diff --git "a/data/train/batch_000058.jsonl" "b/data/train/batch_000058.jsonl" new file mode 100644--- /dev/null +++ "b/data/train/batch_000058.jsonl" @@ -0,0 +1,38 @@ +{"text": "dimensional \u201d including quantum field and string theories. the state - space of quantum mechanics is an infinite - dimensional function space. \u201d \u2013 dimension, wikipedia this use of the term \u201c dimension \u201d should not be confused with the science fiction concept of a \u201c parallel universe \u201d. again to quote wikipedia on the term \u201c dimension \u201d, \u201c science fiction texts often mention the concept of dimension, when really referring to parallel universes, alternate universes, or other planes of existence. this usage is derived from the idea that to travel to parallel / alternate universes / planes of existence one must travel in a direction / dimension besides the standard ones. in effect, the other universes / planes are just a small distance away from our own, but the distance is in a fourth ( or higher ) spatial ( or non - spatial ) dimension, not the standard ones. \u201d the \u201c parallel universe \u201d concept in science fiction actually is very different from the use of the term \u201c dimension \u201d in science, as you can see above. in theory, a \u201c parallel universe \u201d would also have 3 spatial dimensions ( length, width, height ) and a time dimension. that means a \u201c parallel universe \u201d in theory actually has 4 dimensions of its own. additionally the assumption is that there is a 5thdimension to our universe which would be used to allow travel to the parallel world, which has its own 4 dimensions. it would not be accurate to say a \u201c parallel universe \u201d uses the same 4 dimensions that our universe has, because by definition a \u201c universe \u201d is everything that is. so a \u201c parallel universe \u201d would have to have its own construct of dimensions which define its reality and cosmological structure, and not just borrow use of the dimensions inherit in our own universe. this is of course all fictional theories that come from science fiction, which has nothing to do with actual science. and i want to clarify this, as any statement that science has straight theories on \u201c other dimensions \u201d does not have anything to do with the science fiction concept of \u201c parallel universes \u201d. if science were to find some evidence of observation of a \u201c 5th dimension \u201d inherent in our universe, this has nothing to do with a \u201c parallel universe \u201d. the term \u201c dimension \u201d is a science term first, and has been misleadingly borrowed by science fiction in such a way that its meaning is construed. the bible teaches that \u201c in the beginning \u201d god made the \u201c heavens and the earth \u201d, and that at the end of the 6th day god \u201c saw every thing that he had", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6445400068072209, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 2, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.638794"} +{"text": "single brane and the extra dimensions went on forever, as in the randall - sundrum model, gravitational waves could escape altogether and carry away energy from our brane world. this would seem to breach one of the fundamental principles of physics : the law of conservation of energy. the total amount of energy remains the same. however, it appears to be a violation only because our view of what is happening is restricted to the brane. an angel who could see the extra dimensions would know that the energy was the same, just more spread out. \u201d - stephen hawking phd, the universe in a nutshell, pgs. 184 - 192 while giving credence to randall \u2019 s statement, basically hawking says that very large extra - dimensions are possible, and would not violate the known laws of physics. in fact, their existence might help explain some rather large befuddling questions in science that are still unanswered, such as missing mass. as such, science allows for the existence of an invisible spiritual realm, potentially one in which angels are, and the spirit bodies of angels could be composed of the stuff of this extra dimension, this invisible realm. the branch of physics called quantum mechanics deals with particles which are subatomic ( that is smaller than an atom ). quantum mechanics has been well - established through scientific experimentation. unlike string theory, quantum mechanics is a field of practical experimentation. it is in quantum physics that we find the heisenberg uncertainty principle : in quantum physics, the heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. that is, the more precisely one property is known, the less precisely the other can be known. it is impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty. this is not a statement about the limitations of a researcher \u2019 s ability to measure particular quantities of a system, but rather about the nature of the system itself and hence it expresses a property of the universe. - wikipedia, uncertainty principle this basically means that on a subatomic level, that of electrons, quarks, photons, etc., there seems