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In philosophy , Occam's razor (also spelled Ockham's razor or Ocham's razor ; Latin : novacula Occami ) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle of parsimony or the law of parsimony ( Latin : lex parsimoniae ). Attributed to William of Ockham , a 14th-century English philosopher and theologian , it is frequently cited as Entia non sunt multiplicanda praeter necessitatem , which translates as "Entities must not be multiplied beyond necessity", although Occam never used these exact words. Popularly, the principle is sometimes paraphrased as "The simplest explanation is usually the best one."

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132-430: The galah ( / ɡ ə ˈ l ɑː / ; Eolophus roseicapilla ), less commonly known as the pink and grey cockatoo or rose-breasted cockatoo , is an Australian species of cockatoo and the only member of the genus Eolophus . The galah is adapted to a wide variety of modified and unmodified habitats and is one of Australia's most abundant and widespread bird species. The species is endemic to mainland Australia. It

264-517: A circle with the males on the outside and the females and young on the inside. This is an example of a behavior by the males that seems to be altruistic. The behavior is disadvantageous to them individually but beneficial to the group as a whole; thus, it was seen by some to support the group selection theory. Another interpretation is kin selection: if the males are protecting their offspring, they are protecting copies of their own alleles. Engaging in this behavior would be favored by individual selection if

396-409: A clutch. The eggs are incubated for about 25 days, and the male and female share the incubation. The chicks leave the nest about 49 days after hatching. Living in captivity, galahs have been recorded reaching up to 72 years of age when a good-quality diet is strictly followed. They socialise adequately and can engage playfully in entertainment activities to support the overall very intelligent nature of

528-436: A day. The young of all species are born covered in yellowish down, bar the palm cockatoo, whose young are born naked. Cockatoo incubation times are dependent on species size, with the smaller cockatiels having a period of around 20 days and the larger Carnaby's black cockatoo incubating its eggs for up to 29 days. The nestling period also varies by species size, with larger species having longer nestling periods. It

660-655: A discussion of both uses of Occam's razor in biology, see Sober's article "Let's Razor Ockham's Razor" (1990). Other methods for inferring evolutionary relationships use parsimony in a more general way. Likelihood methods for phylogeny use parsimony as they do for all likelihood tests, with hypotheses requiring fewer differing parameters (i.e., numbers or different rates of character change or different frequencies of character state transitions) being treated as null hypotheses relative to hypotheses requiring more differing parameters. Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject

792-432: A greyish breast, crown, and crest, and brown irises with whitish non-carunculated eye rings. The galah can be found throughout Australia, and is absent only from the driest areas and the far north of Cape York Peninsula . The galah has been introduced to Tasmania through anthropogenic means and there were no sightings prior to 1848. A large population expansion occurred in the 1960s following many escapees from captivity. It

924-482: A hundred birds or less, while in droughts or other times of adversity, they may swell up to contain thousands or even tens of thousands of birds; one record from the Kimberley noted a flock of 32,000 little corellas . Species that inhabit open country form larger flocks than those of forested areas. Some species require roosting sites that are located near drinking sites; other species travel great distances between

1056-447: A justified general bias toward the simpler of two competing explanations. To understand why, consider that for each accepted explanation of a phenomenon, there is always an infinite number of possible, more complex, and ultimately incorrect, alternatives. This is so because one can always burden a failing explanation with an ad hoc hypothesis . Ad hoc hypotheses are justifications that prevent theories from being falsified. For example, if

1188-512: A large supply of seed in cones or gumnuts by plant genera such as Eucalyptus , Banksia and Hakea ), a natural feature of the Australian landscape in dryer regions. These woody fruiting bodies are inaccessible to many species and harvested in the main by parrots, cockatoos and rodents in more tropical regions. The larger cones can be opened by the large bills of cockatoos but are too strong for smaller animals. Many nuts and fruits lie on

1320-445: A logical principle, Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data. However, science has shown repeatedly that future data often support more complex theories than do existing data. Science prefers the simplest explanation that is consistent with the data available at a given time, but the simplest explanation may be ruled out as new data become available. That is, science

1452-551: A man, accused of breaking a vase, makes supernatural claims that leprechauns were responsible for the breakage, a simple explanation might be that the man did it, but ongoing ad hoc justifications (e.g., "... and that's not me breaking it on the film; they tampered with that, too") could successfully prevent complete disproof. This endless supply of elaborate competing explanations, called saving hypotheses, cannot be technically ruled out – except by using Occam's razor. Any more complex theory might still possibly be true. A study of

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1584-444: A minimum length of 7 metres. The breeding requirements include the use of upright or tilted logs with a hollow some twenty to thirty centimetres in diameter. Sand and finer grades of wood material are used to construct their nest, the availability of eucalypt leaves for the nest lining is also suggested for captive breeding. The galah has historically been eaten by humans. Galah meat recipes were published in Australian newspapers in

1716-474: A model of a reaction mechanism . Although it is useful as a heuristic in developing models of reaction mechanisms, it has been shown to fail as a criterion for selecting among some selected published models. In this context, Einstein himself expressed caution when he formulated Einstein's Constraint : "It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender

1848-460: A number of functions, including allowing individuals to recognize one another, alerting others of predators, indicating individual moods, maintaining the cohesion of a flock and as warnings when defending nests. The use of calls and number of specific calls varies by species; the Carnaby's black cockatoo has as many as 15 types of call, whereas others, such as the pink cockatoo, have fewer. Some, like

1980-419: A pale grey rump, a pink face and breast, and a light pink mobile crest . It has a bone-coloured beak, and the bare skin of the eye ring is carunculated . It has grey legs. The sexes appear similar; however, adult birds differ in the colour of the irises ; the male has very dark brown (almost black) irises and the female has mid-brown or red irises. Adults are more brightly coloured than juveniles. Juveniles have

2112-415: A particular research problem. The reasonableness of parsimony in one research context may have nothing to do with its reasonableness in another. It is a mistake to think that there is a single global principle that spans diverse subject matter. It has been suggested that Occam's razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption. Most of

