| | this article needs additional citations for verification. ( february 2010 ) | opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. in radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. an opaque object is neither transparent ( allowing all light to pass through ) nor translucent ( allowing some light to pass through ). when light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted ( also see refraction ). reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. an opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. both mirrors and carbon black are opaque. opacity depends on the frequency of the light being considered. for instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. more extreme frequency - dependence is visible in the absorption lines of cold gases. opacity can be quantified in many ways ; for example, see the article mathematical descriptions of opacity. quantitative definition the words " opacity " and " opaque " are often used as colloquial terms for objects or media with the properties described above. however, there is also a specific, quantitative definition of " opacity ", used in astronomy, plasma physics, and other fields, given here. in this use, " opacity " is another term for the mass attenuation coefficient ( or, depending on context, mass absorption coefficient, the difference is described here ) at a particular frequency of electromagnetic radiation. more specifically, if a beam of light with frequency travels through a medium with opacity and mass density, both constant, then the intensity will be reduced with distance x according to the formula - x is the distance the light has traveled through the medium - is the intensity of light remaining at distance x - is the initial intensity of light, at for a given medium at a given frequency, the opacity has a numerical value that may range between 0 and infinity, with units of length2 / mass. planck and rosseland opacity it is customary to define the average opacity, calculated using a certain weighting scheme. planck opacity uses normalized planck black body radiation energy density distribution as


the natural objects that i propose to consider are broadly those physical objects which are studied and referred to by science and by a common sense view, informed by science, of the world. natural objects are, philosophically speaking, individuals ; they are involved as units in dynamic, causal processes. i shall draw a distinction between natural objects and the abstract objects of mathematics, in particular set theory. natural objects encompass atoms and molecules ; cells and organisms, including you and me ; the objects of everyday life such as chairs and automobiles ; nations, continents, ecosystems, mountain ranges, geological faults ; planets, stars and galaxies. each natural object, when regarded internally, is a dynamic system with various interacting parts and components ( some of which may be natural objects in their own right ) ; when regarded externally, a natural object acts as a unit with respect to a larger system or systems ( which may again be natural objects ) of which the given object forms a part or component. it is sometimes argued that objects such as atoms or galaxies are theoretical constructs, as much so as mathematical objects ( or even, according to some, more so ). it is true that any reference to an object rests on epistemological assumptions. the approach here will be not to belittle these important epistemological questions but to leave them aside, and accept as a working assumption the practical viewpoint of people who are dealing with the world : that natural objects exist, act, and are acted upon, independently of the observer - - although any description of them or of their actions is dependent on the describer. scientific theories refer to natural objects as well as to abstractions of them ; they also refer to and quantify over other entities, in particular, the real numbers, points in space, time, and other mathematical spaces such as vector spaces, hilbert space, etc. - - these are abstract objects which are not necessarily abstractions of any natural objects. thus the ontology of natural objects may be said to be more restrictive than, say, a quinesque one. my point, however, is again not to dispute the validity of this or that ontology, but rather to describe a level of existence. no judgment will be presumed about the question of what ontological commitment should be made to abstract objects : rather, our focus of attention will be elsewhere. in the examples above and in what follows, i concentrate on physical objects. i do not mean to rule out psychic or spiritual or intellectual objects. you and i, as objects, have these aspects ; french society


our focus of attention will be elsewhere. in the examples above and in what follows, i concentrate on physical objects. i do not mean to rule out psychic or spiritual or intellectual objects. you and i, as objects, have these aspects ; french society, indian classical music, the theory of natural selection, king lear, king lear, the collective unconscious may all be regarded as natural objects. their ties to physical existence ( in the sense of matter and energy ) or to extensional ( spatial ) existence are various, and there is scope for varied theories about their ontological status ; i tend to follow nicolai hartmann ( 1949 ) in assigning to spiritual and psychic strata " categorial dependence " on the strata of physical existence in spaces : thus these objects are tied, however indirectly, to the physical level of existence. what i have to say will apply to such objects, in so far as they are acknowledged to exist ; and even to purely spiritual or psychic objects not tied to the physical level of existence at all, if they are admitted to exist. but i shall keep largely to physical and biological examples as being less problematic. this will also insulate the discussion from problems of consciousness and free will which inevitably come up but are not my concern here. thus the natural objects to be considered here may correspond more or less to the " natural bodies " of francis bacon : " toward the effecting of works, all that man can do is to put together or put asunder natural bodies. " ( bacon 1620, 39 ) an interesting example of a natural object is a hurricane. it is an open system, exchanging matter, energy and information with its environment, and acting as a whole. it is certainly accorded the status of an individual, in everyday language and in meteorology, even to the extent of being given a proper name ( such as floyd, mitch, zeb or babs ). it cannot be precisely identified with any set of atoms or molecules ; and any boundary in space or time that you try to draw for the hurricane will be arbitrary. meteorologists will draw such a boundary - - say, the point in time when a tropical storm is upgraded to a hurricane - - according to conventions about energy content and wind speeds, but the passing of a boundary is merely the employment of a convenient yardstick and is not supposed to have absolute significance. natural objects may usefully be described as systems. von bertalanffy ( 1968 ) defines a system as " a complex of interacting elements " ( although von bertalanffy '


a convenient yardstick and is not supposed to have absolute significance. natural objects may usefully be described as systems. von bertalanffy ( 1968 ) defines a system as " a complex of interacting elements " ( although von bertalanffy ' s elements are not to be equated with elements in the set - theoretic sense, and to avoid confusion i use " components " ). he goes on to study systems defined in terms of partial differential equations. mesarovic and takahara ( 1975 ) develop a more general, set - based concept of system. they are able to define such notions as cascading, feedback, and open systems. natural objects can be named, or they can be defined by ostension. often, naming and pointing will be essentially the only ways to refer unambiguously to a particular object. 2. natural and abstract objects the words " a logic " of the title are intended to suggest the aim of depicting how we reason or infer about natural objects. set theory, as a foundation for mathematics, is a way of doing this for abstract objects. before examining natural objects more closely, i wish to compare them with abstract objects - - which i shall identify, for concision, with sets - - in order to bring out some properties relevant to both. cantor ( 1895 ) introduced the concept of set as " any comprehension into a whole m of definite and separate objects m of our intuition or our thought ", and the modern development of set theory has retained the spirit of cantor ' s conception, in particular through the fundamental role of the comprehension axiom. even in the limited form necessary to avoid the paradoxes, comprehension formalizes the grouping together of objects with like properties into a single entity. the objects - - sets, classes - - of set theory are abstractions, the product of our mental processes ( " our intuition or our thought " ) which impose an organization on the world we perceive. except under a naive platonist interpretation, sets are not required to have an autonomous existence outside the formal system that creates them : that is to say, outside the language of the observer. ( the same goes for all other mathematical objects, including categories. ) thus set theory may be said to be a part of epistemology, the study of our knowledge of the world. following a hint of graham c. d. griffiths ( 1974, 87 ) i wish to contrast this with ontology, the study of what things exist, independently of any observer. from a scientific perspective, objects such


of our knowledge of the world. following a hint of graham c. d. griffiths ( 1974, 87 ) i wish to contrast this with ontology, the study of what things exist, independently of any observer. from a scientific perspective, objects such as atoms, molecules, organisms ( including persons ), stars, galaxies may be said to have an objective individual existence - - although there are borderline cases where the object ' s existence as a separate individual may be questionable, and the individuality of, say, a quark is of a very different nature from yours or mine. on the other hand, sets of objects, such as the set of all stars, or an arbitrary collection of, say, 100 people chosen at random, can exist as individuals only in an abstract sense ( though the former example may be viewed as a natural kind ). in addition, the " definite and separate " character of the elements of a set is not always found in nature where boundaries are generally ill - defined and separation may be relative and time - dependent. natural objects interact, are born of others, and die. to bring out how natural objects in general differ from sets, let me pause to consider the nature of one particular object, myself, whose autonomy and continuity i feel so clearly ( but proceeding in a different direction from descartes ). can i precisely be identified with a set? what about the set of cells that contain my unique dna? this set provides a good approximation to my physical extent, but there are many problems with identifying " me " with this set : i am not trying to attack set theory as such. i simply wish to note that the common mode of talking about the world leaves philosophical doubts aside and names natural objects ; that the language of science is full of them ( as well as of abstract objects ) ; and that set - theoretic language does not capture the nature of natural objects, as of course it was never intended to. it therefore seems worthwhile to try and develop a theory of natural objects. as jody azzouni puts it ( 1994, 4 ), mathematical objects are metaphysically inert. natural objects, by contrast, interact intensively with the rest of the world, and this interaction in fact cannot be separated from their nature. but great care will be needed because once a mathematical framework for referring to these objects has been established, the referents themselves will be mathematical objects. rigorous separation of levels of discourse will be necessary - - but this is nothing new in logic and metamathematics. sets are


