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Archimedes' screw. A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. Athenaeus of Naucratis quotes a certain Moschion in a description on how King Hiero II commissioned the design of a huge ship, the "Syracusia", which could be used for luxury travel, carrying supplies, and as a display of naval power. The "Syracusia" is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. The ship presumably was capable of carrying 600 people and included garden decorations, a gymnasium, and a temple dedicated to the goddess Aphrodite among its facilities. The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes. Archimedes' screw was turned by hand, and could also be used to transfer water from a body of water into irrigation canals. The screw is still in use today for pumping liquids and granulated solids such as coal and grain. Described by Vitruvius, Archimedes' device may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon. The world's first seagoing steamship with a screw propeller was the SS "Archimedes", which was launched in 1839 and named in honor of Archimedes and his work on the screw.
Archimedes' claw. Archimedes is said to have designed a claw as a weapon to defend the city of Syracuse. Also known as "", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled "Superweapons of the Ancient World" built a version of the claw and concluded that it was a workable device. Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled. Heat ray. As legend has it, Archimedes arranged mirrors as a parabolic reflector to burn ships attacking Syracuse using focused sunlight. While there is no extant contemporary evidence of this feat and modern scholars believe it did not happen, Archimedes may have written a work on mirrors entitled "Catoptrica", and Lucian and Galen, writing in the second century AD, mentioned that during the siege of Syracuse Archimedes had burned enemy ships. Nearly four hundred years later, Anthemius, despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry.
The purported device, sometimes called "Archimedes' heat ray", has been the subject of an ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes, mostly with negative results. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship, but the overall effect would have been blinding, dazzling, or distracting the crew of the ship rather than fire. Using modern materials and larger scale, sunlight-concentrating solar furnaces can reach very high temperatures, and are sometimes used for generating electricity. Astronomical instruments. Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as Aristarchus' heliocentric model of the universe, in the "Sand-Reckoner". Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves), applying correction factors to these measurements, and finally giving the result in the form of upper and lower bounds to account for observational error. Ptolemy, quoting Hipparchus, also references Archimedes' solstice observations in the "Almagest". This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years.
Cicero's "De re publica" portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse in the Second Punic War, Marcellus is said to have taken back to Rome two mechanisms which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets. Cicero also mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome. Marcellus's mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus: This is a description of a small planetarium. Pappus of Alexandria reports on a now lost treatise by Archimedes dealing with the construction of these mechanisms entitled "On Sphere-Making". Modern research in this area has been focused on the Antikythera mechanism, another device built BC designed with a similar purpose, with some scholars regarding Archimedes' device as a precursor. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.
Mathematics. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", though some scholars believe this may be a mischaracterization. Method of exhaustion. Archimedes was able to use indivisibles (a precursor to infinitesimals) in a way that is similar to modern integral calculus. Through proof by contradiction ("reductio ad absurdum"), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the areas of figures and the value of . In "Measurement of a Circle", he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of a circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of lay between 3 (approx. 3.1429) and 3 (approx. 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to multiplied by the square of the radius of the circle (formula_1).
Archimedean property. In "On the Sphere and Cylinder", Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. Archimedes gives the value of the square root of 3 as lying between (approximately 1.7320261) and (approximately 1.7320512) in "Measurement of a Circle". The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results." It is possible that he used an iterative procedure to calculate these values. The infinite series. In "Quadrature of the Parabola", Archimedes proved that the area enclosed by a parabola and a straight line is times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio :
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on. This proof uses a variation of the series which sums to . Myriad of myriads. In "The Sand Reckoner", Archimedes set out to calculate a number that was greater than the grains of sand needed to fill the universe. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote:There are some, King Gelo, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited.To solve the problem, Archimedes devised a system of counting based on the myriad. The word itself derives from the Greek , for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion, or 8.
Writings. The works of Archimedes were written in Doric Greek, the dialect of ancient Syracuse. Many written works by Archimedes have not survived or are only extant in heavily edited fragments; at least seven of his treatises are known to have existed due to references made by other authors. Pappus of Alexandria mentions "On Sphere-Making" and another work on polyhedra, while Theon of Alexandria quotes a remark about refraction from the "Catoptrica". Archimedes made his work known through correspondence with mathematicians in Alexandria. The writings of Archimedes were first collected by the Byzantine Greek architect Isidore of Miletus (), while commentaries on the works of Archimedes written by Eutocius in the same century helped bring his work to a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and into Latin via Arabic by Gerard of Cremona (c. 1114–1187). Direct Greek to Latin translations were later done by William of Moerbeke (c. 1215–1286) and Iacobus Cremonensis (c. 1400–1453).
During the Renaissance, the "Editio princeps" (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin. Surviving works. The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986). "Measurement of a Circle". This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes gives an approximation of the value of pi (), showing that it is greater than (3.1408...) and less than (3.1428...). "The Sand Reckoner". In this treatise, also known as Psammites, Archimedes finds a number that is greater than the grains of sand needed to fill the universe. This book mentions the heliocentric theory of the Solar System proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies, and attempts to measure the apparent diameter of the Sun. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. "The Sand Reckoner" is the only surviving work in which Archimedes discusses his views on astronomy.
"On the Equilibrium of Planes". There are two books to "On the Equilibrium of Planes": the first contains seven postulates and fifteen propositions, while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever, which states that: Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, parallelograms and parabolas. "Quadrature of the Parabola". In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He achieves this in one of his proofs by calculating the value of a geometric series that sums to infinity with the ratio 1/4. "On the Sphere and Cylinder". In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 3 for the sphere, and 23 for the cylinder. The surface area is 42 for the sphere, and 62 for the cylinder (including its two bases), where is the radius of the sphere and cylinder.
"On Spirals". This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in modern polar coordinates (, ), it can be described by the equation formula_3 with real numbers and . This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician. "On Conoids and Spheroids". This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids. "On Floating Bodies". There are two books of "On Floating Bodies". In the first book, Archimedes spells out the law of equilibrium of fluids and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not since he assumes the existence of a point towards which all things fall in order to derive the spherical shape. Archimedes' principle of buoyancy is given in this work, stated as follows:
Any body wholly or partially immersed in fluid experiences an upthrust equal to, but opposite in direction to, the weight of the fluid displaced. In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. "Ostomachion". Also known as Loculus of Archimedes or Archimedes' Box, this is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Reviel Netz of Stanford University argued in 2003 that Archimedes was attempting to determine how many ways the pieces could be assembled into the shape of a square. Netz calculates that the pieces can be made into a square 17,152 ways. The number of arrangements is 536 when solutions that are equivalent by rotation and reflection are excluded. The puzzle represents an example of an early problem in combinatorics.
The origin of the puzzle's name is unclear, and it has been suggested that it is taken from the Ancient Greek word for "throat" or "gullet", "stomachos" (). Ausonius calls the puzzle , a Greek compound word formed from the roots of () and (). The cattle problem. Gotthold Ephraim Lessing discovered this work in a Greek manuscript consisting of a 44-line poem in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. A. Amthor first solved this version of the problem in 1880, and the answer is a very large number, approximately 7.760271. "The Method of Mechanical Theorems". This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses indivisibles, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. He may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with "The Cattle Problem", "The Method of Mechanical Theorems" was written in the form of a letter to Eratosthenes in Alexandria.
Apocryphal works. Archimedes' "Book of Lemmas" or "Liber Assumptorum" is a treatise with 15 propositions on the nature of circles. The earliest known copy of the text is in Arabic. T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The "Lemmas" may be based on an earlier work by Archimedes that is now lost. It has also been claimed that the formula for calculating the area of a triangle from the length of its sides was known to Archimedes, though its first appearance is in the work of Heron of Alexandria in the 1st century AD. Other questionable attributions to Archimedes' work include the Latin poem "Carmen de ponderibus et mensuris" (4th or 5th century), which describes the use of a hydrostatic balance, to solve the problem of the crown, and the 12th-century text "Mappae clavicula", which contains instructions on how to perform assaying of metals by calculating their specific gravities.
Archimedes Palimpsest. The foremost document containing Archimedes' work is the Archimedes Palimpsest. In 1906, the Danish professor Johan Ludvig Heiberg visited Constantinople to examine a 174-page goatskin parchment of prayers, written in the 13th century, after reading a short transcription published seven years earlier by Papadopoulos-Kerameus. He confirmed that it was indeed a palimpsest, a document with text that had been written over an erased older work. Palimpsests were created by scraping the ink from existing works and reusing them, a common practice in the Middle Ages, as vellum was expensive. The older works in the palimpsest were identified by scholars as 10th-century copies of previously lost treatises by Archimedes. The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On 29 October 1998, it was sold at auction to an anonymous buyer for a total of $2.2 million. The palimpsest holds seven treatises, including the only surviving copy of "On Floating Bodies" in the original Greek. It is the only known source of "The Method of Mechanical Theorems", referred to by Suidas and thought to have been lost forever. "Stomachion" was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest was stored at the Walters Art Museum in Baltimore, Maryland, where it was subjected to a range of modern tests including the use of ultraviolet and light to read the overwritten text. It has since returned to its anonymous owner.
The treatises in the Archimedes Palimpsest include: Legacy. Sometimes called the father of mathematics and mathematical physics, Archimedes had a wide influence on mathematics and science. Mathematics and physics. Historians of science and mathematics almost universally agree that Archimedes was the finest mathematician from antiquity. Eric Temple Bell, for instance, wrote: Likewise, Alfred North Whitehead and George F. Simmons said of Archimedes: Reviel Netz, Suppes Professor in Greek Mathematics and Astronomy at Stanford University and an expert in Archimedes notes: Leonardo da Vinci repeatedly expressed admiration for Archimedes, and attributed his invention Architonnerre to Archimedes. Galileo Galilei called him "superhuman" and "my master", while Christiaan Huygens said, "I think Archimedes is comparable to no one", consciously emulating him in his early work. Gottfried Wilhelm Leibniz said, "He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times". Gauss's heroes were Archimedes and Newton, and Moritz Cantor, who studied under Gauss in the University of Göttingen, reported that he once remarked in conversation that "there had been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein".
The inventor Nikola Tesla praised him, saying: Honors and commemorations. Italian numismatist and archaeologist Filippo Paruta (1552–1629) and Leonardo Agostini (1593–1676) reported on a bronze coin in Sicily with the portrait of Archimedes on the obverse and a cylinder and sphere with the monogram ARMD in Latin on the reverse. Although the coin is now lost and its date is not precisely known, Ivo Schneider described the reverse as "a sphere resting on a base – probably a rough image of one of the planetaria created by Archimedes," and suggested it might have been minted in Rome for Marcellus who "according to ancient reports, brought two spheres of Archimedes with him to Rome". There is a crater on the Moon named Archimedes () in his honor, as well as a lunar mountain range, the Montes Archimedes (). The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with a carving illustrating his proof on the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to 1st century AD poet Manilius, which reads in Latin: "Transire suum pectus mundoque potiri" ("Rise above oneself and grasp the world"). Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982), and Spain (1963). The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance, the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California gold rush.
Alternative medicine Alternative medicine is any practice that aims to achieve the healing effects of medicine despite lacking biological plausibility, testability, repeatability or evidence of effectiveness. Unlike modern medicine, which employs the scientific method to test plausible therapies by way of responsible and ethical clinical trials, producing repeatable evidence of either effect or of no effect, alternative therapies reside outside of mainstream medicine and do not originate from using the scientific method, but instead rely on testimonials, anecdotes, religion, tradition, superstition, belief in supernatural "energies", pseudoscience, errors in reasoning, propaganda, fraud, or other unscientific sources. Frequently used terms for relevant practices are New Age medicine, pseudo-medicine, unorthodox medicine, holistic medicine, fringe medicine, and unconventional medicine, with little distinction from quackery. Some alternative practices are based on theories that contradict the established science of how the human body works; others appeal to the supernatural or superstitious to explain their effect or lack thereof. In others, the practice has plausibility but lacks a positive risk–benefit outcome probability. Research into alternative therapies often fails to follow proper research protocols (such as placebo-controlled trials, blind experiments and calculation of prior probability), providing invalid results. History has shown that if a method is proven to work, it eventually ceases to be alternative and becomes mainstream medicine.
