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Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been determined as a unique compound, that known measurement can then be used to determine the same analyte's mass in a mixture, as long as the relative quantities of the other constituents are known. The four main types of this method of analysis are precipitation, volatilization, electro-analytical and miscellaneous physical method. The methods involve changing the phase of the analyte to separate it in its pure form from the original mixture and are quantitative measurements. == Precipitation method == The precipitation method is the one used for the determination of the amount of calcium in water. Using this method, an excess of oxalic acid, H2C2O4, is added to a measured, known volume of water. By adding a reagent, here ammonium oxalate, the calcium will precipitate as calcium oxalate. The proper reagent, when added to aqueous solution, will produce highly insoluble precipitates from the positive and negative ions that would otherwise be soluble with their counterparts (equation 1). The reaction is: Formation of calcium oxalate: Ca2+(aq) + C2O42- → CaC2O4 The precipitate is collected, dried and ignited to high (red) heat which converts it entirely to calcium oxide. The reaction is pure calcium oxide formed CaC2O4 → CaO(s) + CO(g)+ CO2(g) The pure precipitate is cooled, then measured by weighing, and the difference in weights before and after reveals the mass of analyte lost, in this case calcium oxide. That number can then be used to calculate the amount, or the percent concentration, of it in the original mix. == Volatilization methods == Volatilization methods can be either direct or indirect.
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Water eliminated in a quantitative manner from many inorganic substances by ignition is an example of a direct determination. It is collected on a solid desiccant and its mass determined by the gain in mass of the desiccant. Another direct volatilization method involves carbonates which generally decompose to release carbon dioxide when acids are used. Because carbon dioxide is easily evolved when heat is applied, its mass is directly established by the measured increase in the mass of the absorbent solid used. Determination of the amount of water by measuring the loss in mass of the sample during heating is an example of an indirect method. It is well known that changes in mass occur due to decomposition of many substances when heat is applied, regardless of the presence or absence of water. Because one must make the assumption that water was the only component lost, this method is less satisfactory than direct methods. This often faulty and misleading assumption has proven to be wrong on more than a few occasions. There are many substances other than water loss that can lead to loss of mass with the addition of heat, as well as a number of other factors that may contribute to it. The widened margin of error created by this all-too-often false assumption is not one to be lightly disregarded as the consequences could be far-reaching. Nevertheless, the indirect method, although less reliable than direct, is still widely used in commerce. For example, it's used to measure the moisture content of cereals, where a number of imprecise and inaccurate instruments are available for this purpose. === Types of volatilization methods === In volatilization methods, removal of the analyte involves separation by heating or chemically decomposing a volatile sample at a suitable temperature. In other words, thermal or chemical
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energy is used to precipitate a volatile species. For example, the water content of a compound can be determined by vaporizing the water using thermal energy (heat). Heat can also be used, if oxygen is present, for combustion to isolate the suspect species and obtain the desired results. The two most common gravimetric methods using volatilization are those for water and carbon dioxide. An example of this method is the isolation of sodium hydrogen bicarbonate (the main ingredient in most antacid tablets) from a mixture of carbonate and bicarbonate. The total amount of this analyte, in whatever form, is obtained by addition of an excess of dilute sulfuric acid to the analyte in solution. In this reaction, nitrogen gas is introduced through a tube into the flask which contains the solution. As it passes through, it gently bubbles. The gas then exits, first passing a drying agent (here CaSO4, the common desiccant Drierite). It then passes a mixture of the drying agent and sodium hydroxide which lies on asbestos or Ascarite II, a non-fibrous silicate containing sodium hydroxide. The mass of the carbon dioxide is obtained by measuring the increase in mass of this absorbent. This is performed by measuring the difference in weight of the tube in which the ascarite contained before and after the procedure. The calcium sulfate (CaSO4) in the tube retains carbon dioxide selectively as it's heated, and thereby, removed from the solution. The drying agent absorbs any aerosolized water and/or water vapor (reaction 3.). The mix of the drying agent and NaOH absorbs the CO2 and any water that may have been produced as a result of the absorption of the NaOH (reaction 4.). The reactions are: Reaction 3 - absorption of water NaHCO3(aq) + H2SO4(aq) → CO2(g) + H2O(l) + NaHSO4(aq). Reaction 4. Absorption
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of CO2 and residual water CO2(g) + 2 NaOH(s) → Na2CO3(s) + H2O(l). == Example == A chunk of ore is to be analyzed for sulfur content. It is treated with concentrated nitric acid and potassium chlorate to convert all of the sulfur to sulfate (SO2−4). The nitrate and chlorate are removed by treating the solution with concentrated HCl. The sulfate is precipitated with barium (Ba2+) and weighed as BaSO4. == Advantages == Gravimetric analysis, if methods are followed carefully, provides for exceedingly precise analysis. In fact, gravimetric analysis was used to determine the atomic masses of many elements in the periodic table to six figure accuracy. Gravimetry provides very little room for instrumental error and does not require a series of standards for calculation of an unknown. Also, methods often do not require expensive equipment. Gravimetric analysis, due to its high degree of accuracy, when performed correctly, can also be used to calibrate other instruments in lieu of reference standards. Gravimetric analysis is currently used to allow undergraduate chemistry/Biochemistry students to experience a grad level laboratory and it is a highly effective teaching tool to those who want to attend medical school or any research graduate school. == Disadvantages == Gravimetric analysis usually only provides for the analysis of a single element, or a limited group of elements, at a time. Comparing modern dynamic flash combustion coupled with gas chromatography with traditional combustion analysis will show that the former is both faster and allows for simultaneous determination of multiple elements while traditional determination allowed only for the determination of carbon and hydrogen. Methods are often convoluted and a slight mis-step in a procedure can often mean disaster for the analysis (colloid formation in precipitation gravimetry, for example). Compare this with hardy methods such as spectrophotometry and one will find
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that analysis by these methods is much more efficient. == Solubility in the presence of diverse ions == Diverse ions have a screening effect on dissociated ions which leads to extra dissociation. Solubility will show a clear increase in presence of diverse ions as the solubility product will increase. Look at the following example: Find the solubility of AgCl (Ksp = 1.0 x 10−10) in 0.1 M NaNO3. The activity coefficients for silver and chloride are 0.75 and 0.76, respectively. AgCl(s) = Ag+ + Cl− We can no longer use the thermodynamic equilibrium constant (i.e. in absence of diverse ions) and we have to consider the concentration equilibrium constant or use activities instead of concentration if we use Kth: Ksp = aAg+ aCl− Ksp = [Ag+] fAg+ [Cl−] fCl− 1.0 x 10−10 = s x 0.75 x s x 0.76 s = 1.3 x 10−5 M We have calculated the solubility of AgCl in pure water to be 1.0 x 10−5 M, if we compare this value to that obtained in presence of diverse ions we see % increase in solubility = {(1.3 x 10−5 – 1.0 x 10−5) / 1.0 x 10−5} x 100 = 30% Therefore, once again we have an evidence for an increase in dissociation or a shift of equilibrium to right in presence of diverse ions. == References == == External links == Gravimetric Quimociac Technique
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For light and other electromagnetic radiation, the plane of polarization is the plane spanned by the direction of propagation and either the electric vector or the magnetic vector, depending on the convention. It can be defined for polarized light, remains fixed in space for linearly-polarized light, and undergoes axial rotation for circularly-polarized light. Unfortunately the two conventions are contradictory. As originally defined by Étienne-Louis Malus in 1811, the plane of polarization coincided (although this was not known at the time) with the plane containing the direction of propagation and the magnetic vector. In modern literature, the term plane of polarization, if it is used at all, is likely to mean the plane containing the direction of propagation and the electric vector, because the electric field has the greater propensity to interact with matter. For waves in a birefringent (doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction (Poynting vector) or the wave-normal direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig. 1). Malus, as an adherent of the corpuscular theory of light, could only choose the ray direction. But Augustin-Jean Fresnel, in his successful effort to explain double refraction under the wave theory (1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization. In an isotropic medium such as air, the ray and wave-normal directions are the same, and Fresnel's modification makes no difference. Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation. That plane, which became
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known as the plane of vibration, is perpendicular to Fresnel's "plane of polarization" but identical with the plane that modern writers tend to call by that name! It has been argued that the term plane of polarization, because of its historical ambiguity, should be avoided in original writing. One can easily specify the orientation of a particular field vector; and even the term plane of vibration carries less risk of confusion than plane of polarization. == Physics of the term == For electromagnetic (EM) waves in an isotropic medium (that is, a medium whose properties are independent of direction), the electric field vectors (E and D) are in one direction, and the magnetic field vectors (B and H) are in another direction, perpendicular to the first, and the direction of propagation is perpendicular to both the electric and the magnetic vectors. In this case the direction of propagation is both the ray direction and the wave-normal direction (the direction perpendicular to the wavefront). For a linearly-polarized wave (also called a plane-polarized wave), the orientations of the field vectors are fixed (Fig. 2). Because innumerable materials are dielectrics or conductors while comparatively few are ferromagnets, the reflection or refraction of EM waves (including light) is more often due to differences in the electric properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the electric vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation. Indeed, that is the convention used in the online Encyclopædia Britannica, and in Feynman's lecture on polarization. In the latter case one must infer the convention from the context: Feynman keeps emphasizing the
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direction of the electric (E) vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and antennas (Fig. 3). If the medium is magnetically isotropic but electrically non-isotropic (like a doubly-refracting crystal), the magnetic vectors B and H are still parallel, and the electric vectors E and D are still perpendicular to both, and the ray direction is still perpendicular to E and the magnetic vectors, and the wave-normal direction is still perpendicular to D and the magnetic vectors; but there is generally a small angle between the electric vectors E and D, hence the same angle between the ray direction and the wave-normal direction (Fig. 1). Hence D, E, the wave-normal direction, and the ray direction are all in the same plane, and it is all the more natural to define that plane as the "plane of polarization". This "natural" definition, however, depends on the theory of EM waves developed by James Clerk Maxwell in the 1860s — whereas the word polarization was coined about 50 years earlier, and the associated mystery dates back even further. == History of the term == === Three candidates === Whether by accident or by design, the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig. 1, there are three such planes, to which we may assign numbers for ease of reference: (1) the plane containing both electric vectors and both propagation directions (i.e., the plane normal to the magnetic vectors); (2a) the plane containing the magnetic vectors and the wave-normal (i.e., the plane normal to D); (2b) the plane containing the magnetic vectors
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and the ray (i.e., the plane normal to E). In an isotropic medium, E and D have the same direction, so that the ray and wave-normal directions merge, and the planes (2a) and (2b) become one: (2) the plane containing both magnetic vectors and both propagation directions (i.e., the plane normal to the electric vectors). === Malus's choice === Polarization was discovered — but not named or understood — by Christiaan Huygens, as he investigated the double refraction of "Iceland crystal" (transparent calcite, now called Iceland spar). The essence of his discovery, published in his Treatise on Light (1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays. Huygens defined a principal section of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle. This axis was parallel to the axes of the spheroidal secondary waves by which he (correctly) explained the directions of the extraordinary refraction.
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The term polarization was coined by Étienne-Louis Malus in 1811. In 1808, in the midst of confirming Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal. As this behavior had previously been known only in connection with double refraction, Malus described it in that context. In particular, he defined the plane of polarization of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only ordinary refraction. This definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the plane of incidence and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the magnetic vectors of the polarized ray, not the electric vectors. The plane of the ray and the magnetic vectors is the one numbered (2b) above. The implication that the plane of polarization contains the magnetic vectors is still found in the definition given in the online Merriam-Webster dictionary. Even Julius Adams Stratton, having said that "It is customary to define the polarization in terms of E", promptly adds: "In optics, however, the orientation of the vectors is specified traditionally by the 'plane of polarization,' by which is meant the plane normal to E containing both H and the axis of propagation." That definition is identical with Malus's. === Fresnel's choice === In 1821, Augustin-Jean Fresnel announced his hypothesis that light waves
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are exclusively transverse and therefore always polarized in the sense of having a particular transverse orientation, and that what we call unpolarized light is in fact light whose orientation is rapidly and randomly changing. Supposing that light waves were analogous to shear waves in elastic solids, and that a higher refractive index corresponded to a higher density of the luminiferous aether, he found that he could account for the partial reflection (including polarization by reflection) at the interface between two transparent isotropic media, provided that the vibrations of the aether were perpendicular to the plane of polarization. Thus the polarization, according to the received definition, was "in" a certain plane if the vibrations were perpendicular to that plane! Fresnel himself found this implication inconvenient; later that year he wrote: Adopting this hypothesis, it would have been more natural to have called the plane of polarisation that in which the oscillations are supposed to be made: but I wished to avoid making any change in the received appellations. But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront. Hence, if the vibrations were perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray. In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal. The vibrations normal to Malus's plane of polarization are electric, and the electric vibration tangential to the wavefront is D (Fig. 1). Thus, in terms of the above numbering, Fresnel
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changed the "plane of polarization" from (2b) to (2a). Fresnel's definition remains compatible with the Merriam-Webster definition, which fails to specify the propagation direction. And it remains compatible with Stratton's definition, because that is given in the context of an isotropic medium, in which planes (2a) and (2b) merge into (2). What Fresnel called the "more natural" choice was a plane containing D and a direction of propagation. In Fig. 1, the only plane meeting that specification is the one labeled "Plane of vibration" and later numbered (1) — that is, the one that modern authors tend to identify with the "plane of polarization". We might therefore wish that Fresnel had been less deferential to his predecessors. That scenario, however, is less realistic than it may seem, because even after Fresnel's transverse-wave theory was generally accepted, the direction of the vibrations was the subject of continuing debate. === "Plane of vibration" === The principle that refractive index depended on the density of the aether was essential to Fresnel's aether drag hypothesis. But it could not be extended to birefringent crystals — in which at least one refractive index varies with direction — because density is not directional. Hence his explanation of refraction required a directional variation in stiffness of the aether within a birefringent medium, plus a variation in density between media. James MacCullagh and Franz Ernst Neumann avoided this complication by supposing that a higher refractive index corresponded always to the same density but a greater elastic compliance (lower stiffness). To obtain results that agreed with observations on partial reflection, they had to suppose, contrary to Fresnel, that the vibrations were within the plane of polarization. The question called for an experimental determination of the direction of vibration, and the challenge was answered by George Gabriel Stokes. He defined
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the plane of vibration as "the plane passing through the ray and the direction of vibration" (in agreement with Fig. 1). Now suppose that a fine diffraction grating is illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (as MacCullagh and Neumann said), they will be crowded in the same direction; and if the planes of polarization are normal to the planes of vibration (as Fresnel said), the planes of polarization will be crowded in the normal direction. To find the direction of the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual manner. Stokes performed such an experiment in 1849, and it found in favor of Fresnel. In 1852, Stokes noted a much simpler experiment that leads to the same conclusion. Sunlight scattered from a patch of blue sky 90° from the sun is found, by the methods of Malus, to be polarized in the plane containing the line of sight and the sun. But it is obvious from the geometry that the vibrations of that light can only be perpendicular to that plane. There was, however, a sense in which MacCullagh and Neumann were correct. If we attempt an analogy between shear waves in a non-isotropic elastic solid, and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic permeability (both being non-directional), and the compliance must correspond to the electric permittivity (both being directional). The result is that the velocity of the solid corresponds to the H
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field, so that the mechanical vibrations of the shear wave are in the direction of the magnetic vibrations of the EM wave. But Stokes's experiments were bound to detect the electric vibrations, because those have the greater propensity to interact with matter. In short, the MacCullagh-Neumann vibrations were the ones that had a mechanical analog, but Fresnel's vibrations were the ones that were more likely to be detected in experiments. === Modern practice === The electromagnetic theory of light further emphasized the electric vibrations because of their interactions with matter, whereas the old "plane of polarization" contained the magnetic vectors. Hence the electromagnetic theory would have reinforced the convention that the vibrations were normal to the plane of polarization — provided, of course, that one was familiar with the historical definition of the plane of polarization. But if one was influenced by physical considerations alone, then, as Feynman and the Britannica illustrate, one would pay attention to the electric vectors and assume that the "plane" of polarization (if one needed such a concept) contained those vectors. However, it is not clear that a "plane of polarization" is needed at all: knowing what field vectors are involved, one can specify the polarization by specifying the orientation of a particular vector, or, as Born and Wolf suggest, by specifying the "plane of vibration" of that vector. Hecht also prefers the term plane of vibration (or, more usually, plane-of-vibration), which he defines as the plane of E and the wave-normal, in agreement with Fig. 1 above. == Remaining uses == In an optically chiral medium — that is, one in which the direction of polarization gradually rotates as the wave propagates — the choice of definition of the "plane of polarization" does not affect the existence or direction ("handedness") of the rotation. This
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is one context in which the ambiguity of the term plane of polarization causes no further confusion. There is also a context in which the original definition might still suggest itself. In a non-magnetic non-chiral crystal of the biaxial class (in which there is no ordinary refraction, but both refractions violate Snell's law), there are three mutually perpendicular planes for which the speed of light is isotropic within the plane provided that the electric vectors are normal to the plane. This situation naturally draws attention to a plane normal to the vibrations as envisaged by Fresnel, and that plane is indeed the plane of polarization as defined by Fresnel or Malus. In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion. In the words of Born & Wolf, "it is… better not to use this term." == See also == E-plane and H-plane Plane of incidence == Notes == == References == == Bibliography == W.S. Aldis, 1879, A Chapter on Fresnel's Theory of Double Refraction, 2nd Ed., Cambridge: Deighton, Bell, & Co. / London: George Bell & Sons. M. Born and E. Wolf, 1970, Principles of Optics, 4th Ed., Oxford: Pergamon Press. J.Z. Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, ISBN 0-226-07886-8. O. Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, ISBN 978-0-19-964437-7. A. Fresnel, 1822, De la Lumière (On Light), in J. Riffault (ed.), Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th. Thomson, Paris: Chez Méquignon-Marvis, 1822, pp. 1–137, 535–9; reprinted in Fresnel, 1866–70, vol. 2, pp. 3–146;
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translated by T. Young as "Elementary view of the undulatory theory of light", Quarterly Journal of Science, Literature, and Art, vol. 22 (Jan.– Jun. 1827), pp. 127–41, 441–54; vol. 23 (Jul.– Dec. 1827), pp. 113–35, 431–48; vol. 24 (Jan.– Jun. 1828), pp. 198–215; vol. 25 (Jul.– Dec. 1828), pp. 168–91, 389–407; vol. 26 (Jan.– Jun. 1829), pp. 159–65. A. Fresnel, 1827, "Mémoire sur la double réfraction", Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. VII (for 1824, printed 1827), pp. 45–176; reprinted as "Second mémoire…" in Fresnel, 1866–70, vol. 2, pp. 479–596; translated by A.W. Hobson as "Memoir on double refraction", in R. Taylor (ed.), Scientific Memoirs, vol. V (London: Taylor & Francis, 1852), pp. 238–333. (Cited page numbers are from the translation.) A. Fresnel (ed. H. de Senarmont, E. Verdet, and L. Fresnel), 1866–70, Oeuvres complètes d'Augustin Fresnel (3 volumes), Paris: Imprimerie Impériale; vol. 1 (1866), vol. 2 (1868), vol. 3 (1870). E. Hecht, 2017, Optics, 5th Ed., Pearson Education, ISBN 978-1-292-09693-3. C. Huygens, 1690, Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.) B. Powell (July 1856), "On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications", Philosophical Magazine and Journal of Science, Series 4, vol. 12, no. 76, pp. 1–20. J.A. Stratton, 1941, Electromagnetic Theory, New York: McGraw-Hill. E. T. Whittaker, 1910, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, London: Longmans, Green, & Co.