to be a fundamental principal of randomness. particles go where they seem to want to go. particles almost seem to choose what they are doing. however, these choices do form an overall pattern, of statistically calculable probabilities. one of the most well - known and respectable scientists in recent history, instrumental in the development of", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6591252698834722, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 11, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.648255"} +{"text": ". particles almost seem to choose what they are doing. however, these choices do form an overall pattern, of statistically calculable probabilities. one of the most well - known and respectable scientists in recent history, instrumental in the development of quantum mechanics, was richard feynman phd. he worked on the manhattan project developing the atomic bomb, was a recipient of the nobel prize in physics, and is also known for demonstrating the o - ring defects resulting in the space shuttle challenger tragedy. to quote richard feynman phd on the uncertainty principle in quantum mechanics : one might still like to ask : \u201c how does it work? what is the machinery behind the law? \u201d no one has found any machinery behind the law. no one can \u201c explain \u201d any more than we have just \u201c explained. \u201d no one will give you any deeper representation of the situation. we have no ideas about a more basic mechanism from which these results can be deduced. we would like to emphasize a very important difference between classical and quantum mechanics. we have been talking about the probability that an electron will arrive in a given circumstance. we have implied that in our experimental arrangement ( or even in the best possible one ) it would be impossible to predict exactly what would happen. we can only predict the odds! this would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. yes! physics has given up. we do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible \u2014 that the only thing that can be predicted is the probability of different events. it must be recognized that this is a retrenchment in our earlier ideal of understanding nature. it may be a backward step but no one has found a way to avoid it. no one has figured a way out of this puzzle. so at the present time we must limit ourselves to computing probabilities. we say \u201c at the present time, \u201d but we suspect very strongly that it is something that will be with us forever \u2014 that it is impossible to beat that puzzle \u2014 that this is the way nature really is. - richard p. feynman, phd, the feynman lectures on physics, vol. 3, pgs. 1 - 10, 1 - 11 so why is it that at the scale of the tiniest parts of the universe, that there is all this randomness? why has science given up on precise predictability, and accepted that", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6930395751150515, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 12, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.651209"} +{"text": "3, pgs. 1 - 10, 1 - 11 so why is it that at the scale of the tiniest parts of the universe, that there is all this randomness? why has science given up on precise predictability, and accepted that uncertainty and chance rule the microscopic domain of the most basic and fundamental building blocks of the universe? why can only probabilities be known? with the advent of quantum mechanics, we have come to recognize that events cannot be predicted with complete accuracy but that there is always a degree of uncertainty. if one likes, one could ascribe this randomness to the intervention of god, but it would be a very strange kind of intervention : there is no evidence that it is directed toward any purpose. indeed, if it were, it would by definition not be random. in modern times, we have effectively removed the third possibility above by redefining the goal of science : our aim is to formulate a set of laws that enables us to predict events only up to the limit set by the uncertainty principle. - stephen hawking phd, the illustrated brief history of time, pg 224 there is always an element of uncertainty or chance, and this affects the behavior of matter on a small scale in a fundamental way. einstein was almost singlehandedly responsible for general relativity, and he played an important part in the development of quantum mechanics. his feelings about the matter are summed up in the phrase \u201c god does not play dice. \u201d but all the evidence indicates that god is an inveterate gambler and that he throws the dice on every possible occasion. - stephen hawking phd, black holes and baby universes, pg. 70 regarding quantum physics, einstein said that \u201c god does not play dice \u201d, and stephen hawking says, \u201c god throws the dice on every possible occasion \u201d. but what does the bible say on the topic of dice and god? prov 16 : 33 we may throw the dice, but the lord determines how they fall. assuming that whether it is us or the universe that throws the dice, it makes no difference, then what the bible indicates is that god set up the universe to \u201c play dice \u201d