Much of the perceived effect of an alternative practice arises from a belief that it will be effective, the placebo effect, or from the treated condition resolving on its own (the natural course of disease). This is further exacerbated by the tendency to turn to alternative therapies upon the failure of medicine, at which point the condition will be at its worst and most likely to spontaneously improve. In the absence of this bias, especially for diseases that are not expected to get better by themselves such as cancer or HIV infection, multiple studies have shown significantly worse outcomes if patients turn to alternative therapies. While this may be because these patients avoid effective treatment, some alternative therapies are actively harmful (e.g. cyanide poisoning from amygdalin, or the intentional ingestion of hydrogen peroxide) or actively interfere with effective treatments. The alternative medicine sector is a highly profitable industry with a strong lobby, and faces far less regulation over the use and marketing of unproven treatments. Complementary medicine (CM), complementary and alternative medicine (CAM), integrated medicine or integrative medicine (IM), and holistic medicine attempt to combine alternative practices with those of mainstream medicine. Traditional medicine practices become "alternative" when used outside their original settings and without proper scientific explanation and evidence. Alternative methods are often marketed as more "natural" or "holistic" than methods offered by medical science, that is sometimes derogatorily called "Big Pharma" by supporters of alternative medicine. Billions of dollars have been spent studying alternative medicine, with few or no positive results and many methods thoroughly disproven.
Definitions and terminology. The terms "alternative medicine", "complementary medicine", "integrative medicine," "holistic medicine", "natural medicine", "unorthodox medicine", "fringe medicine", "unconventional medicine", and "new age medicine" are used interchangeably as having the same meaning and are almost synonymous in most contexts. Terminology has shifted over time, reflecting the preferred branding of practitioners. For example, the United States National Institutes of Health department studying alternative medicine, currently named the National Center for Complementary and Integrative Health (NCCIH), was established as the "Office of Alternative Medicine" (OAM) and was renamed the "National Center for Complementary and Alternative Medicine" (NCCAM) before obtaining its current name. Therapies are often framed as "natural" or "holistic", implicitly and intentionally suggesting that conventional medicine is "artificial" and "narrow in scope". The meaning of the term "alternative" in the expression "alternative medicine", is not that it is an effective alternative to medical science (though some alternative medicine promoters may use the loose terminology to give the appearance of effectiveness).<ref name="Sampson_6/1995"></ref> Loose terminology may also be used to suggest meaning that a dichotomy exists when it does not (e.g., the use of the expressions "Western medicine" and "Eastern medicine" to suggest that the difference is a cultural difference between the Asian east and the European west, rather than that the difference is between evidence-based medicine and treatments that do not work).
Alternative medicine. Alternative medicine is defined loosely as a set of products, practices, and theories that are believed or perceived by their users to have the healing effects of medicine, but whose effectiveness has not been established using scientific methods, or whose theory and practice is not part of biomedicine, or whose theories or practices are directly contradicted by scientific evidence or scientific principles used in biomedicine. "Biomedicine" or "medicine" is that part of medical science that applies principles of biology, physiology, molecular biology, biophysics, and other natural sciences to clinical practice, using scientific methods to establish the effectiveness of that practice. Unlike medicine, an alternative product or practice does not originate from using scientific methods, but may instead be based on hearsay, religion, tradition, superstition, belief in supernatural energies, pseudoscience, errors in reasoning, propaganda, fraud, or other unscientific sources. Some other definitions seek to specify alternative medicine in terms of its social and political marginality to mainstream healthcare. This can refer to the lack of support that alternative therapies receive from medical scientists regarding access to research funding, sympathetic coverage in the medical press, or inclusion in the standard medical curriculum. For example, a widely used definition devised by the US NCCIH calls it "a group of diverse medical and health care systems, practices, and products that are not generally considered part of conventional medicine". However, these descriptive definitions are inadequate in the present-day when some conventional doctors offer alternative medical treatments and introductory courses or modules can be offered as part of standard undergraduate medical training; alternative medicine is taught in more than half of US medical schools and US health insurers are increasingly willing to provide reimbursement for alternative therapies.
Complementary or integrative medicine. Complementary medicine (CM) or integrative medicine (IM) is when alternative medicine is used together with mainstream medical treatment in a belief that it improves the effect of treatments. For example, acupuncture (piercing the body with needles to influence the flow of a supernatural energy) might be believed to increase the effectiveness or "complement" science-based medicine when used at the same time. Significant drug interactions caused by alternative therapies may make treatments less effective, notably in cancer therapy. Several medical organizations differentiate between complementary and alternative medicine including the UK National Health Service (NHS), Cancer Research UK, and the US Center for Disease Control and Prevention (CDC), the latter of which states that ""Complementary medicine" is used in addition to standard treatments" whereas ""Alternative medicine" is used instead of standard treatments." Complementary and integrative interventions are used to improve fatigue in adult cancer patients.
David Gorski has described integrative medicine as an attempt to bring pseudoscience into academic science-based medicine with skeptics such as Gorski and David Colquhoun referring to this with the pejorative term "quackademia". Robert Todd Carroll described Integrative medicine as "a synonym for 'alternative' medicine that, at its worst, integrates sense with nonsense. At its best, integrative medicine supports both consensus treatments of science-based medicine and treatments that the science, while promising perhaps, does not justify" Rose Shapiro has criticized the field of alternative medicine for rebranding the same practices as integrative medicine. CAM is an abbreviation of the phrase "complementary and alternative medicine". The 2019 World Health Organization (WHO) Global Report on Traditional and Complementary Medicine states that the terms complementary and alternative medicine "refer to a broad set of health care practices that are not part of that country's own traditional or conventional medicine and are not fully integrated into the dominant health care system. They are used interchangeably with traditional medicine in some countries."
In the 1990s, integrative medicine started to be marketed by a new term, functional medicine. The Integrative Medicine Exam by the American Board of Physician Specialties includes the following subjects: Manual Therapies, Biofield Therapies, Acupuncture, Movement Therapies, Expressive Arts, Traditional Chinese Medicine, Ayurveda, Indigenous Medical Systems, Homeopathic Medicine, Naturopathic Medicine, Osteopathic Medicine, Chiropractic, and Functional Medicine. Other terms. Traditional medicine (TM) refers to certain practices within a culture which have existed since before the advent of medical science, Many TM practices are based on "holistic" approaches to disease and health, versus the scientific evidence-based methods in conventional medicine. The 2019 WHO report defines traditional medicine as "the sum total of the knowledge, skill and practices based on the theories, beliefs and experiences indigenous to different cultures, whether explicable or not, used in the maintenance of health as well as in the prevention, diagnosis, improvement or treatment of physical and mental illness." When used outside the original setting and in the absence of scientific evidence, TM practices are typically referred to as "alternative medicine".
is another rebranding of alternative medicine. In this case, the words "balance" and "holism" are often used alongside "complementary" or "integrative", claiming to take into fuller account the "whole" person, in contrast to the supposed reductionism of medicine. Challenges in defining alternative medicine. Prominent members of the science and biomedical science community say that it is not meaningful to define an alternative medicine that is separate from a conventional medicine because the expressions "conventional medicine", "alternative medicine", "complementary medicine", "integrative medicine", and "holistic medicine" do not refer to any medicine at all. Others say that alternative medicine cannot be precisely defined because of the diversity of theories and practices it includes, and because the boundaries between alternative and conventional medicine overlap, are porous, and change. Healthcare practices categorized as alternative may differ in their historical origin, theoretical basis, diagnostic technique, therapeutic practice and in their relationship to the medical mainstream. Under a definition of alternative medicine as "non-mainstream", treatments considered alternative in one location may be considered conventional in another.
Critics say the expression is deceptive because it implies there is an effective alternative to science-based medicine, and that "complementary" is deceptive because it implies that the treatment increases the effectiveness of (complements) science-based medicine, while alternative medicines that have been tested nearly always have no measurable positive effect compared to a placebo. Journalist John Diamond wrote that "there is really no such thing as alternative medicine, just medicine that works and medicine that doesn't", a notion later echoed by Paul Offit: "The truth is there's no such thing as conventional or alternative or complementary or integrative or holistic medicine. There's only medicine that works and medicine that doesn't. And the best way to sort it out is by carefully evaluating scientific studies—not by visiting Internet chat rooms, reading magazine articles, or talking to friends." Types. Alternative medicine consists of a wide range of health care practices, products, and therapies. The shared feature is a claim to heal that is not based on the scientific method. Alternative medicine practices are diverse in their foundations and methodologies. Alternative medicine practices may be classified by their cultural origins or by the types of beliefs upon which they are based. Methods may incorporate or be based on traditional medicinal practices of a particular culture, folk knowledge, superstition, spiritual beliefs, belief in supernatural energies (antiscience), pseudoscience, errors in reasoning, propaganda, fraud, new or different concepts of health and disease, and any bases other than being proven by scientific methods. Different cultures may have their own unique traditional or belief based practices developed recently or over thousands of years, and specific practices or entire systems of practices.
Unscientific belief systems. Alternative medicine, such as using naturopathy or homeopathy in place of conventional medicine, is based on belief systems not grounded in science. Traditional ethnic systems. Alternative medical systems may be based on traditional medicine practices, such as traditional Chinese medicine (TCM), Ayurveda in India, or practices of other cultures around the world. Some useful applications of traditional medicines have been researched and accepted within ordinary medicine, however the underlying belief systems are seldom scientific and are not accepted. Traditional medicine is considered alternative when it is used outside its home region; or when it is used together with or instead of known functional treatment; or when it can be reasonably expected that the patient or practitioner knows or should know that it will not work – such as knowing that the practice is based on superstition. Supernatural energies. Bases of belief may include belief in existence of supernatural energies undetected by the science of physics, as in biofields, or in belief in properties of the energies of physics that are inconsistent with the laws of physics, as in energy medicine.
Herbal remedies and other substances. Substance based practices use substances found in nature such as herbs, foods, non-vitamin supplements and megavitamins, animal and fungal products, and minerals, including use of these products in traditional medical practices that may also incorporate other methods. Examples include healing claims for non-vitamin supplements, fish oil, Omega-3 fatty acid, glucosamine, echinacea, flaxseed oil, and ginseng. Herbal medicine, or phytotherapy, includes not just the use of plant products, but may also include the use of animal and mineral products. It is among the most commercially successful branches of alternative medicine, and includes the tablets, powders and elixirs that are sold as "nutritional supplements". Only a very small percentage of these have been shown to have any efficacy, and there is little regulation as to standards and safety of their contents. NCCIH classification. The United States agency National Center for Complementary and Integrative Health (NCCIH) has created a classification system for branches of complementary and alternative medicine that divides them into five major groups. These groups have some overlap, and distinguish two types of energy medicine: "veritable" which involves scientifically observable energy (including magnet therapy, colorpuncture and light therapy) and "putative", which invokes physically undetectable or unverifiable energy. None of these energies have any evidence to support that they affect the body in any positive or health promoting way.
History. The history of alternative medicine may refer to the history of a group of diverse medical practices that were collectively promoted as "alternative medicine" beginning in the 1970s, to the collection of individual histories of members of that group, or to the history of western medical practices that were labeled "irregular practices" by the western medical establishment.<ref name="RiseRise_6/2004"></ref><ref name="Whorton_9/2002"></ref> It includes the histories of complementary medicine and of integrative medicine. Before the 1970s, western practitioners that were not part of the increasingly science-based medical establishment were referred to "irregular practitioners", and were dismissed by the medical establishment as unscientific and as practicing quackery. Until the 1970s, irregular practice became increasingly marginalized as quackery and fraud, as western medicine increasingly incorporated scientific methods and discoveries, and had a corresponding increase in success of its treatments. In the 1970s, irregular practices were grouped with traditional practices of nonwestern cultures and with other unproven or disproven practices that were not part of biomedicine, with the entire group collectively marketed and promoted under the single expression "alternative medicine".