2244-551: A permit), trapped or gassed (with a permit) by landowners. The galah is very common as a companion parrot or avicultural specimen around the world. They are generally absent from Australian aviaries, although permits are available in South Australia to take a limited number of galahs from the wild per year for avicultural purposes. When tame, it can be an affectionate and friendly bird that can learn to talk , as well as mimic other sounds heard in its environment. While it

2376-783: A person who is assigned to keep watch while others undertake clandestine or illegal activities, particularly gambling, may be referred to as a "cockatoo". Proprietors of small agricultural undertakings are often jocularly or slightly disparagingly referred to as "cocky farmers". Strigopidae – New Zealand parrots Cacatuidae – cockatoos Psittacidae – African and New World parrots Psittaculidae – Old World parrots Calyptorhynchus – black cockatoos (2 species) Zanda – black cockatoos (3 species) Nymphicus – cockatiel Probosciger – palm cockatoo Callocephalon – gang-gang cockatoo Eolophus – galah Lophochroa – pink cockatoo Cacatua – white cockatoos and corellas (13 species) The cockatoos were first defined as

2508-568: A phenomenon called "the selfish herd". Systematics is the branch of biology that attempts to establish patterns of relationship among biological taxa, today generally thought to reflect evolutionary history. It is also concerned with their classification. There are three primary camps in systematics: cladists, pheneticists, and evolutionary taxonomists. Cladists hold that classification should be based on synapomorphies (shared, derived character states), pheneticists contend that overall similarity (synapomorphies and complementary symplesiomorphies )

2640-555: A pink bird named Stella that is intended to be based on a galah. Cockatoo A cockatoo is any of the 21 species of parrots belonging to the family Cacatuidae , the only family in the superfamily Cacatuoidea. Along with the Psittacoidea ( true parrots ) and the Strigopoidea (large New Zealand parrots ), they make up the order Psittaciformes. The family has a mainly Australasian distribution, ranging from

2772-432: A preference for simple theories need not appeal to practical or aesthetic considerations. Our preference for simplicity may be justified by its falsifiability criterion: we prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable". The idea here is that a simple theory applies to more cases than a more complex one, and is thus more easily falsifiable. This

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2904-407: A range of mainly vegetable food items. Seeds form a large part of the diet of all species; these are opened with their large and powerful bills. The galahs, corellas and some of the black cockatoos feed primarily on the ground; others feed mostly in trees. The ground-feeding species tend to forage in flocks, which form tight, squabbling groups where seeds are concentrated and dispersed lines where food

3036-408: A role in clutch size . Some species can lay a second clutch if the first fails. Around 20% of eggs laid are infertile. The cockatoos' incubation and brooding responsibilities may either be undertaken by the female alone in the case of the black cockatoos or shared amongst the sexes as happens in the other species. In the case of the black cockatoos, the female is provisioned by the male several times

3168-499: A shortage of suitable nesting hollows after large mature trees are cleared; conversely, some species have adapted well to human changes and are considered agricultural pests . Cockatoos are popular birds in aviculture , but their needs are difficult to meet. The cockatiel is the easiest cockatoo species to maintain and is by far the most frequently kept in captivity. White cockatoos are more commonly found in captivity than black cockatoos. Illegal trade in wild-caught birds contributes to

3300-411: A simpler explanation for the observed reversibility of both mixing and chemical reactions as simple separation and rearrangements of atomic building blocks. At the time, however, the atomic theory was considered more complex because it implied the existence of invisible particles that had not been directly detected. Ernst Mach and the logical positivists rejected John Dalton 's atomic theory until

3432-518: A subfamily Cacatuinae within the parrot family Psittacidae by the English naturalist George Robert Gray in 1840, with Cacatua the first listed and type genus. This group has alternately been considered as either a full or subfamily by different authorities. The American ornithologist James Lee Peters in his 1937 Check-list of Birds of the World and Sibley and Monroe in 1990 maintained it as

3564-554: A subfamily, while parrot expert Joseph Forshaw classified it as a family in 1973. Subsequent molecular studies indicate that the earliest offshoot from the original parrot ancestors were the New Zealand parrots of the family Strigopidae, and following this the cockatoos, now a well-defined group or clade , split off from the remaining parrots, which then radiated across the Southern Hemisphere and diversified into

3696-406: A third limb when climbing through branches. They generally have long broad wings used in rapid flight, with speeds up to 70 km/h (43 mph) being recorded for galahs. The members of the genus Calyptorhynchus and larger white cockatoos, such as the sulphur-crested cockatoo and the pink cockatoo , have shorter, rounder wings and a more leisurely flight. Cockatoos have a large bill, which

3828-462: A tree. The peregrine falcon and little eagle have been reported taking galahs and the wedge-tailed eagle has been observed killing a sulphur-crested cockatoo. Eggs and nestlings are vulnerable to many hazards. Various species of monitor lizard ( Varanus ) are able to climb trees and enter hollows. Other predators recorded include the spotted wood owl on Rasa Island in the Philippines;

3960-604: A wide range of other possible results. This, again, reflects the mathematical relationship between key concepts in Bayesian inference (namely marginal probability , conditional probability , and posterior probability ). The bias–variance tradeoff is a framework that incorporates the Occam's razor principle in its balance between overfitting (associated with lower bias but higher variance) and underfitting (associated with lower variance but higher bias). Karl Popper argues that

4092-440: A year at least. Females breed for the first time anywhere from three to seven years of age and males are often older. Sexual maturity is delayed so birds can develop the skills for raising and parenting young, which is prolonged compared with other birds; the young of some species remain with their parents for up to a year. Cockatoos may also display site fidelity , returning to the same nesting sites in consecutive years. Courtship

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4224-469: Is a direct result of basic probability theory . By definition, all assumptions introduce possibilities for error; if an assumption does not improve the accuracy of a theory, its only effect is to increase the probability that the overall theory is wrong. There have also been other attempts to derive Occam's razor from probability theory, including notable attempts made by Harold Jeffreys and E. T. Jaynes . The probabilistic (Bayesian) basis for Occam's razor