on a quantum level, but at the same time, god is the one that determines how those \u201c quantum dice \u201d fall. by \u201c quantum dice \u201d i am referring to all of the subatomic particles / energies and their activities on the microscopic scale of the quantum level. however, if the uncertainty principle of quantum physics is correct, then the bible assures us that", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6026212659275112, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 13, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.653331"} +{"text": ". by \u201c quantum dice \u201d i am referring to all of the subatomic particles / energies and their activities on the microscopic scale of the quantum level. however, if the uncertainty principle of quantum physics is correct, then the bible assures us that god still sets the rules and outcomes for the seeming \u201c randomness \u201d of the \u201c quantum dice \u201d. god is in control of the randomness and the probabilities that we see. some christians who are scientists speak on this very issue : john byl has a phd in astronomy, is the author of the book \u201c god and cosmos : a christian view of time, space, and the universe \u201d, and is professor of mathematics and head of the department of mathematical sciences at trinity western university. \u201c w. g. pollard and, more recently, nancey murphy advocate that the apparently random events at the quantum level are all specific, intentional acts of god. god \u2019 s action at this level is limited in that ( 1 ) he respects the integrity of the entities with which he co - operates ( e. g., he doesn \u2019 t change the electron \u2019 s mass arbitrarily ) and ( 2 ) he restricts his action to produce a world that, for all we can tell, is orderly and law - like. god is the hidden variable. murphy asserts that this position is not only theologically preferable to indeterminism, but has the further advantage of consistency with the principle of sufficient reason. of course, if god is directly responsible for quantum events this entails that these are therefore predictable by god. hence we are left with a deterministic universe, at least at the quantum level. \u201d \u201c god \u2019 s sovereignty rules out the possibility of agents acting independently of him. in particular, quantum mechanics does not imply ontological indeterminism, given that determinist interpretations of quantum mechanics are possible, that non - physical secondary causes cannot be ruled out and that god is the primary cause for all events. \u201d - john byl phd, \u201c indeterminacy, divine action and human freedom \u201d william pollard phd, is a nuclear physicist and episcopal priest, with a phd in physics and honorary doctorates in science, divinity, law, and humane letters. he is the author of \u201c chance and providence : god \u2019 s action in a world governed by scientific law \u201d. the entire book is on god operating, instead of \u201c chance \u201d, in quantum mechanics. \u201c in the next chapter i will begin the presentation for your consideration of a quite different approach", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6099840109075748, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 14, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.656157"} +{"text": ": god \u2019 s action in a world governed by scientific law \u201d. the entire book is on god operating, instead of \u201c chance \u201d, in quantum mechanics. \u201c in the next chapter i will begin the presentation for your consideration of a quite different approach to this problem which seems to me to offer an entirely adequate solution for it. under it, as we shall attempt to show, there can emerge again in all of its ancient power the fullness of the biblical response to the living god who is ever active in the whole of his creation sustaining, providing, judging, and redeeming all things, both in heaven and in earth, in accordance with the mysterious and hidden purposes of his might will. at the same time, however, this is accomplished in such a way that the essential integrity and unity of science, both as it is now and as in principle it may become, is fully preserved. \u201d \u201c to einstein \u2019 s famous question expressing his abhorrence of quantum mechanics, \u201c does god throw dice? \u201d the judeo - christian answer is not, as so many have wrongly supposed, a denial, but a very positive affirmative. for only in a world in which the laws of nature govern events in accordance with the casting of dice can a biblical view of a world whose history is responsive to god \u2019 s will prevail. \u201d - william pollard phd, \u201c chance and providence : god \u2019 s action in a world governed by scientific law \u201d, pg. 35, pg. 97 nancey murphy phd, theologian, is professor of christian philosophy at the fuller theological seminary. she also serves as an editorial advisor for theology and science, theology today, and christianity today. she is the author of \u201c divine action in the natural order \u201d. \u201c the second strategy for giving an account of the locus of divine action explores quantum physics and seeks to give an account of god \u2019 s action throughout the natural and human world by means of action at the quantum level ( either alone or in conjunction with top - down action ). my proposal is motivated theologically. if god is immanent in and acting in all creatures, then necessarily god is acting at the quantum level. emphasis on this fact has the advantage of sidestepping the problem of interventionism : the laws of quantum mechanics are only statistical and therefore not subject to violation. if, as most interpreters conclude, events at this level are genuinely indeterminate, then there need be no competition between divine action and physical causation. it is possible from a theistic perspective to interpret current", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6222431608613342, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 15, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.657682"} +{"text": "therefore not subject to violation. if, as most interpreters conclude, events at this level are genuinely indeterminate, then there need be no competition between divine action and physical causation. it is possible from a theistic perspective to interpret current physics as saying that the natural world is intrinsically incomplete and open to divine action at its most basic level. \u201d - nancey murphy phd, dive action in the natural order, pg. 131 in other words, god is in control and constantly interacting with the world at a quantum level. where scientists see randomness and probabilities, they are seeing god determine how the dice fall, all the time, in quantum mechanics. the bible may also present an argument of god controlling the \u201c quantum dice \u201d in col 1 : 16 - 17, referring to jesus christ, \u201c for by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether [ they be ] thrones, or dominions, or principalities, or powers : all things were created by him, and for him : and he is before all things, and by him all things consist. \u201d the word here for \u201c consist \u201d is \u201c synistemi \u201d ( 4921 ) and it means, \u201c to consist of or be composed of, to cohere, put together, hold together or band together \u201d. according to subatomic physics, it is the quantum force particles of bosons, and gluons that hold together atoms, and particles like photons and electrons that hold together different atoms. as such, this verse in the bible could be referring to, that it is by god \u2019 s control over the \u201c quantum dice \u201d that makes these particles we are composed of to hold together. as such, by his actions all things hold together or \u201c by him all things consist \u201d. assuming it is true that god does allow randomness at a quantum level of physics, but also constantly controls the outcome of that randomness, besides \u201c upholding all things \u201d, like the universe, \u201c by the word of his power \u201d ( heb 1 : 3 ), is there another possible reason for god creating the universe to be this way? could it relate to miracles, signs and wonders? this could very well be the case. not only does quantum physics allow for existing particles that we can observe in experiment to act in random ways, but it also allows for particles and antiparticles ( antimatter ) to pop in and out of existence, seemingly randomly.", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.645364214747143, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 16, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.658912"} +{"text": "case. not only does quantum physics allow for existing particles that we can observe in experiment to act in random ways, but it also allows for particles and antiparticles ( antimatter ) to pop in and out of existence, seemingly randomly. these particles usually only exist for a very short time, and are called \u201c virtual particles \u201d. \u201c down at the very tiniest length scale and trillions of times smaller than atoms, is what is known as the planck scale where the concept of length loses its meaning and quantum uncertainty rules. at this level all known laws of physics break down and even space and time become nebulous concepts. any and all conceivable distortions of spacetime will be popping in and out of existence in a random and chaotic dance which is going on all the time everywhere in the universe. terms such as \u201c quantum fluctuations \u201d and the \u201c quantum foam \u201d which are used to describe this chaotic activity certainly do not do it justice. \u201d - jim al - khalili phd, black holes, wormholes, and time machines, pg. 207 phd in theoretical nuclear physics, theoretical physicist at the university of surrey the existence of these seemingly random particles does not violate the laws of physics, especially the law of conservation of energy : \u201c where did all these particles come from? the answer is that relativity and quantum mechanics allow matter to be created out of energy in the form of particle / antiparticle pairs. and where did the energy come from to create this matter? the answer is that it was borrowed from the gravitational energy of the universe. the universe has an enormous debt of negative gravitational energy, which exactly balances the positive