Use of alternative medicine in the west began to rise following the counterculture movement of the 1960s, as part of the rising new age movement of the 1970s. This was due to misleading mass marketing of "alternative medicine" being an effective "alternative" to biomedicine, changing social attitudes about not using chemicals and challenging the establishment and authority of any kind, sensitivity to giving equal measure to beliefs and practices of other cultures (cultural relativism), and growing frustration and desperation by patients about limitations and side effects of science-based medicine. At the same time, in 1975, the American Medical Association, which played the central role in fighting quackery in the United States, abolished its quackery committee and closed down its Department of Investigation. By the early to mid 1970s the expression "alternative medicine" came into widespread use, and the expression became mass marketed as a collection of "natural" and effective treatment "alternatives" to science-based biomedicine. By 1983, mass marketing of "alternative medicine" was so pervasive that the "British Medical Journal" ("BMJ") pointed to "an apparently endless stream of books, articles, and radio and television programmes urge on the public the virtues of (alternative medicine) treatments ranging from meditation to drilling a hole in the skull to let in more oxygen".
An analysis of trends in the criticism of complementary and alternative medicine (CAM) in five prestigious American medical journals during the period of reorganization within medicine (1965–1999) was reported as showing that the medical profession had responded to the growth of CAM in three phases, and that in each phase, changes in the medical marketplace had influenced the type of response in the journals. Changes included relaxed medical licensing, the development of managed care, rising consumerism, and the establishment of the USA Office of Alternative Medicine (later National Center for Complementary and Alternative Medicine, currently National Center for Complementary and Integrative Health). Medical education. Mainly as a result of reforms following the Flexner Report of 1910 medical education in established medical schools in the US has generally not included alternative medicine as a teaching topic. Typically, their teaching is based on current practice and scientific knowledge about: anatomy, physiology, histology, embryology, neuroanatomy, pathology, pharmacology, microbiology and immunology. Medical schools' teaching includes such topics as doctor-patient communication, ethics, the art of medicine, and engaging in complex clinical reasoning (medical decision-making). Writing in 2002, Snyderman and Weil remarked that by the early twentieth century the Flexner model had helped to create the 20th-century academic health center, in which education, research, and practice were inseparable. While this had much improved medical practice by defining with increasing certainty the pathophysiological basis of disease, a single-minded focus on the pathophysiological had diverted much of mainstream American medicine from clinical conditions that were not well understood in mechanistic terms, and were not effectively treated by conventional therapies.
By 2001 some form of CAM training was being offered by at least 75 out of 125 medical schools in the US. Exceptionally, the School of Medicine of the University of Maryland, Baltimore, includes a research institute for integrative medicine (a member entity of the Cochrane Collaboration). Medical schools are responsible for conferring medical degrees, but a physician typically may not legally practice medicine until licensed by the local government authority. Licensed physicians in the US who have attended one of the established medical schools there have usually graduated Doctor of Medicine (MD). All states require that applicants for MD licensure be graduates of an approved medical school and complete the United States Medical Licensing Examination (USMLE). Efficacy. There is a general scientific consensus that alternative therapies lack the requisite scientific validation, and their effectiveness is either unproved or disproved. Many of the claims regarding the efficacy of alternative medicines are controversial, since research on them is frequently of low quality and methodologically flawed. Selective publication bias, marked differences in product quality and standardisation, and some companies making unsubstantiated claims call into question the claims of efficacy of isolated examples where there is evidence for alternative therapies.
"The Scientific Review of Alternative Medicine" points to confusions in the general population – a person may attribute symptomatic relief to an otherwise-ineffective therapy just because they are taking something (the placebo effect); the natural recovery from or the cyclical nature of an illness (the regression fallacy) gets misattributed to an alternative medicine being taken; a person not diagnosed with science-based medicine may never originally have had a true illness diagnosed as an alternative disease category. Edzard Ernst, the first university professor of Complementary and Alternative Medicine, characterized the evidence for many alternative techniques as weak, nonexistent, or negative and in 2011 published his estimate that about 7.4% were based on "sound evidence", although he believes that may be an overestimate. Ernst has concluded that 95% of the alternative therapies he and his team studied, including acupuncture, herbal medicine, homeopathy, and reflexology, are "statistically indistinguishable from placebo treatments", but he also believes there is something that conventional doctors can usefully learn from the chiropractors and homeopath: this is the therapeutic value of the placebo effect, one of the strangest phenomena in medicine.
In 2003, a project funded by the CDC identified 208 condition-treatment pairs, of which 58% had been studied by at least one randomized controlled trial (RCT), and 23% had been assessed with a meta-analysis. According to a 2005 book by a US Institute of Medicine panel, the number of RCTs focused on CAM has risen dramatically. , the Cochrane Library had 145 CAM-related Cochrane systematic reviews and 340 non-Cochrane systematic reviews. An analysis of the conclusions of only the 145 Cochrane reviews was done by two readers. In 83% of the cases, the readers agreed. In the 17% in which they disagreed, a third reader agreed with one of the initial readers to set a rating. These studies found that, for CAM, 38.4% concluded positive effect or possibly positive (12.4%), 4.8% concluded no effect, 0.7% concluded harmful effect, and 56.6% concluded insufficient evidence. An assessment of conventional treatments found that 41.3% concluded positive or possibly positive effect, 20% concluded no effect, 8.1% concluded net harmful effects, and 21.3% concluded insufficient evidence. However, the CAM review used the more developed 2004 Cochrane database, while the conventional review used the initial 1998 Cochrane database.
Alternative therapies do not "complement" (improve the effect of, or mitigate the side effects of) functional medical treatment. Significant drug interactions caused by alternative therapies may instead negatively impact functional treatment by making prescription drugs less effective, such as interference by herbal preparations with warfarin. In the same way as for conventional therapies, drugs, and interventions, it can be difficult to test the efficacy of alternative medicine in clinical trials. In instances where an established, effective, treatment for a condition is already available, the Helsinki Declaration states that withholding such treatment is unethical in most circumstances. Use of standard-of-care treatment in addition to an alternative technique being tested may produce confounded or difficult-to-interpret results. Cancer researcher Andrew J. Vickers has stated: Perceived mechanism of effect. Anything classified as alternative medicine by definition does not have a proven healing or medical effect. However, there are different mechanisms through which it can be perceived to "work". The common denominator of these mechanisms is that effects are mis-attributed to the alternative treatment.
Placebo effect. A placebo is a treatment with no intended therapeutic value. An example of a placebo is an inert pill, but it can include more dramatic interventions like sham surgery. The "placebo effect" is the concept that patients will perceive an improvement after being treated with an inert treatment. The opposite of the placebo effect is the "nocebo effect", when patients who expect a treatment to be harmful will perceive harmful effects after taking it. Placebos do not have a physical effect on diseases or improve overall outcomes, but patients may report improvements in subjective outcomes such as pain and nausea. A 1955 study suggested that a substantial part of a medicine's impact was due to the placebo effect. However, reassessments found the study to have flawed methodology. This and other modern reviews suggest that other factors like natural recovery and reporting bias should also be considered. All of these are reasons why alternative therapies may be credited for improving a patient's condition even though the objective effect is non-existent, or even harmful. David Gorski argues that alternative treatments should be treated as a placebo, rather than as medicine. Almost none have performed significantly better than a placebo in clinical trials. Furthermore, distrust of conventional medicine may lead to patients experiencing the nocebo effect when taking effective medication.
Regression to the mean. A patient who receives an inert treatment may report improvements afterwards that it did not cause. Assuming it was the cause without evidence is an example of the regression fallacy. This may be due to a natural recovery from the illness, or a fluctuation in the symptoms of a long-term condition. The concept of regression toward the mean implies that an extreme result is more likely to be followed by a less extreme result. Other factors. There are also reasons why a placebo treatment group may outperform a "no-treatment" group in a test which are not related to a patient's experience. These include patients reporting more favourable results than they really felt due to politeness or "experimental subordination", observer bias, and misleading wording of questions. In their 2010 systematic review of studies into placebos, Asbjørn Hróbjartsson and Peter C. Gøtzsche write that "even if there were no true effect of placebo, one would expect to record differences between placebo and no-treatment groups due to bias associated with lack of blinding." Alternative therapies may also be credited for perceived improvement through decreased use or effect of medical treatment, and therefore either decreased side effects or nocebo effects towards standard treatment.
Use and regulation. Appeal. Practitioners of complementary medicine usually discuss and advise patients as to available alternative therapies. Patients often express interest in mind-body complementary therapies because they offer a non-drug approach to treating some health conditions. In addition to the social-cultural underpinnings of the popularity of alternative medicine, there are several psychological issues that are critical to its growth, notably psychological effects, such as the will to believe, cognitive biases that help maintain self-esteem and promote harmonious social functioning, and the "post hoc, ergo propter hoc" fallacy. In a 2018 interview with "The BMJ", Edzard Ernst stated: "The present popularity of complementary and alternative medicine is also inviting criticism of what we are doing in mainstream medicine. It shows that we aren't fulfilling a certain need-we are not giving patients enough time, compassion, or empathy. These are things that complementary practitioners are very good at. Mainstream medicine could learn something from complementary medicine."
Marketing. Alternative medicine is a profitable industry with large media advertising expenditures. Accordingly, alternative practices are often portrayed positively and compared favorably to "big pharma". The popularity of complementary & alternative medicine (CAM) may be related to other factors that Ernst mentioned in a 2008 interview in "The Independent": Paul Offit proposed that "alternative medicine becomes quackery" in four ways: by recommending against conventional therapies that are helpful, promoting potentially harmful therapies without adequate warning, draining patients' bank accounts, or by promoting "magical thinking". Promoting alternative medicine has been called dangerous and unethical. Social factors. Authors have speculated on the socio-cultural and psychological reasons for the appeal of alternative medicines among the minority using them "in lieu" of conventional medicine. There are several socio-cultural reasons for the interest in these treatments centered on the low level of scientific literacy among the public at large and a concomitant increase in antiscientific attitudes and new age mysticism. Related to this are vigorous marketing of extravagant claims by the alternative medical community combined with inadequate media scrutiny and attacks on critics. Alternative medicine is criticized for taking advantage of the least fortunate members of society.
There is also an increase in conspiracy theories toward conventional medicine and pharmaceutical companies, mistrust of traditional authority figures, such as the physician, and a dislike of the current delivery methods of scientific biomedicine, all of which have led patients to seek out alternative medicine to treat a variety of ailments. Many patients lack access to contemporary medicine, due to a lack of private or public health insurance, which leads them to seek out lower-cost alternative medicine. Medical doctors are also aggressively marketing alternative medicine to profit from this market. Patients can be averse to the painful, unpleasant, and sometimes-dangerous side effects of biomedical treatments. Treatments for severe diseases such as cancer and HIV infection have well-known, significant side-effects. Even low-risk medications such as antibiotics can have potential to cause life-threatening anaphylactic reactions in a very few individuals. Many medications may cause minor but bothersome symptoms such as cough or upset stomach. In all of these cases, patients may be seeking out alternative therapies to avoid the adverse effects of conventional treatments.
Prevalence of use. According to research published in 2015, the increasing popularity of CAM needs to be explained by moral convictions or lifestyle choices rather than by economic reasoning. In developing nations, access to essential medicines is severely restricted by lack of resources and poverty. Traditional remedies, often closely resembling or forming the basis for alternative remedies, may comprise primary healthcare or be integrated into the healthcare system. In Africa, traditional medicine is used for 80% of primary healthcare, and in developing nations as a whole over one-third of the population lack access to essential medicines. In Latin America, inequities against BIPOC communities keep them tied to their traditional practices and therefore, it is often these communities that constitute the majority of users of alternative medicine. Racist attitudes towards certain communities disable them from accessing more urbanized modes of care. In a study that assessed access to care in rural communities of Latin America, it was found that discrimination is a huge barrier to the ability of citizens to access care; more specifically, women of Indigenous and African descent, and lower-income families were especially hurt. Such exclusion exacerbates the inequities that minorities in Latin America already face. Consistently excluded from many systems of westernized care for socioeconomic and other reasons, low-income communities of color often turn to traditional medicine for care as it has proved reliable to them across generations.