needed because once a mathematical framework for referring to these objects has been established, the referents themselves will be mathematical objects. rigorous separation of levels of discourse will be necessary - - but this is nothing new in logic and metamathematics. sets are abstracted ( from the latin : drawn away ) from direct physical experience. a common example frequently seen in expositions of elementary ( naive ) set theory illustrates the abstract nature of the set concept by explaining how a collection of disparate objects can be grouped together into a set merely by enumerating them or by specifying a common property - - no matter how incongruous and varied their natures or how widely separated they are in space and time. this kind of construction is counter - intuitive to a student who is not accustomed to thinking in terms of abstractions ; the natural objects one is used to dealing with in less abstract contexts do not have these properties. even the pair set axiom does not hold, in general, for natural objects. a pair of objects is not, usually, a single object ( although in special cases one will consider certain pairs as a unit ; for example a married couple is an object in legal considerations ). the same goes for other elementary set - theoretic constructions such as unions and intersections. the distinction between individuals and classes is relevant here. ( some philosophers talk of natural kinds ; others oppose individuals to " sets ". ) this distinction, which goes back to plato and aristotle, was blurred by cantor : his sets are both individuals and classes. indeed, the principle of comprehension is a formalization of the notion that a class of objects is defined, as an individual, by a common property that they share. the subsequent development of set theory reinstated the individual / class distinction in a different form with sets and proper classes ; this happened as early as cantor ( 1899 ). different versions of modern set theory ( zermelo - fraenkel, von neumann - bernays - godel ) vary in the ontological status accorded to proper classes, as do different interpretations of the formalisms. however, the basic point here is that sets are essentially collections ( " multiplicities " - - cantor ) treated as individuals. a natural object is never merely a collection ; the interaction of its components is an essential part of its individuality. it is perhaps of interest to note that ernst zermelo, in his fundamental paper ( 1908 ) on axiomatizing set theory, seemed to be open - minded about whether all objects are sets : "


an essential part of its individuality. it is perhaps of interest to note that ernst zermelo, in his fundamental paper ( 1908 ) on axiomatizing set theory, seemed to be open - minded about whether all objects are sets : " set theory is concerned with a domain b of individuals, which we shall call simply objects and among which are the sets. " ( emphases in original. ) for zermelo, the membership relation is fundamental ; sets are defined in terms of this relation, as objects which have elements, so that a special case is needed for the empty set. so sets are logically posterior to, not prior to, the fundamental binary relation. but unlike later authors zermelo does not rule out the possibility that some objects are nonsets. of course the nonsets which he had principally in mind were atoms or urelements ; these have continued to play a role in set theory, but only in connection with the membership relation. other possible relations or properties of urelements are not considered. natural objects may be urelements - - the raw material for forming sets - - for example, the set of all hurricanes in 1999 may be used, and abstracted, in a statistical analysis. what interests me here is not the properties of natural objects qua urelements, but what other properties they may have, orthogonal as it were to their set - theoretic ones, because not expressed in terms of the membership relation. as a first approximation, let us suppose that an appropriate language for natural objects has a binary relation, analogous to the fundamental binary relation ( " x is an element of y " ) of set theory, but stating rather " x is a component of y ". this relation will have very different properties from. in fact partakes of some of the properties of natural objects : it changes through time and space. its properties in the subatomic and the macroscopic realms diverge. but we can certainly see whether set - theoretic ideas apply to, exploring the correspondence, more than an analogy, between and. as intimated above, basic set - theoretic axioms including comprehension and the pair set axiom do not hold for natural objects under this - interpretation. there is something of a tradition of alternate set theories in which some of the standard axioms are negated. we may gain clues about reasoning with natural objects from what has been learned about reasoning with weak sets. one important line of work in this direction negates the axiom of foundation


set theories in which some of the standard axioms are negated. we may gain clues about reasoning with natural objects from what has been learned about reasoning with weak sets. one important line of work in this direction negates the axiom of foundation. this has been most successfully done by peter aczel ( 1988 ), building on work of boffa ( 1969 ), forti and honsell ( 1983 ), finsler, scott, and others. aczel ' s work in turn has had important applications in situation theory, theory of communicating systems, and elsewhere ( e. g. barwise 1989, barwise and moss 1998 ). aczel has built a universe of set theory, extending and not supplanting the standard universe of set theory, that provides a useful formalism for certain ways of looking at the world ( e. g. situation theory ). the axiom of foundation was historically one of the last of the standard axioms of set theory to be added to the canon. the axiom of choice was introduced earlier ( choice : zermelo 1904 ; well - foundedness and foundation : mirimanoff 1917, skolem 1922 ), but its separate status was recognized from the start, and has, of course, been a central theme in 20th century set theory. other authors have more recently examined the independence of some of the core axioms of set theory from weak base systems, thus bringing into question even these axioms that were, unlike choice, readily accepted. for example, boffa ( 1972 ) proved an independence result concerning the pair set axiom ; gonzalez ( 1992 ) showed the independence of the union axiom in zermelo set theory, using a permutation method ; zarach ( 1998 ) used forcing to show that collection is not implied 3. species and the indescribability in this and the next section i turn from a comparison with set theory to motivating influences from the sciences. problems of behaviour of natural objects, and of the constitution of an individual, have arisen in concrete situations, and i shall attempt to draw some working principles from these lessons. an important case study in the investigation of natural objects is the work of philosophers of biology on the nature of individuals. this has arisen in large part because a set - theoretic framework has been found by many to be inadequate for the ontological status of taxonomic groups. in particular, the traditional conception, which goes back to aristotle, of each species as a class has been questioned, first by michael


a set - theoretic framework has been found by many to be inadequate for the ontological status of taxonomic groups. in particular, the traditional conception, which goes back to aristotle, of each species as a class has been questioned, first by michael ghiselin ( 1966 ; see also 1974, 1981, 1987 ), and then by many other authors ( e. g. holsinger 1984, hull 1978, sober 1984, sober 1993, griffiths 1974 ). they point out that to consider a species as a class, or as defined by a set of properties, is to impose on it a character that it does not have, and to miss the actual nature of species. since darwin we know : this has the added advantage of unifying the biological hierarchy of entities : at each level - - cell, organism, population, species, etc. - - there occur individuals that are defined, not by comprehension in terms of their elements ( this is impossible ), but as dynamical, changing systems whose behaviour can be characterized internally by interactions among their components, or externally by their interactions with their environment. indeed, one can extend this hierarchy to the physical level ( s ) as well ( molecules, atoms,... stars, galaxies,... ) with the same remarks still holding ( griffiths 1974 ). ghiselin ( 1987, 128 ) goes so far as to say that treating species as individuals opens " the prospect that we can develop a single body of knowledge for the entire universe. " thus the practical pursuit of systematics in biology broadens into a picture of the universe as consisting of individuals, each individual being bounded in space and time but not ( necessarily ) contiguous or connected, characterized by a dynamical interplay of its components and its environment, and definable by ostension or by naming and not by comprehension : when anyone tries to find the " defining properties " of an individual, he is wasting his time. this is equally true for homo sapiens, tellurian life, human language, french, and noam chomsky. ( ghiselin 1981, 283 ) another biological science, ecology, similarly encourages us to view biological systems as wholes, with components that are dynamically interdependent ( e. g. levins and lewontin 1980 ). the notion of supervenience ( kim 1978 ) is a good candidate for formalization in any attempt to describe the articulation of the different levels of the hierarchy of natural objects. an important principle suggested by all the above discussions is


1980 ). the notion of supervenience ( kim 1978 ) is a good candidate for formalization in any attempt to describe the articulation of the different levels of the hierarchy of natural objects. an important principle suggested by all the above discussions is the inadequacy of any ( finite ) language to describe any natural object fully, other than by naming or ostension. everyday life, and the example of " me ", tend to confirm this principle ; and of course it is fundamental to quantum mechanics as expressed in the uncertainty principle and complementarity, construed ( as in the copenhagen interpretation ) as precluding a complete objective description of phenomena : i shall say more on this in the next section. the principle of the indescribability of objects provides a contrast between natural objects and abstract objects : in set theory, the exact specification and construction of objects using comprehension and the other constructive axioms is essential. a second principle is, in contrast, shared by natural and abstract objects. in fact it is suggested both by set theory and by recent work in cosmology. cosmologists are facing more and more consciously the problem of describing everything. set theory, among other branches of mathematical logic, has a similar ambition in that an entire universe is to be constructed - - not in this case the physical universe but the " universe of discourse " of mathematics, the aggregate of all the abstract objects studied by mathematicians. incidentally, the habitual use of the term " universe " for the class of all sets is relatively recent. zermelo ( 1908 ) merely spoke, as we have seen, of a " domain " of individuals ; russell and whitehead in principia mathematica ( 1910 ) referred to the " universal class " v, and even godel in his work on v = l, which set the tone for all subsequent set theory, refers to the " universal class " and not the " universe " ( godel 1940, 40 ). the principle i am proposing here is the impossibility of describing everything. in set theory, it was necessitated by the early paradoxes and is articulated in a fundamental series of theorems, including those of lowenheim - skolem, of godel, and the related result of tarski on the undefinability of truth ( these are not confined to set theory ). even before these results, it was realized that sets have a way of spilling over any circumscription that one may attempt to put on them :...