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The Quake-Catcher Network was an initiative run by the University of Southern California that aimed to use computer-based accelerometers to detect earthquakes. It used the BOINC volunteer computing platform (a form of distributed computing, similar to SETI@home). It supported mobile devices (smartphones and some tablets/laptops) that have a built-in accelerometer. It also supported three external USB devices - the codemercs.com JoyWarrior 24F8, the ONavi sensor, and the MotionNode Accel. In 2011, project scientist Elizabeth Cochran was awarded a Presidential Early Career Award from US President Barack Obama in large part due to her founding of the Quake-Catcher Network project. The Quake Catcher Network project started at Stanford University in 2008, then moved to Caltech, and joined the Southern California Earthquake Center (SCEC) and the Incorporated Research Institutions for Seismology (IRIS) in 2016. The Quake-Catcher Network was discontinued on June 1st 2023 == References == == External links == Interactive world map, showing recent earthquakes (day/week/month) – result of QCN
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The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. The ideal Atwood machine consists of two objects of mass m1 and m2, connected by an inextensible massless string over an ideal massless pulley. Both masses experience uniform acceleration. When m1 = m2, the machine is in neutral equilibrium regardless of the position of the weights. == Equation for constant acceleration == An equation for the acceleration can be derived by analyzing forces. Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force (T), and the weight of the two masses (W1 and W2). To find an acceleration, consider the forces affecting each individual mass. Using Newton's second law (with a sign convention of m 1 > m 2 {\displaystyle m_{1}>m_{2}} ) derive a system of equations for the acceleration (a). As a sign convention, assume that a is positive when downward for m 1 {\displaystyle m_{1}} and upward for m 2 {\displaystyle m_{2}} . Weight of m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} is simply W 1 = m 1 g {\displaystyle W_{1}=m_{1}g} and W 2 = m 2 g {\displaystyle W_{2}=m_{2}g} respectively. Forces affecting m1: m 1 g − T = m 1 a {\displaystyle m_{1}g-T=m_{1}a} Forces affecting m2: T − m 2 g = m 2 a {\displaystyle T-m_{2}g=m_{2}a} and adding the two previous equations yields m 1 g − m 2 g = m 1 a + m 2 a , {\displaystyle m_{1}g-m_{2}g=m_{1}a+m_{2}a,} and the concluding formula for acceleration a = g m 1 − m 2 m 1 + m 2
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{\displaystyle a=g{\frac {m_{1}-m_{2}}{m_{1}+m_{2}}}} The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion. == See also == Frictionless plane – simple kinematic model of an object on a ramp under gravityPages displaying wikidata descriptions as a fallback Kater's pendulum – Reversible free swinging pendulum Spherical cow – Humorous concept in scientific models Swinging Atwood's machine – Variation of Atwood's machine incorporating a pendulum == Notes == == External links == A treatise on the rectilinear motion and rotation of bodies; with a description of original experiments relative to the subject by George Atwood, 1764. Drawings appear on page 450. Professor Greenslade's account on the Atwood Machine Atwood's Machine by Enrique Zeleny, The Wolfram Demonstrations Project
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Photosynthetic picoplankton or picophytoplankton is the fraction of the photosynthetic phytoplankton of cell sizes between 0.2 and 2 μm (i.e. picoplankton). It is especially important in the central oligotrophic regions of the world oceans that have very low concentration of nutrients. == History == 1952: Description of the first truly picoplanktonic species, Chromulina pusilla, by Butcher. This species was renamed in 1960 to Micromonas pusilla and a few studies have found it to be abundant in temperate oceanic waters, although very little such quantification data exists for eukaryotic picophytoplankton. 1979: Discovery of marine Synechococcus by Waterbury and confirmation with electron microscopy by Johnson and Sieburth. 1982: The same Johnson and Sieburth demonstrate the importance of small eukaryotes by electron microscopy. 1983: W.K.W Li and colleagues, including Trevor Platt show that a large fraction of marine primary production is due to organisms smaller than 2 μm. 1986: Discovery of "prochlorophytes" by Chisholm and Olson in the Sargasso Sea, named in 1992 as Prochlorococcus marinus. 1994: Discovery in the Thau lagoon in France of the smallest photosynthetic eukaryote known to date, Ostreococcus tauri, by Courties. 2001: Through sequencing of the ribosomal RNA gene extracted from marine samples, several European teams discover that eukaryotic picoplankton are highly diverse. This finding followed on the first discovery of such eukaryotic diversity in 1998 by Rappe and colleagues at Oregon State University, who were the first to apply rRNA sequencing to eukaryotic plankton in the open-ocean, where they discovered sequences that seemed distant from known phytoplankton The cells containing DNA matching one of these novel sequences were recently visualized and further analyzed using specific probes and found to be broadly distributed. == Methods of study == Because of its very small size, picoplankton is difficult to study by classic methods such as optical microscopy. More sophisticated
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"page_id": 7016898,
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methods are needed. Epifluorescence microscopy allows researchers to detect certain groups of cells possessing fluorescent pigments such as Synechococcus which possess phycoerythrin. Flow cytometry measures the size ("forward scatter") and fluorescence of 1,000 in 10,000 cells per second. It allows one to determine very easily the concentration of the various picoplankton populations on marine samples. Three groups of cells (Prochlorococcus, Synechococcus and picoeukaryotes) can be distinguished. For example Synechococcus is characterized by the double fluorescence of its pigments: orange for phycoerythrin and red for chlorophyll. Flow cytometry also allows researchers to sort out specific populations (for example Synechococcus) in order put them in culture, or to make more detailed analyses. Analysis of photosynthetic pigments such as chlorophyll or carotenoids by high precision chromatography (HPLC) allows researchers to determine the various groups of algae present in a sample. Molecular biology techniques: Cloning and sequencing of genes such as that of ribosomal RNA, which allows researchers to determine total diversity within a sample DGGE (denaturing gel electrophoresis) that is faster than the previous approach allows researchers to have an idea of the global diversity within a sample In situ hybridization (FISH) uses fluorescent probes recognizing specific taxon, for example a species, a genus or a class. This original description as a species is now thought to be composed of a number of different cryptic species, a finding that has been confirmed by a genome sequencing project of two strains led by researchers at the Monterey Bay Aquarium Research Institute. Quantitative PCR can be used, as FISH, to determine the abundance of specific groups. It has the main advantage to allow the rapid analysis of a large number of samples simultaneously, but requires more sophisticated controls and calibrations. == Composition == Three major groups of organisms constitute photosynthetic picoplankton: Cyanobacteria belonging to the
|
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"page_id": 7016898,
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"title": "Photosynthetic picoplankton"
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genus Synechococcus of a size of 1 μm (micrometer) were first discovered in 1979 by J. Waterbury (Woods Hole Oceanographic Institution). They are quite ubiquitous, but most abundant in relatively mesotrophic waters. Cyanobacteria belonging to the genus Prochlorococcus are particularly remarkable. With a typical size of 0.6 μm, Prochlorococcus was discovered only in 1988 by two American researchers, Sallie W. (Penny) Chisholm (Massachusetts Institute of Technology) and R.J. Olson (Woods Hole Oceanographic Institution). In spite of its small size, this photosynthetic organism is undoubtedly the most abundant of the planet: indeed its density can reach up to 100 million cells per liter and it can be found down to a depth of 150 m in all the intertropical belt. Picoplanktonic eukaryotes are the least well known, as demonstrated by the recent discovery of major groups. Andersen created in 1993 a new class of brown algae, the Pelagophyceae. More surprising still, the discovery in 1994 of a eukaryote of very small size, Ostreococcus tauri, dominating the phytoplanktonic biomass of a French brackish lagoon (étang de Thau), shows that these organisms can also play a major ecological role in coastal environments. In 1999, yet a new class of alga was discovered, the Bolidophyceae, very close genetically of diatoms, but quite different morphologically. At the present time, about 50 species are known belonging to several classes. The use of molecular approaches implemented since the 1990s for bacteria, were applied to the photosynthetic picoeukaryotes only 10 years later around 2000. They revealed a very wide diversity and brought to light the importance of the following groups in the picoplankton: Prasinophyceae Haptophyta Cryptophyta In temperate coastal environment, the genus Micromonas (Prasinophyceae) seems dominant. However, in numerous oceanic environments, the dominant species of eukaryotic picoplankton remain still unknown. == Ecology == Each picoplanktonic population occupies a
|
{
"page_id": 7016898,
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specific ecological niche in the oceanic environment. The Synechococcus cyanobacterium is generally abundant in mesotrophic environments, such as near the equatorial upwelling or in coastal regions. The Prochlorococcus cyanobacterium replaces it when the waters becomes impoverished in nutrients (i.e., oligotrophic). On the other hand, in temperate regions such as the North Atlantic Ocean, Prochlorococcus is absent because the cold waters prevent its development. The diversity of eukaryotes derives from their presence in a large variety of environments. In oceanic regions, they are often observed at depth, at the base of the well-lit layer (the "euphotic" layer). In coastal regions, certain sorts of picoeukaryotes such as Micromonas dominate. As with larger plankton, their abundance follows a seasonal cycle with a maximum in summer. Thirty years ago, it was hypothesized that the speed of division for micro-organisms in central oceanic ecosystems was very slow, of the order of one week or one month per generation. This hypothesis was supported by the fact that the biomass (estimated for example by the contents of chlorophyll) was very stable over time. However, with the discovery of the picoplankton, it was found that the system was much more dynamic than previously thought. In particular, small predators of a size of a few micrometres which ingest picoplanktonic algae as quickly as they were produced were found to be ubiquitous. This extremely sophisticated predator-prey system is nearly always at equilibrium and results in a quasi-constant picoplankton biomass. This close equivalence between production and consumption makes it extremely difficult to measure precisely the speed at which the system turns over. In 1988, two American researchers, Carpenter and Chang, suggested estimating the speed of cell division of phytoplankton by following the course of DNA replication by microscopy. By replacing the microscope by a flow cytometer, it is possible to follow
|
{
"page_id": 7016898,
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the DNA content of picoplankton cells over time. This allowed researchers to establish that picoplankton cells are highly synchronous: they replicate their DNA and then divide all at the same time at the end of the day. This synchronization could be due to the presence of an internal biological clock. == Genomics == In the 2000s, genomics allowed to cross a supplementary stage. Genomics consists in determining the complete sequence of genome of an organism and to list every gene present. It is then possible to get an idea of the metabolic capacities of the targeted organisms and understand how it adapts to its environment. To date, the genomes of several types of Prochlorococcus and Synechococcus, and of a strain of Ostreococcus have been determined. The complete genomes of two different Micromonas strains revealed that they were quite different (different species) and had similarities with land plants. Several other cyanobacteria and of small eukaryotes (Bathycoccus, Pelagomonas) are under sequencing. In parallel, genome analyses begin to be done directly from oceanic samples (ecogenomics or metagenomics), allowing us to access to large sets of gene for uncultivated organisms. == See also == Bacterioplankton List of eukaryotic picoplankton species Nanophytoplankton Phytoplankton Picoeukaryote == Notes and references == == Bibliography ==
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"page_id": 7016898,
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Compounds are organized into the following lists: List of inorganic compounds, compounds without a C–H bond List of biomolecules == See also == Chemical substance – Form of matter List of alchemical substances List of chemical elements List of minerals – List of minerals with Wikipedia articles List of named alloys List of straight-chain alkanes Polyatomic ion – Ion containing two or more atoms Exotic molecule – a compound containing one or more exotic atoms == External links == Relevant links for chemical compounds are: Chemical Abstracts Service, a division of the American Chemical Society Chemical Abstracts Service (CAS) – substance databases CAS Common Chemistry ChemSpider PubChem
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{
"page_id": 135619,
"source": null,
"title": "List of compounds"
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The Whitley Awards have been awarded annually since 1979 by the Royal Zoological Society of New South Wales (RZSNSW). They commemorate Gilbert Whitley, an eminent Australian ichthyologist, and are presented for outstanding publications, either printed or electronic, that contain new information about the fauna of the Australasian region. For a publication to receive a Whitley Award it must either make a significant contribution of new information, present a new synthesis of existing information, or present existing information in a more acceptable form. All texts must contain a significant proportion of information that relates directly to Australasian zoology. Moreover, all submissions must have been published within 18 months of the awards entry date. A presentation ceremony is held each year in September at the Australian Museum in Sydney when the authors and publishers of the winning titles receive their awards. == Awards == Certificates of Commendation may be awarded to publications judged as the best in various categories including, but not limited to, illustrated publications, textbooks, field guides, reference works, historical zoology, periodicals, handbooks, children’s publications, CD-ROMs, limited editions and videos. === Whitley Medal === The Whitley Medal may be awarded to a publication deemed to be of superior quality that makes a landmark contribution to the understanding, content or dissemination of zoological knowledge. The Whitley Medal is the top award in zoological publishing in Australia and is not necessarily awarded every year, though sometimes more than one medal may be awarded. == See also == Whitley Awards (UK) List of biology awards == References == == External links == About the Whitley Award List of past winners
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{
"page_id": 11407813,
"source": null,
"title": "Whitley Awards (Australia)"
}
|
Membrane stabilizing effects involve the inhibition or total abolishing of action potentials from being propagated across the membrane. This phenomenon is common in nerve tissues as they are the carrier of impulses from the periphery to the central nervous system. Membrane stabilization is the method through which local anesthetics work. They block the propagation of action potentials across nerve cells, thereby producing a nerve block. Some beta-blockers also possess what is referred to as membrane stabilizing activity (MSA). This effect is similar to the membrane stabilizing activity of sodium channel blockers that represent Class I antiarrhythmics. MSA agents produced by beta-blockers reduce the increase of cardiac action potential, while also leading to other electrophysiological effects. However, MSA occurs only at very high concentrations and is not of clinical relevance, except after large doses of MSA compounds. == References ==
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{
"page_id": 15995335,
"source": null,
"title": "Membrane stabilizing effect"
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Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius. == Metric == The original Schwarzschild coordinate expression of the Schwarzschild metric, in natural units (c = G = 1), is given as d s 2 = ( 1 − r s r ) d t 2 − d r 2 1 − r s r − r 2 ( d θ 2 + sin 2 θ d ϕ 2 ) , {\displaystyle ds^{2}=\left(1-{r_{s} \over r}\right)dt^{2}-{dr^{2} \over 1-{r_{s} \over r}}-r^{2}\left(d\theta ^{2}+\sin ^{2}\theta d\phi ^{2}\right)\;,} where d s 2 {\displaystyle ds^{2}} is the invariant interval; r s = 2 G M c 2 {\displaystyle r_{s}={\frac {2GM}{c^{2}}}} is the Schwarzschild radius; M {\displaystyle M} is the mass of the central body; t , r , θ , ϕ {\displaystyle t,r,\theta ,\phi } are the Schwarzschild coordinates (which asymptotically turn into the flat spherical coordinates); c {\displaystyle c} is the speed of light; and G {\displaystyle G} is the gravitational constant. This metric has a coordinate singularity at the Schwarzschild radius r = r s {\displaystyle r=r_{s}} . Georges Lemaître was the first to show that this is not a real physical singularity but simply a manifestation of the fact that the static Schwarzschild coordinates cannot be realized with material bodies inside the Schwarzschild radius. Indeed, inside the Schwarzschild radius everything falls towards the centre and it is impossible for a physical body to keep a constant radius. A transformation of the Schwarzschild coordinate system from { t , r } {\displaystyle \{t,r\}} to the new coordinates { τ , ρ } , {\displaystyle \{\tau ,\rho \},} d τ = d
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"page_id": 13636040,
"source": null,
"title": "Lemaître coordinates"
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t + r s r ( 1 − r s r ) − 1 d r d ρ = d t + r r s ( 1 − r s r ) − 1 d r {\displaystyle {\begin{aligned}d\tau =dt+{\sqrt {\frac {r_{s}}{r}}}\,\left(1-{\frac {r_{s}}{r}}\right)^{-1}dr~\\d\rho =dt+{\sqrt {\frac {r}{r_{s}}}}\,\left(1-{\frac {r_{s}}{r}}\right)^{-1}dr~\end{aligned}}} (the numerator and denominator are switched inside the square-roots), leads to the Lemaître coordinate expression of the metric, d s 2 = d τ 2 − r s r d ρ 2 − r 2 ( d θ 2 + sin 2 θ d ϕ 2 ) {\displaystyle ds^{2}=d\tau ^{2}-{\frac {r_{s}}{r}}d\rho ^{2}-r^{2}(d\theta ^{2}+\sin ^{2}\theta d\phi ^{2})} where r = [ 3 2 ( ρ − τ ) ] 2 / 3 r s 1 / 3 . {\displaystyle r=\left[{\frac {3}{2}}(\rho -\tau )\right]^{2/3}r_{s}^{1/3}\;.} The metric in Lemaître coordinates is non-singular at the Schwarzschild radius r = r s {\displaystyle r=r_{s}} . This corresponds to the point 3 2 ( ρ − τ ) = r s {\displaystyle {\frac {3}{2}}(\rho -\tau )=r_{s}} . There remains a genuine gravitational singularity at the center, where ρ − τ = 0 {\displaystyle \rho -\tau =0} , which cannot be removed by a coordinate change. The time coordinate used in the Lemaître coordinates is identical to the "raindrop" time coordinate used in the Gullstrand–Painlevé coordinates. The other three: the radial and angular coordinates r , θ , ϕ {\displaystyle r,\theta ,\phi } of the Gullstrand–Painlevé coordinates are identical to those of the Schwarzschild chart. That is, Gullstrand–Painlevé applies one coordinate transform to go from the Schwarzschild time t {\displaystyle t} to the raindrop coordinate t r = τ {\displaystyle t_{r}=\tau } . Then Lemaître applies a second coordinate transform to the radial component, so as to get rid of the off-diagonal entry in the Gullstrand–Painlevé chart. The notation τ
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"page_id": 13636040,
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"title": "Lemaître coordinates"