Commentators including David Horrobin have proposed adopting a prize system to reward medical research. This stands in opposition to the current mechanism for funding research proposals in most countries around the world. In the US, the NCCIH provides public research funding for alternative medicine. The NCCIH has spent more than US$2.5 billion on such research since 1992 and this research has not demonstrated the efficacy of alternative therapies. As of 2011, the NCCIH's sister organization in the NIC Office of Cancer Complementary and Alternative Medicine had given out grants of around $105 million each year for several years. Testing alternative medicine that has no scientific basis (as in the aforementioned grants) has been called a waste of scarce research resources. That alternative medicine has been on the rise "in countries where Western science and scientific method generally are accepted as the major foundations for healthcare, and 'evidence-based' practice is the dominant paradigm" was described as an "enigma" in the "Medical Journal of Australia". A 15-year systematic review published in 2022 on the global acceptance and use of CAM among medical specialists found the overall acceptance of CAM at 52% and the overall use at 45%.
In the United States. In the United States, the 1974 Child Abuse Prevention and Treatment Act (CAPTA) required that for states to receive federal money, they had to grant religious exemptions to child neglect and abuse laws regarding religion-based healing practices. Thirty-one states have child-abuse religious exemptions. The use of alternative medicine in the US has increased, with a 50 percent increase in expenditures and a 25 percent increase in the use of alternative therapies between 1990 and 1997 in America. According to a national survey conducted in 2002, "36 percent of U.S. adults aged 18 years and over use some form of complementary and alternative medicine." Americans spend many billions on the therapies annually. Most Americans used CAM to treat and/or prevent musculoskeletal conditions or other conditions associated with chronic or recurring pain. In America, women were more likely than men to use CAM, with the biggest difference in use of mind-body therapies including prayer specifically for health reasons". In 2008, more than 37% of American hospitals offered alternative therapies, up from 27 percent in 2005, and 25% in 2004. More than 70% of the hospitals offering CAM were in urban areas.
A survey of Americans found that 88 percent thought that "there are some good ways of treating sickness that medical science does not recognize". Use of magnets was the most common tool in energy medicine in America, and among users of it, 58 percent described it as at least "sort of scientific", when it is not at all scientific. In 2002, at least 60 percent of US medical schools have at least some class time spent teaching alternative therapies. "Therapeutic touch" was taught at more than 100 colleges and universities in 75 countries before the practice was debunked by a nine-year-old child for a school science project. Prevalence of use of specific therapies. The most common CAM therapies used in the US in 2002 were prayer (45%), herbalism (19%), breathing meditation (12%), meditation (8%), chiropractic medicine (8%), yoga (5–6%), body work (5%), diet-based therapy (4%), progressive relaxation (3%), mega-vitamin therapy (3%) and visualization (2%). In Britain, the most often used alternative therapies were Alexander technique, aromatherapy, Bach and other flower remedies, body work therapies including massage, Counseling stress therapies, hypnotherapy, meditation, reflexology, Shiatsu, Ayurvedic medicine, nutritional medicine, and yoga. Ayurvedic medicine remedies are mainly plant based with some use of animal materials. Safety concerns include the use of herbs containing toxic compounds and the lack of quality control in Ayurvedic facilities.
According to the National Health Service (England), the most commonly used complementary and alternative medicines (CAM) supported by the NHS in the UK are: acupuncture, aromatherapy, chiropractic, homeopathy, massage, osteopathy and clinical hypnotherapy. In palliative care. Complementary therapies are often used in palliative care or by practitioners attempting to manage chronic pain in patients. Integrative medicine is considered more acceptable in the interdisciplinary approach used in palliative care than in other areas of medicine. "From its early experiences of care for the dying, palliative care took for granted the necessity of placing patient values and lifestyle habits at the core of any design and delivery of quality care at the end of life. If the patient desired complementary therapies, and as long as such treatments provided additional support and did not endanger the patient, they were considered acceptable." The non-pharmacologic interventions of complementary medicine can employ mind-body interventions designed to "reduce pain and concomitant mood disturbance and increase quality of life."
Regulation. The alternative medicine lobby has successfully pushed for alternative therapies to be subject to far less regulation than conventional medicine. Some professions of complementary/traditional/alternative medicine, such as chiropractic, have achieved full regulation in North America and other parts of the world and are regulated in a manner similar to that governing science-based medicine. In contrast, other approaches may be partially recognized and others have no regulation at all. In some cases, promotion of alternative therapies is allowed when there is demonstrably no effect, only a tradition of use. Despite laws making it illegal to market or promote alternative therapies for use in cancer treatment, many practitioners promote them. Regulation and licensing of alternative medicine ranges widely from country to country, and state to state. In Austria and Germany complementary and alternative medicine is mainly in the hands of doctors with MDs, and half or more of the American alternative practitioners are licensed MDs. In Germany herbs are tightly regulated: half are prescribed by doctors and covered by health insurance.
Government bodies in the US and elsewhere have published information or guidance about alternative medicine. The U.S. Food and Drug Administration (FDA), has issued online warnings for consumers about medication health fraud. This includes a section on Alternative Medicine Fraud, such as a warning that Ayurvedic products generally have not been approved by the FDA before marketing. Risks and problems. The National Science Foundation has studied the problematic side of the public's attitudes and understandings of science fiction, pseudoscience, and belief in alternative medicine. They use a quote from Robert L. Park to describe some issues with alternative medicine: Negative outcomes. According to the Institute of Medicine, use of alternative medical techniques may result in several types of harm: Interactions with conventional pharmaceuticals. Forms of alternative medicine that are biologically active can be dangerous even when used in conjunction with conventional medicine. Examples include immuno-augmentation therapy, shark cartilage, bioresonance therapy, oxygen and ozone therapies, and insulin potentiation therapy. Some herbal remedies can cause dangerous interactions with chemotherapy drugs, radiation therapy, or anesthetics during surgery, among other problems. An example of these dangers was reported by Associate Professor Alastair MacLennan of Adelaide University, Australia regarding a patient who almost bled to death on the operating table after neglecting to mention that she had been taking "natural" potions to "build up her strength" before the operation, including a powerful anticoagulant that nearly caused her death.
To "ABC Online", MacLennan also gives another possible mechanism: Side-effects. Conventional treatments are subjected to testing for undesired side-effects, whereas alternative therapies, in general, are not subjected to such testing at all. Any treatment – whether conventional or alternative – that has a biological or psychological effect on a patient may also have potential to possess dangerous biological or psychological side-effects. Attempts to refute this fact with regard to alternative therapies sometimes use the "appeal to nature" fallacy, i.e., "That which is natural cannot be harmful." Specific groups of patients such as patients with impaired hepatic or renal function are more susceptible to side effects of alternative remedies. An exception to the normal thinking regarding side-effects is homeopathy. Since 1938, the FDA has regulated homeopathic products in "several significantly different ways from other drugs." Homeopathic preparations, termed "remedies", are extremely dilute, often far beyond the point where a single molecule of the original active (and possibly toxic) ingredient is likely to remain. They are, thus, considered safe on that count, but "their products are exempt from good manufacturing practice requirements related to expiration dating and from finished product testing for identity and strength", and their alcohol concentration may be much higher than allowed in conventional drugs.
Treatment delay. Alternative medicine may discourage people from getting the best possible treatment. Those having experienced or perceived success with one alternative therapy for a minor ailment may be convinced of its efficacy and persuaded to extrapolate that success to some other alternative therapy for a more serious, possibly life-threatening illness. For this reason, critics argue that therapies that rely on the placebo effect to define success are very dangerous. According to mental health journalist Scott Lilienfeld in 2002, "unvalidated or scientifically unsupported mental health practices can lead individuals to forgo effective treatments" and refers to this as opportunity cost. Individuals who spend large amounts of time and money on ineffective treatments may be left with precious little of either, and may forfeit the opportunity to obtain treatments that could be more helpful. In short, even innocuous treatments can indirectly produce negative outcomes. Between 2001 and 2003, four children died in Australia because their parents chose ineffective naturopathic, homeopathic, or other alternative medicines and diets rather than conventional therapies.
Unconventional cancer "cures". There have always been "many therapies offered outside of conventional cancer treatment centers and based on theories not found in biomedicine. These alternative cancer cures have often been described as 'unproven,' suggesting that appropriate clinical trials have not been conducted and that the therapeutic value of the treatment is unknown." However, "many alternative cancer treatments have been investigated in good-quality clinical trials, and they have been shown to be ineffective... The label 'unproven' is inappropriate for such therapies; it is time to assert that many alternative cancer therapies have been 'disproven'." Edzard Ernst has stated: Rejection of science. Complementary and alternative medicine (CAM) is not as well researched as conventional medicine, which undergoes intense research before release to the public. Practitioners of science-based medicine also discard practices and treatments when they are shown ineffective, while alternative practitioners do not. Funding for research is also sparse making it difficult to do further research for effectiveness of CAM. Most funding for CAM is funded by government agencies. Proposed research for CAM are rejected by most private funding agencies because the results of research are not reliable. The research for CAM has to meet certain standards from research ethics committees, which most CAM researchers find almost impossible to meet. Even with the little research done on it, CAM has not been proven to be effective. Studies that have been done will be cited by CAM practitioners in an attempt to claim a basis in science. These studies tend to have a variety of problems, such as small samples, various biases, poor research design, lack of controls, negative results, etc. Even those with positive results can be better explained as resulting in false positives due to bias and noisy data.
Alternative medicine may lead to a false understanding of the body and of the process of science. Steven Novella, a neurologist at Yale School of Medicine, wrote that government-funded studies of integrating alternative medicine techniques into the mainstream are "used to lend an appearance of legitimacy to treatments that are not legitimate." Marcia Angell considered that critics felt that healthcare practices should be classified based solely on scientific evidence, and if a treatment had been rigorously tested and found safe and effective, science-based medicine will adopt it regardless of whether it was considered "alternative" to begin with. It is possible for a method to change categories (proven vs. unproven), based on increased knowledge of its effectiveness or lack thereof. Prominent supporters of this position are George D. Lundberg, former editor of the "Journal of the American Medical Association" ("JAMA") and the journal's interim editor-in-chief Phil Fontanarosa. Writing in 1999 in "CA: A Cancer Journal for Clinicians" Barrie R. Cassileth mentioned a 1997 letter to the United States Senate's Subcommittee on Public Health and Safety, which had deplored the lack of critical thinking and scientific rigor in OAM-supported research, had been signed by four Nobel Laureates and other prominent scientists. (This was supported by the National Institutes of Health (NIH).)
In March 2009, a staff writer for "The Washington Post" reported that the impending national discussion about broadening access to health care, improving medical practice and saving money was giving a group of scientists an opening to propose shutting down the National Center for Complementary and Alternative Medicine. They quoted one of these scientists, Steven Salzberg, a genome researcher and computational biologist at the University of Maryland, as saying "One of our concerns is that NIH is funding pseudoscience." They noted that the vast majority of studies were based on fundamental misunderstandings of physiology and disease, and had shown little or no effect. Writers such as Carl Sagan, a noted astrophysicist, advocate of scientific skepticism and the author of "The Demon-Haunted World: Science as a Candle in the Dark" (1996), have lambasted the lack of empirical evidence to support the existence of the putative energy fields on which these therapies are predicated. Sampson has also pointed out that CAM tolerated contradiction without thorough reason and experiment. Barrett has pointed out that there is a policy at the NIH of never saying something does not work, only that a different version or dose might give different results. Barrett also expressed concern that, just because some "alternatives" have merit, there is the impression that the rest deserve equal consideration and respect even though most are worthless, since they are all classified under the one heading of alternative medicine.