4356-500: Is a noisy bird that may be unsuitable for apartment living, it is comparatively quieter than other cockatoo species. Like most parrots, the galah requires plenty of exercise and play time out of its cage as well as several hours of daily social interaction with humans or other birds in order to thrive in captivity. It may also be prone to obesity if not provided with a suitable, nutritionally-balanced diet. The World Parrot Trust recommends that captive galahs should be kept in an aviary with

4488-671: Is again comparing a simple theory to a more complex theory where both explain the data equally well. The philosopher of science Elliott Sober once argued along the same lines as Popper, tying simplicity with "informativeness": The simplest theory is the more informative, in the sense that it requires less information to a question. He has since rejected this account of simplicity, purportedly because it fails to provide an epistemic justification for simplicity. He now believes that simplicity considerations (and considerations of parsimony in particular) do not count unless they reflect something more fundamental. Philosophers, he suggests, may have made

4620-419: Is also affected by season and environmental factors and by competition with siblings in species with clutch sizes greater than one. Much of what is known about the nestling period of some species is dependent on aviary studies – aviary cockatiels can fledge after 5 weeks and the large palm cockatoos after 11 weeks. During this period, the young become covered in juvenile plumage while remaining in

4752-506: Is also potentially true for any type of phylogenetic inference, unless the model used to estimate the tree reflects the way that evolution actually happened. Because this information is not empirically accessible, the criticism of statistical inconsistency against parsimony holds no force. For a book-length treatment of cladistic parsimony, see Elliott Sober 's Reconstructing the Past: Parsimony, Evolution, and Inference (1988). For

4884-405: Is amenable to empirical testing. Another interpretation of the razor's statement would be that "simpler hypotheses are generally better than the complex ones". The procedure to test the former interpretation would compare the track records of simple and comparatively complex explanations. If one accepts the first interpretation, the validity of Occam's razor as a tool would then have to be rejected if

5016-441: Is an ultimate a priori epistemic principle that simplicity is evidence for truth. According to Swinburne, since our choice of theory cannot be determined by data (see Underdetermination and Duhem–Quine thesis ), we must rely on some criterion to determine which theory to use. Since it is absurd to have no logical method for settling on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose

5148-690: Is better than particular because it produces knowledge from fewer premises. Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal." The Summa Theologica of Thomas Aquinas (1225–1274) states that "it is superfluous to suppose that what can be accounted for by a few principles has been produced by many." Aquinas uses this principle to construct an objection to God's existence , an objection that he in turn answers and refutes generally (cf. quinque viae ), and specifically, through an argument based on causality . Hence, Aquinas acknowledges

5280-524: Is called the " Zebra ": a physician should reject an exotic medical diagnosis when a more commonplace explanation is more likely, derived from Theodore Woodward 's dictum "When you hear hoofbeats, think of horses not zebras". Ernst Mach formulated the stronger version of Occam's razor into physics , which he called the Principle of Economy stating: "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by

5412-482: Is common in metropolitan areas such as Adelaide , Perth , and Melbourne , and abundant in open habitats that offer at least some scattered trees for shelter. It is common in all habitats in its range except for dense forests, especially those with high rainfall. While it is mostly found in inland areas, the galah is rapidly colonising coastal regions. The changes brought by European settlement , which have been disastrous for many species, have been highly beneficial for

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5544-553: Is elaborated by David J. C. MacKay in chapter 28 of his book Information Theory, Inference, and Learning Algorithms , where he emphasizes that a prior bias in favor of simpler models is not required. William H. Jefferys and James O. Berger (1991) generalize and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data. They state, "A hypothesis with fewer adjustable parameters will automatically have an enhanced posterior probability, due to

5676-629: Is generally simple, particularly for established pairs, with the black cockatoos alone engaging in courtship feeding . Established pairs do engage in preening each other , but all forms of courtship drop off after incubation begins, possibly due to the strength of the pair-bond. Like most parrots, the cockatoos are cavity nesters , nesting in holes in trees, which they are unable to excavate themselves. These hollows are formed from decay or destruction of wood by branches breaking off, fungi or insects such as termites or even woodpeckers where their ranges overlap. In many places these holes are scarce and

5808-405: Is kept sharp by rasping the two jaws together when resting. The bill is complemented by a large muscular tongue which helps manipulate seeds inside the bill so that they can be de-husked before eating. During the de-husking, the lower jaw applies the pressure, the tongue holds the seed in place and the upper jaw acts as an anvil. The eye region of the skull is reinforced to support muscles which move

5940-405: Is more sparsely distributed; they also prefer open areas where visibility is good. The western and long-billed corellas have elongated bills to excavate tubers and roots and the pink cockatoo walks in a circle around the doublegee ( Emex australis ) to twist out and remove the underground parts. Many species forage for food in the canopy of trees, taking advantage of serotiny (the storage of

6072-714: Is not found in any of William's writings, one can cite statements such as Numquam ponenda est pluralitas sine necessitate ("Plurality must never be posited without necessity"), which occurs in his theological work on the Sentences of Peter Lombard ( Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi ; ed. Lugd., 1495, i, dist. 27, qu. 2, K). Nevertheless, the precise words sometimes attributed to William of Ockham, Entia non sunt multiplicanda praeter necessitatem (Entities must not be multiplied beyond necessity), are absent in his extant works; this particular phrasing comes from John Punch , who described

6204-481: Is not the simplest and most basic explanation. Dawkins argues the way evolution works is that the genes propagated in most copies end up determining the development of that particular species, i.e., natural selection turns out to select specific genes, and this is really the fundamental underlying principle that automatically gives individual and group selection as emergent features of evolution. Zoology provides an example. Muskoxen , when threatened by wolves , form

6336-484: Is open to the possibility that future experiments might support more complex theories than demanded by current data and is more interested in designing experiments to discriminate between competing theories than favoring one theory over another based merely on philosophical principles. When scientists use the idea of parsimony, it has meaning only in a very specific context of inquiry. Several background assumptions are required for parsimony to connect with plausibility in

6468-563: Is similar in most species. The plumage of the female cockatiel is duller than the male, but the most marked sexual dimorphism occurs in the gang-gang cockatoo and the two species of black cockatoos in the subgenus Calyptorhynchus , namely the red-tailed and glossy black cockatoos . The iris colour differs in a few species, being pink or red in the female galah and the pink cockatoo and red-brown in some other female white cockatoo species. The males all have dark brown irises. Cockatoos maintain their plumage with frequent preening throughout