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{\displaystyle \tau } used in this article for the time coordinate should not be confused with the proper time. It is true that τ {\displaystyle \tau } gives the proper time for radially infalling observers; it does not give the proper time for observers traveling along other geodesics. == Geodesics == The trajectories with ρ constant are timelike geodesics with τ the proper time along these geodesics. They represent the motion of freely falling particles which start out with zero velocity at infinity. At any point their speed is just equal to the escape velocity from that point. The Lemaître coordinate system is synchronous, that is, the global time coordinate of the metric defines the proper time of co-moving observers. The radially falling bodies reach the Schwarzschild radius and the centre within finite proper time. Radial null geodesics correspond to d s 2 = 0 {\displaystyle ds^{2}=0} , which have solutions d τ = ± β d ρ {\displaystyle d\tau =\pm \beta d\rho } . Here, β {\displaystyle \beta } is just a short-hand for β ≡ β ( r ) = r s r {\displaystyle \beta \equiv \beta (r)={\sqrt {r_{s} \over r}}} The two signs correspond to outward-moving and inward-moving light rays, respectively. Re-expressing this in terms of the coordinate r {\displaystyle r} gives d r = ( ± 1 − r s r ) d τ {\displaystyle dr=\left(\pm 1-{\sqrt {r_{s} \over r}}\right)d\tau } Note that d r < 0 {\displaystyle dr<0} when r < r s {\displaystyle r<r_{s}} . This is interpreted as saying that no signal can escape from inside the Schwarzschild radius, with light rays emitted radially either inwards or outwards both end up at the origin as the proper time τ {\displaystyle \tau } increases. The Lemaître coordinate chart is not geodesically complete. This can
|
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"page_id": 13636040,
"source": null,
"title": "Lemaître coordinates"
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be seen by tracing outward-moving radial null geodesics backwards in time. The outward-moving geodesics correspond to the plus sign in the above. Selecting a starting point r > r s {\displaystyle r>r_{s}} at τ = 0 {\displaystyle \tau =0} , the above equation integrates to r → + ∞ {\displaystyle r\to +\infty } as τ → + ∞ {\displaystyle \tau \to +\infty } . Going backwards in proper time, one has r → r s {\displaystyle r\to r_{s}} as τ → − ∞ {\displaystyle \tau \to -\infty } . Starting at r < r s {\displaystyle r<r_{s}} and integrating forward, one arrives at r = 0 {\displaystyle r=0} in finite proper time. Going backwards, one has, once again that r → r s {\displaystyle r\to r_{s}} as τ → − ∞ {\displaystyle \tau \to -\infty } . Thus, one concludes that, although the metric is non-singular at r = r s {\displaystyle r=r_{s}} , all outward-traveling geodesics extend to r = r s {\displaystyle r=r_{s}} as τ → − ∞ {\displaystyle \tau \to -\infty } . == See also == Kruskal-Szekeres coordinates Eddington–Finkelstein coordinates Lemaître–Tolman metric Introduction to the mathematics of general relativity Stress–energy tensor Metric tensor (general relativity) Relativistic angular momentum == References ==
|
{
"page_id": 13636040,
"source": null,
"title": "Lemaître coordinates"
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Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. The result of this integration is it allows calculation of the posterior distribution of the prior, providing an updated probability estimate. Frequentist statistics may yield conclusions seemingly incompatible with those offered by Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. As the approaches answer different questions the formal results aren't technically contradictory but the two approaches disagree over which answer is relevant to particular applications. Bayesians argue that relevant information regarding decision-making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling, as its name implies, retains nested data structure, and is used when information is available at several different levels of observational units. For example, in epidemiological modeling to describe infection trajectories for multiple countries, observational units are countries, and each country has its own time-based profile of daily infected cases. In decline curve analysis to describe oil or gas production decline curve for multiple wells, observational units are oil or gas wells in a reservoir region, and each well has each own time-based profile of oil or gas production rates (usually, barrels per month). Hierarchical modeling is used to devise computatation based strategies for multiparameter problems. == Philosophy == Statistical
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{
"page_id": 42734031,
"source": null,
"title": "Bayesian hierarchical modeling"
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methods and models commonly involve multiple parameters that can be regarded as related or connected in such a way that the problem implies a dependence of the joint probability model for these parameters. Individual degrees of belief, expressed in the form of probabilities, come with uncertainty. Amidst this is the change of the degrees of belief over time. As was stated by Professor José M. Bernardo and Professor Adrian F. Smith, “The actuality of the learning process consists in the evolution of individual and subjective beliefs about the reality.” These subjective probabilities are more directly involved in the mind rather than the physical probabilities. Hence, it is with this need of updating beliefs that Bayesians have formulated an alternative statistical model which takes into account the prior occurrence of a particular event. == Bayes' theorem == The assumed occurrence of a real-world event will typically modify preferences between certain options. This is done by modifying the degrees of belief attached, by an individual, to the events defining the options. Suppose in a study of the effectiveness of cardiac treatments, with the patients in hospital j having survival probability θ j {\displaystyle \theta _{j}} , the survival probability will be updated with the occurrence of y, the event in which a controversial serum is created which, as believed by some, increases survival in cardiac patients. In order to make updated probability statements about θ j {\displaystyle \theta _{j}} , given the occurrence of event y, we must begin with a model providing a joint probability distribution for θ j {\displaystyle \theta _{j}} and y. This can be written as a product of the two distributions that are often referred to as the prior distribution P ( θ ) {\displaystyle P(\theta )} and the sampling distribution P ( y ∣ θ )
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"page_id": 42734031,
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{\displaystyle P(y\mid \theta )} respectively: P ( θ , y ) = P ( θ ) P ( y ∣ θ ) {\displaystyle P(\theta ,y)=P(\theta )P(y\mid \theta )} Using the basic property of conditional probability, the posterior distribution will yield: P ( θ ∣ y ) = P ( θ , y ) P ( y ) = P ( y ∣ θ ) P ( θ ) P ( y ) {\displaystyle P(\theta \mid y)={\frac {P(\theta ,y)}{P(y)}}={\frac {P(y\mid \theta )P(\theta )}{P(y)}}} This equation, showing the relationship between the conditional probability and the individual events, is known as Bayes' theorem. This simple expression encapsulates the technical core of Bayesian inference which aims to deconstruct the probability, P ( θ ∣ y ) {\displaystyle P(\theta \mid y)} , relative to solvable subsets of its supportive evidence. == Exchangeability == The usual starting point of a statistical analysis is the assumption that the n values y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} are exchangeable. If no information – other than data y – is available to distinguish any of the θ j {\displaystyle \theta _{j}} ’s from any others, and no ordering or grouping of the parameters can be made, one must assume symmetry of prior distribution parameters. This symmetry is represented probabilistically by exchangeability. Generally, it is useful and appropriate to model data from an exchangeable distribution as independently and identically distributed, given some unknown parameter vector θ {\displaystyle \theta } , with distribution P ( θ ) {\displaystyle P(\theta )} . === Finite exchangeability === For a fixed number n, the set y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable if the joint probability P ( y 1 , y 2 , … , y n )
|
{
"page_id": 42734031,
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{\displaystyle P(y_{1},y_{2},\ldots ,y_{n})} is invariant under permutations of the indices. That is, for every permutation π {\displaystyle \pi } or ( π 1 , π 2 , … , π n ) {\displaystyle (\pi _{1},\pi _{2},\ldots ,\pi _{n})} of (1, 2, …, n), P ( y 1 , y 2 , … , y n ) = P ( y π 1 , y π 2 , … , y π n ) . {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})=P(y_{\pi _{1}},y_{\pi _{2}},\ldots ,y_{\pi _{n}}).} The following is an exchangeable, but not independent and identical (iid), example: Consider an urn with a red ball and a blue ball inside, with probability 1 2 {\displaystyle {\frac {1}{2}}} of drawing either. Balls are drawn without replacement, i.e. after one ball is drawn from the n balls, there will be n − 1 remaining balls left for the next draw. Let Y i = { 1 , if the i th ball is red , 0 , otherwise . {\displaystyle {\text{Let }}Y_{i}={\begin{cases}1,&{\text{if the }}i{\text{th ball is red}},\\0,&{\text{otherwise}}.\end{cases}}} The probability of selecting a red ball in the first draw and a blue ball in the second draw is equal to the probability of selecting a blue ball on the first draw and a red on the second, both of which are 1/2: [ P ( y 1 = 1 , y 2 = 0 ) = P ( y 1 = 0 , y 2 = 1 ) = 1 2 ] {\displaystyle [P(y_{1}=1,y_{2}=0)=P(y_{1}=0,y_{2}=1)={\frac {1}{2}}]} ) This makes y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} exchangeable. But the probability of selecting a red ball on the second draw given that the red ball has already been selected in the first is 0. This is not equal to the probability that the red ball is selected in
|
{
"page_id": 42734031,
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the second draw, which is 1/2: [ P ( y 2 = 1 ∣ y 1 = 1 ) = 0 ≠ P ( y 2 = 1 ) = 1 2 ] {\displaystyle [P(y_{2}=1\mid y_{1}=1)=0\neq P(y_{2}=1)={\frac {1}{2}}]} ). Thus, y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} are not independent. If x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are independent and identically distributed, then they are exchangeable, but the converse is not necessarily true. === Infinite exchangeability === Infinite exchangeability is the property that every finite subset of an infinite sequence y 1 {\displaystyle y_{1}} , y 2 , … {\displaystyle y_{2},\ldots } is exchangeable. For any n, the sequence y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable. == Hierarchical models == === Components === Bayesian hierarchical modeling makes use of two important concepts in deriving the posterior distribution, namely: Hyperparameters: parameters of the prior distribution Hyperpriors: distributions of Hyperparameters Suppose a random variable Y follows a normal distribution with parameter θ {\displaystyle \theta } as the mean and 1 as the variance, that is Y ∣ θ ∼ N ( θ , 1 ) {\displaystyle Y\mid \theta \sim N(\theta ,1)} . The tilde relation ∼ {\displaystyle \sim } can be read as "has the distribution of" or "is distributed as". Suppose also that the parameter θ {\displaystyle \theta } has a distribution given by a normal distribution with mean μ {\displaystyle \mu } and variance 1, i.e. θ ∣ μ ∼ N ( μ , 1 ) {\displaystyle \theta \mid \mu \sim N(\mu ,1)} . Furthermore, μ {\displaystyle \mu } follows another distribution given, for example, by the standard normal distribution, N ( 0 , 1 ) {\displaystyle {\text{N}}(0,1)} . The parameter μ {\displaystyle \mu } is
|
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"page_id": 42734031,
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"title": "Bayesian hierarchical modeling"
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called the hyperparameter, while its distribution given by N ( 0 , 1 ) {\displaystyle {\text{N}}(0,1)} is an example of a hyperprior distribution. The notation of the distribution of Y changes as another parameter is added, i.e. Y ∣ θ , μ ∼ N ( θ , 1 ) {\displaystyle Y\mid \theta ,\mu \sim N(\theta ,1)} . If there is another stage, say, μ {\displaystyle \mu } following another normal distribution with a mean of β {\displaystyle \beta } and a variance of ϵ {\displaystyle \epsilon } , then μ ∼ N ( β , ϵ ) {\displaystyle \mu \sim N(\beta ,\epsilon )} , {\displaystyle {\mbox{ }}} β {\displaystyle \beta } and ϵ {\displaystyle \epsilon } can also be called hyperparameters with hyperprior distributions. === Framework === Let y j {\displaystyle y_{j}} be an observation and θ j {\displaystyle \theta _{j}} a parameter governing the data generating process for y j {\displaystyle y_{j}} . Assume further that the parameters θ 1 , θ 2 , … , θ j {\displaystyle \theta _{1},\theta _{2},\ldots ,\theta _{j}} are generated exchangeably from a common population, with distribution governed by a hyperparameter ϕ {\displaystyle \phi } . The Bayesian hierarchical model contains the following stages: Stage I: y j ∣ θ j , ϕ ∼ P ( y j ∣ θ j , ϕ ) {\displaystyle {\text{Stage I: }}y_{j}\mid \theta _{j},\phi \sim P(y_{j}\mid \theta _{j},\phi )} Stage II: θ j ∣ ϕ ∼ P ( θ j ∣ ϕ ) {\displaystyle {\text{Stage II: }}\theta _{j}\mid \phi \sim P(\theta _{j}\mid \phi )} Stage III: ϕ ∼ P ( ϕ ) {\displaystyle {\text{Stage III: }}\phi \sim P(\phi )} The likelihood, as seen in stage I is P ( y j ∣ θ j , ϕ ) {\displaystyle P(y_{j}\mid \theta _{j},\phi )} , with P ( θ
|
{
"page_id": 42734031,
"source": null,
"title": "Bayesian hierarchical modeling"
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j , ϕ ) {\displaystyle P(\theta _{j},\phi )} as its prior distribution. Note that the likelihood depends on ϕ {\displaystyle \phi } only through θ j {\displaystyle \theta _{j}} . The prior distribution from stage I can be broken down into: P ( θ j , ϕ ) = P ( θ j ∣ ϕ ) P ( ϕ ) {\displaystyle P(\theta _{j},\phi )=P(\theta _{j}\mid \phi )P(\phi )} [from the definition of conditional probability] With ϕ {\displaystyle \phi } as its hyperparameter with hyperprior distribution, P ( ϕ ) {\displaystyle P(\phi )} . Thus, the posterior distribution is proportional to: P ( ϕ , θ j ∣ y ) ∝ P ( y j ∣ θ j , ϕ ) P ( θ j , ϕ ) {\displaystyle P(\phi ,\theta _{j}\mid y)\propto P(y_{j}\mid \theta _{j},\phi )P(\theta _{j},\phi )} [using Bayes' Theorem] P ( ϕ , θ j ∣ y ) ∝ P ( y j ∣ θ j ) P ( θ j ∣ ϕ ) P ( ϕ ) {\displaystyle P(\phi ,\theta _{j}\mid y)\propto P(y_{j}\mid \theta _{j})P(\theta _{j}\mid \phi )P(\phi )} === Example calculation === As an example, a teacher wants to estimate how well a student did on the SAT. The teacher uses the current grade point average (GPA) of the student for an estimate. Their current GPA, denoted by Y {\displaystyle Y} , has a likelihood given by some probability function with parameter θ {\displaystyle \theta } , i.e. Y ∣ θ ∼ P ( Y ∣ θ ) {\displaystyle Y\mid \theta \sim P(Y\mid \theta )} . This parameter θ {\displaystyle \theta } is the SAT score of the student. The SAT score is viewed as a sample coming from a common population distribution indexed by another parameter ϕ {\displaystyle \phi } , which is the high
|
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"page_id": 42734031,
"source": null,
"title": "Bayesian hierarchical modeling"
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school grade of the student (freshman, sophomore, junior or senior). That is, θ ∣ ϕ ∼ P ( θ ∣ ϕ ) {\displaystyle \theta \mid \phi \sim P(\theta \mid \phi )} . Moreover, the hyperparameter ϕ {\displaystyle \phi } follows its own distribution given by P ( ϕ ) {\displaystyle P(\phi )} , a hyperprior. These relationships can be used to calculate the likelihood of a specific SAT score relative to a particular GPA: P ( θ , ϕ ∣ Y ) ∝ P ( Y ∣ θ , ϕ ) P ( θ , ϕ ) {\displaystyle P(\theta ,\phi \mid Y)\propto P(Y\mid \theta ,\phi )P(\theta ,\phi )} P ( θ , ϕ ∣ Y ) ∝ P ( Y ∣ θ ) P ( θ ∣ ϕ ) P ( ϕ ) {\displaystyle P(\theta ,\phi \mid Y)\propto P(Y\mid \theta )P(\theta \mid \phi )P(\phi )} All information in the problem will be used to solve for the posterior distribution. Instead of solving only using the prior distribution and the likelihood function, using hyperpriors allows a more nuanced distinction of relationships between given variables. === 2-stage hierarchical model === In general, the joint posterior distribution of interest in 2-stage hierarchical models is: P ( θ , ϕ ∣ Y ) = P ( Y ∣ θ , ϕ ) P ( θ , ϕ ) P ( Y ) = P ( Y ∣ θ ) P ( θ ∣ ϕ ) P ( ϕ ) P ( Y ) {\displaystyle P(\theta ,\phi \mid Y)={P(Y\mid \theta ,\phi )P(\theta ,\phi ) \over P(Y)}={P(Y\mid \theta )P(\theta \mid \phi )P(\phi ) \over P(Y)}} P ( θ , ϕ ∣ Y ) ∝ P ( Y ∣ θ ) P ( θ ∣ ϕ ) P ( ϕ ) {\displaystyle P(\theta ,\phi \mid Y)\propto P(Y\mid
|
{
"page_id": 42734031,
"source": null,
"title": "Bayesian hierarchical modeling"
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\theta )P(\theta \mid \phi )P(\phi )} === 3-stage hierarchical model === For 3-stage hierarchical models, the posterior distribution is given by: P ( θ , ϕ , X ∣ Y ) = P ( Y ∣ θ ) P ( θ ∣ ϕ ) P ( ϕ ∣ X ) P ( X ) P ( Y ) {\displaystyle P(\theta ,\phi ,X\mid Y)={P(Y\mid \theta )P(\theta \mid \phi )P(\phi \mid X)P(X) \over P(Y)}} P ( θ , ϕ , X ∣ Y ) ∝ P ( Y ∣ θ ) P ( θ ∣ ϕ ) P ( ϕ ∣ X ) P ( X ) {\displaystyle P(\theta ,\phi ,X\mid Y)\propto P(Y\mid \theta )P(\theta \mid \phi )P(\phi \mid X)P(X)} == Bayesian nonlinear mixed-effects model == A three stage version of Bayesian hierarchical modeling could be used to calculate probability at 1) an individual level, 2) at the level of population and 3) the prior, which is an assumed probability distribution that takes place before evidence is initially acquired: Stage 1: Individual-Level Model y i j = f ( t i j ; θ 1 i , θ 2 i , … , θ l i , … , θ K i ) + ϵ i j , ϵ i j ∼ N ( 0 , σ 2 ) , i = 1 , … , N , j = 1 , … , M i . {\displaystyle {y}_{ij}=f(t_{ij};\theta _{1i},\theta _{2i},\ldots ,\theta _{li},\ldots ,\theta _{Ki})+\epsilon _{ij},\quad \epsilon _{ij}\sim N(0,\sigma ^{2}),\quad i=1,\ldots ,N,\,j=1,\ldots ,M_{i}.} Stage 2: Population Model θ l i = α l + ∑ b = 1 P β l b x i b + η l i , η l i ∼ N ( 0 , ω l 2 ) , i = 1 , … , N , l
|
{
"page_id": 42734031,
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"title": "Bayesian hierarchical modeling"
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= 1 , … , K . {\displaystyle \theta _{li}=\alpha _{l}+\sum _{b=1}^{P}\beta _{lb}x_{ib}+\eta _{li},\quad \eta _{li}\sim N(0,\omega _{l}^{2}),\quad i=1,\ldots ,N,\,l=1,\ldots ,K.} Stage 3: Prior σ 2 ∼ π ( σ 2 ) , α l ∼ π ( α l ) , ( β l 1 , … , β l b , … , β l P ) ∼ π ( β l 1 , … , β l b , … , β l P ) , ω l 2 ∼ π ( ω l 2 ) , l = 1 , … , K . {\displaystyle \sigma ^{2}\sim \pi (\sigma ^{2}),\quad \alpha _{l}\sim \pi (\alpha _{l}),\quad (\beta _{l1},\ldots ,\beta _{lb},\ldots ,\beta _{lP})\sim \pi (\beta _{l1},\ldots ,\beta _{lb},\ldots ,\beta _{lP}),\quad \omega _{l}^{2}\sim \pi (\omega _{l}^{2}),\quad l=1,\ldots ,K.} Here, y i j {\displaystyle y_{ij}} denotes the continuous response of the i {\displaystyle i} -th subject at the time point t i j {\displaystyle t_{ij}} , and x i b {\displaystyle x_{ib}} is the b {\displaystyle b} -th covariate of the i {\displaystyle i} -th subject. Parameters involved in the model are written in Greek letters. The variable f ( t ; θ 1 , … , θ K ) {\displaystyle f(t;\theta _{1},\ldots ,\theta _{K})} is a known function parameterized by the K {\displaystyle K} -dimensional vector ( θ 1 , … , θ K ) {\displaystyle (\theta _{1},\ldots ,\theta _{K})} . Typically, f {\displaystyle f} is a `nonlinear' function and describes the temporal trajectory of individuals. In the model, ϵ i j {\displaystyle \epsilon _{ij}} and η l i {\displaystyle \eta _{li}} describe within-individual variability and between-individual variability, respectively. If the prior is not considered, the relationship reduces to a frequentist nonlinear mixed-effect model. A central task in the application of the Bayesian nonlinear mixed-effect models is to evaluate
|
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"page_id": 42734031,
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"title": "Bayesian hierarchical modeling"
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posterior density: π ( { θ l i } i = 1 , l = 1 N , K , σ 2 , { α l } l = 1 K , { β l b } l = 1 , b = 1 K , P , { ω l } l = 1 K | { y i j } i = 1 , j = 1 N , M i ) {\displaystyle \pi (\{\theta _{li}\}_{i=1,l=1}^{N,K},\sigma ^{2},\{\alpha _{l}\}_{l=1}^{K},\{\beta _{lb}\}_{l=1,b=1}^{K,P},\{\omega _{l}\}_{l=1}^{K}|\{y_{ij}\}_{i=1,j=1}^{N,M_{i}})} ∝ π ( { y i j } i = 1 , j = 1 N , M i , { θ l i } i = 1 , l = 1 N , K , σ 2 , { α l } l = 1 K , { β l b } l = 1 , b = 1 K , P , { ω l } l = 1 K ) {\displaystyle \propto \pi (\{y_{ij}\}_{i=1,j=1}^{N,M_{i}},\{\theta _{li}\}_{i=1,l=1}^{N,K},\sigma ^{2},\{\alpha _{l}\}_{l=1}^{K},\{\beta _{lb}\}_{l=1,b=1}^{K,P},\{\omega _{l}\}_{l=1}^{K})} = π ( { y i j } i = 1 , j = 1 N , M i | { θ l i } i = 1 , l = 1 N , K , σ 2 ) ⏟ S t a g e 1 : I n d i v i d u a l − L e v e l M o d e l × π ( { θ l i } i = 1 , l = 1 N , K | { α l } l = 1 K , { β l b } l = 1 , b = 1 K , P , { ω l } l = 1 K ) ⏟ S t a g e 2 : P o p u l a t