energy of the matter. \u201d - stephen hawking, phd, black holes and baby universes, pg. 97 virtual particles have been shown, through experiments, to exist, as seen in the lamb shift and the casimir effect. \u201c these particles are called virtual because, unlike \u201c real \u201d particles, they cannot be observed directly with a particle detector. their indirect effects can nonetheless be measured, and their existence has been confirmed by a small shift ( the \u201c lamb shift \u201d ) they produce in the spectrum of light from excited hydrogen atoms. \u201d - stephen hawking phd, black holes and baby universes, pg 107 regarding the casimir effect, \u201c as we saw in chapter 7, even what we think of as \u201c empty \u201d space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and come back together and annihilate each other.", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6796703178723833, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 17, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.660133"} +{"text": ", \u201c as we saw in chapter 7, even what we think of as \u201c empty \u201d space is filled with pairs of virtual particles and antiparticles that appear together, move apart, and come back together and annihilate each other. now, suppose one has two metal plates a short distance apart. the plates will act like mirrors for the virtual photons or particles of light. in fact they will form a cavity between them, a bit like an organ pipe that will resonate only at certain notes. this means that virtual photons can occur in the space between the plates only if their wavelengths ( the distance between the crest of one wave and the next ) fit a whole number of times into the gap between the plates. if the width of a cavity is a whole number of wavelengths plus a fraction of a wavelength, then after some reflections backward and forward between the plates, the crests of one wave with coincide with the troughs of another and the waves will cancel out. because the virtual photons between the plates can have only the resonant wavelengths, there will be slightly fewer of them than in the region outside the plates where virtual photons can have any wavelength. thus there will be slightly fewer virtual photons hitting the inside surfaces of the plates than the outside surfaces. one would therefore expect a force on the plates, pushing them toward each other. this force has actually been detected and has the predicted value. thus we have experimental evidence that virtual particles exist and have real effects. \u201d - stephen hawking phd, the illustrated brief history of time, pgs. 204 - 206 virtual particles can include all types of particles, including photons, electrons, gluons, bosons, and quarks. according to physicists, under certain conditions in the universe, virtual particles can exist for longer periods of time and therefore become \u201c real \u201d particles. this particular example relates to conditions of space near a black hole, but in principle this shows that science does generally allow for the possibility of virtual particles popping into existence and becoming real particles. \u201c we can understand this in the following way : what we think of as \u201c empty \u201d space cannot be completely empty because that would mean that all the fields, such as the gravitational and electromagnetic fields, would have to be exactly zero. however, the value of a field and its rate of change with time are like the position and velocity of a particle : the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one can know the other. so in", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.688921143852423, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 18, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.661262"} +{"text": "however, the value of a field and its rate of change with time are like the position and velocity of a particle : the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one can know the other. so in empty space the field cannot be fixed at exactly zero, because then it would have both a precise value ( zero ) and a precise rate of change ( also zero ). there must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field. one can think of these fluctuations as pairs of particle of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other. these particles are virtual particles like carry the gravitational force of the sun : unlike real particles, they cannot be observed directly with a particle detector. however, their indirect effects, such as small changes in the electron orbits in atoms, can be measured and agree with the theoretical predictions to a remarkable degree of accuracy. the uncertainty principle also predicts that there will be similar virtual pairs of matter particles, such as electrons or quarks. in this case, however, one member of the pair will be a particle, and the other an antiparticle ( the antiparticles of light and gravity are the same as the particles ). because energy cannot be created out of nothing, one of the partners in a particle / antiparticle pair will have positive energy, and the other partner negative energy. the one with negative energy is condemned