undefinability of truth ( these are not confined to set theory ). even before these results, it was realized that sets have a way of spilling over any circumscription that one may attempt to put on them :... quel que soit l ' ensemble qu ' on envisage ( pourvu qu ' il existe ), des individus nouveaux surgissent, et un ensemble plus vaste apparait necessairement ; on est bien en presence d ' une extension indefinie qui ne comporte pas d ' arret ni borne. ( mirimanoff 1917, 48 ) since godel ' s work, there has been what akihiro kanamori ( 1996, 46 ) calls a " cornucopia of models of set theory " ( i. e. models of everything ) and in fact these are a basic research tool. in cosmology, the attention of some researchers has been focussed more recently on the problem of everything. it arises acutely when the universe ( defined, perhaps, as what emerged from the big bang ) turns out not to be everything : when in order to account for the observed properties of our universe, it is found that the best explanation is a theory incorporating the existence of many universes, of which ours is just one. several modern cosmological theories call for multiple universes, including lee smolin ' s theory of the creation and natural selection of universes ( smolin 1997 ). andrei linde ' s " chaotic inflation " and " eternally self - reproducing universe " ( e. g. linde 1990 ) also call for many, perhaps infinitely many, universes - - if by universe we mean everything that we can in principle communicate with. smolin ( 1997, 14 ) has addressed the issues that emerge when attempting to describe everything : the problem of how to make a theory of the whole universe is thus the problem of how to construct a theory without making any reference to anything that exists, or anything that we might have imagined happened, outside of the system we are describing. a related lesson is taught by quantum theory ; thus heinz r. pagels ( 1982, 103 ) : bohr ' s principle of complementarity implies that knowing everything at one time about the world - - a requirement of determinism - - is impossible because the conditions for knowing one thing necessarily exclude knowledge of others. the separation of observer and observed, in the copenhagen interpretation, carries the


expressed in terms of a space and time that were absolute and prior to the physical universe. newton himself realized this and had recourse to a metaphysical notion of space and time. leibniz also realized it and made it a central part of his criticisms of the newtonian cosmos, proposing instead a relational view of space and time. it was part of the achievement of einstein to remove space and time from their privileged position as the " stage " on which the events of the universe are played out, and replace them by a concept of space and time as part of the fabric of the universe, acting and acted upon by matter and energy in a dynamical system. analogously, in " classical " logic one first specifies the language ( syntax and rules of inference ) and then constructs " universes " with this language as the stage - setting. a way to avoid the paradoxes and limitations to which this gives rise is a description in which the language is no longer separate from and prior to the object being described. ( barwise and etchemendy ( 1987 ) use just such a strategy to deal with the liar paradox, although the limitations of logic to abstract objects are not challenged. i comment further on situation semantics below. ) such descriptions would be impredicative - - physicists might call them non - local - - in that the specification of a single object would involve the whole universe or a substantial part of it : that each singular substance expresses the whole universe in its own way, and that in its concept are included all of the experiences belonging to it together with all of their circumstances and the entire sequence of exterior events. ( leibniz 1686, 308 ) mach ' s principle may be regarded as an expression of this in dynamics. in quantum theory, bohr frequently noted the following corollary to, or instance of, complementarity : on the lines of objective description, it is indeed more appropriate to use the word phenomenon to refer only to observations obtained under circumstances whose description includes an account of the whole experimental arrangement. ( bohr 1961, 73 ) this means, in fact, since it is not clear where to draw the line that separates the " whole experimental arrangement " ( and the laws governing it ) from the rest of the world, that the description of a phenomenon implicitly includes the whole universe. such impredicativity has the consequence that one cannot construct from scratch models of a universe consisting of " singular substances ". this would be considered by logicians a drawback of impredicativity ;


implicitly includes the whole universe. such impredicativity has the consequence that one cannot construct from scratch models of a universe consisting of " singular substances ". this would be considered by logicians a drawback of impredicativity ; but in the context of the problem of smolin, it may be an advantage that not only are there no obvious models of the system which are describable from outside, but perhaps such models are in principle not possible. situation semantics ( barwise and perry 1983 ; barwise 1989 ) is a different kind of attempt to address the problem of the impossibility of describing everything in the context of the analysis of natural language. the approach of viewing utterances and inferences as situated activities differs from the present one in that it is epistemological rather than ontological. it " shifts attention from truth preservation to information extraction and information processing " ( barwise 1989, xiv ; emphases in original ). furthermore, its syntax presupposes the existence and discreteness - - the abstractness - - of objects. ian hacking ( 1972, 148 ), discussing leibniz ' s notion of individual substance, makes an important point : which bundles [ of qualities ] are substances? only those bundles that are active, in the sense of having laws of their own. laws provide the active principle of unity. there is a tendency in much analytic philosophy to conceive things as given, and then to speculate on what laws they enter into. on the contrary, things are in the first instance recognized by regularities. ( emphasis in original ) thus a logic of natural objects will put priority on addressing the question : what makes an individual an individual? as hacking points out, leibniz shares with berkeley the view that substances are bundles of qualities ; the important question, as in the quote above, is the converse. with the principle that each object ( or singular substance, or thing, or individual, or phenomenon ) irreducibly reflects its entire surroundings, we have come to a fusion of the first two principles mooted : the indescribability of the individual and of the universe. in combination with either of these, it implies the other. in leibniz ' s case, this third principle is a consequence of the principle of reason ( or of " predicate - in - notion " ) - - as is another principle, that no two individuals are exactly alike. the identity of indiscernibles has not received attention here but is indeed logically


of the principle of reason ( or of " predicate - in - notion " ) - - as is another principle, that no two individuals are exactly alike. the identity of indiscernibles has not received attention here but is indeed logically linked to the principles adduced above. the principle of reason does not stand up to scrutiny in the light of contemporary logic, but some of its consequences may be recast for our use. in the novum organum bacon ( 1620, 41 ) criticizes aristotelian logic thus : the syllogism is not applied to the first principles of sciences, and is applied in vain to intermediate axioms, being no match for the subtlety of nature. it commands assent therefore to the proposition, but does not take hold of the thing. a modern logic of natural objects would aim to take hold of the thing, aiming to secure sound principles for reasoning with individuals without need of leibniz ' s metaphysical starting point. 1. i am grateful to john wahlert for elucidating this example for me. aczel, peter ( 1988 ). non - well - founded sets, csli lecture notes 14, stanford. azzouni, jody ( 1994 ). metaphysical myths, mathematical practice : the ontology and epistemology of the exact sciences, cambridge university press. bacon, francis ( 1620 ). the new organon, ed. fulton h. anderson, the library of liberal arts, bobbs - merrill, 1960. barwise, jon ( 1989 ). the situation in logic, csli lecture notes 17, stanford. barwise, jon and john etchemendy ( 1987 ). the liar, oxford university press. barwise, jon and lawrence moss ( 1998 ). vicious circles. csli lecture notes 60. barwise, jon and j. perry ( 1983 ). situations and attitudes, mit press, cambridge, mass. and london. bertalanffy, ludwig von ( 1968 ). general systems theory, george braziller, new york. boffa, m ( 1969 ). sur la theorie des ensembles sans axiome de fondement, bull soc. math. belg. 31, 16 - 56. boffa, m ( 1972 ). l ' axiome de paire dans le systeme de zermelo, arch. math. logik grundlagenforsch. 15, 97 - 98. bohr, niels ( 1961 ). atomic physics and human knowledge, science editions,


, ian ( 1972 ). individual substance, in : leibniz : a collection of critical essays, ed. harry g. frankfurt, anchor books. hartmann, nicolai ( 1949 ). new ways of ontology, greenwood press, henry regnery co., 1975. translation of neue wege der ontologie, w. kohlhammer, stuttgart. holsinger, kent e. ( 1984 ). the nature of biological species, philosophy of science 51, 293 - 307. hull, david l. ( 1978 ). a matter of individuality, philosophy of science 45, 335 - 360. kanamori, akihiro ( 1996 ). the mathematical development of set theory from cantor to cohen, bull. symbolic logic 2 ( 1 ), 1 - 71. kim, jaegwon ( 1978 ). supervenience and nomological incommensurables, american philosophical quarterly, 15 ( 2 ), 149 - 156. leibniz, gottfried wilhelm ( 1686 ). discourse on metaphysivs, in philosophical papers and letters, trans. leroy e. loemker, 2nd ed., d. reidel, 1969. levins, richard and richard lewontin ( 1980 ). dialectics and reduction in ecology, synthese 43, 47 - 78. linde, andrei ( 1990 ). inflation and quantum cosmology, academic press. mayr, ernst ( 1976 ). evolution and the diversity of life, belknap press, harvard university press. mesarovic, m. d. and yasuhiko takahara ( 1975 ). general systems theory : mathematical foundations, academic press. mirimanoff, d. ( 1917 ). remarques sur la theorie des ensembles et les antinomies cantoriennes, i, l ' enseignement math. 19, 209 - 217. pagels, heinz r. ( 1982 ). the cosmic code : quantum physics as the language of nature, simon & schuster, new york. russell, bertrand, and alfred north whitehead ( 1910 ). principia mathematica, cambridge university press, 1962. skolem, thoralf ( 1922 ). some remarks on axiomatized set theory, translated in van heijenoort ( 1967, 290 - 301 ). smolin, lee ( 1997 ). the life of the cosmos, oxford university press. sober, elliott ( 1984 ). sets, species, and evolution : comments on philip kitcher '