|
{
"page_id": 42734031,
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"title": "Bayesian hierarchical modeling"
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i o n M o d e l × p ( σ 2 , { α l } l = 1 K , { β l b } l = 1 , b = 1 K , P , { ω l } l = 1 K ) ⏟ S t a g e 3 : P r i o r {\displaystyle =\underbrace {\pi (\{y_{ij}\}_{i=1,j=1}^{N,M_{i}}|\{\theta _{li}\}_{i=1,l=1}^{N,K},\sigma ^{2})} _{Stage1:Individual-LevelModel}\times \underbrace {\pi (\{\theta _{li}\}_{i=1,l=1}^{N,K}|\{\alpha _{l}\}_{l=1}^{K},\{\beta _{lb}\}_{l=1,b=1}^{K,P},\{\omega _{l}\}_{l=1}^{K})} _{Stage2:PopulationModel}\times \underbrace {p(\sigma ^{2},\{\alpha _{l}\}_{l=1}^{K},\{\beta _{lb}\}_{l=1,b=1}^{K,P},\{\omega _{l}\}_{l=1}^{K})} _{Stage3:Prior}} The panel on the right displays Bayesian research cycle using Bayesian nonlinear mixed-effects model. A research cycle using the Bayesian nonlinear mixed-effects model comprises two steps: (a) standard research cycle and (b) Bayesian-specific workflow. A standard research cycle involves 1) literature review, 2) defining a problem and 3) specifying the research question and hypothesis. Bayesian-specific workflow stratifies this approach to include three sub-steps: (b)–(i) formalizing prior distributions based on background knowledge and prior elicitation; (b)–(ii) determining the likelihood function based on a nonlinear function f {\displaystyle f} ; and (b)–(iii) making a posterior inference. The resulting posterior inference can be used to start a new research cycle. == References ==
|
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"page_id": 42734031,
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"title": "Bayesian hierarchical modeling"
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The placenta of humans, and certain other mammals contains structures known as cotyledons, which transmit fetal blood and allow exchange of oxygen and nutrients with the maternal blood. == Ruminants == The Artiodactyla have a cotyledonary placenta. In this form of placenta, the chorionic villi form a number of separate circular structures (cotyledons) which are distributed over the surface of the chorionic sac. Sheep, goats and cattle have between 72 and 125 cotyledons whereas deer have 4-6 larger cotyledons. == Human == The form of the human placenta is generally classified as a discoid placenta. Within this, the cotyledons are the approximately 15-25 separations of the decidua basalis of the placenta, separated by placental septa. Each cotyledon consists of a main stem of a chorionic villus as well as its branches and sub-branches. == Vasculature == The cotyledons receive fetal blood from chorionic vessels, which branch off cotyledon vessels into the cotyledons, which, in turn, branch into capillaries. The cotyledons are surrounded by maternal blood, which can exchange oxygen and nutrients with the fetal blood in the capillaries. == References == == External links == Diagram (page in French)
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{
"page_id": 8196559,
"source": null,
"title": "Placental cotyledon"
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In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). For an intended output t = ±1 and a classifier score y, the hinge loss of the prediction y is defined as ℓ ( y ) = max ( 0 , 1 − t ⋅ y ) {\displaystyle \ell (y)=\max(0,1-t\cdot y)} Note that y {\displaystyle y} should be the "raw" output of the classifier's decision function, not the predicted class label. For instance, in linear SVMs, y = w ⋅ x + b {\displaystyle y=\mathbf {w} \cdot \mathbf {x} +b} , where ( w , b ) {\displaystyle (\mathbf {w} ,b)} are the parameters of the hyperplane and x {\displaystyle \mathbf {x} } is the input variable(s). When t and y have the same sign (meaning y predicts the right class) and | y | ≥ 1 {\displaystyle |y|\geq 1} , the hinge loss ℓ ( y ) = 0 {\displaystyle \ell (y)=0} . When they have opposite signs, ℓ ( y ) {\displaystyle \ell (y)} increases linearly with y, and similarly if | y | < 1 {\displaystyle |y|<1} , even if it has the same sign (correct prediction, but not by enough margin). == Extensions == While binary SVMs are commonly extended to multiclass classification in a one-vs.-all or one-vs.-one fashion, it is also possible to extend the hinge loss itself for such an end. Several different variations of multiclass hinge loss have been proposed. For example, Crammer and Singer defined it for a linear classifier as ℓ ( y ) = max ( 0 , 1 + max y ≠ t w y x − w t x ) {\displaystyle \ell (y)=\max(0,1+\max _{y\neq t}\mathbf {w} _{y}\mathbf {x} -\mathbf
|
{
"page_id": 33100241,
"source": null,
"title": "Hinge loss"
}
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{w} _{t}\mathbf {x} )} , where t {\displaystyle t} is the target label, w t {\displaystyle \mathbf {w} _{t}} and w y {\displaystyle \mathbf {w} _{y}} are the model parameters. Weston and Watkins provided a similar definition, but with a sum rather than a max: ℓ ( y ) = ∑ y ≠ t max ( 0 , 1 + w y x − w t x ) {\displaystyle \ell (y)=\sum _{y\neq t}\max(0,1+\mathbf {w} _{y}\mathbf {x} -\mathbf {w} _{t}\mathbf {x} )} . In structured prediction, the hinge loss can be further extended to structured output spaces. Structured SVMs with margin rescaling use the following variant, where w denotes the SVM's parameters, y the SVM's predictions, φ the joint feature function, and Δ the Hamming loss: ℓ ( y ) = max ( 0 , Δ ( y , t ) + ⟨ w , ϕ ( x , y ) ⟩ − ⟨ w , ϕ ( x , t ) ⟩ ) = max ( 0 , max y ∈ Y ( Δ ( y , t ) + ⟨ w , ϕ ( x , y ) ⟩ ) − ⟨ w , ϕ ( x , t ) ⟩ ) {\displaystyle {\begin{aligned}\ell (\mathbf {y} )&=\max(0,\Delta (\mathbf {y} ,\mathbf {t} )+\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {y} )\rangle -\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {t} )\rangle )\\&=\max(0,\max _{y\in {\mathcal {Y}}}\left(\Delta (\mathbf {y} ,\mathbf {t} )+\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {y} )\rangle \right)-\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {t} )\rangle )\end{aligned}}} . == Optimization == The hinge loss is a convex function, so many of the usual convex optimizers used in machine learning can work with it. It is not differentiable, but has a subgradient with respect to model parameters w of a linear
|
{
"page_id": 33100241,
"source": null,
"title": "Hinge loss"
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SVM with score function y = w ⋅ x {\displaystyle y=\mathbf {w} \cdot \mathbf {x} } that is given by ∂ ℓ ∂ w i = { − t ⋅ x i if t ⋅ y < 1 , 0 otherwise . {\displaystyle {\frac {\partial \ell }{\partial w_{i}}}={\begin{cases}-t\cdot x_{i}&{\text{if }}t\cdot y<1,\\0&{\text{otherwise}}.\end{cases}}} However, since the derivative of the hinge loss at t y = 1 {\displaystyle ty=1} is undefined, smoothed versions may be preferred for optimization, such as Rennie and Srebro's ℓ ( y ) = { 1 2 − t y if t y ≤ 0 , 1 2 ( 1 − t y ) 2 if 0 < t y < 1 , 0 if 1 ≤ t y {\displaystyle \ell (y)={\begin{cases}{\frac {1}{2}}-ty&{\text{if}}~~ty\leq 0,\\{\frac {1}{2}}(1-ty)^{2}&{\text{if}}~~0<ty<1,\\0&{\text{if}}~~1\leq ty\end{cases}}} or the quadratically smoothed ℓ γ ( y ) = { 1 2 γ max ( 0 , 1 − t y ) 2 if t y ≥ 1 − γ , 1 − γ 2 − t y otherwise {\displaystyle \ell _{\gamma }(y)={\begin{cases}{\frac {1}{2\gamma }}\max(0,1-ty)^{2}&{\text{if}}~~ty\geq 1-\gamma ,\\1-{\frac {\gamma }{2}}-ty&{\text{otherwise}}\end{cases}}} suggested by Zhang. The modified Huber loss L {\displaystyle L} is a special case of this loss function with γ = 2 {\displaystyle \gamma =2} , specifically L ( t , y ) = 4 ℓ 2 ( y ) {\displaystyle L(t,y)=4\ell _{2}(y)} . == See also == Multivariate adaptive regression spline § Hinge functions == References ==
|
{
"page_id": 33100241,
"source": null,
"title": "Hinge loss"
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The molecular formula C24H26N2O2 (molar mass: 374.47 g/mol, exact mass: 374.1994 u) may refer to: Carmoxirole Evocalcet Furanylfentanyl
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{
"page_id": 58069459,
"source": null,
"title": "C24H26N2O2"
}
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Growing Up in the Universe was a series of televised public lectures given by British evolutionary biologist Richard Dawkins as part of the Royal Institution Christmas Lectures, in which he discussed the evolution of life in the universe. The lectures were first broadcast on the BBC in 1991, in the form of five one-hour episodes. The Richard Dawkins Foundation for Reason and Science was granted the rights to the televised lectures, and a DVD version was released by the foundation on 20 April 2007. Dawkins' book Climbing Mount Improbable (1996) was developed from the ideas presented in the lectures, and the title itself was taken from the third lecture in the series. == Parts == === Part 1: Waking Up in the Universe === To start off part one, Dawkins discusses the amazing capabilities of the human body and contrasts these with the limited capabilities of computers and other man-made machines. He uses a small totem pole (which is used in ancestor worship) to illustrate the importance of studying our ancestors to understand how we've evolved. To contrast ease of reproduction with the difficulty of becoming an ancestor, Dawkins uses the example of paper folding to explain exponential growth. Dawkins then tells the audience that exponential growth does not generally happen in the real world – natural factors come into play which control the population numbers, meaning that only an elite group of organisms will actually become distant ancestors. To be in this elite group, the organism must "have what it takes" to survive and pass on their genes to offspring. The long chain of successful ancestors means that the probability of our existence is very small, and we are lucky to be alive. By turning down the lights and shining a small spotlight on a large ruler in front
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{
"page_id": 11080148,
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of him, Dawkins illustrates the darkness of the distant past and of the unknown future. After expounding on how lucky we are to be alive, and urging us not to waste the precious time that we have, Dawkins brings up the usefulness of science in aiding our understanding of the universe. He mentions the reply that Michael Faraday gave to Sir Robert Peel when asked about the use of science. Faraday's response was "What is the use of a baby?" Dawkins explains that Faraday was either referring to the vast potential of a baby, or to the idea that there must be something more to life than growing up, working, getting old, and dying. There must be a point to it all; Perhaps science can uncover the answers to our biggest questions. To shake off the "anesthetic of familiarity," Dawkins shows the audience a number of strange terrestrial organisms which he humorously nicknames "By-Jovians," playing off a term we might use to refer to living organisms from another planet, for instance Jupiter. He uses a scanning electron microscope to look at small organisms including mites, mosquitoes, and a bee being parasitized by a strepsiptera. Using a model of a eukaryotic cell, he discusses the mitochondria and presents the audience with a complicated diagram of the metabolic pathways. Dawkins suggests that we can also shake off the familiarity by stepping backwards in time. By using a single pace to represent going back 1000 years, he starts at year zero and takes four steps in front of his desk, going back to 4000 BCE. Pointing to a portrait of Homo habilis, he states that to go back to the time of habilis, he would have to walk about two kilometers. He has audience members hold up portraits of other human ancestors, telling
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{
"page_id": 11080148,
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them how far he would have to walk to get back to the time of each one. By imagining what an advanced alien species would think of humans if they were to arrive on Earth, Dawkins suggests that their science would be similar to ours. They would know about pi, the Pythagorean theorem, and the theory of relativity. However, Dawkins explains that the alien anthropologists would most likely scoff at our local, parochial religious beliefs. He then contrasts evidence-based beliefs with revealed, tradition-based, and authority-based beliefs. To explain the problem with beliefs in the supernatural, Dawkins conducts a small experiment with the audience to "find the psychic." Using a coin, he assigns half the audience to will it to land on heads, and assigns the other half to will it to land on tails. After each flip, the section of the audience that was wrong is eliminated from the experiment, and he repeats the experiment using the remainder. After eight coin flips, only one boy in the audience remains. Dawkins then asks the question "Is he psychic?" Obviously, because of how the experiment was set up, one person was bound to have been correct about the result of each coin flip. Dawkins argues that this is exactly how seemingly supernatural events occur in the real world, especially when the "audience" is the entire population of the planet. To conclude the lecture, Dawkins claims that there is nothing wrong with having faith in a proper scientific prediction. To illustrate this, he takes a cannonball which has been suspended from the ceiling with a rope, pulls it aside and touches it to his forehead. He announces that he is going to release the cannonball, letting it swing away from him, and that when it comes back to him, he is going to
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{
"page_id": 11080148,
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ignore his natural instinct to run because he has faith in his scientific prediction of what will happen – the cannonball should stop about an inch short of his forehead. He releases the cannonball, and his prediction is proved correct. === Part 2: Designed and Designoid Objects === Dawkins' second lecture of the series examines the problem of design. He presents the audience with a number of simple objects, such as rocks and crystals, and notes that these objects have been formed by simple laws of physics and are therefore not designed. He then examines some designed objects – including a microscope, an electronic calculator, a pocket watch, and a clay pot – and notes that none of these objects could have possibly come about by sheer luck. Dawkins then discusses what he calls "designoid objects", which are complex objects that are neither simple, nor designed. Not only are they complex on the outside, they are also complex on the inside – perhaps billions of times more complex than a designed object such as a microscope. Dawkins then shows the audience a number of designed and designoid objects, including the pitcher plant, megalithic mounds built by the compass termite, and pots made by trapdoor spiders, potter wasps, and mason bees. He examines some designoid objects that use camouflage, such as a grasshopper that looks like a stone, a sea horse that looks like sea weed, a leaf insect, a green snake, a stick insect, and a collection of butterflies that look like dead leaves when their wings are closed. Dawkins notes that many animals share similar types of camouflage or protection because of a process called convergent evolution. Examples of such designoid objects include the hedgehog and the spiny anteater (both of which evolved pointed spines along their back) and
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{
"page_id": 11080148,
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the marsupial wolf (which looks like a dog but is actually a marsupial). He illustrates the reason why convergent evolution occurs by using two small models of commercial aircraft. The reason they look similar isn't due to industrial espionage, it is due to the fact that they are both built to fly, so they must make use of similar design principles. Using a camera and a model eye, Dawkins then compares the designed camera with the designoid eye. Both are involved in similar processes – using a lens to direct light onto a film or a retina. Both the camera and the eye also have an iris, which is used to control the amount of light which is allowed in. Using a volunteer from the audience, Dawkins demonstrates the contraction of the human iris by shining a light into her right eye. The lecture then moves into an explanation of natural selection, which brings forth designoid objects. To explain natural selection, Dawkins first explains artificial selection by discussing the evolution of wild cabbage into broccoli, cauliflower, cabbage, red cabbage, kohlrabi, and Brussels sprouts. He continues the discussion of artificial selection by explaining the evolution of the ancestral wolf into the many varieties of modern dog. Starting with the ancestral wolf, Dawkins imagines that everyone on one side of the room is breeding for small wolves, while everyone on the other side is breeding for big wolves. By selectively breeding the smallest or largest of each litter for a number of years, you may eventually end up with something like the Chihuahua on one side of the room, and something like a Great Dane on the other side of the room. Dawkins then introduces an Arthromorphs computer program (similar to the Biomorphs program), explaining how it works while a volunteer uses
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{
"page_id": 11080148,
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the computer to selectively breed more and more generations. At this point, Dawkins switches from explaining artificial selection to explaining natural selection. To demonstrate natural selection in a computer program, Dawkins uses a program written by Peter Fuchs to simulate the evolution of the spiderweb. The program builds "genetic" variations of a parent web, as if the web was actually being built by a child spider. For each generation, a simulation is run which randomly generates flies – some of which will hit the web, and others that will miss it. The child web that is able to capture the highest number of flies is selected as the parent for the next generation of webs. Dawkins shows the audience the "fossil record" that the program recorded after simulating a large number of generations overnight. The web starts off very simple and inefficient, but by the end it has evolved into a web that is highly efficient and highly complex. This is the same process that has led to the existence of all designoid objects. Dawkins now discusses the most popular alternative to natural selection, which is known as creationism. He explains that creationists mistakenly believe designoid objects to be designed objects created by a divine being. Quoting from William Paley's Natural Theology, Dawkins discusses the argument from design using the example of the watch and the watchmaker. Even though designoid objects appear to be designed, Darwin proved that this is not the case. Although Darwin's theory was discovered well after Paley developed his watchmaker argument, Dawkins explains that the argument of a divine watchmaker was still a bad argument, even in Paley's day. Paraphrasing David Hume, Dawkins explains that anything capable of creating humans must itself be highly complicated. Thus, the argument from design actually explains nothing – "shooting itself
|
{
"page_id": 11080148,
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in the foot." While it is true that designoid objects cannot come about by chance, evolution provides a non-random method of creation – namely, natural selection. After developing the argument against a divine creator, Dawkins examines a number of designoid objects that contain imperfections, which is something you would not expect to find in an object that is supposedly created by a divine being. Showing the audience a halibut flatfish, he explains how they evolved from an upright swimming ancestor with one eye on each side of the head into a bottom-hugging flatfish with a distorted set of eyes on one side of the body. Dawkins claims that this is poorly designed, as any proper engineer would design an organism more like a skate, which flattened out on its belly instead of on its side. This is an example of something you would expect from an evolved/designoid object, but not something you would expect from a created/designed object. Using labeled building blocks, Dawkins shows the audience how designed objects came to be. He starts off by placing the simple block on the bottom, and explaining that you don't have to start with a complex being, but can start with a very simple foundation. If you have a simple foundation, you can place the next block on top – the designoid block. From this block, you can get complex organisms. Only after complex designoid objects come to be can you get the final building block of design (microscopes, clay pots, etc.). === Part 3: Climbing Mount Improbable === Dawkins starts the lecture coming in with a stick insect on his hand. He describes with how many details such a being imitates its environment, its almost like a key that fits a lock. He then shows another insect, namely a Leaf Insect,