6600-462: Is superfluous to do it by means of several; for we observe that nature does not employ two instruments [if] one suffices." Beginning in the 20th century, epistemological justifications based on induction , logic , pragmatism , and especially probability theory have become more popular among philosophers. Occam's razor has gained strong empirical support in helping to converge on better theories (see Uses section below for some examples). In

6732-502: Is that theories (or models) of natural law must be consistent with repeatable experimental observations. This ultimate arbiter (selection criterion) rests upon the axioms mentioned above. If multiple models of natural law make exactly the same testable predictions, they are equivalent and there is no need for parsimony to choose a preferred one. For example, Newtonian , Hamiltonian and Lagrangian classical mechanics are equivalent. Physicists have no interest in using Occam's razor to say

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6864-584: Is the determining criterion, while evolutionary taxonomists say that both genealogy and similarity count in classification (in a manner determined by the evolutionary taxonomist). It is among the cladists that Occam's razor is applied, through the method of cladistic parsimony . Cladistic parsimony (or maximum parsimony ) is a method of phylogenetic inference that yields phylogenetic trees (more specifically, cladograms). Cladograms are branching, diagrams used to represent hypotheses of relative degree of relationship, based on synapomorphies . Cladistic parsimony

6996-483: Is the more parsimonious theory. In doing so he is invoking a variant of Occam's razor known as Morgan's Canon : "In no case is an animal activity to be interpreted in terms of higher psychological processes, if it can be fairly interpreted in terms of processes which stand lower in the scale of psychological evolution and development." (Morgan 1903). However, more recent biological analyses, such as Richard Dawkins 's The Selfish Gene , have contended that Morgan's Canon

7128-540: Is unknown, as is the cause, although a parrot papilloma virus has been isolated from a grey parrot with the condition. Cockatoos have been shown to learn new skills through social interaction. In New South Wales , researchers and citizen scientists were able to track the spread of lid-flipping skills as cockatoos learned from each other to open garbage bins. Bin-opening spread more quickly to neighbouring suburbs than suburbs further away. In addition, birds in different areas developed their own variants for accomplishing

7260-465: Is used to select as the preferred hypothesis of relationships the cladogram that requires the fewest implied character state transformations (or smallest weight, if characters are differentially weighted). Critics of the cladistic approach often observe that for some types of data, parsimony could produce the wrong results, regardless of how much data is collected (this is called statistical inconsistency, or long branch attraction ). However, this criticism

7392-550: The Philippines and the eastern Indonesian islands of Wallacea to New Guinea , the Solomon Islands and Australia . Cockatoos are recognisable by the prominent crests and curved bills . Their plumage is generally less colourful than that of other parrots, being mainly white, grey or black and often with coloured features in the crest, cheeks or tail. On average they are larger than other parrots; however,

7524-640: The Philippines , and some Pacific regions. Eleven of the 21 species exist in the wild only in Australia, while seven species occur only in the islands of the Philippines , Indonesia, Papua New Guinea and the Solomon Islands . No cockatoo species are found in Borneo , despite their presence on nearby Palawan and Sulawesi or many Pacific islands, although fossil remains have been recorded from New Caledonia . Three species occur in both New Guinea and Australia. Some species have widespread distributions, with

7656-454: The Wien and Jeans radiation laws and used Occam's razor logic to formulate the quantum hypothesis, even resisting that hypothesis as it became more obvious that it was correct. Appeals to simplicity were used to argue against the phenomena of meteorites, ball lightning , continental drift , and reverse transcriptase . One can argue for atomic building blocks for matter, because it provides

7788-493: The amethystine python , black butcherbird and rodents including the giant white-tailed rat in Cape York; and brushtail possum on Kangaroo Island. Furthermore, galahs and little corellas competing for nesting space with the glossy black cockatoo on Kangaroo Island have been recorded killing nestlings of the latter species there. Severe storms may also flood hollows drowning the young and termite or borer activity may lead to

7920-513: The cockatiel , the smallest cockatoo species, is medium-sized. The phylogenetic position of the cockatiel remains unresolved, except that it is one of the earliest offshoots of the cockatoo lineage. The remaining species are in two main clades. The five large black-coloured cockatoos of the genus Calyptorhynchus form one branch. The second and larger branch is formed by the genus Cacatua , comprising 12 species of white-plumaged cockatoos and three monotypic genera that branched off earlier; namely

8052-405: The subgenera Licmetis , commonly known as corellas , and Cacatua , referred to as white cockatoos. Confusingly, the term "white cockatoo" has also been applied to the whole genus. The five cockatoo species of the genus Calyptorhynchus are commonly known as black cockatoos, and are divided into two subgenera— Calyptorhynchus and Zanda . The former group are sexually dichromatic , with

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8184-441: The 1930s, alongside jokes about the alleged toughness and unpalatable nature of the bird's flesh. "Galah" is also derogatory Australian slang, synonymous with "fool", "clown", or "idiot". Because of the bird's distinctive bright pink colour, it is also used for gaudy dress. A detailed description of the Australian slang term can be found in the standup comedy performance of Paul Hogan , titled Stand Up Hoges . Another famous user of

8316-437: The 20th century, it was a commonly held belief that nature itself was simple and that simpler hypotheses about nature were thus more likely to be true. This notion was deeply rooted in the aesthetic value that simplicity holds for human thought and the justifications presented for it often drew from theology . Thomas Aquinas made this argument in the 13th century, writing, "If a thing can be done adequately by means of one, it

8448-586: The Posterior Analytics Books ( Commentarius in Posteriorum Analyticorum Libros ) ( c.  1217–1220 ), declares: "That is better and more valuable which requires fewer, other circumstances being equal... For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration

8580-460: The Soul , gives him credit for the phrase, speaking of " novacula occami ". Ockham did not invent this principle, but its fame—and its association with him—may be due to the frequency and effectiveness with which he used it. Ockham stated the principle in various ways, but the most popular version, "Entities are not to be multiplied without necessity" ( Non sunt multiplicanda entia sine necessitate )