| foundation of quantum theory | the following well - known experiments serve as a motivation for studying quantum theory. the experimental results cannot be explained using ideas from classical physics. | 1. blackbody radiation | | 2. photoelectric effect | | 3. compton effect | it is well - known that when a body is heated it emits electromagnetic radiation. for example, if a piece of iron is heated to a few hundred degrees, it gives off e. m. radiation which is predominantly in the infra - red region. when the temperature is raised to 1000c it will begin to glow with reddish color which means that the radiation emitted by it is in the visible red region having wavelengths shorter than in the previous case. if heated further it will become white - hot and the radiation emitted is shifted towards the still shorter wave - length blue color in the visible spectrum. thus the nature of the radiation depends on the temperature of the emitter. a heated body not only emits radiation but it also absorbs a part of radiation falling on it. if a body absorbs all the radiant energy falling on it, then its absorptive power is unity. such a body is called a black body. an ideal blackbody is realized in practice by heating to any desired temperature a hollow enclosure ( cavity ) and with a very small orifice. the inner surface is coated with lamp - black. thus radiation entering the cavity through the orifice is incident on its blackened inner surface and is partly absorbed and partly reflected. the reflected component is again incident at another point on the inner surface and gets partly absorbed and partly reflected. this process of absorption and reflection continues until the incident beam is totally absorbed by the body. the inner walls of the heated cavity also emit radiation, a part of which can come out through the orifice. this radiation has the characteristics of blackbody radiation - the spectrum of which can be analyzed by an infra - red spectrometer. experimental results show that the blackbody radiation has a continuous spectrum ( shown in the graph ). the intensity of the emitted radiation el is plotted as a function of the wavelength l for different temperatures. the wavelength of the emitted radiation ranges continuously from zero to infinity. el increases with increasing temperature for all wavelengths. it has very low values for both very short and very long wavelengths and has a maximum in between at some wavelength lmax. lmax depends on the temperature of the blackbody and decreases with increasing temperature. the shift in the peak of the intensity distribution curve obeys an empirical relationship known as


short and very long wavelengths and has a maximum in between at some wavelength lmax. lmax depends on the temperature of the blackbody and decreases with increasing temperature. the shift in the peak of the intensity distribution curve obeys an empirical relationship known as wien ' s displacement law : lmax t = constant. the total power radiated per unit area of a blackbody can be derived from thermodynamics. this is known as stefan - boltzmann law which can be expressed mathematically as : e = s t4, where s = 5. 67 x 10 - 8 w m - 2 k - 4 is known as stefan ' s constant. note that the total power e radiated is obtained by integrating el over all wavelengths. w. wien proposed an empirical relationship between el with l for a given temperature t : el ( t ) = a exp ( - b / lt ) / l5, where the constants a and b are chosen arbitrarily so as to fit the experimental energy distribution curves. but it was later found that the experimental data don ' t follow wien ' s empirical relation at larger wavelengths [ see fig. below ]. wien ' s theory of intensity of radiation was based only on arguments from thermodynamics not on any plausible model. considering the radiation system as composed of a bunch of harmonic oscillators rayleigh and jeans derived ( using thermodynamics ) an expression for the emitted radiation el : el = ( c / 4 ) ( 8pkbt / l4 ). ' kb ' is the boltzman constant ( kb = 1. 345 x 10 - 23 j / k ). the above expression agrees well with the experimental results at long wavelengths but drastically fails at shorter wavelengths. in the limit l - > 0, el - > infinity from the expression above, but in the experiments el - > 0, as l - > 0. this serious disagreement between theory and experiment indicates the limitations of classical mechanics. max planck later derived an expression for the emitted radiation using quantum mechanics. he made a bold new postulate that an oscillator can have only energies which are discrete, i. e., an integral multiple of a finite quantum of energy hf where h is planck ' s constant ( h = 6. 55 x 10 - 34 j. s ) and f is the frequency of the oscillator. thus the energy of the oscillator is, e = nhf, where n is an integer or zero. planck further assumed that


. 55 x 10 - 34 j. s ) and f is the frequency of the oscillator. thus the energy of the oscillator is, e = nhf, where n is an integer or zero. planck further assumed that the change in energy of the oscillator due to emission or absorption of radiant energy can also take place by a discrete amount hf. since radiation is emitted from the oscillators, and since according to planck, the change in energy of the oscillators can only take discrete values, the energy carried by the emitted radiation, which is called a photon, will be hf, and that is also equal to the loss of energy of the oscillator. again, this is also the energy gain of the oscillator when it absorbs a photon. based on these ideas planck derived the expression for the energy distribution of blackbody radiation : el = ( c / 4 ) ( 8phc / l5 ) ( 1 / [ exp ( hc / lkbt ) - 1 ] ). rayleigh - jean ' s expression and wien ' s displacement law are special cases of planck ' s law of radiation. planck ' s formula for the energy distribution of blackbody radiation agrees well with the experimental results, both for the long wavelengths and the short wavelengths of the energy spectrum. please on the simulation below to see nice interactive demonstration of the physics of blackbody radiation. simulation on blackbody radiation back to top planck ' s postulate regarding the discrete nature of the possible energy states of an oscillator marked a radical departure from the ideas of classical physics. according to the laws of classical mechanics, the energy of an oscillator can vary continuously, depending only on the amplitude of the vibrations - this is in total contrast to planck ' s hypothesis of discrete energy states of an oscillator. photoelectric effect is another classic example which can not be explained with classical physics. einstein was awarded nobel prize for his explanation of the physics of photoelectric effect. the basic experiment of photoelectric effect is simple. it was observed that a metal plate when exposed to ultraviolet radiation became positively charged which showed that it has lost negative charges from its surface. these negatively charged particles were later identified to be electrons ( later named photoelectrons ). this phenomenon is known as photoelectric effect. please out the physics applet below which shows the effect of light on various metals. simulation on photoelectric effect the main results of the


to be electrons ( later named photoelectrons ). this phenomenon is known as photoelectric effect. please out the physics applet below which shows the effect of light on various metals. simulation on photoelectric effect the main results of the experiment can be summarized as follows : on exposure to the incident light, photoelectrons with all possible velocities ranging from 0 upto a maximum vm are emitted from the metal plate. when a positive potential is applied to the collector ( which collects the emitted photoelectrons ), a fraction of the total number emitted is collected by the collector. this fraction increases as the voltage is increased. for potentials above about + 10 volts, all the electrons emitted by the light are collected by the collector which accounts for the saturation of the photoelectric current [ figs. ( a ) and ( b ) below ]. on the other hand, when a negative retarding potential is applied on the collector, the lower energy electrons are unable to reach the collector so that the current gradually decreases with increasing negative potential. finally for a potential - v0 ( known as the stopping potential ), the photoelectrons of all velocities upto the maximum vm are prevented from reaching the collector. at this point, the maximum kinetic energy of the emitted electrons equals the energy required to overcome the effect of the retarding potential - so we can write mvm2 / 2 = ev0. conclusion from the experimental results : ( 1 ) the photoelectric current depends upon the intensity of the light used. it is independent of the wavelength of the light [ see fig. ( a ) above ]. ( 2 ) the photoelectrons are emitted with all possible velocities from 0 upto a maximum vm which is independent of the intensity of the incident light, but depends only on its wavelength ( or frequency ). it is found that if f is the frequency of the light used, then the maximum kinetic energy of the photoelectrons increases linearly with f [ see figs. ( b ) and ( c ) above ]. ( 3 ) photoelectron emission is an instantaneous effect. there is no time gap between the incidence of the light and the emission of the photoelectrons. ( 4 ) the straight line graph showing the variation of the maximum kinetic energy of the emitted electrons with the frequency f of the light intersects the abscissa at some point f0. no photoelectron emission takes


the photoelectrons. ( 4 ) the straight line graph showing the variation of the maximum kinetic energy of the emitted electrons with the frequency f of the light intersects the abscissa at some point f0. no photoelectron emission takes place in the frequency range f < f0. this minimum frequency f0 is known as the threshold frequency. its value depends on the nature of the emitting material [ see fig. ( c ) above ]. breakdown of classical physics : according to classical physics - ( a ) light is an electromagnetic wave - the intensity of light is determined by the amplitudes of these electromagnetic oscillations. when light falls on an electron bound in an atom, it gains energy from the oscillating electric field. larger the amplitude of oscillations, larger is the energy gained by the emitted electron - thus energy of the emitted electrons should depend on the intensity of the incident light. this is in contrast to what has been observed in experiment ( point 2 above ). ( b ) according to the electromagnetic theory, the velocity of the emitted electrons should not depend on the frequency of the incident light. whatever may be the frequency of the incident light, the electron would be emitted if it gets sufficient time to collect the necessary energy for emission. so the photoelectric emission is not an instantaneous effect. these are in contrary to points 3 and 4 above. ( c ) finally, the incident electromagnetic wave acts equally on all the electrons of the metal surface. there is no reason why only some electrons will be able to collect the necessary energy for emission from the incident waves. given sufficient time, all electrons should be able to collect the energy necessary for emission. so there is no reason why the photoelectric current should depend upon the intensity of the incident light. however, this is again in contrary to the observed facts ( point 1 above ). einstein ' s light quantum hypothesis and photoelectric equation : we have seen from above that the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident light. in terms of equation we have mvm2 / 2 = ev0 = af - w where a and w are constants. w is known as the work function of the emitting material. the constant a was determined experimentally and is found to be equal to the planck ' s constant h. we can then rewrite the above equation as - mvm2 / 2 = ev0 = hf - w. for the special value of f =