|
{
"page_id": 11080148,
"source": null,
"title": "Growing Up in the Universe"
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which basically looks exactly like a dead leaf. He gives some more examples for this amazing imitation of the surrounding, e.g. a Potoo, which looks like a branch of tree and a thorn bug, which gains protection by looking like a rose thorn. He, once again, makes the point that you can compare these beings with a key, which they represent themselves, whereas nature is the lock. Professor Richard Dawkins then explains that a key has to fit a lock exactly, and demonstrates this with a model of a lock. He mentions that a key is something very improbable. However it is hard to measure the probability of such a key, therefore Dawkins takes a bicycle lock for illustration, where you can calculate how likely it is to open the lock, because there is a fixed number of dials with a fixed number of positions. In Dawkin's case we have 3 dials, with 6 positions each, so the probability that you open the lock by sheer luck is one in 216. Dawkins then shows the mechanism of the lock with a big model: Each dial has to be in the correct position in order to open up the lock. The model is then adapted to demonstrate a staged or gradualist solution to finding the right combination to open the lock. The probability of unlocking the combination in three separate phases falls to one in eighteen. In this illustration, Dawkins identifies the role of sub-stages in Darwinian evolution. It is to increase the efficiency of mutation without affecting the probability of evolutionary success. The single stage requires 216, while the series of sub-stages requires only 18 non-random mutations at 100% probability of evolutionary success. That is an efficiency factor of 12 for mutations due to sub-staging without any change in probability.
|
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"page_id": 11080148,
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Similar efficiencies are achieved with random mutation without any change in probability. After addressing the claim by Fred Hoyle that probability alone could not produce the complexity of a typed text by Shakespeare, Dawkins introduces the notion of inherited improvements over a number of generations. Nature proceeds through small evolutionary steps, rather than large leaps. This idea is illustrated by a model of the ascent of Mount Improbable, which provides the title for this lecture. Dawkins then illustrates the difference between the reproduction of inanimate phenomena, such as fires spread through sparks, with the inter-generational transmission of DNA in living structures. The gradual evolutionary adaption of these organisms is demonstrated through the examples of the eye, varieties of wings and protective camouflage. The example of the gradual emergence of the eye is first shown: starting with a simple light sensitive flat surface and demonstrating the evolutionary benefits of a cone shaped proto-eye for detecting shadows and shapes. Dawkins then relates this model to the simple pinhole eye structure of a nautilus mollusc. The benefit of wing structures is illustrated by way of body flattening behaviour in tree snakes, the web like skin of flying squirrels and similar adaptions to be found on flying lizards. === Part 4: The Ultraviolet Garden === Dawkins begins by relating the story of asking a little girl "what she thought flowers were 'for'." Her response is anthropocentric, that flowers are there for our benefit. Dawkins points out that many people throughout history have thought that the natural world existed for our benefit, with examples from Genesis and other literature. Author Douglas Adams, who is sitting in the audience, is called to read a relevant passage from his novel The Restaurant at the End of the Universe. Dawkins then asks his audience to put off the
|
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"page_id": 11080148,
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idea that the natural world exists for our benefit. He considers the question of flowers seen through the eyes of bees and other pollinators, and performs a series of demonstrations which use ultraviolet light to excite fluorescence in various substances. === Part 5: The Genesis of Purpose === Dawkins opens by talking how organisms "grow up" to understand the universe around them, which requires certain apparatus, such as a brain. But before brains can become large enough to model the universe they must develop from intermediate forms. Dawkins then discusses the digger wasp and the set of experiments conducted by Nikolaas Tinbergen of how the digger wasp models the local geography around its nest. He then talks about the limitations of the digger wasps' brain and concludes that only the human brain is sufficiently developed to model large-scale phenomena about the world. He then shows an MRI scan of a human brain (later revealed to be his own brain) and describes how an image develops from the eye onto the visual cortex. Dawkins discusses how the image on the retina is upside-down and in two dimensions but the overlapping images from each of the eyes are composited to form a three-dimensional model in the brain. He shows this by asking the audience to focus on him while holding their hand at eye level which causes them to see two images of their hand; one from each eye. He then describes how using his finger to wriggle his eyeball that the outside world appears to move because he is moving the image on his retina. However this does not happen when he voluntary rolls his eyes from side to side. This is due to the brain using the internal model to compensate for the relative change in position of images on
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"page_id": 11080148,
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"title": "Growing Up in the Universe"
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the retina. Dawkins gets someone to wear a virtual reality headset and move around in a 3-D computer generated world and draws an analogy between the model of the universe developed in one's head with the virtual reality universe developed in the computer. He then goes on the show that the brain uses models to describe the universe by looking at how the brain interprets various optical illusions, such as the hollow-face illusion using a rotating hollow mask of Charlie Chaplin, the "impossible" geometry of a Penrose triangle, the shifting interpretations of the Necker cube and the ability of humans to find faces in random shapes. Dawkins then begins to discuss the evolution of the human brain. He shows an animation of the increasing skull size from Australopithecus to Homo habilis to Homo erectus and then finally to modern day humans. The ability of a brain to run complex simulations is a powerful evolutionary advantage. Dawkins talks about how this ability to model future events by showing a painting suggesting a hypothetical situation in which a female Homo erectus uses a mental model of a tree fallen across a gorge as a possible solution to crossing the gorge. The group then burns a tree so that it would create a bridge over the gap. He goes on to describe how the complex modelling ability of the brain may have developed due to this imaginative simulation of various possible scenarios or by the development of language, which would allow ideas to be passed from generation to generation, or by technology, which is an extension of human hands and eyes; or, indeed, if it is a combination of all three. Dawkins concludes that purpose has arisen in the Universe due to human brains. The simulations developed in our brain allow us to
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{
"page_id": 11080148,
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"title": "Growing Up in the Universe"
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develop intent and purpose; and over time our collective understanding of the Universe will improve as we continue to study and exchange ideas. == Quotations == Life makes the wonders of technology seem commonplace. So where does life come from? What is it? Why are we here? What are we for? What is the meaning of life? There's a conventional wisdom which says that science has nothing to say about such questions. Well, all I can say is that if science has nothing to say, it's certain that no other discipline can say anything at all. But in fact, science has a great deal to say about such questions. And that's what these five lectures are going to be about. Life "grows up" in the universe by gradual degrees – evolution – and we grow up in our understanding of our origins and our meaning. The present century is a tiny spotlight, inching its way along a gigantic ruler of time. Everything before the spotlight is the darkness of the dead past. Everything after the spotlight is in the darkness of the unknown future. We live in the spotlight. Of all the 200,000,000 centuries along the ruler of time, 199,999,999 centuries are in darkness. Only one is lit up, and that is the one in which we happen – by sheer luck – to be alive. The odds against our century happening to be the present century are the same as the odds against a penny tossed out at random on the road from London to Istanbul happening to fall on a particular ant. We do of course, have an ordinary life to get on with. We do have a living to earn. We've got to earn our living being a solicitor or a lavatory cleaner or something like that.
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"page_id": 11080148,
"source": null,
"title": "Growing Up in the Universe"
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But nevertheless, it is worthwhile also from time to time shaking off the anaesthetic of familiarity and awakening to the wonder that is really all around us all the time. Natural selection – nature – is constantly choosing which individual shall live, [and] which individual shall breed. And the result, after many generations of natural selection, is much the same as the result after many generations of artificial selection. In any case, all creation, all design, all machines and houses and paintings and computers and airplanes, everything designed and made by us, everything made by other creatures, is only made possible because there are already brains put together as designoid objects – and designoid objects come about only through gradual evolution. Creation, when it does occur in the universe, is an afterthought. When creation appeared on this planet it came locally, and it came late. Creation does not belong in any account of the fundamentals of the universe. Creation is something that, rather late in the day, grows up in the universe. == Notes and references == == External links == Growing Up in the Universe - Richard Dawkins - YouTube
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"page_id": 11080148,
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"title": "Growing Up in the Universe"
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Decrepitation is the noise produced when certain chemical compounds are heated, or it refers to the cracking, or breaking up of lumps of limestone during heating. Such compounds include lead nitrate and calcine. == Mineralogy == Decrepitation is one of the most accurate ways to calculate a mineral-deposit scale so that the analysis of the hydrothermal system is advanced and improved. Fluid inclusions are important in regard to decrepitation because they are the microscopic areas of gas and liquid within crystals that are decrepitated, or broken, with the application of heat. When decrepitating the crystal or salt, the liquid pressure is released which can result in a crack. However, in some cases the fluid inclusions are not fully decrepitated, in which case other methods must be used. Despite this shortcoming, decrepitation is the preferred procedure for identifying minerals because it allows for the quickest and greatest number of inclusions to be measured. The pressure necessary to spur decrepitation is reliant upon the size of the fluid inclusions; bigger inclusions decrepitate more easily at pressures between 700 and 900 atmospheres, while smaller fluid inclusions may require upwards of 1200 atmospheres, contrastingly, when fluid inclusions become even smaller, the amount of pressure applied will have no effect and decrepitation will not occur. == Decrepitation in metamorphic rock == If the decrepitation begins at a temperature less than the temperature required to form the mineral, it is likely that the rate of decrepitation will speed up once the temperature exceeds that of the initial heating. For metamorphic rocks, there are certain principles for measuring the decrepitations. What is known as D1 decrepitation, is classified as a temperature range of about 200-300 °C and is caused by the liquid phase which occupies intricate inclusions, as in hydrothermal minerals. D2 decrepitation is characterized by a
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{
"page_id": 9572821,
"source": null,
"title": "Decrepitation"
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|
starting heat range of about 300-700 °C, the temperature can also increase rapidly for a few hundred degrees, such as in solid inclusions. D3 decrepitation is continuously heated until the rate reaches its maximum out at about 350-450 °C, D3 decrepitation can be observed in carbonates and is defined by the effect of an inversion of the mineral. Once decrepitation of a D4 mineral is reached it should reach completion within a few degrees, which is seen in the decrepitation of quartz. Decrepitation as a result of decomposition is known as D5 decrepitation, it is characterized by a sharp upwards rate, a definite peak, and a sharp downwards rate, this can be detected by comparing the peaks of various minerals within a rock. == References ==
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{
"page_id": 9572821,
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"title": "Decrepitation"
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Gunpowder is the first explosive to have been developed. Popularly listed as one of the "Four Great Inventions" of China, it was invented during the late Tang dynasty (9th century) while the earliest recorded chemical formula for gunpowder dates to the Song dynasty (11th century). Knowledge of gunpowder spread rapidly throughout Asia and Europe, possibly as a result of the Mongol conquests during the 13th century, with written formulas for it appearing in the Middle East between 1240 and 1280 in a treatise by Hasan al-Rammah, and in Europe by 1267 in the Opus Majus by Roger Bacon. It was employed in warfare to some effect from at least the 10th century in weapons such as fire arrows, bombs, and the fire lance before the appearance of the gun in the 13th century. While the fire lance was eventually supplanted by the gun, other gunpowder weapons such as rockets and fire arrows continued to see use in China, Korea, India, and this eventually led to its use in the Middle East, Europe, and Africa. Bombs too never ceased to develop and continued to progress into the modern day as grenades, mines, and other explosive implements. Gunpowder has also been used for non-military purposes such as fireworks for entertainment, or in explosives for mining and tunneling. The evolution of guns led to the development of large artillery pieces, popularly known as bombards, during the 15th century, pioneered by states such as the Duchy of Burgundy. Firearms came to dominate early modern warfare in Europe by the 17th century. The gradual improvement of cannons firing heavier rounds for a greater impact against fortifications led to the invention of the star fort and the bastion in the Western world, where traditional city walls and castles were no longer suitable for defense. The use
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"title": "History of gunpowder"
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of gunpowder technology also spread throughout the Islamic world and to India, Korea, and Japan. The so-called Gunpowder Empires of the early modern period consisted of the Mughal Empire, Safavid Empire, and Ottoman Empire. The use of gunpowder in warfare during the course of the 19th century diminished due to the invention of smokeless powder. Gunpowder is often referred to today as "black powder" to distinguish it from the propellant used in contemporary firearms. == Chinese beginnings == === Gunpowder formula === Gunpowder was invented in China sometime during the first millennium AD. The earliest possible reference to gunpowder appeared in 142 AD during the Eastern Han dynasty when the alchemist Wei Boyang, also known as the "father of alchemy", wrote about a substance with gunpowder-like properties. He described a mixture of three powders that would "fly and dance" violently in his Cantong qi, otherwise known as the Book of the Kinship of Three, a Taoist text on the subject of alchemy. At this time, saltpeter was produced in Hanzhong, but would shift to Gansu and Sichuan later on. Wei Boyang is considered to be a semi-legendary figure meant to represent a "collective unity", and the Cantong qi was probably written in stages from the Han dynasty to 450 AD. While it was almost certainly not their intention to create a weapon of war, Taoist alchemists continued to play a major role in gunpowder development due to their experiments with sulfur and saltpeter involved in searching for eternal life and ways to transmute one material into another. Historian Peter Lorge notes that despite the early association of gunpowder with Taoism, this may be a quirk of historiography and a result of the better preservation of texts associated with Taoism, rather than being a subject limited to only Taoists. The Taoist
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quest for the elixir of life attracted many powerful patrons, one of whom was Emperor Wu of Han. One of the resulting alchemical experiments involved heating 10% sulfur and 75% saltpeter to transform them. The next reference to gunpowder occurred in the year 300 during the Jin dynasty (266–420). A Taoist philosopher by the name of Ge Hong wrote down the ingredients of gunpowder in his surviving works, collectively known as the Baopuzi ("The Master Who Embraces Simplicity"). The "Inner Chapters" (neipian) on Taoism contains records of his experiments to create gold with heated saltpeter, pine resin, and charcoal among other carbon materials, resulting in a purple powder and arsenic vapours. In 492, Taoist alchemists noted that saltpeter, one of the most important ingredients in gunpowder, burns with a purple flame, allowing for practical efforts at purifying the substance. During the Tang dynasty, alchemists used saltpeter in processing the "four yellow drugs" (sulfur, realgar, orpiment, arsenic trisulfide). The first confirmed references to what can be considered gunpowder in China occurred more than three hundred years later during the Tang dynasty in two Taoist texts. The first in a formula contained in the Taishang Shengzu Jindan Mijue (太上聖祖金丹秘訣) in 808, and then about 50 years later in a text known as the Zhenyuan miaodao yaolüe (真元妙道要略). The first formula was a combination of six parts sulfur to six parts saltpeter to one part birthwort herb. The second text warned against an assortment of dangerous formulas, one of which corresponds with gunpowder: "Some have heated together sulfur, realgar (arsenic disulfide), and saltpeter with honey; smoke [and flames] result, so that their hands and faces have been burnt, and even the whole house burned down." Alchemists called this discovery fire medicine ("huoyao" 火藥), and the term has continued to refer to gunpowder in
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China into the present day, a reminder of its heritage as a side result in the search for longevity increasing drugs. A book published in 1185 called Gui Dong (The Control of Spirits) also contains a story about a Tang dynasty alchemist whose furnace exploded, but it is not known if this was caused by gunpowder. The earliest surviving chemical formula of gunpowder dates to 1044 in the form of the military manual Wujing Zongyao, also known in English as the Complete Essentials for the Military Classics, which contains a collection of entries on Chinese weaponry. However the 1044 edition has since been lost and the only currently extant copy is dated to 1510 during the Ming dynasty. The Wujing Zongyao served as a repository of antiquated or fanciful weaponry, and this applied to gunpowder as well, suggesting that it had already been weaponized long before the invention of what would today be considered conventional firearms. These types of gunpowder weapons had an assortment of odd names such as "flying incendiary club for subjugating demons", "caltrop fire ball", "ten-thousand fire flying sand magic bomb", "big bees nest", "burning heaven fierce fire unstoppable bomb", and "fire bricks" which released "flying swallows", "flying rats", "fire birds", and "fire oxen". Eventually they gave way and coalesced into a smaller number of dominant weapon types, notably gunpowder arrows, bombs, and early guns. This was most likely because some weapons were deemed too onerous or ineffective to deploy. === Fire arrows === The early gunpowder formula contained too little saltpeter (about 50%) to be explosive, but the mixture was highly flammable, and contemporary weapons reflected this in their deployment as mainly shock and incendiary weapons. One of the first, if not the first of these weapons was the fire arrow. The first possible reference to