Some critics of alternative medicine are focused upon health fraud, misinformation, and quackery as public health problems, notably Wallace Sampson and Paul Kurtz founders of Scientific Review of Alternative Medicine and Stephen Barrett, co-founder of The National Council Against Health Fraud and webmaster of Quackwatch. Grounds for opposing alternative medicine include that: Many alternative medical treatments are not patentable, which may lead to less research funding from the private sector. In addition, in most countries, alternative therapies (in contrast to pharmaceuticals) can be marketed without any proof of efficacy – also a disincentive for manufacturers to fund scientific research. English evolutionary biologist Richard Dawkins, in his 2003 book "A Devil's Chaplain", defined alternative medicine as a "set of practices that cannot be tested, refuse to be tested, or consistently fail tests." Dawkins argued that if a technique is demonstrated effective in properly performed trials then it ceases to be alternative and simply becomes medicine.
CAM is also often less regulated than conventional medicine. There are ethical concerns about whether people who perform CAM have the proper knowledge to treat patients. CAM is often done by non-physicians who do not operate with the same medical licensing laws which govern conventional medicine, and it is often described as an issue of non-maleficence. According to two writers, Wallace Sampson and K. Butler, marketing is part of the training required in alternative medicine, and propaganda methods in alternative medicine have been traced back to those used by Hitler and Goebels in their promotion of pseudoscience in medicine. In November 2011 Edzard Ernst stated that the "level of misinformation about alternative medicine has now reached the point where it has become dangerous and unethical. So far, alternative medicine has remained an ethics-free zone. It is time to change this." Harriet Hall criticized the low standard of evidence accepted by the alternative medicine community: Conflicts of interest.
Use of health and research resources. Research into alternative therapies has been criticized for "diverting research time, money, and other resources from more fruitful lines of investigation in order to pursue a theory that has no basis in biology." Research methods expert and author of "Snake Oil Science", R. Barker Bausell, has stated that "it's become politically correct to investigate nonsense." A commonly cited statistic is that the US National Institute of Health had spent $2.5 billion on investigating alternative therapies prior to 2009, with none being found to be effective.
Archimedean solid The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygons, but not all alike, and whose vertices are all symmetric to each other. The solids were named after Archimedes, although he did not claim credit for them. They belong to the class of uniform polyhedra, the polyhedra with regular faces and symmetric vertices. Some Archimedean solids were portrayed in the works of artists and mathematicians during the Renaissance. The elongated square gyrobicupola or "" is an extra polyhedron with regular faces and congruent vertices, but it is not generally counted as an Archimedean solid because it is not vertex-transitive. The solids. The Archimedean solids have a single vertex configuration and highly symmetric properties. A vertex configuration indicates which regular polygons meet at each vertex. For instance, the configuration formula_1 indicates a polyhedron in which each vertex is met by alternating two triangles and two pentagons. Highly symmetric properties in this case mean the symmetry group of each solid were derived from the Platonic solids, resulting from their construction. Some sources say the Archimedean solids are synonymous with the semiregular polyhedron. Yet, the definition of a semiregular polyhedron may also include the infinite prisms and antiprisms, including the elongated square gyrobicupola.
The construction of some Archimedean solids begins from the Platonic solids. The truncation involves cutting away corners; to preserve symmetry, the cut is in a plane perpendicular to the line joining a corner to the center of the polyhedron and is the same for all corners, and an example can be found in truncated icosahedron constructed by cutting off all the icosahedron's vertices, having the same symmetry as the icosahedron, the icosahedral symmetry. If the truncation is exactly deep enough such that each pair of faces from adjacent vertices shares exactly one point, it is known as a rectification. Expansion involves moving each face away from the center (by the same distance to preserve the symmetry of the Platonic solid) and taking the convex hull. An example is the rhombicuboctahedron, constructed by separating the cube or octahedron's faces from the centroid and filling them with squares. Snub is a construction process of polyhedra by separating the polyhedron faces, twisting their faces in certain angles, and filling them up with equilateral triangles. Examples can be found in snub cube and snub dodecahedron. The resulting construction of these solids gives the property of chirality, meaning they are not identical when reflected in a mirror. However, not all of them can be constructed in such a way, or they could be constructed alternatively. For example, the icosidodecahedron can be constructed by attaching two pentagonal rotunda base-to-base, or rhombicuboctahedron that can be constructed alternatively by attaching two square cupolas on the bases of octagonal prism.
At least ten of the Archimedean solids have the Rupert property: each can pass through a copy of itself, of the same size. They are the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron, truncated dodecahedron, and the truncated tetrahedron. The dual polyhedron of an Archimedean solid is a Catalan solid. Background of discovery. The names of Archimedean solids were taken from Ancient Greek mathematician Archimedes, who discussed them in a now-lost work. Although they were not credited to Archimedes originally, Pappus of Alexandria in the fifth section of his titled compendium "Synagoge" referring that Archimedes listed thirteen polyhedra and briefly described them in terms of how many faces of each kind these polyhedra have. During the Renaissance, artists and mathematicians valued pure forms with high symmetry. Some Archimedean solids appeared in Piero della Francesca's "De quinque corporibus regularibus", in attempting to study and copy the works of Archimedes, as well as include citations to Archimedes. Yet, he did not credit those shapes to Archimedes and know of Archimedes' work but rather appeared to be an independent rediscovery. Other appearance of the solids appeared in the works of Wenzel Jamnitzer's "Perspectiva Corporum Regularium", and both "Summa de arithmetica" and "Divina proportione" by Luca Pacioli, drawn by Leonardo da Vinci. The net of Archimedean solids appeared in Albrecht Dürer's "Underweysung der Messung", copied from the Pacioli's work. By around 1620, Johannes Kepler in his "Harmonices Mundi" had completed the rediscovery of the thirteen polyhedra, as well as defining the prisms, antiprisms, and the non-convex solids known as Kepler–Poinsot polyhedra.
Kepler may have also found another solid known as elongated square gyrobicupola or "pseudorhombicuboctahedron". Kepler once stated that there were fourteen Archimedean solids, yet his published enumeration only includes the thirteen uniform polyhedra. The first clear statement of such solid existence was made by Duncan Sommerville in 1905. The solid appeared when some mathematicians mistakenly constructed the rhombicuboctahedron: two square cupolas attached to the octagonal prism, with one of them rotated in forty-five degrees. The thirteen solids have the property of vertex-transitive, meaning any two vertices of those can be translated onto the other one, but the elongated square gyrobicupola does not. observed that it meets a weaker definition of an Archimedean solid, in which "identical vertices" means merely that the parts of the polyhedron near any two vertices look the same (they have the same shapes of faces meeting around each vertex in the same order and forming the same angles). Grünbaum pointed out a frequent error in which authors define Archimedean solids using some form of this local definition but omit the fourteenth polyhedron. If only thirteen polyhedra are to be listed, the definition must use global symmetries of the polyhedron rather than local neighborhoods. In the aftermath, the elongated square gyrobicupola was withdrawn from the Archimedean solids and included into the Johnson solids instead, a convex polyhedron in which all of the faces are regular polygons.
Antiprism In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are triangles, rather than quadrilaterals. The dual polyhedron of an -gonal antiprism is an -gonal trapezohedron. History. In his 1619 book "Harmonices Mundi", Johannes Kepler observed the existence of the infinite family of antiprisms. This has conventionally been thought of as the first discovery of these shapes, but they may have been known earlier: an unsigned printing block for the net of a hexagonal antiprism has been attributed to Hieronymus Andreae, who died in 1556. The German form of the word "antiprism" was used for these shapes in the 19th century; Karl Heinze credits its introduction to . Although the English "anti-prism" had been used earlier for an optical prism used to cancel the effects of a primary optical element, the first use of "antiprism" in English in its geometric sense appears to be in the early 20th century in the works of H. S. M. Coxeter.
Special cases. Right antiprism. For an antiprism with regular -gon bases, one usually considers the case where these two copies are twisted by an angle of degrees. The axis of a regular polygon is the line perpendicular to the polygon plane and lying in the polygon centre. For an antiprism with congruent regular -gon bases, twisted by an angle of degrees, more regularity is obtained if the bases have the same axis: are "coaxial"; i.e. (for non-coplanar bases): if the line connecting the base centers is perpendicular to the base planes. Then the antiprism is called a right antiprism, and its side faces are isosceles triangles. The symmetry group of a right -antiprism is of order known as an antiprismatic symmetry, because it could be obtained by rotation of the bottom half of a prism by formula_1 in relation to the top half. A concave polyhedron created in this way would have this symmetry group, hence prefix "anti" before "prismatic". There are two exceptions having groups different than : If a right 2- or 3-antiprism is not uniform, then its symmetry group is or as usual.
The symmetry group contains inversion if and only if is odd. The rotation group is of order , except in the cases of: If a right 2- or 3-antiprism is not uniform, then its rotation group is or as usual. The right -antiprisms have congruent regular -gon bases and congruent isosceles triangle side faces, thus have the same (dihedral) symmetry group as the uniform -antiprism, for . Uniform antiprism. A uniform -antiprism has two congruent "regular" -gons as base faces, and "equilateral" triangles as side faces. As do uniform prisms, the uniform antiprisms form an infinite class of vertex-transitive polyhedra. For , one has the digonal antiprism (degenerate antiprism), which is visually identical to the regular tetrahedron; for , the regular octahedron is a "triangular antiprism" (non-degenerate antiprism). The Schlegel diagrams of these semiregular antiprisms are as follows: Cartesian coordinates. Cartesian coordinates for the vertices of a right -antiprism (i.e. with regular -gon bases and isosceles triangle side faces, circumradius of the bases equal to 1) are:
where ; if the -antiprism is uniform (i.e. if the triangles are equilateral), then: formula_3 Volume and surface area. Let be the edge-length of a uniform -gonal antiprism; then the volume is: formula_4 and the surface area is: formula_5 Furthermore, the volume of a regular right -gonal antiprism with side length of its bases and height is given by: formula_6 Derivation. The circumradius of the horizontal circumcircle of the regular formula_7-gon at the base is The vertices at the base are at the vertices at the top are at Via linear interpolation, points on the outer triangular edges of the antiprism that connect vertices at the bottom with vertices at the top are at and at By building the sums of the squares of the formula_13 and formula_14 coordinates in one of the previous two vectors, the squared circumradius of this section at altitude formula_15 is The horizontal section at altitude formula_17 above the base is a formula_18-gon (truncated formula_7-gon) with formula_7 sides of length formula_21 alternating with formula_7 sides of length formula_23.
It can be dissected into formula_7 isoceless triangles of edges formula_25 and formula_26 (semiperimeter formula_27) plus formula_7 isoceless triangles of edges formula_25 and formula_30 (semiperimeter formula_31). According to Heron's formula the areas of these triangles are and The area of the section is formula_34, and the volume is The volume of a right -gonal prism with the same and is: formula_36 which is smaller than that of an antiprism. Generalizations. In higher dimensions. Four-dimensional antiprisms can be defined as having two dual polyhedra as parallel opposite faces, so that each three-dimensional face between them comes from two dual parts of the polyhedra: a vertex and a dual polygon, or two dual edges. Every three-dimensional convex polyhedron is combinatorially equivalent to one of the two opposite faces of a four-dimensional antiprism, constructed from its canonical polyhedron and its polar dual. However, there exist four-dimensional polychora that cannot be combined with their duals to form five-dimensional antiprisms.