to be a short - lived virtual particle because real particles always have positive energy in normal situations. it must therefore seek out its partner and annihilate with it. however, a real particle close to a massive body has less energy than if it were far away, because it would take energy to lift it far away against the gravitational attraction of the body. normally, the energy of the particle is still positive, but the gravitational field inside a black hole is so strong that even a real particle can have negative energy there. it is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle or antiparticle. in this case it no longer has to annihilate with its partner. its forsaken partner may fall into the black hole as well. or, having positive energy, it might also escape from the vicinity of the black hole as a real particle or antiparticle. to an observer", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6639049277119236, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 19, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.662529"} +{"text": "a little ; if it happens twice in a row, i shift even more. if it happens three times in a row, i shift even more. \" an optimal learning strategy? using the same set of data, shams and wozny published in the aug. 5, 2010, issue of the journal plos computational biology a computational model that allows them to analyze why subjects perceive the sounds and sights in a particular way and what computations occur in their brains when they hear the sounds and see flashes. ( ulrik beierholm, a former ucla graduate student of shams, who is currently a postdoctoral fellow at university college london ' s gatsby computational neuroscience unit, was a co - author. ) \" by analyzing the data using three models, we can determine which model best explains the data and can characterize the strategy the subjects ' brains use to make perceptual decisions, shams said. determining the locations of sights and sounds is a basic brain function, and scientists assume that such functions are performed optimally because they have been refined over millions of years of evolution, shams said. because this is a basic task, neuroscientists would expect almost all brains to perform it in the same way. \" surprisingly, we found the perceptual task is not performed uniformly across subjects. different people use different strategies to perform this task, \" shams said. \" secondly, the vast majority of people, at least 75 percent, use a strategy that is considered seriously sub - optimal. \" what is this sub - optimal strategy? by way of analogy, shams says, if there is a 70 percent chance of rain, you would be wise to take an umbrella with you. \" what we found is that instead of people taking the umbrella every time there is, say, a 70 percent chance of rain, so to speak, they match the probability : they take the umbrella only 70 percent of the time, \" she said. when subjects were presented with a noise and a flash and were asked where they perceived the noise and flash to be coming from, their brains had to figure out whether the sound and flash were coming from the same location or from different locations. \" if they infer there is a 70 percent chance that the sound and flash are coming from the same object, for the majority of observers, 70 percent of the time they go with that estimate and 30 percent of the time they go with the unlikely estimate, \" shams said. \" under conventional measures of optimality, which implicitly assume", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.61158441546646, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 3, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.746305"} +{"text": "( phys. org ) \u2014 scientists at the university of texas at austin and cornell university have fabricated the first ordered arrays of silicon nanocrystals reported to date. brian a. korgel and colleagues developed a new chemical method to generate tiny silicon crystals \u2014 or quantum dots \u2014 with precisely controlled size and then relied on nature to organize them into regular structures. the new self - assembled arrays, presented in the journal chemphyschem, could help researchers exploit the promising light - emitting properties of one of the most commercially important semiconductors. bulk silicon is used in a wide range of applications, mainly in the electronics industry, but it is a weak light absorber and an extremely poor light emitter, so it is not suitable for uses that require light emission. these properties change when the crystal shrinks to the nanoscale. si quantum dots can exhibit very bright visible luminescence with size - tunable color, which makes them interesting for the fabrication of light - emitting diodes ( leds ) \u2014 or even as a possible laser source. during the last years there has been great interest in understanding these unique properties and using them to create new technologies. however, most of the applications require arrays of nanocrystals, and although there have been efforts to fabricate them, the collections of si quantum dots obtained to date have been disordered, usually with a significant size distribution. korgel and co - workers have now developed a new chemical method that allows them to obtain monodisperse silicon particles in the exact size range needed for nanoscale properties, such as bright light emission. \" we have made the first ordered arrays, or superlattices, of nanoscale silicon crystals. these collections of tiny silicon crystals are self - assembled \u2014 much in the same way that macromolecules self - assemble in living organisms \", korgel says. \" this is necessary because the dimensions are far too small to be obtained using conventional means like the lithographic patterning techniques used to make integrated circuits \", he adds. the scientists also found that the new si nanocrystal superlattices are much more thermally stable than other types of nanocrystal superlattices reported before. korgel ' s team synthesized si nanocrystals by thermal decomposition of hydrogen silsesquioxane ( hsq ), followed by etching with hf, reaction with 1 - dodecene, and size - selective precipitation of the obtained nanoparticles", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.632307526405069, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.757027"} +{"text": "' s gaze in the voyeur example cited earlier, our bodily intentionality ( what he calls \u201c the body as for - itself \u201d ) is revealing an ontological reality. the case at hand is an artistic way of conveying what sartre in being and nothingness will call \u201c the phenomenon of being. \u201d he agrees with the tradition that \u201c being \u201d or \u201c to be \u201d is not a concept. but if not that, how is it to be indexed? what does it mean \u201c to be \u201d? sartre ' s existential phenomenology appeals to certain kinds of experience such as nausea and joy to articulate the \u201c transphenomenal \u201d character of being. pace kant, \u201c being \u201d does not denote a realm behind the phenomena that the descriptive method analyzes. neither is it the object of an \u201c eidetic \u201d reduction ( the phenomenological method that would grasp it as an essence ). rather, being accompanies all phenomena as their existential dimension. but this dimension is revealed by certain experiences such as that of the utter contingency which roquentin felt. this is scarcely rationalism, but neither is it mysticism. anyone can experience this contingency and, once brought to reflective awareness, can ponder its implications. what this novel does imaginatively, being and nothingness, subtitled \u201c a phenomenological ontology, \u201d pursues conceptually, though with the aid of phenomenological \u201c arguments, \u201d as we have seen. in a series of essays published as what is literature? ( 1947 ), sartre expounds his notion of \u201c committed \u201d literature, a turn in his thought first indicated in the inaugural issue of les temps modernes two years earlier. though steeped in the polemics of the day, this continues to be a seminal text of criticism. it underscores what i have called the \u201c pragmatist \u201d dimension of sartre ' s thought : writing is a form of acting in the world ; it produces effects for which the author must assume responsibility. addressing the problem of \u201c writing for our time, \u201d sartre underscores the harsh facts of oppression and exploitation that were not erased by the upheaval of world war. ours remains \u201c a society based on violence. \u201d accordingly, the author is responsible for addressing that violence with a counter - violence ( for example, by his choice of topics to discuss ) or sharing in it by his silence. drawing a distinction between prose, which can be committed, and", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6014229519250689, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 15, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:05.828274"} +{"text": "- bolshevik revolution - coup organized by vladimir i. lenin and carried out by the bolshevik radical group of the russian social democratic labor party to overthrow the provisional government of russia in november 1917. also known as the - commonwealth of independent states ( cis ) - official designation of the former republics of the soviet union that remained loosely federated in economic and security matters after the soviet union disbanded as a unified state in 1991. members in 1996 were armenia, azerbaijan, belarus, georgia, kazakstan, kyrgyzstan, moldova, russia, tajikistan, turkmenistan, ukraine, and uzbekistan. - conventional forces in europe ( cfe ) treaty - an agreement signed in 1990 by members of the warsaw pact and the north atlantic treaty organization ( nato - - q. v. ) to establish parity in conventional weapons between the two organizations from the atlantic to the urals. included a strict system of inspections and information exchange. in 1995 russia requested exemptions for forces stationed in the caucasus region, and substantial changes were negotiated by the thirty signatory nations in 1997. - economic cooperation organization ( eco ) - established in 1985, an economic union of islamic countries to promote regional cooperation in trade, transportation, communications, culture, and overall economic development. members in 1996 were