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the use of fire arrows was by the Southern Wu in 904 during the siege of Yuzhang. An officer under Yang Xingmi by the name of Zheng Fan (鄭璠) ordered his troops to "shoot off a machine to let fire and burn the Longsha Gate", after which he and his troops dashed over the fire into the city and captured it, and he was promoted to Prime Minister Inspectorate for his efforts and the burns his body endured. A later account of this event corroborated with the report and explained that "by let fire (飛火) is meant things like firebombs and fire arrows." Arrows carrying gunpowder were possibly the most applicable form of gunpowder weaponry at the time. Early gunpowder may have only produced an effective flame when exposed to oxygen, thus the rush of air around the arrow in flight would have provided a suitably ample supply of reactants for the reaction. ==== Rockets ==== The first fire arrows were arrows strapped with gunpowder incendiaries but they eventually became gunpowder propelled projectiles (rockets). It's not certain when this happened. According to the History of Song, in 969 two Song generals, Yue Yifang and Feng Jisheng (馮繼升), invented a variant fire arrow which used gunpowder tubes as propellants. These fire arrows were shown to the emperor in 970 when the head of a weapons manufacturing bureau sent Feng Jisheng to demonstrate the gunpowder arrow design, for which he was heavily rewarded. However Joseph Needham argues that rockets could not have existed before the 12th century, since the gunpowder formulas listed in the Wujing Zongyao are not suitable as rocket propellant. According to Stephen G. Haw, there is only slight evidence that rockets existed prior to 1200 and it is more likely they were not produced or used for warfare until
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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the latter half of the 13th century. Rockets are recorded to have been used by the Song navy in a military exercise dated to 1245. Internal-combustion rocket propulsion is mentioned in a reference to 1264, recording that the 'ground-rat,' a type of firework, had frightened the Empress-Mother Gongsheng at a feast held in her honor by her son the Emperor Lizong. In 975, the state of Wuyue sent to the Song dynasty a unit of soldiers skilled in the handling of fire arrows and in the same year, the Song used fire arrows to destroy the fleet of Southern Tang. In 994, the Liao dynasty attacked the Song and laid siege to Zitong with 100,000 troops. They were repelled with the aid of fire arrows. In 1000 a soldier by the name of Tang Fu (唐福) also demonstrated his own designs of gunpowder arrows, gunpowder pots (a proto-bomb which spews fire), and gunpowder caltrops, for which he was richly rewarded as well. The imperial court took great interest in the progress of gunpowder developments and actively encouraged as well as disseminated military technology. For example, in 1002 a local militia man named Shi Pu (石普) showed his own versions of fireballs and gunpowder arrows to imperial officials. They were so astounded that the emperor and court decreed that a team would be assembled to print the plans and instructions for the new designs to promulgate throughout the realm. The Song court's policy of rewarding military innovators was reported to have "brought about a great number of cases of people presenting technology and techniques" (器械法式) according to the official History of Song. Production of gunpowder and fire arrows heavily increased in the 11th century as the court centralized the production process, constructing large gunpowder production facilities, hiring artisans, carpenters, and tanners
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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for the military production complex in the capital of Kaifeng. One surviving source circa 1023 lists all the artisans working in Kaifeng while another notes that in 1083 the imperial court sent 100,000 gunpowder arrows to one garrison and 250,000 to another. Evidence of gunpowder in the Liao dynasty and Western Xia is much sparser than in Song, but some evidence such as the Song decree of 1073 that all subjects were henceforth forbidden from trading sulfur and saltpeter across the Liao border, suggests that the Liao were aware of gunpowder developments to the south and coveted gunpowder ingredients of their own. === Explosives === Gunpowder bombs had been mentioned since the 11th century. In 1000 AD, a soldier by the name of Tang Fu (唐福) demonstrated a design of gunpowder pots (a proto-bomb which spews fire) and gunpowder caltrops, for which he was richly rewarded. In the same year, Xu Dong wrote that trebuchets used bombs that were like "flying fire", suggesting that they were incendiaries. In the military text Wujing Zongyao of 1044, bombs such as the "ten-thousand fire flying sand magic bomb", "burning heaven fierce fire unstoppable bomb", and "thunderclap bomb" (pilipao) were mentioned. However detailed accounts of their use did not appear until the 12th century. The Jurchen people of Manchuria united under Wanyan Aguda and established the Jin dynasty in 1115. Allying with the Song, they rose rapidly to the forefront of East Asian powers and defeated the Liao dynasty in a shockingly short span of time, destroying the 150-year balance of power between the Song, Liao, and Western Xia. Remnants of the Liao fled to the west and became known as the Qara Khitai, or Western Liao to the Chinese. In the east, the fragile Song-Jin alliance dissolved once the Jin saw how badly
|
{
"page_id": 12063194,
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"title": "History of gunpowder"
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the Song army had performed against Liao forces. Realizing the weakness of Song, the Jin grew tired of waiting and captured all five of the Liao capitals themselves. They proceeded to make war on Song, initiating the Jin-Song Wars. For the first time, two major powers would have access to equally formidable gunpowder weapons. Initially the Jin expected their campaign in the south to proceed smoothly given how poorly the Song had fared against the Liao. However they were met with stout resistance upon besieging Kaifeng in 1126 and faced the usual array of gunpowder arrows and fire bombs, but also a weapon called the "thunderclap bomb" (霹靂炮), which one witness wrote, "At night the thunderclap bombs were used, hitting the lines of the enemy well, and throwing them into great confusion. Many fled, screaming in fright." The thunderclap bomb was previously mentioned in the Wujing Zongyao, but this was the first recorded instance of its use. Its description in the text reads thus: The thunderclap bomb contains a length of two or three internodes of dry bamboo with a diameter of 1.5 in. There must be no cracks, and the septa are to be retained to avoid any leakage. Thirty pieces of thin broken porcelain the size of iron coins are mixed with 3 or 4 lb of gunpowder, and packed around the bamboo tube. The tube is wrapped within the ball, but with about an inch or so protruding at each end. A (gun)powder mixture is then applied all over the outer surface of the ball. Jin troops withdrew with a ransom of Song silk and treasure but returned several months later with their own gunpowder bombs manufactured by captured Song artisans. According to historian Wang Zhaochun, the account of this battle provided the "earliest truly detailed descriptions
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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of the use of gunpowder weapons in warfare." Records show that the Jin used gunpowder arrows and trebuchets to hurl gunpowder bombs while the Song responded with gunpowder arrows, fire bombs, thunderclap bombs, and a new addition called the "molten metal bomb" (金汁炮). As the Jin account describes, when they attacked the city's Xuanhua Gate, their "fire bombs fell like rain, and their arrows were so numerous as to be uncountable." The Jin captured Kaifeng despite the appearance of the molten metal bomb and secured another 20,000 fire arrows for their arsenal. The molten metal bomb appeared again in 1129 when Song general Li Yanxian (李彥仙) clashed with Jin forces while defending a strategic pass. The Jin assault lasted day and night without respite, using siege carts, fire carts, and sky bridges, but each assault was met with Song soldiers who "resisted at each occasion, and also used molten metal bombs. Wherever the gunpowder touched, everything would disintegrate without a trace." The molten metal bomb was likely an explosive that contained molten metal and gunpowder. === Fire lance === The Song relocated their capital to Hangzhou and the Jin followed. The fighting that ensued would see the first proto-gun, the fire lance, in action – with earliest confirmed employment by Song dynasty forces against the Jin in 1132 during the siege of De'an (modern Anlu, Hubei), Most Chinese scholars reject the appearance of the fire lance prior to the Jin-Song wars, but its first appearance in art with a silk banner painting from Dunhuang dates to the Five Dynasties and Ten Kingdoms period in the mid-10th century. The siege of De'an marks an important transition and landmark in the history of gunpowder weapons as the fire medicine of the fire lances were described using a new word: "fire bomb medicine"
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{
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(火炮藥), rather than simply "fire medicine." This could imply the use of a new more potent formula, or simply an acknowledgement of the specialized military application of gunpowder. Peter Lorge suggests that this "bomb powder" may have been corned, making it distinct from normal gunpowder. Evidence of gunpowder firecrackers also points to their appearance at roughly around the same time fire medicine was making its transition in the literary imagination. Fire lances continued to be used as anti-personnel weapons into the Ming dynasty, and were even attached to battle carts on one situation in 1163. Song commander Wei Sheng constructed several hundred of these carts known as "at-your-desire-war-carts" (如意戰車), which contained fire lances protruding from protective covering on the sides. They were used to defend mobile trebuchets that hurled fire bombs. They were used as cavalry weapons by the 13th century. === Naval bombs === Gunpowder technology also spread to naval warfare and in 1129 Song decreed that all warships were to be fitted with trebuchets for hurling gunpowder bombs. Older gunpowder weapons such as fire arrows were also used. In 1159 a Song fleet of 120 ships caught a Jin fleet at anchor near Shijiu Island (石臼島) off the shore of Shandong peninsula. The Song commander "ordered that gunpowder arrows be shot from all sides, and wherever they struck, flames and smoke rose up in swirls, setting fire to several hundred vessels." Song forces took another victory in 1161 when Song paddle boats ambushed a Jin transport fleet, launched thunderclap bombs, and drowned the Jin force in the Yangtze. The men inside them paddled fast on the treadmills, and the ships glided forwards as though they were flying, yet no one was visible on board. The enemy thought that they were made of paper. Then all of a sudden
|
{
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a thunderclap bomb was let off: It was made with paper (carton) and filled with lime and sulphur. (Launched from trebuchets) these thunderclap bombs came dropping down from the air, and upon meeting the water exploded with a noise like thunder, the sulphur bursting into flames. The carton case rebounded and broke, scattering the lime to form a smoky fog which blinded the eyes of men and horses so that they could see nothing. Our ships then went forward to attack theirs, and their men and horses were all drowned, so that they were utterly defeated. According to a minor military official by the name of Zhao Wannian (趙萬年), thunderclap bombs were used again to great effect by the Song during the Jin siege of Xiangyang in 1206–1207. Both sides had gunpowder weapons, but the Jin troops only used gunpowder arrows for destroying the city's moored vessels. The Song used fire arrows, fire bombs, and thunderclap bombs. Fire arrows and bombs were used to destroy Jin trebuchets. The thunderclap bombs were used on Jin soldiers themselves, causing foot soldiers and horsemen to panic and retreat. "We beat our drums and yelled from atop the city wall, and simultaneously fired our thunderclap missiles out from the city walls. The enemy cavalry was terrified and ran away." The Jin were forced to retreat and make camp by the riverside. In a rare occurrence, the Song made a successful offensive on Jin forces and conducted a night assault using boats. They were loaded with gunpowder arrows, thunderclap bombs, a thousand crossbowmen, five hundred infantry, and a hundred drummers. Jin troops were surprised in their encampment while asleep by loud drumming, followed by an onslaught of crossbow bolts, and then thunderclap bombs, which caused a panic of such magnitude that they were unable to
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even saddle themselves and trampled over each other trying to get away. Two to three thousand Jin troops were slaughtered along with eight to nine hundred horses. === Hard-shell explosives === Traditionally the inspiration for the development of the iron bomb is ascribed to the tale of a fox hunter named Iron Li. According to the story, around the year 1189 Iron Li developed a new method for hunting foxes which used a ceramic explosive to scare foxes into his nets. The explosive consisted of a ceramic bottle with a mouth, stuffed with gunpowder, and attached with a fuse. Explosive and net were placed at strategic points of places such as watering holes frequented by foxes, and when they got near enough, Iron Li would light the fuse, causing the ceramic bottle to explode and scaring the frightened foxes right into his nets. Although the veracity of this story is uncertain, the tradition holds that this ceramic bomb inspired the Jin to create an iron version. The iron bomb made its first appearance in 1221 at the siege of Qizhou (in modern Hubei), and this time it would be the Jin who possessed the technological advantage. The Song commander Zhao Yurong (趙與褣) survived and was able to relay his account for posterity. Qizhou was a major fortress city situated near the Yangtze and a 25 thousand strong Jin army advanced on it in 1221. News of the approaching army reached Zhao Yurong in Qizhou, and despite being outnumbered nearly eight to one, he decided to hold the city. Qizhou's arsenal consisted of some three thousand thunderclap bombs, twenty thousand "great leather bombs" (皮大炮), and thousands of gunpowder arrows and gunpowder crossbow bolts. While the formula for gunpowder had become potent enough to consider the Song bombs to be true explosives,
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they were unable to match the explosive power of the Jin iron bombs. Yurong describes the uneven exchange thus, "The barbaric enemy attacked the Northwest Tower with an unceasing flow of catapult projectiles from thirteen catapults. Each catapult shot was followed by an iron fire bomb [catapult shot], whose sound was like thunder. That day, the city soldiers in facing the catapult shots showed great courage as they maneuvered [our own] catapults, hindered by injuries from the iron fire bombs. Their heads, their eyes, their cheeks were exploded to bits, and only one half [of the face] was left." Jin artillerists were able to successfully target the command center itself: "The enemy fired off catapult stones ... nonstop day and night, and the magistrate's headquarters [帳] at the eastern gate, as well as my own quarters ..., were hit by the most iron fire bombs, to the point that they struck even on top of [my] sleeping quarters and [I] nearly perished! Some said there was a traitor. If not, how would they have known the way to strike at both of these places?" Zhao was able to examine the new iron bombs himself and described thus, "In shape they are like gourds, but with a small mouth. They are made with pig iron, about two inches thick, and they cause the city's walls to shake." Houses were blown apart, towers battered, and defenders blasted from their placements. Within four weeks all four gates were under heavy bombardment. Finally the Jin made a frontal assault on the walls and scaled them, after which followed a merciless hunt for soldiers, officers, and officials of every level. Zhao managed an escape by clambering over the battlement and making a hasty retreat across the river, but his family remained in the city. Upon
|
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"title": "History of gunpowder"
}
|
returning at a later date to search the ruins, he found that the "bones and skeletons were so mixed up that there was no way to tell who was who." === Hand cannon === The early fire lance, considered to be the ancestor of firearms, is not considered a true gun because it did not include projectiles, whereas a gun by definition uses "the explosive force of the gunpowder to propel a projectile from a tube: cannons, muskets, and pistols are typical examples.". Even later on when shrapnel such as ceramics and bits of iron were added to the fire lance, these didn't occlude the barrel, and were only swept along with the discharge rather than making use of windage, and so are referred to as "co-viatives." In 1259 a type of "fire-emitting lance" (tuhuoqiang 突火槍) made an appearance and according to the History of Song: "It is made from a large bamboo tube, and inside is stuffed a pellet wad (子窠). Once the fire goes off it completely spews the rear pellet wad forth, and the sound is like a bomb that can be heard for five hundred or more paces." The pellet wad mentioned is possibly the first true bullet in recorded history depending on how bullet is defined, as it did occlude the barrel, unlike previous co-viatives used in the fire lance. Fire lances transformed from the "bamboo- (or wood- or paper-) barreled firearm to the metal-barreled firearm" to better withstand the explosive pressure of gunpowder. From there it branched off into several different gunpowder weapons known as "eruptors" in the late 12th and early 13th centuries, with different functions such as the "filling-the-sky erupting tube" which spewed out poisonous gas and porcelain shards, the "orifice-penetrating flying sand magic mist tube" (鑽穴飛砂神霧筒) which spewed forth sand and
|
{
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poisonous chemicals into orifices, and the more conventional "phalanx-charging fire gourd" which shot out lead pellets. The earliest artistic depiction of what might be a hand cannon – a rock sculpture found among the Dazu Rock Carvings – is dated to 1128, much earlier than any recorded or precisely dated archaeological samples, so it is possible that the concept of a cannon-like firearm has existed since the 12th century. This has been challenged by others such as Liu Xu, Cheng Dong, and Benjamin Avichai Katz Sinvany. According to Liu, the weight of the cannon would have been too much for one person to hold, especially with just one arm, and points out that fire lances were being used a decade later at De'an. Cheng Dong believes that the figure depicted is actually a wind spirit letting air out of a bag rather than a cannon emitting a blast. Stephen Haw also considered the possibility that the item in question was a bag of air but concludes that it is a cannon because it was grouped with other weapon wielding sculptures. Sinvany believes in the wind bag interpretation and that the cannonball indentation was added later on. Archaeological samples of the gun, specifically the hand cannon (huochong), have been dated starting from the 13th century. The oldest extant gun whose dating is unequivocal is the Xanadu Gun because it contains an inscription describing its date of manufacture corresponding to 1298. It is so called because it was discovered in the ruins of Xanadu, the Mongol summer palace in Inner Mongolia. The Xanadu Gun is 34.7 cm in length and weighs 6.2 kg. The design of the gun includes axial holes in its rear which some speculate could have been used in a mounting mechanism. Like most early guns it is small,