a was determined experimentally and is found to be equal to the planck ' s constant h. we can then rewrite the above equation as - mvm2 / 2 = ev0 = hf - w. for the special value of f = f0 = w / h, the k. e. of the emitted photoelectrons becomes zero. so there will be no photoelectron emission if f < f0. f0 is the threshold frequency. the equation, mvm2 / 2 = ev0 = hf - hf0 is known as the famous einstein ' s photoelectric equation. einstein used the quantum hypothesis of planck to explain the photoelectric effect. he postulated that light is emitted from a source in the form of energy packets of the amount hf known as the light quantum or photon. this is known as einstein ' s light quantum hypothesis. when a photon of energy hf falls on an electron bound inside an atom, the electron absorbs the energy hf and is emitted from the atom provided that hf is greater than the energy of binding of the electron in the atom which is equal to the work function w of the metal. the surplus of energy ( hf - w ) is taken away by the electron as its kinetic energy. obviously if hf < w, i. e. f < f0, no photoelectric emission can take place. this explains the existence of the threshold frequency. furthermore, according to einstein ' s theory, larger the number of photons falling on the metal, greater is the probability of their encounter with the atomic electrons and hence greater is the photoelectric current. so the increase of photoelectric current with the increasing light intensity can be easily explained. finally, as soon as the photon of energy hf > w falls on an electron, the latter absorbs it and is emitted instantaneously. note that einstein ' s light quantum hypothesis postulates the corpuscular nature of light in contrast to the wave nature. we will talk about this wave - particle duality later on in this course. back to top the discovery of compton scattering of x - rays provides direct support that light consists of pointlike quanta of energy called photons. a schematic diagram of the apparatus used by compton is shown in the figure below. a graphite target was bombarded with monochromatic x - rays and the wavelength of the scattered radiation was measured with a rotating crystal spectrometer. the intensity was determined by a movable ionization chamber


compton is shown in the figure below. a graphite target was bombarded with monochromatic x - rays and the wavelength of the scattered radiation was measured with a rotating crystal spectrometer. the intensity was determined by a movable ionization chamber that generated a current proportional to the x - ray intensity. compton measured the dependence of scattered x - ray intensity on wavelength at three different scattering angles of 45o, 90o, and 135o. the experimental intensity vs. wavelength plots observed by compton for the above three scattering angles ( see fig. below ) show two peaks, one at the wavelength l of the incident x - rays and the other at a longer wavelength l '. the functional dependence of l ' on the scattering angle and l was predicted by compton to be : l ' - l = ( h / mec ) [ 1 - cosq ] = l0 [ 1 - cosq ]. the factor l0 = h / mec, also known as compton wavelength can be calculated to be equal to 0. 00243 nm. the physics of compton effect : to explain his observations compton assumed that light consists of photons each of which carries an energy hf and a momentum hf / c ( as p = e / c = hf / c ). when such a photon strikes a free electron the electron gets some momentum ( pe ) and kinetic energy ( te ) due to the collision, as a result of which the momentum and energy of the photon are reduced. considering energy and momentum conservation ( for the detail derivation please here ) one can derive the change in wavelength due to compton scattering : l ' - l = ( h / mec ) [ 1 - cosq ]. note that the result is independent of the scattering material and depends only on the angle of scattering. the appearance of the peak at the longer wavelength in the intensity vs. wavelength curve is due to compton scattering from the electron which may be considered free, since its energy of binding in the atom is small compared to the energy hf of the photon. the appearance of the other peak at the wavelength of the incident radiation is due to scattering from a bound electron. in this case the recoil momentum is taken up by the entire atom, which being much heavier compared to the electron, produces negligible wavelength shift. compton effect gives conclusive evidence in support of the corpuscular character of electromagnetic radiation. please out the simulation below which shows compton scattering. simulation on compton scattering back to top © kingshuk majumdar ( 2000 )


/ 1998 ] what are dominant terms, and how do you obtain their values? - donkey grazing half a field [ 08 / 08 / 1997 ] a donkey is attached by a rope to a point on the perimeter of a circular field. how long should the rope be so that the donkey can graze exactly half the field? - double integration in polar coordinates [ 03 / 27 / 2003 ] evaluate double integral x - y / x * 2 + y * 2 over x * 2 + y * 2 equal to or less - e as a series and a limit [ 03 / 30 / 1998 ] why does e = 1 + 1 / 2! + 1 / 3! + 1 / 4! +... and lim ( 1 + 1 / n ) ^ n, as n - - - an easy definition of calculus [ 9 / 4 / 1995 ] what is calculus? - e ^ ( e ^ x ) = 2 [ 01 / 28 / 2002 ] i have been trying to solve e ^ ( e ^ x ) = 2. help! - an ellipse or a circle? - parametric equations [ 12 / 05 / 1998 ] is this parametric equation elliptical or a circle?... and how do i compute the slopes at points 0, pi / 4, pi / 2, 3pi / 2, and 2pi? - an elliptic integral [ 01 / 05 / 2003 ] - epsilon / delta definition of limits [ 08 / 26 / 1999 ] can you explain how to use the epsilon / delta definition of limits? - epsilon - delta proofs [ 09 / 28 / 2004 ] an explanation of the thinking behind two epsilon - delta proofs, one from a calculus textbook and one from an answer in our archives.


newton ' s first law states that an object will keep doing what it is doing if left alone, in other words - the natural state of an object is static - unchanging - motion. newton ' s second law clarifies the first. acceleration, or any change in motion, is an unnatural state for an arbitrary object left to its laurels, however it is a state that clearly exists all around us. newton defines the " thing " that forces an object to change its state of being - a force. in this most rigorous sense, a force is defined to be that which causes a change in motion. the observation of a change in momentum necessitates that there is some force driving that change, so in this sense the two are equivalent ( there is an equals sign there after all ) - wherever you see a ( net ) force you will see an acceleration, wherever you see an acceleration you will find a force responsible for it. however, going back to the first law, acceleration is a change in the ( kinetic ) state of an object, an objects natural tendency is to statically maintain its state. the observation of an unnatural state of being would logically imply that there is a cause. intuitively it seems unnatural that accelerations would happen spontaneously and that the universe will invent a force just to balance the books if you will.


methods | statistics | clinical | educational | industrial | professional items | world psychology | a word is a unit of language that carries meaning and consists of one or more morphemes which are linked more or less tightly together. typically a word will consist of a root or stem and zero or more affixes. words can be combined to create phrases, clauses and sentences. a word consisting of two or more stems joined together is called a compound. difficulty in defining the term edit the precise definition of what a word is depends on which language the definition is for, and the dividing line between words and phrases is not always clear. in most writing systems, a word is usually marked out in the text by interword separation such as spaces or word dividers used in some languages such as amharic. in other languages such as chinese and japanese, and in many ancient languages such as sanskrit, word boundaries are not shown. even in writing systems that use interword separation, word boundaries are not always clear ; for example, even though ice cream is written like two words, it is a single compound because it cannot be separated by another morpheme or rephrased like iced cream or cream of ice. likewise, a proper noun is a word, however long it is. a space may not be even the main morpheme boundary in a word ; the word new yorker is a compound of new york and - er, not of new and yorker. in english, many common words have historically progressed from being written as two separate words ( e. g. to day ) to hyphenated ( to - day ) to a single word ( today ), a process which is still ongoing, as in the common spelling of all right as alright. words in different classes of languages edit in synthetic languages, a single word stem ( for example, love ) may have a number of different forms ( for example, loves, loving, and loved ). however, these are not usually considered to be different words, but different forms of the same word. in these languages, words may be considered to be constructed from a number of morphemes ( such as love and - s ). in polysynthetic languages, the number of morphemes per word can become so large that the word performs the same grammatical role as a phrase or clause in less synthetic languages ( for example, in yupik, angyaghllangyugtuq means " he wants to acquire a big boat " ). these large - construction words are


one half of optics was missing at optical frequencies, electromagnetic waves interact with an ordinary optical material ( e. g., glass ) via the electronic polarizability of the material. in contrast, the corresponding magnetizability is negligible for frequencies above a few thz, or in other words, its magnetic permeability is identical to unity ( μ ( ω ) = 1 ). consequently, the optical properties of an ordinary optical material are completely characterized by its electric permittivity ε ( ω ) ( or dielectric function ). as a result, we can only directly manipulate the electric component of light with an appropriate optical device while we have no immediate handle on the corresponding magnetic component. one half of optics has been missing. artificial magnetism at optical frequencies photonic metamaterials open up a way to overcome this constraint. the basic idea is to create an artificial crystal with significantly sub - wavelength periods. analogous to an ordinary optical material, such a photonic metamaterial can approximately be treated as an effective medium characterized by effective material parameters ε ( ω ) and μ ( ω ). however, the proper design of the elementary building blocks ( or " artificial atoms " or " meta - atoms " ) of the photonic metamaterial allows for a non - vanishing magnetic response and even for μ < 0 at optical frequencies – despite the fact that the constituent materials of the photonic metamaterial are completely non - magnetic. negative refractive index … much of the early excitement in the field has been about achieving a negative index of refraction n < 0 by simultaneous ε < 0 and µ < 0 at near - infrared or even at visible frequencies. a negative refractive index means that the phase velocity of light is opposite to the electromagnetic energy flow ( the poynting vector ). this unusual situation has inspired fascinating ideas like the so - called " perfect lens ", which employs the fact that the optical path length between two spatially separate points can be made equal to zero, rendering the two points equivalent for the purpose of optics. … and beyond artificial magnetism is also a necessary prerequisite for obtaining strong optical activity and circular dichroism. these phenomena are based on magnetic dipoles excited by the electric component of the light field and vice versa. three - dimensional metal helices have been a corresponding paradigm building block in optical textbooks, but their nanofabrication has not been possible until quite recently. such gold - helix metamaterials can be applied as compact and broadband ( more than one octave ) circular


metal helices have been a corresponding paradigm building block in optical textbooks, but their nanofabrication has not been possible until quite recently. such gold - helix metamaterials can be applied as compact and broadband ( more than one octave ) circular polarizers - the circular analogue of the good old wire - grid linear polarizer ( already used by heinrich hertz in his pioneering experiments on electromagnetic waves in karlsruhe in 1887 ) and possibly a first down - to - earth application of the deceptively simple but far - reaching ideas of photonic metamaterials. transforming optical space further flexibility for achieving certain functions arises from intentionally spatially inhomogeneous optical metamaterials. such structures can be designed using the concepts of transformation optics, which is inspired by albert einstein ’ s theory of general relativity. in essence, distortions of actual space ( e. g., due to heavy masses ) can equivalently be mimicked by distortions of optical space, i. e., by tailoring the local index of refraction. invisibility cloaking structures have been a demanding benchmark example for the strength of transformation optics because invisibility cloaks would have been considered " impossible " just five years ago. today, direct laser writing has allowed for the first three - dimensional invisibility cloaking structures. lately, even visible operation frequencies have become accessible. a complete list of publications can be found here.