8712-405: The adequate representation of a single datum of experience." An often-quoted version of this constraint (which cannot be verified as posited by Einstein himself) reduces this to "Everything should be kept as simple as possible, but not simpler." In the scientific method , Occam's razor is not considered an irrefutable principle of logic or a scientific result; the preference for simplicity in

8844-418: The behaviors of individual organisms acting in their own self-interest (or in the interest of their genes, via kin selection). Williams was arguing against the perspective of others who propose selection at the level of the group as an evolutionary mechanism that selects for altruistic traits (e.g., D. S. Wilson & E. O. Wilson, 2007). The basis for Williams's contention is that of the two, individual selection

8976-425: The best way to explain altruism among animals is based on low-level (i.e., individual) selection as opposed to high-level group selection. Altruism is defined by some evolutionary biologists (e.g., R. Alexander, 1987; W. D. Hamilton, 1964) as behavior that is beneficial to others (or to the group) at a cost to the individual, and many posit individual selection as the mechanism that explains altruism solely in terms of

9108-461: The bird. In their natural habitat, galahs are unlikely to reach the age of 20 years, falling victim to traffic, predators such as the little eagle and black and peregrine falcons , and human activities in some agricultural areas. Like most other cockatoos, galahs create strong, lifelong bonds with their partners. The galah readily hybridizes with several species, including the sulphur-crested cockatoo, little corella, Major Mitchell's cockatoo, and

9240-415: The black palm cockatoo ( Probosciger ), the grey and reddish galah ( Eolophus ), and the gang-gang cockatoo ( Callocephalon ), although Probosciger is sometimes placed basal to all other species. The remaining species are mainly white or slightly pinkish and all belong to the genus Cacatua . The genera Eolophus and Cacatua are hypomelanistic . The genus Cacatua is further subdivided into

9372-463: The characteristic curved beak shape and a zygodactyl foot, with the two middle toes forward and the two outer toes backward. They differ in the presence of an erectile crest and their lack of the Dyck texture feather composition which causes the bright blues and greens seen in true parrots. Like other parrots, cockatoos have short legs, strong claws, a waddling gait and often use their strong bill as

9504-425: The cockatiel, is considerably smaller and slimmer than the other species, being 32 cm (13 in) long (including its long pointed tail feathers) and 80–100 g (2.8–3.5 oz) in weight. The movable headcrest , which is present in all cockatoos, is spectacular in many species; it is raised when the bird lands from flying or when it is aroused. Cockatoos share many features with other parrots, including

9636-520: The cockatiel. Galah x cockatiel hybrids are often referred to as "galatiels". Aviary-bred hybrids of galah x Major Mitchell's cockatoo have been bred in Sydney, with the tapered wings of the galah and the crest and colours of the Major Mitchell's, as well as the plaintive cry of the latter. In the state of South Australia , galahs are considered "unprotected native fauna" and may be shot (without

9768-419: The cockatoo family Cacatuidae including recognized subspecies. The current subdivision of this family is as follows: Subfamily Nymphicinae Subfamily Calyptorhynchinae: Black cockatoos Subfamily Cacatuinae The cockatoos are generally medium to large parrots of stocky build, which range from 30–60 cm (12–24 in) in length and 300–1,200 g (0.66–2.65 lb) in weight; however, one species,

9900-450: The colours of the plumage and in the extent of the carunculation of the eye rings among the three subspecies. The south-eastern form, E. r. albiceps , is clearly distinct from the paler-bodied Western Australian nominate subspecies , E. r. roseicapilla , although the extent and nature of the central hybrid zone remains undefined. Most pet birds outside Australia are the south-eastern form. The third form, E. r. kuhli , found right across

10032-633: The complex task. Human activities have had positive effects on some species of cockatoo and negative effects on others. Many species of open country have benefited greatly from anthropogenic changes to the landscape, with the great increase in reliable seed food sources, and available water contributing to their survival, as well as their adaption to a diet including foreign foodstuffs. This benefit appears to be restricted to Australian species, as cockatoos favouring open country outside Australia have not become more abundant. Predominantly forest-dwelling species have suffered greatly from habitat destruction ; in

10164-404: The cones in its foot and shreds them with its powerful bill before removing the seeds with its tongue. Some species take large numbers of insects, particularly when breeding; in fact the bulk of the yellow-tailed black cockatoo 's diet is made up of insects. The large bill is used in order to extract grubs and larvae from rotting wood. The amount of time cockatoos have to spend foraging varies with

10296-408: The continent where they are not native. Cockatoos occupy a wide range of habitats from forests in subalpine regions to mangroves. However, no species is found in all types of habitat. The most widespread species, such as the galah and cockatiel, are open-country specialists that feed on grass seeds. They are often highly mobile fast flyers and are nomadic. Flocks of birds move across large areas of

10428-464: The cost to the male musk ox is less than half of the benefit received by his calf – which could easily be the case if wolves have an easier time killing calves than adult males. It could also be the case that male musk oxen would be individually less likely to be killed by wolves if they stood in a circle with their horns pointing out, regardless of whether they were protecting the females and offspring. That would be an example of regular natural selection –

10560-452: The course of incubation. They range in size from 55 mm × 37 mm (2.2 in × 1.5 in) in the palm and red-tailed black cockatoos, to 26 mm × 19 mm (1.02 in × 0.75 in) in the cockatiel. Clutch size varies within the family, with the palm cockatoo and some other larger cockatoos laying only a single egg and the smaller species laying anywhere between two and eight eggs. Food supply also plays

10692-465: The crest or tail. The galah and Major Mitchell's cockatoo are more broadly coloured in pink tones. Several species have a brightly coloured bare area around the eye and face known as a periophthalmic ring; the large red patch of bare skin of the palm cockatoo is the most extensive and covers some of the face, while it is more restricted in some other species of white cockatoo, notably the corellas and blue-eyed cockatoo . The plumage of males and females