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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weighing just over six kilograms and thirty-five centimeters in length. Although the Xanadu Gun is the most precisely dated gun from the 13th century, other extant samples with approximate dating likely predate it. The Heilongjiang hand cannon is dated a decade earlier to 1288, but the dating method is based on contextual evidence; the gun bears no inscription or era date. According to the History of Yuan, in 1287, a group of soldiers equipped with hand cannons led by the Jurchen commander Li Ting (李庭) attacked the rebel prince Nayan's camp. The History reports that the hand cannons not only "caused great damage," but also caused "such confusion that the enemy soldiers attacked and killed each other." The hand cannons were used again in the beginning of 1288. Li Ting's "gun-soldiers" or chongzu (銃卒) were able to carry the hand cannons "on their backs". The passage on the 1288 battle is also the first to coin the name chong (銃) for metal-barrel firearms. Chong was used instead of the earlier and more ambiguous term huo tong (fire tube; 火筒), which may refer to the tubes of fire lances, proto-cannons, or signal flares. Another specimen, the Wuwei Bronze Cannon, was discovered in 1980 and may possibly be the oldest as well as largest cannon of the 13th century: a 100 centimeter 108 kilogram bronze cannon discovered in a cellar in Wuwei, Gansu containing no inscription, but has been dated by historians to the late Western Xia period between 1214 and 1227. The gun contained an iron ball about nine centimeters in diameter, which is smaller than the muzzle diameter at twelve centimeters, and 0.1 kilograms of gunpowder in it when discovered, meaning that the projectile might have been another co-viative. Ben Sinvany and Dang Shoushan believe that the ball used to
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{
"page_id": 12063194,
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be much larger prior to its highly corroded state at the time of discovery. While large in size, the weapon is noticeably more primitive than later Yuan dynasty guns, and is unevenly cast. A similar weapon was discovered not far from the discovery site in 1997, but much smaller in size at only 1.5 kg. Chen Bingying disputes this however, and argues there were no guns before 1259, while Dang Shoushan believes the Western Xia guns point to the appearance of guns by 1220, and Stephen Haw goes even further by stating that guns were developed as early as 1200. Sinologist Joseph Needham and renaissance siege expert Thomas Arnold provide a more conservative estimate of around 1280 for the appearance of the "true" cannon. Whether or not any of these are correct, it seems likely that the gun was born sometime during the 13th century. == Use by the Mongols == The Mongols and their rise in world history as well as conflicts with both the Jin and Song played a key role in the evolution of gunpowder technology. Mongol aptitude in incorporating foreign experts extended to the Chinese, who provided artisans that followed Mongol armies willingly and unwillingly far into the west and even east, to Japan. Unfortunately textual evidence for this is scant as the Mongols left few documents. This lack of primary source documents has caused some historians and scholars such as Kate Raphael to doubt the Mongol's role in disseminating gunpowder throughout Eurasia. On the opposite side stand historians such as Tonio Andrade and Stephen Haw, who believe that the Mongol Empire not only used gunpowder weapons but deserves the moniker "the first gunpowder empire." === Conquest of the Jin dynasty === The first concerted Mongol invasion of Jin occurred in 1211 and total conquest was
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{
"page_id": 12063194,
"source": null,
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not accomplished until 1234. In 1232 the Mongols besieged the Jin capital of Kaifeng and deployed gunpowder weapons along with other more conventional siege techniques such as building stockades, watchtowers, trenches, guardhouses, and forcing Chinese captives to haul supplies and fill moats. Jin scholar Liu Qi (劉祈) recounts in his memoir, "the attack against the city walls grew increasingly intense, and bombs rained down as [the enemy] advanced." The Jin defenders also deployed gunpowder bombs as well as fire arrows (huo jian 火箭) launched using a type of early solid-propellant rocket. Of the bombs, Liu Qi writes, "From within the walls the defenders responded with a gunpowder bomb called the heaven-shaking-thunder bomb (震天雷). Whenever the [Mongol] troops encountered one, several men at a time would be turned into ashes." A more fact based and clear description of the bomb exists in the History of Jin: "The heaven-shaking-thunder bomb is an iron vessel filled with gunpowder. When lighted with fire and shot off, it goes off like a crash of thunder that can be heard for a hundred li [thirty miles], burning an expanse of land more than half a mu [所爇圍半畝之上, a mu is a sixth of an acre], and the fire can even penetrate iron armor." A Ming official named He Mengchuan would encounter an old cache of these bombs three centuries later in the Xi'an area: "When I went on official business to Shaanxi Province, I saw on top of Xi'an's city walls an old stockpile of iron bombs. They were called 'heaven-shaking-thunder' bombs, and they were like an enclosed rice bowl with a hole at the top, just big enough to put your finger in. The troops said they hadn't been used for a very long time." Furthermore, he wrote, "When the powder goes off, the bomb
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{
"page_id": 12063194,
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rips open, and the iron pieces fly in all directions. That is how it is able to kill people and horses from far away." Heaven-shaking-thunder bombs, also known as thunder crash bombs, were used prior to the siege in 1231 when a Jin general made use of them in destroying a Mongol warship. The Jin general named Wanyan Eke had lost the defense of Hezhong to the Mongols and fled on ships with 3,000 of his men. The Mongols pursued them with their ships until the Jin broke through by using thunder crash bombs that caused flashes and flames. However during the siege the Mongols responded by protecting themselves with elaborate screens of thick cowhide. This was effective enough for workers to get right up to the walls to undermine their foundations and excavate protective niches. Jin defenders countered by tying iron cords and attaching them to heaven-shaking-thunder bombs, which were lowered down the walls until they reached the place where the miners worked. The protective leather screens were unable to withstand the explosion, and were penetrated, killing the excavators. Another weapon the Jin employed was an improved version of the fire lance called the flying fire lance. The History of Jin provides a detailed description: "To make the lance, use chi-huang paper, sixteen layers of it for the tube, and make it a bit longer than two feet. Stuff it with willow charcoal, iron fragments, magnet ends, sulfur, white arsenic [probably an error that should mean saltpeter], and other ingredients, and put a fuse to the end. Each troop has hanging on him a little iron pot to keep fire [probably hot coals], and when it's time to do battle, the flames shoot out the front of the lance more than ten feet, and when the gunpowder is depleted,
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{
"page_id": 12063194,
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the tube isn't destroyed." While Mongol soldiers typically held a view of disdain toward most Jin weapons, apparently they greatly feared the flying fire lance and heaven-shaking-thunder bomb. Kaifeng managed to hold out for a year before the Jin emperor fled and the city capitulated. In some cases Jin troops still fought with some success, scoring isolated victories such as when a Jin commander led 450 fire lancers against a Mongol encampment, which was "completely routed, and three thousand five hundred were drowned." Even after the Jin emperor committed suicide in 1234, one loyalist gathered all the metal he could find in the city he was defending, even gold and silver, and made explosives to lob against the Mongols, but the momentum of the Mongol Empire could not be stopped. By 1234, both the Western Xia and Jin dynasty had been conquered. === Conquest of the Song dynasty === The Mongol war machine moved south and in 1237 attacked the Song city of Anfeng (modern Shouxian, Anhui) "using gunpowder bombs [huo pao] to burn the [defensive] towers." These bombs were apparently quite large. "Several hundred men hurled one bomb, and if it hit the tower it would immediately smash it to pieces." The Song defenders under commander Du Gao (杜杲) rebuilt the towers and retaliated with their own bombs, which they called the "Elipao," after a famous local pear, probably in reference to the shape of the weapon. Perhaps as another point of military interest, the account of this battle also mentions that the Anfeng defenders were equipped with a type of small arrow to shoot through eye slits of Mongol armor, as normal arrows were too thick to penetrate. By the mid 13th century, gunpowder weapons had become central to the Song war effort. In 1257 the Song official
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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Li Zengbo was dispatched to inspect frontier city arsenals. Li considered an ideal city arsenal to include several hundred thousand iron bombshells, and also its own production facility to produce at least a couple thousand a month. The results of his tour of the border were severely disappointing and in one arsenal he found "no more than 85 iron bomb-shells, large and small, 95 fire-arrows, and 105 fire-lances. This is not sufficient for a mere hundred men, let alone a thousand, to use against an attack by the ... barbarians. The government supposedly wants to make preparations for the defense of its fortified cities, and to furnish them with military supplies against the enemy (yet this is all they give us). What chilling indifference!" Fortunately for the Song, Möngke Khan died in 1259 and the war would not continue until 1269 under the leadership of Kublai Khan, but when it did the Mongols came in full force. Blocking the Mongols' passage south of the Yangtze were the twin fortress cities of Xiangyang and Fancheng. What resulted was one of the longest sieges the world had ever known, lasting from 1268 to 1273. In 1273 the Mongols enlisted the expertise of two Muslim engineers, one from Persia and one from Syria, who helped in the construction of counterweight trebuchets. These new siege weapons had the capability of throwing larger missiles further than the previous traction trebuchets. One account records, "when the machinery went off the noise shook heaven and earth; every thing that [the missile] hit was broken and destroyed." The fortress city of Xiangyang fell in 1273. The next major battle to feature gunpowder weapons was during a campaign led by the Mongol general Bayan, who commanded an army of around two hundred thousand, consisting of mostly Chinese soldiers. It
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{
"page_id": 12063194,
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was probably the largest army the Mongols had ever used. Such an army was still unable to successfully storm Song city walls, as seen in the 1274 Siege of Shayang. Thus Bayan waited for the wind to change to a northerly course before ordering his artillerists to begin bombarding the city with molten metal bombs, which caused such a fire that "the buildings were burned up and the smoke and flames rose up to heaven." Shayang was captured and its inhabitants massacred. Gunpowder bombs were used again in the 1275 Siege of Changzhou in the latter stages of the Mongol-Song Wars. Upon arriving at the city, Bayan gave the inhabitants an ultimatum: "if you ... resist us ... we shall drain your carcasses of blood and use them for pillows." This didn't work and the city resisted anyway, so the Mongol army bombarded them with fire bombs before storming the walls, after which followed an immense slaughter claiming the lives of a quarter million. The war lasted for only another four years during which some remnants of the Song held up last desperate defenses. In 1277, 250 defenders under Lou Qianxia conducted a suicide bombing and set off a huge iron bomb when it became clear defeat was imminent. Of this, the History of Song writes, "the noise was like a tremendous thunderclap, shaking the walls and ground, and the smoke filled up the heavens outside. Many of the troops [outside] were startled to death. When the fire was extinguished they went in to see. There were just ashes, not a trace left." So came an end to the Mongol-Song Wars, which saw the deployment of all the gunpowder weapons available to both sides at the time, which for the most part meant gunpowder arrows, bombs, and lances, but in
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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retrospect, another development would overshadow them all, the birth of the gun. In 1280, a large store of gunpowder at Weiyang in Yangzhou accidentally caught fire, producing such a massive explosion that a team of inspectors at the site a week later deduced that some 100 guards had been killed instantly, with wooden beams and pillars blown sky high and landing at a distance of over 10 li (~2 mi. or ~3 km) away from the explosion, creating a crater more than ten feet deep. By the time of Jiao Yu and his Huolongjing (a book that describes military applications of gunpowder in great detail) in the mid 14th century, the explosive potential of gunpowder was perfected, as the level of nitrate in gunpowder formulas had risen from a range of 12% to 91%, with at least 6 different formulas in use that are considered to have maximum explosive potential for gunpowder. By that time, the Chinese had discovered how to create explosive round shot by packing their hollow shells with this nitrate-enhanced gunpowder. === Invasions of Europe and Japan === Gunpowder may have been used during the Mongol invasions of Europe. "Fire catapults", "pao", and "naphtha-shooters" are mentioned in some sources. However, according to Timothy May, "there is no concrete evidence that the Mongols used gunpowder weapons on a regular basis outside of China." Shortly after the Mongol invasions of Japan (1274–1281), the Japanese produced a scroll painting depicting a bomb. Called tetsuhau in Japanese, the bomb is speculated to have been the Chinese thunder crash bomb. Archaeological findings by the Kyushu Okinawa Society for Underwater Archaeology confirmed the existence of bombs in the Yuan invasion's arsenal. Multiple bomb shells were discovered in an underwater shipwreck off the shore of Japan and X-rays of the excavated shells show that
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{
"page_id": 12063194,
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they contained gunpowder and were also packed with scrap iron. Japanese descriptions of the invasions also talk of iron and bamboo pao causing "light and fire" and emitting 2–3,000 iron bullets. The Nihon Kokujokushi, written around 1300, mentions huo tong (fire tubes) at the Battle of Tsushima in 1274 and the second coastal assault led by Holdon in 1281. The Hachiman Gudoukun of 1360 mentions iron pao "which caused a flash of light and a loud noise when fired." The Taiheki of 1370 mentions "iron pao shaped like a bell." The commanding general kept his position on high ground, and directed the various detachments as need be with signals from hand-drums. But whenever the (Mongol) soldiers took to flight, they sent iron bomb-shells (tetsuho) flying against us, which made our side dizzy and confused. Our soldiers were frightened out of their wits by the thundering explosions; their eyes were blinded, their ears deafened, so that they could hardly distinguish east from west. According to our manner of fighting, we must first call out by name someone from the enemy ranks, and then attack in single combat. But they (the Mongols) took no notice at all of such conventions; they rushed forward all together in a mass, grappling with any individuals they could catch and killing them. == Historiography of gunpowder and gun transmission == According to historian Tonio Andrade, "Scholars today overwhelmingly concur that the gun was invented in China," however multiple independent gunpowder and gun invention theories continue to exist today, advocating for European, Islamic, or Indian origins. Opponents of Chinese invention and transmission criticize the vagueness of Chinese records on specific gunpowder usage in weaponry, the possible lack of gunpowder in incendiary weapons as described by Chinese documents, the weakness of Chinese firearms, the lack of evidence of
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{
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guns between Europe and China before 1326, and emphasize the appearance of earlier or superior gunpowder weapons. For example, Stephen Morillo, Jeremy Black, and Paul Lococo's War in World History argues that "the sources are not entirely clear about Chinese use of gunpowder in guns. There are references to bamboo and iron cannons, or perhaps proto-cannons, but these seem to have been small, unreliable, handheld weapons in this period. The Chinese do seem to have invented guns independently of the Europeans, at least in principle; but, in terms of effective cannon, the edge goes to Europe." Independent invention theories include examples such as the attribution of gunpowder to Berthold Schwarz (Black Berthold), the usage of cannons by Mamluks at the Battle of Ain Jalut in 1260, and descriptions of gunpowder and firearms to various Sanskrit texts. The problem with all theories of non-Chinese invention boils down to lack of evidence and dating. It's not certain who exactly Berthold Schwarz was since there are no contemporary records of him. According to J.R. Partington, Black Berthold is a purely legendary figure invented for the purpose of providing a German origin for gunpowder and cannon. The source for Mamluk usage of cannons in the Battle of Ain Jalut is a text dated to the late 14th century. The dating of the cited Sanskrit texts is often dubious at best, with one example, Sukraniti, containing descriptions of a musket and a cart-drawn gun. Proponents of Chinese invention and transmission point out the lack of any significant evidence of evolution or experimentation with gunpowder or gunpowder weapons leading up to the gun outside of China. Gunpowder appeared in Europe primed for military usage as an explosive and propellant, bypassing a process which took centuries of Chinese experimentation with gunpowder weaponry to reach, making a nearly
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{
"page_id": 12063194,
"source": null,
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instantaneous and seamless transition into firearm warfare, as its name suggests. Furthermore, early European gunpowder recipes shared identical defects with Chinese recipes such as the inclusion of the poisons sal ammoniac and arsenic, which provide no benefit to gunpowder. Bert S. Hall explains this phenomenon in his Weapons and Warfare in Renaissance Europe: Gunpowder, Technology, and Tactics by drawing upon the gunpowder transmission theory, explaining that "gunpowder came [to Europe], not as an ancient mystery, but as a well-developed modern technology, in a manner very much like twentieth-century 'technology-transfer' projects." In a similar vein, Peter Lorge supposes that the Europeans experienced gunpowder "free from preconceived notions of what could be done," in contrast to China, "where a wide range of formulas and a broad variety of weapons demonstrated the full range of possibilities and limitations of the technologies involved." There is also the vestige of Chinese influence on Muslim terminology of key gunpowder related items such as saltpeter, which has been described as either Chinese snow or salt, fireworks which were called Chinese flowers, and rockets which were called Chinese arrows. Moreover, Europeans in particular experienced great difficulty in obtaining saltpeter, a primary ingredient of gunpowder which was relatively scarce in Europe compared to China, and had to be obtained from "distant lands or extracted at high cost from soil rich in dung and urine." Thomas Arnold believes that the similarities between early European cannons and contemporary Chinese models suggests a direct transmission of cannon making knowledge from China rather than a home grown development. == Spread throughout Eurasia and Africa == === Middle East === The Muslim world acquired the gunpowder formula some time after 1240, but before 1280, by which time Hasan al-Rammah had written, in Arabic, recipes for gunpowder, instructions for the purification of saltpeter, and descriptions