the gap at the desired arm position. the slotted optical switch operates in the same fashion as the infrared reflectance sensor, with the exception that a different value of pull - up resistor must be added externally for the particular model of optical switch we use. the modulated infrared light detector is a device that combines an infrared phototransistor with specialized signal processing circuitry to detect only light that is pulsing at a particular rate. the elec 201 kit includes the sharp gp1u52 sensor, which detects the presence of infrared light modulated ( pulsed ) at 40, 000 hz. normal room light, which is not modulated, does not effect the sensor, a big advantage. this type of sensor is used for the remote control function on televisions, vcrs, etc. in elec 201 this sensor is used to detect the specially modulated infrared light emitted by the beacon on the opponent robot. the software can distinguish different pulse patterns in order to distinguish between the beacons on the two robots. ( in a television remote, different pulse patterns would correspond to different functions, such a changing the channel up or down. ) the principles of operation and use are explained further in section 5. 8, which also discusses the circuit used to create the modulated infrared light for the beacon. an explanation of the software interface to the sharp sensors is given in section 10. 11. 2. the elec 201 kit contains both an analog sensor that provides information about the strength of the magnetic field and a digital sensor, a magnetic switch. a device called a hall effect sensor can be used to detect the presence and strength of magnetic fields. the hall effect sensors have an output voltage even when no magnetic field is present, and the output changes when a magnetic field is present, the direction of change depending on the polarity of the field. the digital magnetic sensors are simple switches that are open or closed. internally the switches have an arm made of magnetic material that is attracted to a magnet and moves to short out the switch contacts. these switches are commonly used as door and window position sensors in home security systems. the switch will close when it comes within 1 ' ' of its companion magnet. either sensor can be used to detect magnets or magnetic strips that may be present on the elec 201 game board table. with the magnets typically used on the game board, the hall effect sensor output voltage changes only a small amount when a field is present. the no - field voltage varies between sensors, but it is very stable for a particular sensor


to what some historians might consider outlandish neologisms. interest was developed in group dynamics, in the behavior of small groups, in mass psychology, in competition and cooperation, and in other forms of human behavior with which the historian must on occasion be concerned. the use of scientific analogies likewise continued. certain patterns of thought developed by the natural scientists had attracted or repelled social scientists and humanists since the days of isaac newton and john locke. within the memories of many of us, historians had been looking for law, for dynamic interpretation. edward p. cheyney developed a concept of law in history. henry adams professed to see in the physicists ' second law of thermodynamics the doom of man ' s intellect. others pondered over concepts of relativity, uncertainty, and the immaterial nature of matter. historians in some instances were no longer so confident that they could discover just how eigentlich things might have gewesen. during this period of fragmentation, however, the tradition of synthesis was by no means forgotten. there was a deliberate interest in continuing it and, incidentally, in arresting the chaotic influence of specialization and fragmentation upon the historian ' s capacity to generalize. various efforts were made in the early years of the twentieth century to restore the desire and the power to scan wider horizons. one of these was the use of a civilization concept such as employed in different ways by arnold toynbee, charles and mary beard, and later by william mcneill. another very significant instrument for this purpose was the culture concept borrowed not from scholars in belles - lettres, but adopted in broader terms from social anthropologists. as i have found this cultural concept one of the most useful aids available to historians in developing the synthesis, which is one of their main responsibilities, i propose to dwell upon some of its implications for members of this association. the term " culture " used in this sense is all - inclusive, embracing as it does all the behavior patterns employed by any given society. it also supplies the concept of a unity greater than even the sum of its definable parts. into such a synthesis can be fitted any specialized, any personal, or any national experience. each of us can relate his interest to any such concept of image, national character, or gestalt that appeals to the individual ' s sense of the all - embracing. viewing any specific problems in the light of such over - all interpretation supplies whatever each of us may do with a maximum of significance and interpretive meaning. there


, or gestalt that appeals to the individual ' s sense of the all - embracing. viewing any specific problems in the light of such over - all interpretation supplies whatever each of us may do with a maximum of significance and interpretive meaning. there are various types of cultural definitions, but one in particular can be especially useful : namely, i believe, the design most indicative of the nature and the identity of any society. this is its plan of operation, the force or influence that organizes it and keeps within it a semblance of recognizable structure and order. in highly complicated societies this plan takes the form of government, the customs of rule, of the exercise of authority, of the structure of power. a culture therefore may be known as a democracy, an empire, a totalitarian state. any such designation is not merely derived from constitutional institutions, but it embraces attitudes, ideas of community identification, and social as well as political relationships. the distinguishing characteristic of the society known as the united states of america is the fact that it is a democratic culture dedicated to a self - government in which all are technically involved and in which this interest is demonstrably central to the self - identification of the people. it can be used as the hallmark of the culture. this use is appropriate likewise because a basic, if not the basic, historical problem in this culture is how a society expanding so quickly in so large an area became and has remained self - governing. the study of this problem has involved me and many others in working out the process of the evolution and the operation of this culture and has also concentrated much interest on a particular phase of it, namely the stresses and strains that eventually led to the destructive social war of 1861 - 1865, which nearly destroyed it. this culture concept, which has dominated and determined the history of the united states, is broader and older than the boundaries of the united states would imply. it has involved consideration of the european origin of folkways and institutions. the proper definition of this broader field of analysis is the anglo - american culture, including much that evolved in the british isles and was transported to america. there it was transplanted and eventually matured in a new society. the employment of this very broad culture concept is extremely useful not only in overcoming the disadvantages of fragmentation but in quickening the capacity for synthesis. likewise, it has sharpened our understanding of historical process by giving greater opportunity for more sophisticated conceptualization of certain of our historical responsibilities. setting significant chronological limits to the study of the evolution of the anglo - american


minute a variety of alternatives might have taken over. in the end i feel that a series of accidents rather than destiny, or great forces, or any deus ex machina decided the issue. eventually, after bitter and expensive conflict, the republic righted itself - - but that was a century ago. this description of the concept of american self - governing culture, which we have used in our search to overcome fragmentation and to re - establish synthesis, and of the observable tendency to periodic resorts to violence to change our patterns of self - government, not only indicates an interesting paradox, but also gives us food for thought as we ponder certain problems which today ' s necessities call upon us to face and which we may illustrate by asking ourselves certain questions in this year of 1966. since that holiday season when channing asked his questions, nearly a half century ago, many more things have changed than the fashions of history writing about which we have just been thinking. many new conditions of life have appeared and have added much to the complexity of our task and thus to our responsibility. now wars seem never to end, and where there is no war there may be racial tension, for a world - wide reorientation of peoples is in process. the energy of the atom has been released ; population is exploding. time and space seem no longer to be limiting concepts ; man not only stands on the verge of outer space, but on occasions walks in its vastness. a mechanism is replacing the human brain in some forms of computation. we are told that the genetic code has been broken and that the universe has lost its parity and is lopsided. we are reminded that upon occasion when some basic irregularity, operating contrary to the accepted laws of the universe, has been discovered, such observation can be the prelude to significant new knowledge. a drift in the perihelion of the orbit of the planet mercury was eventually accounted for when the general theory of relativity was formulated. with all these aberrations and incongruities may we not be on the eve of certain discoveries in human knowledge? at any rate this wide variety of new circumstances carries us far away from the days of white and channing, and certainly into a period of new responsibility. in the light of this possible new experience we are justified in asking questions, even as channing asked them - - though they will be of a different nature. the main question that we raise is this : if we are on the verge or in the midst of certain basic changes, not only


volume 9, issue 2 tricks of the trade in and out download this issue learning about differential equations from their symmetries application of mathsym to analyzing an ordinary differential equation in the previous section we used a scaling symmetry to help understand the solutions of a pair of differential equations. in each case, the scaling symmetry was found by inspection. here i present the computation of the complete set of point symmetries for two additional differential equations. our third example is a nonlinear ordinary differential that we analyze using its two symmetries. the final example is the partial differential equation known as the cubic nonlinear schrodinger equation. example three is the ordinary differential equation that arises in the study of nonlinear water wave equations. i also show that we can use its two symmetries to begin to learn something about the structure of its solutions. mathsym returns a system of equations, the determining equations, whose solutions generate the symmetries of equation ( 8 ). internally, the mathsym package denotes all independent variables in an equation as and dependent variables as. this way it can be run on systems of equations with arbitrary numbers of independent and dependent variables without needing to know how to treat different variable names. furthermore, constants are represented as internally and printed as. with this notation, constants are treated correctly by mathematica ' s differentiation routine dt. mathsym ' s output is the following list of determining equations. with the output from mathsym we can continue our analysis of equation ( 8 ). first, we solve the determining equations : the functions and determine two symmetries that can be used to convert equation ( 8 ) into two integrals. the reader is directed to similar computations for the blasius boundary layer equation which appear on pages 118 - 120 of. we begin by considering the symmetry that occurs because of the term. setting and produces a transformation and. we next look for two quantities that do not change under this transformation. obvious choices are and. if we assume that is a function of and write the differential equation for that arises by insisting that satisfy equation ( 8 ), we find this is a standard reduction of order for autonomous equations that may be found in a sophomore differential equations text such as. this equation in and has a symmetry that is generated by the constant appearing in equations ( 9 ) and ( 10 ). from this symmetry we can derive new variables and and consider as a function of. in terms of and, equation ( 11 ) becomes we have now converted the problem of solving the original equation into