Self-crossing polyhedra. Uniform star antiprisms are named by their star polygon bases, and exist in prograde and in retrograde (crossed) solutions. Crossed forms have intersecting vertex figures, and are denoted by "inverted" fractions: instead of ; example: (5/3) instead of (5/2). A right star -antiprism has two congruent coaxial regular convex or star polygon base faces, and isosceles triangle side faces. Any star antiprism with "regular" convex or star polygon bases can be made a "right" star antiprism (by translating and/or twisting one of its bases, if necessary). In the retrograde forms, but not in the prograde forms, the triangles joining the convex or star bases intersect the axis of rotational symmetry. Thus: Also, star antiprism compounds with regular star -gon bases can be constructed if and have common factors. Example: a star (10/4)-antiprism is the compound of two star (5/2)-antiprisms. Number of uniform crossed antiprisms. If the notation is used for an antiprism, then for the antiprism is crossed (by definition) and for is not. In this section all antiprisms are assumed to be non-degenerate, i.e. , . Also, the condition ( and are relatively prime) holds, as compounds are exluded from counting. The number of uniform crossed antiprisms for fixed can be determined using simple inequalities. The condition on possible is Examples: In the first column of the following table, the symbols are Schoenflies, Coxeter, and orbifold notation, in this order.
Natural history of Africa The natural history of Africa encompasses some of the well known megafauna of that continent. Natural history is the study and description of organisms and natural objects, especially their origins, evolution, and interrelationships. Flora. The vegetation of Africa follows very closely the distribution of heat and moisture. The northern and southern temperate zones have a flora distinct from that of the continent generally, which is tropical. In the countries bordering the Mediterranean, there are groves of orange and olive trees, evergreen oaks, cork trees and pines, intermixed with cypresses, myrtles, arbutus and fragrant tree-heaths. South of the Atlas Mountains, the conditions alter. The zones of minimum rainfall have a very scanty flora, consisting of plants adapted to resist the great dryness. Characteristic of the Sahara is the date palm, which flourishes where other vegetation can scarcely maintain existence, while in the semidesert regions the acacia, from which gum arabic is obtained, is abundant.
The more humid regions have a richer vegetation; dense forest where the rainfall is greatest and variations of temperature least, conditions found chiefly on the tropical coasts, and in the west African equatorial basin with its extension towards the upper Nile; and savanna interspersed with trees on the greater part of the plateaus, passing as the desert regions are approached into a scrub vegetation consisting of thorny acacias, etc. Forests also occur on the humid slopes of mountain ranges up to a certain elevation. In the coast regions, the typical tree is the mangrove, which flourishes wherever the soil is of a swamp character. The dense forests of West Africa contain, in addition to a great variety of hardwoods, two palms, "Elaeis guineensis" (oil palm) and "Raphia vinifera" (bamboo palm), not found, generally speaking, in the savanna regions. "Bombax" or silk cotton trees attain gigantic proportions in the forests, which are the home of the India rubber-producing plants and of many valuable kinds of timber trees, such as odum ("Chlorophora excelsa"), ebony, mahogany ("Khaya senegalensis"), "Oldfieldia" ("Oldfieldia africana") and camwood ("Baphia nitida"). The climbing plants in the tropical forests are exceedingly luxuriant and the undergrowth or "bush" is extremely dense.
In the savannas the most characteristic trees are the monkey-bread tree or baobab ("Adansonia digitata"), doum palm ("Hyphaene") and euphorbias. The coffee plant grows wild in such widely separated places as Liberia and southern Ethiopia. The higher mountains have a special flora showing close agreement over wide intervals of space, as well as affinities with the mountain flora of the eastern Mediterranean, the Himalaya and Indo-China. In the swamp regions of north-east Africa, papyrus and associated plants, including the soft-wooded ambach, flourished in immense quantities, and little else is found in the way of vegetation. South Africa is largely destitute of forest, save in the lower valleys and coast regions. Tropical flora disappears, and in the semi-desert plains the fleshy, leafless, contorted species of kapsias, mesembryanthemums, aloes and other succulent plants make their appearance. There are, too, valuable timber trees, such as the yellowwood ("Podocarpus elongatus"), stinkwood ("Ocotea"), sneezewood or Cape ebony ("Pteroxylon utile") and ironwood. Extensive miniature woods of heaths are found in almost endless variety and covered throughout the greater part of the year with innumerable blossoms in which red is very prevalent. Of the grasses of Africa, alfa is very abundant in the plateaus of the Atlas range.
Fauna. The fauna again shows the effect of the characteristics of the vegetation. The open savannas are the home of large ungulates, especially antelopes, the giraffe (peculiar to Africa), zebra, buffalo, wild donkey and four species of rhinoceros; and of carnivores, such as the lion, leopard, hyena, etc. The okapi (a genus restricted to Africa) is found only in the dense forests of the Congo basin. Bears are confined to the Atlas region, wolves and foxes to North Africa. The elephant (though its range has become restricted through the attacks of hunters) is found both in the savannas and forest regions, the latter being otherwise poor in large game, though the special habitat of the chimpanzee and gorilla. Baboons and mandrills, with few exceptions, are peculiar to Africa. The single-humped camel, as a domestic animal, is especially characteristic of the northern deserts and steppes. The rivers in the tropical zone abound with hippopotami and crocodiles, the former entirely confined to Africa. The vast herds of game, formerly so characteristic of many parts of Africa, have much diminished with the increase of intercourse with the interior. Game reserves have, however, been established in South Africa, Central Africa, East Africa, Somaliland, etc., while measures for the protection of wild animals were laid down in an international convention signed in May 1900.
The ornithology of northern Africa presents a close resemblance to that of southern Europe, scarcely a species being found which does not also occur in the other countries bordering the Mediterranean. Among the birds most characteristic of Africa are the ostrich and the secretarybird. The ostrich is widely dispersed, but is found chiefly in the desert and steppe regions. The secretarybird is common in the south. The weaver birds and their allies, including the long-tailed whydahs, are abundant, as are, among game-birds, the francolin and guineafowl. Many of the smaller birds, such as the sunbirds, bee-eaters, the parrots and kingfishers, as well as the larger plantain-eaters, are noted for the brilliance of their feathers. Of reptiles, the lizard and chameleon are common, and there are a number of venomous snakes, though these are not so numerous as in other tropical countries. The scorpion is abundant. Of insects, Africa has many thousand different kinds; of these the locust is the proverbial scourge of the continent, and the ravages of the termites are almost incredible. The spread of malaria by means of mosquitoes is common. The tsetse fly, whose bite is fatal to all domestic animals, is common in many districts of South and East Africa. It is found nowhere outside Africa.
Geography of Africa Africa is a continent comprising 63 political territories, representing the largest of the great southward projections from the main mass of Earth's surface. Within its regular outline, it comprises an area of , excluding adjacent islands. Its highest mountain is Kilimanjaro; its largest lake is Lake Victoria. Separated from Europe by the Mediterranean Sea and from much of Asia by the Red Sea, Africa is joined to Asia at its northeast extremity by the Isthmus of Suez (which is transected by the Suez Canal), wide. For geopolitical purposes, the Sinai Peninsula of Egypt – east of the Suez Canal – is often considered part of Africa. From the most northerly point, Ras ben Sakka in Tunisia, at 37°21′ N, to the most southerly point, Cape Agulhas in South Africa, 34°51′15″ S, is a distance approximately of ; from Cap-Vert, 17°31′13″W, the westernmost point, to Ras Hafun in the Somali Puntland region, in the Horn of Africa, 51°27′52″ E, the most easterly projection, is a distance (also approximately) of .
The main structural lines of the continent show both the east-to-west direction characteristic, at least in the eastern hemisphere, of the more northern parts of the world, and the north-to-south direction seen in the southern peninsulas. Africa is thus mainly composed of two segments at right angles, the northern running from east to west, and the southern from north to south. Main features. The average elevation of the continent approximates closely to above sea level, roughly near to the mean elevation of both North and South America, but considerably less than that of Asia, . In contrast with other continents, it is marked by the comparatively small area of either very high or very low ground, lands under occupying an unusually small part of the surface; while not only are the highest elevations inferior to those of Asia or South America, but the area of land over is also quite insignificant, being represented almost entirely by individual peaks and mountain ranges. Moderately elevated tablelands are thus the characteristic feature of the continent, though the surface of these is broken by higher peaks and ridges. (So prevalent are these isolated peaks and ridges that a specialised term—"Inselberg-Landschaft", island mountain landscape—has been adopted in Germany to describe this kind of country, thought to be in great part the result of wind action.)
As a general rule, the higher tablelands lie to the east and south, while a progressive diminution in altitude towards the west and north is observable. Apart from the lowlands and the Atlas Mountains, the continent may be divided into two regions of higher and lower plateaus, the dividing line (somewhat concave to the northwest) running from the middle of the Red Sea to about 6 degrees south on the west coast. Africa can be divided into a number of geographic zones: Plateau region. There are many plateaus in Africa. The high southern and eastern plateaus, rarely falling below , have a mean elevation of about . The South African plateau, as far as about 12° S, is bounded east, west and south by bands of high ground which fall steeply to the coasts. On this account South Africa has a general resemblance to an inverted saucer. Due south, the plateau rim is formed by three parallel steps with level ground between them. The largest of these level areas, the Great Karoo, is a dry, barren region, and a large tract of the plateau proper is of a still more arid character and is known as the Kalahari Desert.
The South African plateau is connected towards East African plateau, with probably a slightly greater average elevation, and marked by some distinct features. It is formed by a widening out of the eastern axis of high ground, which becomes subdivided into a number of zones running north and south and consisting in turn of ranges, tablelands and depressions. The most striking feature is the existence of two great lines of depression, due largely to the subsidence of whole segments of the Earth's crust, the lowest parts of which are occupied by vast lakes. Towards the south the two lines converge and give place to one great valley (occupied by Lake Nyasa), the southern part of which is less distinctly due to rifting and subsidence than the rest of the system. Farther north the western hollow, known as the Albertine Rift, is occupied for more than half its length by water, forming the Great Lakes of Tanganyika, Kivu, Lake Edward and Lake Albert, the first-named over long and the longest freshwater lake in the world. Associated with these great valleys are a number of volcanic peaks, the greatest of which occur on a meridional line east of the eastern trough. The eastern branch of the East African Rift, contains much smaller lakes, many of them brackish and without outlet, the only one comparable to those of the western trough being Lake Turkana or Basso Norok.
A short distance east of this rift valley is Mount Kilimanjaro – with its two peaks Kibo and Mawenzi, the latter being , and the culminating point of the whole continent – and Mount Kenya, which is . Hardly less important is the Ruwenzori Range, over , which lies east of the western trough. Other volcanic peaks rise from the floor of the valleys, some of the Kirunga (Mfumbiro) group, north of Lake Kivu, being still partially active. This could cause most of the cities and states to be flooded with lava and ash. The third division of the higher region of Africa is formed by the Ethiopian Highlands, a rugged mass of mountains forming the largest continuous area of its altitude in the whole continent, little of its surface falling below , while the summits reach heights of 4400 m to 4550 m. This block of country lies just west of the line of the great East African Trough, the northern continuation of which passes along its eastern escarpment as it runs up to join the Red Sea. There is, however, in the centre a circular basin occupied by Lake Tsana.
Both in the east and west of the continent the bordering highlands are continued as strips of plateau parallel to the coast, the Ethiopian mountains being continued northwards along the Red Sea coast by a series of ridges reaching in places a height of . In the west the zone of high land is broader but somewhat lower. The most mountainous districts lie inland from the head of the Gulf of Guinea (Adamawa, etc.), where heights of are reached. Exactly at the head of the gulf the great peak of the Cameroon, on a line of volcanic action continued by the islands to the south-west, has a height of , while Clarence Peak, in Fernando Po, the first of the line of islands, rises to over . Towards the extreme west the Futa Jallon highlands form an important diverging point of rivers, but beyond this, as far as the Atlas chain, the elevated rim of the continent is almost wanting. Plains. Much of Africa is made up of plains of the pediplain and etchplain type often occurring as steps. The etchplains are commonly associated with laterite soil and inselbergs. Inselberg-dotted plains are common in Africa including Tanzania, the Anti-Atlas of Morocco, Namibia, and the interior of Angola. One of the most wideaspread plain is the African Surface, a composite etchplain occurring across much of the continent.