10824-425: The day. They remove dirt and oil and realign feather barbs by nibbling their feathers. They also preen other birds' feathers that are otherwise hard to get at. Cockatoos produce preen-oil from a gland on their lower back and apply it by wiping their plumage with their heads or already oiled feathers. Powder-down is produced by specialised feathers in the lumbar region and distributed by the preening cockatoo all over

10956-552: The decline of some cockatoo species in the wild. The word cockatoo dates from the 17th century and is derived from Dutch kaketoe , which in turn is from the Indonesian / Malay kakatua . Seventeenth-century variants include cacato, cockatoon and crockadore, and cokato, cocatore and cocatoo were used in the eighteenth century. The derivation has also been used for the family and generic names Cacatuidae and Cacatua , respectively. In Australian slang or vernacular speech,

11088-409: The end of small branches which are unable to support the weight of the foraging cockatoo, which instead bends the branch towards itself and holds it with its foot. While some cockatoos are generalists taking a wide range of foods, others are specialists. The glossy black cockatoo specialises in the cones of trees of the genus Allocasuarina , preferring a single species, A. verticillata . It holds

11220-404: The error of hypostatizing simplicity (i.e., endowed it with a sui generis existence), when it has meaning only when embedded in a specific context (Sober 1992). If we fail to justify simplicity considerations on the basis of the context in which we use them, we may have no non-circular justification: "Just as the question 'why be rational?' may have no non-circular answer, the same may be true of

11352-414: The fact that the predictions it makes are sharp." The use of "sharp" here is not only a tongue-in-cheek reference to the idea of a razor, but also indicates that such predictions are more accurate than competing predictions. The model they propose balances the precision of a theory's predictions against their sharpness, preferring theories that sharply make correct predictions over theories that accommodate

11484-512: The females having prominently barred plumage. The two are also distinguished by differences in the food-begging calls of juveniles. The fossil record of cockatoos is even more limited than that of parrots in general, with only one truly ancient cockatoo fossil known: a species of Cacatua , most probably subgenus Licmetis , found in Early Miocene (16–23 million years ago) deposits of Riversleigh , Australia. Although fragmentary,

11616-545: The food supply is more stable and predictable. Several species have adapted well to human modified habitats and are found in agricultural areas and even busy cities. Cockatoos are diurnal and require daylight to find their food. They are not early risers, instead waiting until the sun has warmed their roosting sites before feeding. All species are generally highly social and roost, forage and travel in colourful and noisy flocks . These vary in size depending on availability of food; in times of plenty, flocks are small and number

11748-420: The galah, because of the clearing of forests in fertile areas and the provision of stock-watering points in arid zones. The galah has been introduced to New Zealand . The classification of the galah was difficult. It was separated in the monotypic genus Eolophus , but the further relationships were not clear. Obvious morphological similarities are shared between the galah and the white cockatoos that make up

11880-701: The galah, for example, occurring over most of Australia, whereas other species have tiny distributions, confined to a small part of the continent, such as the Baudin's black cockatoo of Western Australia or to a small island group, such as the Tanimbar corella , which is restricted to the Tanimbar Islands of Indonesia. Some cockatoos have been introduced accidentally to areas outside their natural range such as New Zealand, Singapore, and Palau , while two Australian corella species have been introduced to parts of

12012-472: The gang-gang cockatoo, are comparatively quiet but do have softer growling calls when feeding. In addition to vocalisations, palm cockatoos communicate over large distances by drumming on a dead branch with a stick. Cockatoo species also make a characteristic hissing sound when threatened. Cockatoos have a much more restricted range than the true parrots, occurring naturally only in Australia , Indonesia ,

12144-445: The genus Cacatua and indeed the galah was initially described as Cacatua roseicapilla . Early DNA studies allied the galah with the cockatiel or placed it close to some Cacatua species of completely different appearance. In consequence, the ancestors of the galah, the cockatiel and Major Mitchell's cockatoo were thought to have diverged from the main white cockatoo line at some stage prior to that group's main radiation; this

12276-435: The ground for food in open, grassy areas. Flocks of independent juvenile galahs will often disperse from their birth flock haphazardly. The galah feeds on seeds gathered on the ground, mainly feeding in the morning and late afternoon. Idly, it will strip leaves and bark from trees, and large flocks have been observed to kill trees through defoliation . The galah nests in tree cavities. The eggs are white, usually two to five in

12408-542: The hollow. Wings and tail feathers are slow to grow initially but more rapid as the primary feathers appear. Nestlings quickly reach about 80–90% of adult weight about two-thirds of the time through this period, plateauing before they leave the hollow; they fledge at this weight with wing and tail feathers still to grow a little before reaching adult dimensions. Growth rate of the young, as well as numbers fledged, are adversely impacted by reduced food supply and poor weather conditions. Cockatoos are versatile feeders and consume

12540-496: The hypothesis that requires the fewest assumptions, and that this is not meant to be a way of choosing between hypotheses that make different predictions. Similarly, in science, Occam's razor is used as an abductive heuristic in the development of theoretical models rather than as a rigorous arbiter between candidate models. The phrase Occam's razor did not appear until a few centuries after William of Ockham's death in 1347. Libert Froidmont , in his On Christian Philosophy of

12672-466: The inland, locating and feeding on seed and other food sources. Drought may force flocks from more arid areas to move further into farming areas. Other cockatoo species, such as the glossy black cockatoo, inhabit woodlands, rainforests, shrublands and even alpine forests. The red-vented cockatoo inhabits mangroves and its absence from northern Luzon may be related to the lack of mangrove forests there. Forest-dwelling cockatoos are generally sedentary, as

12804-454: The internal collapse of nests. Like other parrots, cockatoos can be afflicted by psittacine beak and feather disease (PBFD). The viral infection causes feather loss and beak malformation and reduces the bird's overall immunity. Particularly prevalent in sulphur-crested cockatoos, little corellas and galahs, it has been recorded in 14 species of cockatoo to date. Although unlikely to significantly impact on large, healthy populations of birds in

12936-650: The issue. Today, the galah is seen, along with Major Mitchell's cockatoo, as an early divergence from the white cockatoo lineage, which has not completely lost its ability to produce an overall pink (Major Mitchell's) or pink and grey (galah) body plumage, while already being light in colour and non-sexually dimorphic. The significance of these two (and other) characteristics shared by the Cacatuinae had previously been explained away in earlier studies by strict application of parsimony on misinterpreted data. Three subspecies are usually recognised. Slight variation exists in