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{
"page_id": 12063194,
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of gunpowder incendiaries. Early Muslim sources suggest that knowledge of gunpowder was acquired from China and may have been introduced by invading Mongols. This is implied by al-Rammah's usage of "terms that suggested he derived his knowledge from Chinese sources." Early Arab texts on gunpowder refer to saltpeter as "Chinese snow" (Arabic: ثلج الصين thalj al-ṣīn), fireworks as "Chinese flowers" and rockets as "Chinese arrows" (sahm al-Khitai). Similarly, the Persians called saltpeter "Chinese salt" or "salt from Chinese salt marshes" (namak shūra chīnī Persian: نمک شوره چيني). Fireworks listed by al-Rammah include "wheels of China" and "flowers of China". The gunpowder formula of al-Rammah has a saltpeter content of 68% to 75%, which is more explosive than is necessary for rockets, however no explosives are mentioned. Al-Rammah's text, The Book of Military Horsemanship and Ingenious War Devices (Kitab al-Furusiya wa'l-Munasab al-Harbiya), does however mention fuses, incendiary bombs, naphtha pots, fire lances, and an illustration and description of the earliest torpedo. The torpedo was called the "egg which moves itself and burns." Two iron sheets were fastened together and tightened using felt. The flattened pear shaped vessel was filled with gunpowder, metal filings, "good mixtures," two rods, and a large rocket for propulsion. Judging by the illustration, it was evidently supposed to glide across the water. Hasan al-Rammah was the first Muslim to describe the purification of saltpeter using the chemical processes of solution and crystallization. This was the first clear method for the purification of saltpeter. According to Joseph Needham, fire lances were used in battles between the Muslims and Mongols in 1299 and 1303. The earliest surviving documentary evidence for cannons in the Islamic world is from an Arabic manuscript dated to the early 14th century. The author's name is uncertain but may have been Shams al-Din Muhammad, who
|
{
"page_id": 12063194,
"source": null,
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died in 1350. Dating from around 1320–1350, the illustrations show gunpowder weapons such as gunpowder arrows, bombs, fire tubes, and fire lances or proto-guns. The manuscript describes a type of gunpowder weapon called a midfa which uses gunpowder to shoot projectiles out of a tube at the end of a stock. Some consider this to be a cannon while others do not. The problem with identifying cannons in early 14th century Arabic texts is the term midfa, which appears from 1342 to 1352 but cannot be proven to be true hand-guns or bombards. Contemporary accounts of a metal-barrel cannon in the Islamic world do not occur until 1365. Needham believes that in its original form the term midfa refers to the tube or cylinder of a naphtha projector (flamethrower), then after the invention of gunpowder it meant the tube of fire lances, and eventually it applied to the cylinder of hand-gun and cannon. Description of the drug (mixture) to be introduced in the madfa'a (cannon) with its proportions: barud, ten; charcoal two drachmes, sulphur one and a half drachmes. Reduce the whole into a thin powder and fill with it one third of the madfa'a. Do not put more because it might explode. This is why you should go to the turner and ask him to make a wooden madfa'a whose size must be in proportion with its muzzle. Introduce the mixture (drug) strongly; add the bunduk (balls) or the arrow and put fire to the priming. The madfa'a length must be in proportion with the hole. If the madfa'a was deeper than the muzzle's width, this would be a defect. Take care of the gunners. Be careful According to Paul E. J. Hammer, the Mamluks certainly used cannons by 1342. According to J. Lavin, cannons were used by Moors
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{
"page_id": 12063194,
"source": null,
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at the siege of Algeciras in 1343. A metal cannon firing an iron ball was described by Shihab al-Din Abu al-Abbas al-Qalqashandi between 1365 and 1376. === Europe === A common theory of how gunpowder came to Europe is that it made its way along the Silk Road through the Middle East. Another is that it was brought to Europe during the Mongol invasion in the first half of the 13th century. Some sources claim that Chinese firearms and gunpowder weapons may have been deployed by Mongols against European forces at the Battle of Mohi in 1241. It may also have been due to subsequent diplomatic and military contacts. Some authors have speculated that William of Rubruck, who served as an ambassador to the Mongols from 1253 to 1255, was a possible intermediary in the transmission of gunpowder. His travels were recorded by Roger Bacon, who was the first European to mention gunpowder, but the records of William's journey do not contain any mention of gunpowder. The earliest European references to gunpowder are found in Roger Bacon's Opus Majus from 1267, in which he mentions a firecracker toy found in various parts of the world. The passage reads: "We have an example of these things (that act on the senses) in [the sound and fire of] that children's toy which is made in many [diverse] parts of the world; i.e., a device no bigger than one's thumb. From the violence of that salt called saltpeter [together with sulfur and willow charcoal, combined into a powder] so horrible a sound is made by the bursting of a thing so small, no more than a bit of parchment [containing it], that we find [the ear assaulted by a noise] exceeding the roar of strong thunder, and a flash brighter than the most
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{
"page_id": 12063194,
"source": null,
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brilliant lightning." In the early 20th century, British artillery officer Henry William Lovett Hime proposed that another work tentatively attributed to Bacon, Epistola de Secretis Operibus Artis et Naturae, et de Nullitate Magiae contained an encrypted formula for gunpowder. This claim has been disputed by historians of science including Lynn Thorndike, John Maxson Stillman and George Sarton and by Bacon's editor Robert Steele, both in terms of authenticity of the work, and with respect to the decryption method. In any case, the formula claimed to have been decrypted (7:5:5 saltpeter:charcoal:sulfur) is not useful for firearms use or even firecrackers, burning slowly and producing mostly smoke. However, if Bacon's recipe is taken as measurements by volume rather than weight, a far more potent and serviceable explosive powder is created suitable for firing hand-cannons, albeit less consistent due to the inherent inaccuracies of measurements by volume. One example of this composition resulted in 100 parts saltpeter, 27 parts charcoal, and 45 parts sulfur, by weight. The oldest written recipes for gunpowder in Europe were recorded under the name Marcus Graecus or Mark the Greek between 1280 and 1300 in the Liber Ignium, or Book of Fires. One recipe for "flying fire" (ignis volatilis) involves saltpeter, sulfur, and colophonium, which, when inserted into a reed or hollow wood, "flies away suddenly and burns up everything." Another recipe, for artificial "thunder", specifies a mixture of one pound native sulfur, two pounds linden or willow charcoal, and six pounds of saltpeter. Another specifies a 1:3:9 ratio. The text is likely a translation from Arabic through a Spanish intermediary due to the terminology used and recipes for items found in 12th century Arabic texts. The earliest known European depiction of a gun appeared in 1326 in a manuscript by Walter de Milemete, although not necessarily drawn
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
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by him, known as De Nobilitatibus, sapientii et prudentiis regum (Concerning the Majesty, Wisdom, and Prudence of Kings), which displays a gun with a large arrow emerging from it and its user lowering a long stick to ignite the gun through the touchole In the same year, another similar illustration showed a darker gun being set off by a group of knights, which also featured in another work of de Milemete's, De secretis secretorum Aristotelis. On 11 February of that same year, the Signoria of Florence appointed two officers to obtain canones de mettallo and ammunition for the town's defense. In the following year a document from the Turin area recorded a certain amount was paid "for the making of a certain instrument or device made by Friar Marcello for the projection of pellets of lead." The bronze vase-shaped gun from Mantua, unfortunately disappeared in 1849, but of which we have drawings and measurements taken in 1786, dates back to 1322. It was 16.4 cm long, weighed about 5 kg and had a caliber of 5.5 cm. The 1320s seem to have been the takeoff point for guns in Europe according to most modern military historians. Scholars suggest that the lack of gunpowder weapons in a well-traveled Venetian's catalogue for a new crusade in 1321 implies that guns were unknown in Europe up until this point. From the 1320s guns spread rapidly across Europe. The French raiding party that sacked and burned Southampton in 1338 brought with them a ribaudequin and 48 bolts (but only 3 pounds of gunpowder). By 1341 the town of Lille had a "tonnoire master," and a tonnoire was an arrow-hurling gun. In 1345, two iron cannons were present in Toulouse. In 1346 Aix-la-Chapelle too possessed iron cannons which shot arrows (busa ferrea ad sagittandum tonitrum).
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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The Battle of Crécy in 1346 was one of the first in Europe where cannons were used. By 1350 Petrarch wrote that the presence of cannons on the battlefield was 'as common and familiar as other kinds of arms'. Around the late 14th century European and Ottoman guns began to deviate in purpose and design from guns in China, changing from small anti-personnel and incendiary devices to the larger artillery pieces most people imagine today when using the word "cannon." If the 1320s can be considered the arrival of the gun on the European scene, then the end of the 14th century may very well be the departure point from the trajectory of gun development in China. In the last quarter of the 14th century, European guns grew larger and began to blast down fortifications. === Southeast Asia === In Southeast Asia, cannons were used by the Ayutthaya Kingdom in 1352 during its invasion of the Khmer Empire. Within a decade large quantities of gunpowder could be found in the Khmer Empire. By the end of the century firearms were also used by the Trần dynasty in Đại Việt. The Mongol invasion of Java in 1293 brought gunpowder technology to the Nusantara archipelago in the form of cannon (Chinese: 炮—Pào). The knowledge of making gunpowder-based weapon has been known after the failed Mongol invasion of Java.: 1–2 : 220 The predecessor of firearms, the pole gun (bedil tombak), was recorded as being used in Java by 1413,: 245 while the knowledge of making "true" firearms came much later, after the middle of 15th century. It was brought by the Muslim traders from West Asia, most probably the Arabs. The precise year of introduction is unknown, but it may be safely concluded to be no earlier than 1460.: 23 Portuguese influence
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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to local weaponry after the capture of Malacca (1511) resulted in a new type of hybrid tradition matchlock firearm, the istinggar.: 53 Saltpeter harvesting was recorded by Dutch and German travelers as being common in even the smallest villages and was collected from the decomposition process of large dung hills specifically piled for this purpose. The Dutch punishment for possession of non-permitted gunpowder appears to have been amputation.: 180–181 Ownership and manufacture of gunpowder was later prohibited by the colonial Dutch occupiers. According to colonel McKenzie quoted in the book The History of Java (1817) by Thomas Stamford Raffles, the purest sulfur was supplied from a crater from a mountain near the straits of Bali.: 180–181 === India === Gunpowder technology is believed to have arrived in India by the mid-14th century, but could have been introduced much earlier by the Mongols, who had conquered both China and some borderlands of India, perhaps as early as the mid-13th century. The unification of a large single Mongol Empire resulted in the free transmission of Chinese technology into Mongol conquered parts of India. Regardless, it is believed that the Mongols used Chinese gunpowder weapons during their invasions of India. It was written in the Tarikh-i Firishta (1606–1607) that the envoy of the Mongol ruler Hulegu Khan was presented with a dazzling pyrotechnics display upon his arrival in Delhi in 1258. The first gunpowder device, as opposed to naphtha-based pyrotechnics, introduced to India from China in the second half of the 13th century, was a rocket called the "hawai" (also called "ban"). The rocket was used as an instrument of war from the second half of the 14th century onward, and the Delhi sultanate as well as the Bahmani Sultanate made good use of them. As a part of an embassy to India
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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by Timurid leader Shah Rukh (1405–1447), 'Abd al-Razzaq mentioned naphtha-throwers mounted on elephants and a variety of pyrotechnics put on display. Roger Pauly has written that "while gunpowder was primarily a Chinese innovation," the saltpeter that led to the invention of gunpowder may have arrived from India, although it is also likely that it originated indigenously in China. Firearms known as top-o-tufak also existed in the Vijayanagara Empire of Southern India by as early as 1366. In 1368–1369, the Bahmani Sultanate may have used firearms against Vijayanagara, but these weapons could have been pyrotechnics as well. By 1442 guns had a clearly felt presence in India as attested to by historical records. From then on the employment of gunpowder warfare in India was prevalent, with events such as the siege of Belgaum in 1473 by Muhammad Shah III. Muslim and Hindu states in the south were advanced in artillery compared to the Delhi rulers of this period because of their contact with the outside world, especially Turkey, through the sea route. The south Indian kingdoms imported their gunners (topci) and artillery from Turkey and the Arab countries, with whom they had developed good relations. === Korea === Korea had already come into possession of cannons by 1373, when a Korean mission was sent to China requesting gunpowder supplies for the artillery on their ships. However Korea did not natively produce gunpowder until the years 1374–76. In the 14th century a Korean scholar named Ch'oe Mu-sŏn discovered a way to produce it after visiting China and bribing a merchant by the name of Li Yuan for the gunpowder formula. In 1377 he figured out how to extract potassium nitrate from the soil and subsequently invented the juhwa, Korea's first rocket, and further developments led to the birth of singijeons, Korean arrow
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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rockets. Korea also began producing cannons in 1377. The multiple rocket launcher known as hwacha ("fire cart" 火車) was developed from the juhwa and singijeon in Korea by 1409 during the Joseon Dynasty. Its inventors include Yi To (이도, not to be mistaken for Sejong the Great) and Ch'oe Hae-san, the son of Ch'oe Mu-sŏn. However the first hwachas did not fire rockets, but used mounted bronze guns that shot iron-fletched darts. Rocket launching hwachas were developed in 1451 under the decree of King Munjong and his younger brother Pe. ImYung (Yi Gu, 임영대군 이구). This "Munjong Hwacha" is the well-known type today, and could fire 100 rocket arrows or 200 small Chongtong bullets at one time with changeable modules. At the time, 50 units were deployed in Hanseong (present-day Seoul), and another 80 on the northern border. By the end of 1451, hundreds of hwachas were deployed throughout Korea. Naval gunpowder weapons also appeared and were rapidly adopted by Korean ships for conflicts against Japanese pirates in 1380 and 1383. By 1410, 160 Korean ships were reported to have equipped artillery of some sort. Mortars firing thunder-crash bombs are known to have been used, and four types of cannons are mentioned: chonja (heaven), chija (earth), hyonja (black), and hwangja (yellow), but their specifications are unknown. These cannons typically shot wooden arrows tipped with iron, the longest of which were nine feet long, but stone and iron balls were sometimes used as well. === Japan === Firearms seem to have been known in Japan around 1270 as proto-cannons invented in China, which the Japanese called teppō (鉄砲 lit. "iron cannon"). Gunpowder weaponry exchange between China and Japan was slow and only a small number of hand guns ever reached Japan. However Japanese samurai used Fire lances in 15th-century. The first
|
{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
|
recorded appearance of the Fire lances in Japan was in 1409. The use of gunpowder bombs in the style of Chinese explosives is known to have occurred in Japan from at least the mid-15th century onward. The first recorded appearance of the cannon in Japan was in 1510 when a Buddhist monk presented Hōjō Ujitsuna with a teppō iron cannon that he had acquired during his travels in China. Firearms saw very little use in Japan until Portuguese matchlocks were introduced in 1543. During the Japanese invasions of Korea (1592–1598), the forces of Toyotomi Hideyoshi effectively used matchlock firearms against the Korean forces of Joseon, although they would ultimately be defeated and forced to withdraw from the Korean peninsula. === Africa === In Africa, the Adal Empire and the Abyssinian Empire both deployed gunpowder weapons during the Adal-Abyssinian War. Imported from Arabia, and the wider Islamic world, the Adalites, led by Ahmed ibn Ibrahim al-Ghazi, were the first African power to introduce cannon warfare to the African continent. Later on as the Portuguese Empire entered the war it would supply and train the Abyssinians with cannon and muskets, while the Ottoman Empire sent soldiers and cannon to back Adal. The conflict proved, through their use on both sides, the value of firearms such as the matchlock musket, cannon, and the arquebus over traditional weapons. Ernest Gellner in his book 'Nations and Nationalism' argues that the centralizing potential of the gun and the book, enabled both the Somali people and the Amhara people to dominate the political history of a vast area in Africa, despite neither of them being numerically predominant. "In the Horn of Africa both the Amharas and the Somalis possessed both gun and Book (not the same Book, but rival and different editions), and neither bothered greatly with
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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the wheel. Each of these ethnic groups was aided in its use of these two pieces of cultural equipment by its link to other members of the wider religious civilization which habitually used them, and were willing to replenish their stock." – Ernest Gellner == Transition to early modern warfare == === Early Ming firearms === Gun development and proliferation in China continued under the Ming dynasty. The success of its founder Zhu Yuanzhang, who declared his reign to be the era of Hongwu, or "Great Martiality," has often been attributed to his effective use of guns. Most early Ming guns weighed two to three kilograms while guns considered "large" at the time weighed around only seventy-five kilograms. Ming sources suggest guns such as these shot stones and iron balls, but were primarily used against men rather than for causing structural damage to ships or walls. Accuracy was low and they were limited to a range of only 50 paces or so. Despite the relatively small size of early Ming guns, some elements of gunpowder weapon design followed world trends. The growing length to muzzle bore ratio matched the rate at which European guns were developing up until the 1450s. The practice of corning gunpowder had been developed by 1370 for the purpose of increasing explosive power in land mines, and was arguably used in guns as well according to one record of a fire-tube shooting a projectile 457 meters, which was probably only possible at the time with the usage of corned powder. Around the same year Ming guns transitioned from using stone shots to iron ammunition, which has greater density and increased firearm power. Aside from firearms, the Ming pioneered in the usage of rocket launchers known as "wasp nests", which it manufactured for the army in 1380
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{
"page_id": 12063194,
"source": null,
"title": "History of gunpowder"
}
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