The area between the east and west coast highlands, which north of 17° N is mainly desert, is divided into separate basins by other bands of high ground, one of which runs nearly centrally through North Africa in a line corresponding roughly with the curved axis of the continent as a whole. The best marked of the basins so formed (the Congo Basin) occupies a circular area bisected by the equator, once probably the site of an inland sea. Running along the south of desert is the plains region known as the Sahel. The arid region, the Sahara — the largest hot desert in the world, covering — extends from the Atlantic to the Red Sea. Though generally of slight elevation, it contains mountain ranges with peaks rising to Bordered N.W. by the Atlas range, to the northeast a rocky plateau separates it from the Mediterranean; this plateau gives place at the extreme east to the delta of the Nile. That river (see below) pierces the desert without modifying its character. The Atlas range, the north-westerly part of the continent, between its seaward and landward heights encloses elevated steppes in places broad. From the inner slopes of the plateau numerous wadis take a direction towards the Sahara. The greater part of that now desert region is, indeed, furrowed by old water-channels.
Mountains. The mountains are an exception to Africa's general landscape. Geographers came up with the idea of "high Africa" and "low Africa" to help distinguish the difference in Geography; "high Africa" extending from Ethiopia down south to South Africa and the Cape of Good Hope while "low Africa" representing the plains of the rest of the continent. The following table gives the details of the chief mountains and ranges of the continent: Rivers. From the outer margin of the African plateaus, a large number of streams run to the sea with comparatively short courses, while the larger rivers flow for long distances on the interior highlands, before breaking through the outer ranges. The main drainage of the continent is to the north and west, or towards the basin of the Atlantic Ocean. To the main African rivers belong: Nile (the longest river of Africa), Congo (river with the highest water discharge on the continent) and the Niger, which flows half of its length through the arid areas. The largest lakes are the following: Lake Victoria (Lake Ukerewe), Lake Chad, in the centre of the continent, Lake Tanganyika, lying between the Democratic Republic of Congo, Burundi, Tanzania and Zambia. There is also the considerably large Lake Malawi stretching along the eastern border of Malawi. There are also numerous water dams throughout the continent: Kariba on the river of Zambezi, Asuan in Egypt on the river of Nile, and Akosombo, the continent's biggest dam on the Volta River in Ghana (Fobil 2003).
The high lake plateau of the African Great Lakes region contains the headwaters of both the Nile and the Congo. The break-up of Gondwana in Late Cretaceous and Cenozoic times led to a major reorganization of the river courses of various large African rivers including the Congo, Niger, Nile, Orange, Limpopo and Zambezi rivers. Flowing to the Mediterranean Sea. The upper Nile receives its chief supplies from the mountainous region adjoining the Central African trough in the neighborhood of the equator. From there, streams pour eastward into Lake Victoria, the largest lake in Africa (covering over 26,000 square m.), and to the west and north into Lake Edward and Lake Albert. To the latter of these, the effluents of the other two lakes add their waters. Issuing from there, the Nile flows northward, and between the latitudes of 7 and 10 degrees north it traverses a vast marshy level, where its course is liable to being blocked by floating vegetation. After receiving the Bahr-el-Ghazal from the west and the Sobat, Blue Nile and Atbara from the Ethiopian Highlands (the chief gathering ground of the flood-water), it separates the great desert with its fertile watershed, and enters the Mediterranean at a vast delta.
Flowing to the Atlantic Ocean. The most remote head-stream of the Congo is the Chambezi, which flows southwest into the marshy Lake Bangweulu. From this lake issues the Congo, known in its upper course by various names. Flowing first south, it afterwards turns north through Lake Mweru and descends to the forest-clad basin of west equatorial Africa. Traversing this in a majestic northward curve, and receiving vast supplies of water from many great tributaries, it finally turns southwest and cuts a way to the Atlantic Ocean through the western highlands. The area of the Congo basin is greater than that of any other river except the Amazon, while the African inland drainage area is greater than that of any continent but Asia, where the corresponding area is . West of Lake Chad is the basin of the Niger, the third major river of Africa. With its principal source in the far west, it reverses the direction of flow exhibited by the Nile and Congo, and ultimately flows into the Atlantic — a fact that eluded European geographers for many centuries. An important branch, however — the Benue — flows from the southeast.
These four river basins occupy the greater part of the lower plateaus of North and West Africa — the remainder consists of arid regions watered only by intermittent streams that do not reach the sea. Of the remaining rivers of the Atlantic basin, the Orange, in the extreme south, brings the drainage from the Drakensberg on the opposite side of the continent, while the Kunene, Kwanza, Ogowe and Sanaga drain the west coastal highlands of the southern limb; the Volta, Komoe, Bandama, Gambia and Senegal the highlands of the western limb. North of the Senegal, for over of coast, the arid region reaches to the Atlantic. Farther north are the streams, with comparatively short courses, reaching the Atlantic and Mediterranean from the Atlas mountains. Flowing to the Indian Ocean. Of the rivers flowing to the Indian Ocean, the only one draining any large part of the interior plateaus is the Zambezi, whose western branches rise in the western coastal highlands. The main stream has its rise in 11°21′3″ S 24°22′ E, at an elevation of . It flows to the west and south for a considerable distance before turning eastward. All the largest tributaries, including the Shire, the outflow of Lake Nyasa, flow down the southern slopes of the band of high ground stretching across the continent from 10° to 12° S. In the southwest, the Zambezi system interlaces with that of the Taukhe (or Tioghe), from which it at times receives surplus water. The rest of the water of the Taukhe, known in its middle course as the Okavango, is lost in a system of swamps and saltpans that was formerly centred in Lake Ngami, now dried up.
Farther south, the Limpopo drains a portion of the interior plateau, but breaks through the bounding highlands on the side of the continent nearest its source. The Rovuma, Rufiji and Tana principally drain the outer slopes of the African Great Lakes highlands. In the Horn region to the north, the Jubba and the Shebelle rivers begin in the Ethiopian Highlands. These rivers mainly flow southwards, with the Jubba emptying in the Indian Ocean. The Shebelle River reaches a point to the southwest. After that, it consists of swamps and dry reaches before finally disappearing in the desert terrain near the Jubba River. Another large stream, the Hawash, rising in the Ethiopian mountains, is lost in a saline depression near the Gulf of Aden. Inland basins. Between the basins of the Atlantic and Indian Oceans, there is an area of inland drainage along the centre of the Ethiopian plateau, directed chiefly into the lakes in the Great Rift Valley. The largest river is the Omo, which, fed by the rains of the Ethiopian highlands, carries down a large body of water into Lake Turkana. The rivers of Africa are generally obstructed either by bars at their mouths, or by cataracts at no great distance upstream. But when these obstacles have been overcome, the rivers and lakes afford a vast network of navigable waters.
North of the Congo basin, and separated from it by a broad undulation of the surface, is the basin of Lake Chad — a flat-shored, shallow lake filled principally by the Chari coming from the southeast. Lakes. The principal lakes of Africa are situated in the African Great Lakes plateau. The lakes found within the Great Rift Valley have steep sides and are very deep. This is the case with the two largest of the type, Tanganyika and Nyasa, the latter with depths of . Others, however, are shallow, and hardly reach the steep sides of the valleys in the dry season. Such are Lake Rukwa, in a subsidiary depression north of Nyasa, and Eiassi and Manyara in the system of the Great Rift Valley. Lakes of the broad type are of moderate depth, the deepest sounding in Lake Victoria being under . Besides the African Great Lakes, the principal lakes on the continent are: Lake Chad, in the northern inland watershed; Bangweulu and Mweru, traversed by the head-stream of the Congo; and Lake Mai-Ndombe and Ntomba (Mantumba), within the great bend of that river. All, except possibly Mweru, are more or less shallow, and Lake Chad appears to be drying up.
Divergent opinions have been held as to the mode of origin of the African Great Lakes, especially Tanganyika, which some geologists have considered to represent an old arm of the sea, dating from a time when the whole central Congo basin was under water; others holding that the lake water has accumulated in a depression caused by subsidence. The former view is based on the existence in the lake of organisms of a decidedly marine type. They include jellyfish, molluscs, prawns, crabs, etc. Islands. With the exception of Madagascar, the African islands are small. Madagascar, with an area of , is, after Greenland, New Guinea and Borneo, the fourth largest island on the Earth. It lies in the Indian Ocean, off the southeast coast of the continent, from which it is separated by the deep Mozambique Channel, wide at its narrowest point. Madagascar in its general structure, as in flora and fauna, forms a connecting link between Africa and southern Asia. East of Madagascar are the small islands of Mauritius and Réunion. There are also islands in the Gulf of Guinea on which lies the Republic of São Tomé and Príncipe (islands of São Tomé and Príncipe). Part of the Republic of Equatorial Guinea is lying on the island of Bioko (with the capital Malabo and the town of Lubu) and the island of Annobón. Socotra lies E.N.E. of Cape Guardafui. Off the north-west coast are the Canary and Cape Verde archipelagoes. which, like some small islands in the Gulf of Guinea, are of volcanic origin. The South Atlantic Islands of Saint Helena and Ascension are classed as Africa but are situated on the Mid-Atlantic Ridge halfway to South America.
Climatic conditions. Lying almost entirely within the tropics, and equally to north and south of the equator, Africa does not show excessive variations of temperature. Great heat is experienced in the lower plains and desert regions of North Africa, removed by the great width of the continent from the influence of the ocean, and here, too, the contrast between day and night, and between summer and winter, is greatest. (The rarity of the air and the great radiation during the night cause the temperature in the Sahara to fall occasionally to freezing point.) Farther south, the heat is to some extent modified by the moisture brought from the ocean, and by the greater elevation of a large part of the surface, especially in East Africa, where the range of temperature is wider than in the Congo basin or on the Guinea coast. In the extreme north and south the climate is a warm temperate one, the northern countries being on the whole hotter and drier than those in the southern zone; the south of the continent being narrower than the north, the influence of the surrounding ocean is more felt.
The most important climatic differences are due to variations in the amount of rainfall. The wide heated plains of the Sahara, and in a lesser degree the corresponding zone of the Kalahari in the south, have an exceedingly scanty rainfall, the winds which blow over them from the ocean losing part of their moisture as they pass over the outer highlands, and becoming constantly drier owing to the heating effects of the burning soil of the interior; while the scarcity of mountain ranges in the more central parts likewise tends to prevent condensation. In the inter-tropical zone of summer precipitation, the rainfall is greatest when the sun is vertical or soon after. It is therefore greatest of all near the equator, where the sun is twice vertical, and less in the direction of both tropics. The rainfall zones are, however, somewhat deflected from a due west-to-east direction, the drier northern conditions extending southwards along the east coast, and those of the south northwards along the west. Within the equatorial zone certain areas, especially on the shores of the Gulf of Guinea and in the upper Nile basin, have an intensified rainfall, but this rarely approaches that of the rainiest regions of the world. The rainiest district in all Africa is a strip of coastland west of Mount Cameroon, where there is a mean annual rainfall of about as compared with a mean of at Cherrapunji, in Meghalaya, India.
The two distinct rainy seasons of the equatorial zone, where the sun is vertical at half-yearly intervals, become gradually merged into one in the direction of the tropics, where the sun is overhead but once. Snow falls on all the higher mountain ranges, and on the highest the climate is thoroughly Alpine. The countries bordering the Sahara are much exposed to a very dry wind, full of fine particles of sand, blowing from the desert towards the sea. Known in Egypt as the khamsin, on the Mediterranean as the sirocco, it is called on the Guinea coast the harmattan. This wind is not invariably hot; its great dryness causes so much evaporation that cold is not infrequently the result. Similar dry winds blow from the Kalahari Desert in the south. On the eastern coast the monsoons of the Indian Ocean are regularly felt, and on the southeast hurricanes are occasionally experienced. Health. The climate of Africa lends itself to certain environmental diseases, the most serious of which are: malaria, sleeping sickness and yellow fever. Malaria is the most deadly environmental disease in Africa. It is transmitted by a genus of mosquito (anopheles mosquito) native to Africa, and can be contracted over and over again. There is not yet a vaccine for malaria, which makes it difficult to prevent the disease from spreading in Africa. Recently, the dissemination of mosquito netting has helped lower the rate of malaria.