13068-430: The jaws sideways. The bills of male cockatoos are generally slightly larger than those of their female counterparts, but this size difference is quite marked in the palm cockatoo. The plumage of the cockatoos is less brightly coloured than that of the other parrots, with species generally being either black, grey or white. Many species have smaller areas of colour on their plumage, often yellow, pink and red, usually on

13200-405: The main, they appear to have a more specialised diet and have not been able to incorporate exotic food into their diet. A notable exception is the yellow-tailed black cockatoo in eastern Australia. Occam%27s razor This philosophical razor advocates that when presented with competing hypotheses about the same prediction and both hypotheses have equal explanatory power, one should prefer

13332-427: The many species of parrots, parakeets , macaws , lories, lorikeets , lovebirds and other true parrots of the superfamily Psittacoidea . The relationships among various cockatoo genera are largely resolved, although the placement of the cockatiel ( Nymphicus hollandicus ) at the base of the cockatoos remains uncertain. The cockatiel is alternatively placed basal to all other cockatoo species, as

13464-399: The more complex explanations were more often correct than the less complex ones (while the converse would lend support to its use). If the latter interpretation is accepted, the validity of Occam's razor as a tool could possibly be accepted if the simpler hypotheses led to correct conclusions more often than not. Even if some increases in complexity are sometimes necessary, there still remains

13596-512: The next symbol based upon a given series of symbols. The only assumption is that the environment follows some unknown but computable probability distribution. This theory is a mathematical formalization of Occam's razor. Another technical approach to Occam's razor is ontological parsimony . Parsimony means spareness and is also referred to as the Rule of Simplicity. This is considered a strong version of Occam's razor. A variation used in medicine

13728-524: The northern part of the continent, tends to be a little smaller and is distinguished by differences in the shape and colour of the crest, although its status as a valid subspecies is uncertain. The galah is often found in flocks of 10 to 1,000 individuals. These can be mixed flocks , the members of which may include Major Mitchell's cockatoo, the little corella , and the sulphur-crested cockatoo . The galah readily hybridizes with all of these species (see below). Flocks of galahs often congregate and forage on

13860-531: The other two are wrong. Likewise, there is no demand for simplicity principles to arbitrate between wave and matrix formulations of quantum mechanics. Science often does not demand arbitration or selection criteria between models that make the same testable predictions. Biologists or philosophers of biology use Occam's razor in either of two contexts both in evolutionary biology : the units of selection controversy and systematics . George C. Williams in his book Adaptation and Natural Selection (1966) argues that

13992-399: The pink and grey galah , the mainly grey gang-gang cockatoo and the large black-plumaged palm cockatoo . Cockatoos prefer to eat seeds, tubers , corms , fruit, flowers and insects. They often feed in large flocks, particularly when ground-feeding. Cockatoos are monogamous and nest in tree hollows . Some cockatoo species have been adversely affected by habitat loss , particularly from

14124-399: The plumage. Moulting is very slow and complex. Black cockatoos appear to replace their flight feathers one at a time, their moult taking two years to complete. This process is much shorter in other species, such as the galah and long-billed corella , which each take around six months to replace all their flight feathers. The vocalisations of cockatoos are loud and harsh. They serve

14256-418: The predictive validity of Occam's razor found 32 published papers that included 97 comparisons of economic forecasts from simple and complex forecasting methods. None of the papers provided a balance of evidence that complexity of method improved forecast accuracy. In the 25 papers with quantitative comparisons, complexity increased forecast errors by an average of 27 percent. One justification of Occam's razor

14388-621: The principle as a "common axiom" ( axioma vulgare ) of the Scholastics. William of Ockham himself seems to restrict the operation of this principle in matters pertaining to miracles and God's power, considering a plurality of miracles possible in the Eucharist simply because it pleases God. This principle is sometimes phrased as Pluralitas non est ponenda sine necessitate ("Plurality should not be posited without necessity"). In his Summa Totius Logicae , i. 12, William of Ockham cites

14520-455: The principle of economy, Frustra fit per plura quod potest fieri per pauciora ("It is futile to do with more things that which can be done with fewer"; Thorburn, 1918, pp. 352–53; Kneale and Kneale, 1962, p. 243.) To quote Isaac Newton , "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, as far as possible, assign

14652-624: The principle that today is known as Occam's razor, but prefers causal explanations to other simple explanations (cf. also Correlation does not imply causation ). William of Ockham ( circa 1287–1347) was an English Franciscan friar and theologian , an influential medieval philosopher and a nominalist . His popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam's razor. The term razor refers to distinguishing between two hypotheses either by "shaving away" unnecessary assumptions or cutting apart two similar conclusions. While it has been claimed that Occam's razor

14784-414: The question 'why should simplicity be considered in evaluating the plausibility of hypotheses? ' " Richard Swinburne argues for simplicity on logical grounds: ... the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it

14916-617: The reality of atoms was more evident in Brownian motion , as shown by Albert Einstein . In the same way, postulating the aether is more complex than transmission of light through a vacuum . At the time, however, all known waves propagated through a physical medium, and it seemed simpler to postulate the existence of a medium than to theorize about wave propagation without a medium. Likewise, Isaac Newton 's idea of light particles seemed simpler than Christiaan Huygens 's idea of waves, so many favored it. In this case, as it turned out, neither

15048-565: The related concept of overfitting , excessively complex models are affected by statistical noise (a problem also known as the bias–variance tradeoff ), whereas simpler models may capture the underlying structure better and may thus have better predictive performance. It is, however, often difficult to deduce which part of the data is noise (cf. model selection , test set , minimum description length , Bayesian inference , etc.). The razor's statement that "other things being equal, simpler explanations are generally better than more complex ones"

15180-509: The remains are similar to the western corella and the galah. In Melanesia , subfossil bones of Cacatua species which apparently did not survive early human settlement have been found on New Caledonia and New Ireland . The bearing of these fossils on cockatoo evolution and phylogeny is fairly limited, although the Riversleigh fossil does allow tentative dating of the divergence of subfamilies. There are about 44 different birds in

