currently of synthetic origin. […] Roughly 49% of diamonds originate from Central and Southern Africa, although significant sources of the mineral have been discovered in Canada, India, Russia, Brazil, and Australia.”
iv. Gropecunt Lane (featured – NSFW?).
“Gropecunt Lane /ˈɡroʊpkʌnt ˈleɪn/ was a street name found in English towns and cities during the Middle Ages, believed to be a reference to the prostitution centred on those areas; it was normal practice for a medieval street name to reflect the street’s function or the economic activity taking place within it. Gropecunt, the earliest known use of which is in about 1230, appears to have been derived as a compound of the words grope and cunt. Streets with that name were often in the busiest parts of medieval towns and cities, and at least one appears to have been an important thoroughfare. […]
Although some medieval street names such as Addle Street (stinking urine, or other liquid filth; mire) and Fetter Lane (once Fewterer, meaning “idle and disorderly person”) have survived, others have been changed in deference to contemporary attitudes. Sherborne Lane in London was in 1272–73 known as Shitteborwelane, later Shite-burn lane and Shite-buruelane (possibly due to nearby cesspits). Pissing Alley, one of several identically named streets whose names survived the Great Fire of London, was called Little Friday Street in 1848, before being absorbed into Cannon Street in 1853–54. Petticoat Lane, the meaning of which is sometimes misinterpreted as related to prostitution, was in 1830 renamed as Middlesex Street, following complaints about the street being named after an item of underwear. […] As the most ubiquitous and explicit example of such street names, with the exception of Shrewsbury and possibly Newcastle (where a Grapecuntlane was mentioned in 1588) the use of Gropecunt seems to have fallen out of favour by the 14th century. Its steady disappearance from the English vernacular may have been the result of a gradual cleaning-up of the name; Gropecuntelane in 13th-century Wells became Grope Lane, and then in the 19th century, Grove Lane.”
v. Mary Toft (featured).
“Mary Toft (née Denyer; c. 1701–1763), also spelled Tofts, was an English woman from Godalming, Surrey, who in 1726 became the subject of considerable controversy when she tricked doctors into believing that she had given birth to rabbits.”
If that introduction doesn’t make you want to read this article, we probably can’t be friends… Here’s the rest of the introduction:
“In 1726 Toft became pregnant, but following her reported fascination with the sighting of a rabbit, she miscarried. Her claim to have given birth to various animal parts prompted the arrival of John Howard, a local surgeon, who investigated the matter. He delivered several pieces of animal flesh and duly notified other prominent physicians, which brought the case to the attention of Nathaniel St. André, surgeon to the Royal Household of King George I. St. André concluded that Toft’s case was genuine but the king also sent surgeon Cyriacus Ahlers, who remained sceptical. By then quite famous, Toft was brought to London and studied at length, where under intense scrutiny and producing no more rabbits she confessed to the hoax, and was subsequently imprisoned as a fraud.
The resultant public mockery created panic within the medical profession and ruined the careers of several prominent surgeons. The affair was satirised on many occasions, not least by the pictorial satirist and social critic William Hogarth, who was notably critical of the medical profession’s gullibility. Toft was eventually released without charge and returned home.”
The story is completely absurd, but also quite funny. I laughed out loud when I read this part, “The timing of Toft’s confession [7 December] proved awkward for St. André, who on 3 December had published his forty-page pamphlet A Short Narrative of an Extraordinary Delivery of Rabbets.” Naturally this article is yet another gem from the wikipedia list of unusual articles.
vi. Small shelly fauna (‘good article’).
“The small shelly fauna or small shelly fossils, abbreviated to SSF, are mineralized fossils, many only a few millimetres long, with a nearly continuous record from the latest stages of the Ediacaran to the end of the Early Cambrian period. They are very diverse, and there is no formal definition of “small shelly fauna” or “small shelly fossils”. Almost all are from earlier rocks than more familiar fossils such as trilobites. Since most SSFs were preserved by being covered quickly with phosphate and this method of preservation is mainly limited to the Late Ediacaran and Early Cambrian periods, the animals that made them may actually have arisen earlier and persisted after this time span.
Some of the fossils represent the entire skeletons of small organisms, including the mysterious Cloudina and some snail-like molluscs. However, the bulk of the fossils are fragments or disarticulated remains of larger organisms, including sponges, molluscs, slug-like halkieriids, brachiopods, echinoderms, and onychophoran-like organisms that may have been close to the ancestors of arthropods.
One of the early explanations for the appearance of the SSFs – and therefore the evolution of mineralized skeletons – suggested a sudden increase in the ocean’s concentration of calcium. However, many SSFs are constructed of other minerals, such as silica. Because the first SSFs appear around the same time as organisms first started burrowing to avoid predation, it is more likely that they represent early steps in an evolutionary arms race between predators and increasingly well-defended prey. On the other hand mineralized skeletons may have evolved simply because they are stronger and cheaper to produce than all-organic skeletons like those of insects. Nevertheless it is still true that the animals used minerals that were most easily accessible.
Although the small size and often fragmentary nature of SSFs makes it difficult to identify and classify them, they provide very important evidence for how the main groups of marine invertebrates evolved, and particularly for the pace and pattern of evolution in the Cambrian explosion. Besides including the earliest known representatives of some modern phyla, they have the great advantage of presenting a nearly continuous record of Early Cambrian organisms whose bodies include hard parts. […]
Small shelly fossils are typically, although not always, preserved in phosphate. Whilst some shellies were originally phosphatic, in most cases the phosphate represents a replacement of the original calcite. They are usually extracted from limestone by placing the limestone in a weak acid, typically acetic acid; the phosphatized fossils remain after the rock is dissolved away. Preservation of microfossils by phosphate seems to have become less common after the early Cambrian, perhaps as a result of increased disturbance of sea-floors by burrowing animals. Without this fossil-forming mode, many small shelly fossils may not have been preserved – or been impossible to extract from the rock; hence the animals that produced these fossils may have lived beyond the Early Cambrian – the apparent extinction of most SSFs by the end of the Cambrian may be an illusion. For decades it was thought that halkieriids, whose “armor plates” are a common type of SSF, perished in the end-Botomian mass extinction; but in 2004 halkieriid armor plates were reported from Mid Cambrian rocks in Australia, a good 10 million years more recent than that. […]
Biomineralization is the production of mineralized parts by organisms. Hypotheses to explain the evolution of biomineralization include physiological adaptation to changing chemistry of the oceans, defense against predators and the opportunity to grow larger. The functions of biomineralization in SSFs vary: some SSFs are not yet understood; some are components of armor; and some are skeletons. A skeleton is any fairly rigid structure of an animal, irrespective of whether it has joints and irrespective of whether it is biomineralized. Although some SSFs may not be skeletons, SSFs are biomineralized by definition, being shelly. Skeletons provide a wide range of possible advantages, including : protection, support, attachment to a surface, a platform or set of levers for muscles to act on, traction when moving on a surface, food handling, provision of filtration chambers and storage of essential substances.”
Incidentally I’ve now read the first half of George Martin’s A Clash of Kings – I’ll probably blog it tomorrow.