Yellow fever is a disease also transmitted by mosquitoes native to Africa. Unlike malaria, it cannot be contracted more than once. Like chicken pox, it is a disease that tends to be severe the later in life a person contracts the disease. Sleeping sickness, or African trypanosomiasis, is a disease that usually affects animals, but has been known to be fatal to some humans as well. It is transmitted by the tsetse fly and is found almost exclusively in Sub-Saharan Africa. This disease has had a significant impact on African development not because of its deadly nature, like Malaria, but because it has prevented Africans from pursuing agriculture (as the sleeping sickness would kill their livestock).
Approval voting Approval voting is a single-winner rated voting system where voters can approve of all the candidates as they like instead of choosing one. The method is designed to eliminate vote-splitting while keeping election administration simple and easy-to-count (requiring only a single score for each candidate). Approval voting has been used in both organizational and political elections to improve representativeness and voter satisfaction. Critics of approval voting have argued the simple ballot format is a disadvantage, as it forces a binary choice for each candidate (instead of the expressive grades of other rated voting rules). Effect on elections. Research by social choice theorists Steven Brams and Dudley R. Herschbach found that approval voting would increase voter participation, prevent minor-party candidates from being spoilers, and reduce negative campaigning. Brams' research concluded that approval can be expected to elect majority-preferred candidates in practical election scenarios, avoiding the center squeeze common to ranked-choice voting and primary elections.
One study showed that approval would not have chosen the same two winners as plurality voting (Jacques Chirac and Jean-Marie Le Pen) in the first round of the 2002 French presidential election; it instead would have chosen Chirac and Lionel Jospin as the top two candidates to proceed to the runoff. In the actual election, Le Pen lost by an overwhelming margin in the runoff, 82.2% to 17.8%, a sign that the true top two candidates had not been found. In the approval voting survey primary, Chirac took first place with 36.7%, compared to Jospin at 32.9%. Le Pen, in that study, received 25.1% and so would not have made the cut to the second round. In the real primary election, the top three were Chirac, 19.9%, Le Pen, 16.9%, and Jospin, 16.2%. A study of various evaluative voting methods (approval and score voting) during the 2012 French presidential election showed that "unifying" candidates tended to do better, and polarizing candidates did worse, as compared to under plurality voting. Use. Current electoral use.
Latvia. The Latvian parliament uses a modified version of approval voting within open list proportional representation, in which voters can cast either positive (approval) votes, negative votes or neither for any number of candidates. United States. In November 2020, St. Louis, Missouri, passed Proposition D with 70% voting to authorize a variant of approval (unified primary) for municipal offices. In 2021, the first mayoral election with approval voting saw Tishaura Jones and Cara Spencer move on to the general with 57% and 46% support. Lewis Reed and Andrew Jones were eliminated with 39% and 14% support, resulting in an average of 1.6 candidates supported by each voter in the 4 person race. In 2018, Fargo, North Dakota, passed a local ballot initiative adopting approval for the city's local elections, becoming the first United States city and jurisdiction to adopt approval. Previously in 2015, a Fargo city commissioner election had suffered from six-way vote-splitting, resulting in a candidate winning with an unconvincing 22% plurality of the vote.
The first election was held June 9, 2020, selecting two city commissioners, from seven candidates on the ballot. Both winners received over 50% approval, with an average 2.3 approvals per ballot, and 62% of voters supported the change to approval in a poll. A poll by opponents of approval was conducted to test whether voters had in fact voted strategically according to the Burr dilemma. They found that 30% of voters who bullet voted did so for strategic reasons, while 57% did so because it was their sincere opinion. Fargo's second approval election took place in June 2022, for mayor and city commission. The incumbent mayor was re-elected from a field of 7 candidates, with an estimated 65% approval, with voters expressing 1.6 approvals per ballot, and the two commissioners were elected from a field of 15 candidates, with 3.1 approvals per ballot. In 2023, the North Dakota legislature passed a bill which intended to ban approval voting. The bill was vetoed by governor Doug Burgum, citing the importance of "home rule" and allowing citizens control over their local government. The legislature attempted to overrule the veto but failed.
Use by organizations. Approval has been used in privately administered nomination contests by the Independent Party of Oregon in 2011, 2012, 2014, and 2016. Oregon is a fusion voting state, and the party has cross-nominated legislators and statewide officeholders using this method; its 2016 presidential preference primary did not identify a potential nominee due to no candidate earning more than 32% support. The party switched to using STAR voting in 2020. It is also used in internal elections by the American Solidarity Party; the Green Parties of Texas and Ohio; the Libertarian National Committee; the Libertarian parties of Texas, Colorado, Arizona, and New York; Alliance 90/The Greens in Germany; and the Czech and German Pirate Party. Approval has been adopted by several societies: the Society for Social Choice and Welfare (1992), Mathematical Association of America (1986), the American Mathematical Society, the Institute of Management Sciences (1987) (now the Institute for Operations Research and the Management Sciences), the American Statistical Association (1987), and the Institute of Electrical and Electronics Engineers (1987).
Steven Brams' analysis of the 5-candidate 1987 Mathematical Association of America presidential election shows that 79% of voters cast a ballot for one candidate, 16% for 2 candidates, 5% for 3, and 1% for 4, with the winner earning the approval of 1,267 (32%) of 3,924 voters. The IEEE board in 2002 rescinded its decision to use approval. IEEE Executive Director Daniel J. Senese stated that approval was abandoned because "few of our members were using it and it was felt that it was no longer needed." Approval voting was used for Dartmouth Alumni Association elections for seats on the College Board of Trustees, but after some controversy it was replaced with traditional runoff elections by an alumni vote of 82% to 18% in 2009. Dartmouth students started to use approval voting to elect their student body president in 2011. In the first election, the winner secured the support of 41% of voters against several write-in candidates. In 2012, Suril Kantaria won with the support of 32% of the voters. In 2013, 2014 and 2016, the winners also earned the support of under 40% of the voters. Results reported in "The Dartmouth" show that in the 2014 and 2016 elections, more than 80 percent of voters approved of only one candidate. Students replaced approval voting with plurality voting before the 2017 elections.
Historical. Robert J. Weber coined the term "Approval Voting" in 1971. It was more fully published in 1978 by political scientist Steven Brams and mathematician Peter Fishburn. Historically, several voting methods that incorporate aspects of approval have been used: The idea of approval was adopted by X. Hu and Lloyd Shapley in 2003 in studying authority distribution in organizations. Strategic voting. Overview. Approval voting allows voters to select all the candidates whom they consider to be reasonable choices. "Strategic approval" differs from ranked voting (aka preferential voting) methods where voters are generally forced to "reverse" the preference order of two options, which if done on a larger scale can cause an unpopular candidate to win. Strategic approval, with more than two options, involves the voter changing their approval threshold. The voter decides which options to give the "same" rating, even if they were to have a preference order between them. This leaves a tactical concern any voter has for approving their second-favorite candidate, in the case that there are three or more candidates. Approving their second-favorite means the voter harms their favorite candidate's chance to win. Not approving their second-favorite means the voter helps the candidate they least desire to beat their second-favorite and perhaps win.
Approval technically allows for but is strategically immune to push-over and burying. Bullet voting occurs when a voter approves "only" candidate "a" instead of "both" "a" and "b" for the reason that voting for "b" can cause "a" to lose. The voter would be satisfied with either "a" or "b" but has a moderate preference for "a". Were "b" to win, this hypothetical voter would still be satisfied. If supporters of both "a" and "b" do this, it could cause candidate "c" to win. This creates the "chicken dilemma", as supporters of "a" and "b" are playing chicken as to which will stop strategic voting first, before both of these candidates lose. Compromising occurs when a voter approves an "additional" candidate who is otherwise considered unacceptable to the voter to prevent an even worse alternative from winning. Sincere voting. Approval experts describe sincere votes as those "... that directly reflect the true preferences of a voter, i.e., that do not report preferences 'falsely. They also give a specific definition of a sincere approval vote in terms of the voter's ordinal preferences as being any vote that, if it votes for one candidate, it also votes for any more preferred candidate. This definition allows a sincere vote to treat strictly preferred candidates the same, ensuring that every voter has at least one sincere vote. The definition also allows a sincere vote to treat equally preferred candidates differently. When there are two or more candidates, every voter has at least three sincere approval votes to choose from. Two of those sincere approval votes do not distinguish between any of the candidates: vote for none of the candidates and vote for all of the candidates. When there are three or more candidates, every voter has more than one sincere approval vote that distinguishes between the candidates.
Examples. Based on the definition above, if there are four candidates, A, B, C, and D, and a voter has a strict preference order, preferring A to B to C to D, then the following are the voter's possible sincere approval votes: If the voter instead equally prefers B and C, while A is still the most preferred candidate and D is the least preferred candidate, then all of the above votes are sincere and the following combination is also a sincere vote: The decision between the above ballots is equivalent to deciding an arbitrary "approval cutoff." All candidates preferred to the cutoff are approved, all candidates less preferred are not approved, and any candidates equal to the cutoff may be approved or not arbitrarily. Sincere strategy with ordinal preferences. A sincere voter with multiple options for voting sincerely still has to choose which sincere vote to use. Voting strategy is a way to make that choice, in which case strategic approval includes sincere voting, rather than being an alternative to it. This differs from other voting systems that typically have a unique sincere vote for a voter.
When there are three or more candidates, the winner of an approval election can change, depending on which sincere votes are used. In some cases, approval can sincerely elect any one of the candidates, including a Condorcet winner and a Condorcet loser, without the voter preferences changing. To the extent that electing a Condorcet winner and not electing a Condorcet loser is considered desirable outcomes for a voting system, approval can be considered vulnerable to sincere, strategic voting. In one sense, conditions where this can happen are robust and are not isolated cases. On the other hand, the variety of possible outcomes has also been portrayed as a virtue of approval, representing the flexibility and responsiveness of approval, not just to voter ordinal preferences, but cardinal utilities as well. Dichotomous preferences. Approval avoids the issue of multiple sincere votes in special cases when voters have dichotomous preferences. For a voter with dichotomous preferences, approval is strategyproof. When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval is guaranteed to elect a Condorcet winner. However, having dichotomous preferences when there are three or more candidates is not typical. It is an unlikely situation for all voters to have dichotomous preferences when there are more than a few voters.
Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group. A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences. Being strategy-proof for a voter means that there is a unique way for the voter to vote that is a strategically best way to vote, regardless of how others vote. In approval, the strategy-proof vote, if it exists, is a sincere vote. Approval threshold. Another way to deal with multiple sincere votes is to augment the ordinal preference model with an approval or acceptance threshold. An approval threshold divides all of the candidates into two sets, those the voter approves of and those the voter does not approve of. A voter can approve of more than one candidate and still prefer one approved candidate to another approved candidate. Acceptance thresholds are similar. With such a threshold, a voter simply votes for every candidate that meets or exceeds the threshold.
With threshold voting, it is still possible to not elect the Condorcet winner and instead elect the Condorcet loser when they both exist. However, according to Steven Brams, this represents a strength rather than a weakness of approval. Without providing specifics, he argues that the pragmatic judgments of voters about which candidates are acceptable should take precedence over the Condorcet criterion and other social choice criteria. Strategy with cardinal utilities. Voting strategy under approval is guided by two competing features of approval. On the one hand, approval fails the later-no-harm criterion, so voting for a candidate can cause that candidate to win instead of a candidate more preferred by that voter. On the other hand, approval satisfies the monotonicity criterion, so not voting for a candidate can never help that candidate win, but can cause that candidate to lose to a less preferred candidate. Either way, the voter can risk getting a less preferred election winner. A voter can balance the risk-benefit trade-offs by considering the voter's cardinal utilities, particularly via the von Neumann–Morgenstern utility theorem, and the probabilities of how others vote.

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