7. praxeological prediction praxeological knowledge makes it possible to predict with apodictic certainty the outcome of various modes of action. but, of course, such prediction can never imply anything regarding quantitative matters. quantitative problems are in the field of human action open [ p. 118 ] to no other elucidation than that by understanding. we can predict, as will be shown later, that? - - other things being equal? - - a fall in the demand for a will result in a drop in the price of a. but we cannot predict the extent of this drop. this question can be answered only by understanding. the fundamental deficiency implied in every quantitative approach to economic problems consists in the neglect of the fact that there are no constant relations between what are called economic dimensions. there is neither constancy nor continuity in the valuations and in the formation of exchange ratios between various commodities. every new datum brings about a reshuffling of the whole price structure. understanding, by trying to grasp what is going on in the minds of the men concerned, can approach the problem of forecasting future conditions. we may call its methods unsatisfactory and the positivists may arrogantly scorn it. but such arbitrary judgments must not and cannot obscure the fact that understanding is the only appropriate method of dealing with the uncertainty of future conditions. [ p. 119 ]


joined : 16 mar 2004 | posted : tue may 27, 2008 11 : 36 am post subject : assembly lines for nanotechnology. | 24 august 2007 rsc publishing - chemical technology nano production lines researchers in switzerland have built nanoscale cargo loading stations and shuttles, an important step towards assembly lines for nanotechnology. drawing of a nano conveyor belt biological assembly lines consist of kinesin proteins which carry cargo, like organelles or vesicles, and literally walk along microtubules. however, as far as man - made systems go, ' nothing comparable to a macroscopic assembly line exists at the nanoscale, ' according to viola vogel of the department of materials at the swiss federal institute of technology ( eth ) in zurich. ' imagine if you wanted to build a car by fabricating all of its components, putting them in a glass full of water and hoping that they would self - assemble spontaneously into the finished car. ' the challenge is to tune the interactions in the system so that the cargo remains stuck to the station when not needed, but can be picked up easily by the shuttle. as a test of principle, vogel and colleagues used gold nanoparticles coated in anti - biotin antibodies as cargo, and compared loading stations made of biotin - tipped dna with biotin - tipped polyethylene glycol. biotinylated microtubules, powered by kinesin motors, act as shuttles rather than conveyor belts, as they do in cells. vogel and team then tracked the fate of the gold nanoparticles with scanning electron microscopy. they found that the shuttles did indeed pick up the nanoparticles and that they held on to them, with a loss rate of about 28 % over 12 minutes. they also found that dna stations are more effective than polymer ones. ' future challenges will be to combine the main components of a transport system : pick - up of cargo from defined locations, guided transport, and controlled discharge of the load at the final destination, ' commented vogel. she went on to caution : ' the problems are always in the details of working through the engineering challenges of interfacing biological molecules with synthetic devices. ' story posted : 24th august 2007


quarks are completely confined within protons and neutrons : a phenomenon that we do not completely understand. the artist ' s view below represents the two interlinked phenomena that drive confinement : the long - range correlations in the physical vacuum that surround the proton and excludes the color - field emanating from quarks and the extremely strong gluon - fields between the quarks. to make progress on confinement we need to separate these two effects and study each individually. one way to do this is to make a much larger system of quarks and gluons where the role of the vacuum at the surface of the larger system is much reduced. such a large system can be produced by compressing or heating nuclear matter so that the neutrons and protons begin to overlap. as the boundaries between each neutron and proton disappear, a large volume of a new state of matter should be formed - the quark gluon plasma ( qgp ). the strong interactions between quarks and gluons dominate the properties of the qgp, and because of the larger volume of the system, the influence of the correlated vacuum is much reduced. collisions between two heavy nuclei take place at relativistic heavy ion collider ( rhic ). our first results from phenix indicate that the plasma may be formed in these reactions. leading the evidence for the qgp is the reduced yield of particles at high transverse momenta ( pt ). these particles predominantly come from rare, high - momentum collisions between quarks and gluons ( partons ) that occur in the hot, early stage of the reaction. as high momentum partons travel through the forming plasma, they are predicted to lose a considerable fraction of their energy. outside the collision zone high - momentum partons fragment into hadrons, and any energy - loss in the plasma softens the hadronic spectrum, i. e. lowers the measured yield of hadrons at high - pt. the first high - pt spectra from au + au collisions measured by phenix at rhic were published in 2001 with the key observation that the high - pt spectra are softer in central than in peripheral collisions. because a central reaction would produce a larger volume of qgp, this result is consistent with the hard - scattered parton losing energy in a qgp. the overall caution remains that a heavy - ion reaction is a very complex, challenging environment. a strong case for the existence and properties of the qgp must rely on a broad range of


in a synthetic chemical soup thomas latimer ’ s unfortunate experience what ’ s in the synthetic chemical soup? synthetic flows and assumptions the flow of information about synthetic flows you cannot do just one thing : two examples mathematics : food, soil, water, air, free speech the " hour glass " industrial agriculture machine industrial agriculture logic vs. the logic of life fast foods, few foods, and fossil fuels genetic engineering : one mathematical perspective toxic sludge is good for you! oceans : rising acidity and disappearing life stocks, flows and distributions of food my definition of food choices : central vs. diverse decision making mathematics and energy how much solar energy is there? solar energy is there, do we know how to get it? nuclear power : is it too cheap to meter? net primary productivity and ecological footprints npp, soil, biofuels, and the super grid the brower – cousteau model of the earth how heavily do we weigh upon the earth? mining and damming : massive rearrangements fish, forests, deserts, and soil : revisited the cousteau – brower earth model fuzzy logic, sharp logic, frames, and bigger pictures sharp ( aristotelian ) logic : a standard syllogism measuring truth values : fuzzy / measured logic definitions, assumptions and the frame of debate humans in denial — nature cannot be fooled — gravity exists the bigger picture principle the dunbar number the sustainability hypothesis : is it true? the dunbar number public relations, political power, and the organization of society political uses of fear confronting fear ( and apathy ) : organizing your community for self - preservation and sustainability math and nature : the nature of math one pattern viewed via geometry and numbers : mathese the square numbers of pythagoras the language of mathematics : mathese a general expression in mathese : a formula for odd numbers an important word in mathese : σ sentences in mathese : equations with σ and a dummy variable induction, deduction, mathematical research, and mathematical proofs what is a mathematical proof? what is a deductive system? originalidad es volver al origen axioms and atoms molecules and atoms ; the atomic number and the atomic mass number of an atom scaling and our first two axioms for numbers our first axiom for numbers number 1 : its definition, properties, uniqueness the definition of multiplicative inverse our second axiom for numbers if …, then …. our first proofs return to the problem : how many protons in one gram of protons? what is a mole?


definition, properties, uniqueness the definition of multiplicative inverse our second axiom for numbers if …, then …. our first proofs return to the problem : how many protons in one gram of protons? what is a mole? scaling up from the atomic to the human scale five more axioms for numbers associativity, identity, and inverses for + commutativity of + and * what patterns can be deduced in our deductive system? playing the mathematics game rules for playing the mathematics game the usual rules for fractions are part of our deductive system can you tell the difference between true and false patterns? one of the oldest mathematical patterns a short story and some numberless mathematics relations defined as collections of ordered pairs transitive and reflexive relations relations that are functions a set of social rules for the warlpiri people the section rule the mother relation rules the marriage rules the father relation rules cultural contexts in which mathematics is done counting social security numbers among other things permutations : order matters there are n! permutations of n distinct objects counting connections : order does not matter equivalence relations and counting using equivalence relations to count combinations : order does not matter additional counting problems box models : population, money, recycling some population numbers counting people in the world a fundamental axiom of population ecology counting people in the united states basic mathematical patterns in population growth schwartz charts are box - flow models our first population model : simple boxes and flows three basic operations : addition, multiplication, and exponentiation defining logarithm functions computing formulas for doubling times logarithms to any base further study : more complicated models and chaos theory the world ’ s human population : one box box models : money, recycling, epidemics some obvious laws humans continue to ignore a linear multiplier effect : some mathematics of money multiplier effects arising from cycles : the mathematics of recycling a simple model of an influenza epidemic chance : health, surveillance, spies, and voting chance : health and news if you test hiv positive, are you infected? chance and the " news surveillance, spies, snitches, loss of privacy, and life is someone watching you? why? living with a police escort? i ’ m not worried, i ’ ve done nothing wrong identity theft, encryption, torture, planespotting encryption mathematics and identity protection extraordinary rendition = kidnapping and torture planespotting : a self - organizing countermeasure the cia did not anticipate bigger pictures and the cia voting in the 21st century stealing elections is