15312-552: The roosting and feeding sites. Cockatoos have several characteristic methods of bathing; they may hang upside down or fly about in the rain or flutter in wet leaves in the canopy. Cockatoos have a preferred "footedness" analogous to human handedness. Most species are left-footed with 87–100% of individuals using their left feet to eat, but a few species favor their right foot. Cockatoos are monogamous breeders, with pair bonds that can last many years. Many birds pair up in flocks before they reach sexual maturity and delay breeding for

15444-451: The same causes." In the sentence hypotheses non fingo , Newton affirms the success of this approach. Bertrand Russell offers a particular version of Occam's razor: "Whenever possible, substitute constructions out of known entities for inferences to unknown entities." Around 1960, Ray Solomonoff founded the theory of universal inductive inference , the theory of prediction based on observations – for example, predicting

15576-441: The scientific method is based on the falsifiability criterion. For each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives. Since failing explanations can always be burdened with ad hoc hypotheses to prevent them from being falsified, simpler theories are preferable to more complex ones because they tend to be more testable . As

15708-483: The season. During times of plenty they may need to feed for only a few hours in the day, in the morning and evening, then spend the rest of the day roosting or preening in trees, but during the winter most of the day may be spent foraging. The birds have increased nutritional requirements during the breeding season, so they spend more time foraging for food during this time. Cockatoos have large crops , which allow them to store and digest food for some time after retiring to

15840-414: The senses." This principle goes back at least as far as Aristotle, who wrote "Nature operates in the shortest way possible." The idea of parsimony or simplicity in deciding between theories, though not the intent of the original expression of Occam's razor, has been assimilated into common culture as the widespread layman's formulation that "the simplest explanation is usually the correct one." Prior to

15972-545: The simplest theory: "Either science is irrational [in the way it judges theories and predictions probable] or the principle of simplicity is a fundamental synthetic a priori truth." From the Tractatus Logico-Philosophicus : and on the related concept of "simplicity": In science , Occam's razor is used as a heuristic to guide scientists in developing theoretical models rather than as an arbiter between published models. In physics , parsimony

16104-423: The sister taxon to the black cockatoo species of the genus Calyptorhynchus or as the sister taxon to a clade consisting of the white and pink cockatoo genera as well as the palm cockatoo . The remaining species are within two main clades, one consisting of the black species of the genus Calyptorhynchus while the other contains the remaining species. According to most authorities, the second clade includes

16236-404: The slang "galah" is Alf Stewart from Home and Away , who is often heard saying "Flaming galah!" when he is riled by somebody. The Australian representative team of footballers who played a series of test matches of international rules football against Irish sides in the late 1960s adopted the nickname "The Galahs" after a disparaging reference to their uniform. Angry Birds includes

16368-635: The source of competition, both with other members of the same species and with other species and types of animal. In general, cockatoos choose hollows only a little larger than themselves, hence different-sized species nest in holes of corresponding (and different) sizes. If given the opportunity, cockatoos prefer nesting over 7 or 8 metres (23 or 26 ft) above the ground and close to water and food. The nesting hollows are lined with sticks, wood chips and branches with leaves. The eggs of cockatoos are oval and initially white, as their location makes camouflage unnecessary. However, they do become discoloured over

16500-596: The superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." Ptolemy ( c.  AD 90  – c.  168 ) stated, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible." Phrases such as "It is vain to do with more what can be done with fewer" and "A plurality is not to be posited without necessity" were commonplace in 13th-century scholastic writing. Robert Grosseteste, in Commentary on [Aristotle's]

16632-414: The time, however, Occam's razor is a conservative tool, cutting out "crazy, complicated constructions" and assuring "that hypotheses are grounded in the science of the day", thus yielding "normal" science: models of explanation and prediction. There are, however, notable exceptions where Occam's razor turns a conservative scientist into a reluctant revolutionary. For example, Max Planck interpolated between

16764-509: The wave—nor the particle—explanation alone suffices, as light behaves like waves and like particles . Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam's razor and parsimony support, but do not prove, these axioms of science. The general principle of science

16896-573: The wild, PBFD may pose a high risk to smaller stressed populations. A white cockatoo and a sulphur-crested cockatoo were found to be infected with the protozoon Haemoproteus and another sulphur-crested cockatoo had the malaria parasite Plasmodium on analysis of faecal samples at Almuñecar ornithological garden in Granada in Spain. Like amazon parrots and macaws, cockatoos frequently develop cloacal papillomas . The relationship with malignancy

17028-472: Was introduced to Tasmania , where it is now widespread, in the mid-19th century and much more recently to New Zealand . The term galah is derived from gilaa , a word from the Yuwaalaraay and neighbouring Aboriginal languages spoken in north-western New South Wales . The galah is about 35 cm (14 in) in length, and weighs 270–350 g (10–12 oz). It has a pale silver to grey back,

17160-463: Was an important heuristic in the development and application of the principle of least action by Pierre Louis Maupertuis and Leonhard Euler , in Albert Einstein 's formulation of special relativity , and in the development of quantum mechanics by Max Planck , Werner Heisenberg and Louis de Broglie . In chemistry , Occam's razor is often an important heuristic when developing

17292-522: Was formulated by the Irish Franciscan philosopher John Punch in his 1639 commentary on the works of Duns Scotus . The origins of what has come to be known as Occam's razor are traceable to the works of earlier philosophers such as John Duns Scotus (1265–1308), Robert Grosseteste (1175–1253), Maimonides (Moses ben-Maimon, 1138–1204), and even Aristotle (384–322 BC). Aristotle writes in his Posterior Analytics , "We may assume

17424-442: Was indeed correct except for the placement of the cockatiel. Ignorance of this fact, however, led to attempts to resolve the evolutionary history and prehistoric biogeography of the cockatoos, which ultimately proved fruitless because they were based on invalid assumptions to start with. It fell to the study of Brown & Toft (1999) to compare the previously available data with their mitochondrial 12S rRNA sequence to resolve

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