encryption, torture, planespotting encryption mathematics and identity protection extraordinary rendition = kidnapping and torture planespotting : a self - organizing countermeasure the cia did not anticipate bigger pictures and the cia voting in the 21st century stealing elections is a time honored tradition a simple solution exists two modest proposals what exactly is economics? it takes the longest time to think of the simplest things a preview of two laws of nature three kinds of economists the human economy depends on nature ’ s flows of energy and entropy nature ’ s services and human wealth : important calculations how we treat each other : how we treat nature — the tragedy of the commons mathematical concepts and economics new mathematical patterns : self - organizing systems finding a niche : habits and habitats the concept of money financial wealth and real wealth is financial collapse possible now? follow the money are you paying more or less than your fair share of taxes? financial growth vs. fish growth fractional reserve banking : an amazing mathematical trick distributed vs. centralized control and decision making farms : to be run by few or by many? utilities : muni or investor - owned? linux vs. microsoft medicine for people or for profit or both? a little history an example of the need for fuzzy logic : the definition of poverty energy and thermodynamics energy and the first law of thermodynamics the first law of thermodynamics entropy and the second law of thermodynamics early statements of the second law of thermodynamics algebraic statement of the second law of thermodynamics so what is entropy and can we measure it? some applications of the second law of thermodynamics : power plants and hurricanes hiking up a mountain understanding entropy with a little mathematics the financial mathematics of loans, debts, and compound interest simple and compound interest : a review how much does a debt really cost you? buying on time and / or installment plans. amortization. the four important numbers : p, r, r, n examples of individual debt : rent - to - own, credit cards, and loans information flow in the 21st century investigative journalism requires cash thesis : the range of debate is too narrow now time series test and multiple source test measuring the range of debate distractions and illusions media literacy : censorship and propaganda filters and censors censorship : external and internal conclusion and epilog : where are the adults? martin walter is a professor in the department of mathematics at the university of colorado at boulder. dr. walter is a sloan, woodrow wilson, and national science foundation fellow


right now, the accelerator is stopped for the annual maintenance shutdown. this is the opportunity to fix all problems that occurred during the past year both on the accelerator and the experiments. the detectors are opened and all accessible malfunctioning equipment is being repaired or replaced. in the 27 - km long lhc tunnel, surveyors are busy getting everything realigned to a high precision, while various repairs and maintenance operations are on their way. by early march, all magnets will have been cooled down again and prepared for operation. the experimentalists are not only working on their detectors but also improving all aspects of their software : the detector simulations, event reconstruction algorithms, particle identification schemes and analysis techniques are all being revised. by late march, the lhc will resume colliding protons with the goal of delivering about 16 inverse femtobarns of data, compared to 5 inverse femtobarns in 2011. this will enable the experiments to improve the precision of all measurements achieved so far, push all searches for new phenomena slightly further and explore areas not yet tackled. the hope is to discover particles associated with new physics revealing the existence of new phenomena. the cms and atlas physicists are looking for dozens of hypothetical particles, the higgs boson being the most publicized but only one of many. when protons collide in the lhc accelerator, the energy released materializes in the form of massive but unstable particles. this is a consequence of the well - known equation e = mc2, which simply states that energy ( represented by e ) and mass ( m ) are equivalent, each one can change into the other. the symbol c2 represents the speed of light squared and acts like a conversion factor. this is why in particle physics we measure particle masses in units of energy like gev ( giga electronvolt ) or tev ( tera electronvolt ). one electronvolt is the energy acquired by an electron through a potential difference of one volt. it is therefore easier to create lighter particles since less energy is required. over the past few decades, we have already observed the lighter particles countless times in various experiments. so we know fairly well how many events containing them we should observe. we can tell when new particles are created when we see more events of a certain topology than what we expect from those well - known phenomena, which we refer to as the background. we can claim that something additional and new is also occurring when we see an excess of events. of course, the bigger the excess, the easier


certain topology than what we expect from those well - known phenomena, which we refer to as the background. we can claim that something additional and new is also occurring when we see an excess of events. of course, the bigger the excess, the easier it is to claim something new is happening. this is the reason why we accumulate so many events, each one being a snap - shots of the debris coming out of a proton - proton collisions. we want to be sure the excess cannot be due to some random fluctuation. some of the particles we are looking for are expected to have a mass in the order of a few hundred gev. this is the case for the higgs boson and we already saw possible signs of its presence last year. if the observed excess continues to grow as we collect more data in 2012, it will be enough to claim the higgs boson discovery beyond any doubt in 2012 or rule it out forever. other hypothetical particles may have masses as large as a few thousand gev or equivalently, a few tev. in 2011, the accelerator provided 7 tev of energy at the collision point. the more energy the accelerator has, the higher the reach in masses, just like one cannot buy a 7000 chf car with 5000 chf. so to create a pair of particles with a mass of 3. 5 tev ( or 3500 gev ), one needs to provide at least 7 tev to produce them. but since some of the energy is shared among many particles, the effective limit is lower than the accelerator energy. there are ongoing discussions right now to decide if the lhc will be operating at 8 tev this year instead of 7 tev as in 2011. the decision will be made in early february. if cern decides to operate at 8 tev, the chances of finding very heavy particles will slightly increase, thanks to the extra energy available. this will be the case for searches for particles like the w ’ or z ’, a heavier version of the well - known w and z bosons. for these, collecting more data in 2012 will probably not be enough to push the current limits much farther. we will need to wait until the lhc reaches full energy at 13 or 14 tev in 2015 to push these searches higher than in 2011 where limits have already been placed around 1 tev. for lhcb and alice, the main goal is not to find new particles. lhcb aims at making extremely precise measurements to see if there are any weak points in


july 17, 1998 july 15, 1998 : a unique levitation furnace that flew on the space shuttle in 1998 is being eyed for upgrades to fly on future shuttle and international space station missions. " tempus on msl - 1 provided it was operationally reliable, " said dr. ivan egry, the project scientist at the german space agency ( dlr ). " i am really surprised at how much scientific data we are still squeezing out of it. " egry spoke tuesday morning to the third biennial microgravity materials science conference sponsored by nasa. tempus - built by the dlr and used jointly by dlr and nasa - is the german acronym for containerless electromagnetic processing in weightlessness. that, simply put, is what tempus does. an electromagnetic coil inside the tempus facility positions metal samples with about 1 / 1, 000th the force needed on the ground to work against gravity and keep the samples from touching the container walls. a second coil pumps in radio wave energy - a bit like a microwave oven - to melt the sample. this approach is vital in a number of research areas because touching the container walls will instantly cool the sample and levitation on the ground often involve forces great enough to disturb the sample. scientist don ' t want either to happen when they are trying to make precise measurements of fundamental properties that can help them refine manufacturing processes on earth. tempus flew on the microgravity sciences laboratory - 1 mission in 1998, and on the second international microgravity laboratory ( iml - 2 ) in 1994. data are still being analyzed, but egry gave a preview tuesday, including benchmark data that will let scientists correct the surface tension measurements for one type of metal, and make the first - ever reliable viscosity measurements. " many things were surprising, " egry said when asked about the data from tempus. among them were the first experimental measurements of the electrical conductivity of cobalt - palladium in both its liquid and solid states. tempus demonstrated its value by making repeat measurements that matched very closely with one another. consistency is crucial when one is trying to establish basic physical properties. for example, one line of experiments involved cooling metals, such as zirconium, far below their normal freezing point and then recording the point where they froze, how much heat they gave off, and other details. the zirconium sample was put through 120 melt / freeze cycles. " it ' s really amazing to see how


learn something new every day more info... by email dark energy is a very sparse, uniform negative pressure that permeates the entire observable universe. it accounts for 70 % of the mass / energy in the universe and is responsible for its accelerating rate of expansion. dark energy is unlike the energy we are familiar with because it is not concentrated locally, as is the case with stars and galaxies, manifestations of conventional matter and energy. there are many other important differences between conventional energy and dark energy, which physicists continue to investigate. the exact form or mechanism of operation of dark energy is unknown. in this respect, it is similar to its cousin, dark matter, which can only be observed by the influence it has on normal matter and energy. there are two major theories for the form of dark energy, although one is more prominent than the other. the first theory, quintessence, describes the dark energy as a fluctuating field that changes its intensity based on location. the second theory, that of a cosmological constant, describes dark energy as constant and uniform. it is this second theory that is believed by most physicists and forms the basis of the lambda - cdm model, the prevailing model of the structure of the cosmos. the negative pressure of the cosmological constant is thought to originate from vacuum fluctuations at extremely small scales in all space. so - called virtual particles are continuously created and destroyed in this vacuum, creating a quantum foam that itself has energy. the existence of dark energy has implications for the ultimate fate of the universe. if dark energy is an intrinsic property of space, as it looks to be, then it will continue to be exist indefinitely. if dark energy is the cause of the universe ’ s accelerating expansion, then it will also be the cause of reducing the average density of any parcel of space in the long run. as the universe grows more and more sparse, it will also grow more cold and hostile to life. therefore, dark energy can justifiably be blamed for bringing on the “ heat death ” of the universe. is europe using some type of dark energy device to power the earth?? my dad read it to me from a news paper. i just could not find anything about it