afghanistan, azerbaijan, iran, kazakstan, kyrgyzstan, pakistan, tajikistan, turkey, the \" turkish republic of northern cyprus, \" turkmenistan, and uzbekistan. - russian term, literally meaning \" public voicing. \" applied in the soviet union beginning in 1987 to official permission for public discussion of issues and public access to information, initially intended as a means for the regime of mikhail s. gorbachev to publicize the need for political and economic reform. - gross domestic product ( gdp ) - the total value of goods and services produced exclusively within a nation ' s domestic economy, in contrast to the gross national product ( gnp - - q. v. ). normally computed over one - year periods. - gross national product ( gnp ) - the total value of goods and services produced within a country ' s borders and the income received from abroad by residents, minus payments remitted abroad by nonresidents. normally computed over one - year - hard currency - national currencies that are freely convertible and traded on international currency markets. - international monetary fund ( imf ) - established with the world bank ( q. v. ) in 1945, a specialized agency affiliated with the united nations and responsible for stabilizing international exchange rates and payments. its main function is to provide loans to its members", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6046507493761145, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.122807"} +{"text": "inventor of the week archive for a different invention or inventor one of the most popular labs at mit is the one directed by toyoichi tanaka, whose polymer gels have shown their potential to transform the technology of medicine, energy, food production born and raised in japan, tanaka received his higher education at the university of tokyo, where he earned a b. s. ( 1968 ), m. s. ( 1970 ), and d. sc. ( 1973 ), in physics. in 1975, he joined the faculty of mit, where he has risen to the rank of professor of physics as well as morningstar professor of science. tanaka ' s field of expertise is gels. a gel is typically a mixture of a polymer \" matrix, \" that is, a chain of individual molecules, and a fluid \" solute, \" in a ratio of about 1 : 30. the obvious example is jell - o, which has a matrix of gelatin in a solute of sugar water. however, synthetic gels can be made in which the polymers are very tightly bonded - - - with sometimes surprising in the mid - 1970s, tanaka discovered that certain synthetic ( polyacrylamide ) gels had remarkable properties : for example, they responded to minute changes in their environment by drastically swelling up or changing color. any substance will respond to its environment to some extent ; but tanaka learned to fine - tune his gels to undergo radical changes, or \" phase transitions, \" when they encounter either a chemical or a change in conditions ( temperature, light, electricity, magnetism, etc. ). at this stage, tanaka ' s gels have valuable applications because they can expand and contract up to 1, 000 times their original volume in response to predictable stimuli : for example, these gels could be used as artificial muscles, set in motion by a specific electrical pulse. more importantly, the polymers in the gels can capture or expel specific substances as they grow or shrink, so that the gels could be used, for example, as super - sponges to absorb and immobilize toxic waste, or as molecular filters of various sorts. the more complex stage of tanaka ' s research has been to develop \" smart \" gels which imitate proteins by recognizing conditions and responding to their environment. for example, smart gels can be fine - tuned to draw humidity from the air when it is over a given temperature, or even to release insulin when the glucose level around them drops below a given point. by 1992, tanaka had", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6098553792567964, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.421762"} +{"text": "key : \" s : \" = show synset ( semantic ) relations, \" w : \" = show word ( lexical ) relations display options for sense : ( gloss ) \" an example sentence \" - s : ( n ) fire ( the event of something burning ( often destructive ) ) \" they lost everything in the fire \" - s : ( n ) fire, firing ( the act of firing weapons or artillery at an enemy ) \" hold your fire until you can see the whites of their eyes \" ; \" they retreated in the face of withering enemy fire \" - s : ( n ) fire, flame, flaming ( the process of combustion of inflammable materials producing heat and light and ( often ) smoke ) \" fire was one of our ancestors ' first discoveries \" - s : ( n ) fire ( a fireplace in which a relatively small fire is burning ) \" they sat by the fire and talked \" - s : ( n ) fire ( once thought to be one of four elements composing the universe ( empedocles ) ) - s : ( n ) ardor, ardour, fervor, fervour, fervency, fire, fervidness ( feelings of great warmth and intensity ) \" he spoke with great ardor \" - s : ( n ) fire ( fuel that is burning and is used as a means for cooking ) \" put the kettle on the fire \" ; \" barbecue over an open fire \" - s : ( n ) fire ( a severe trial ) \" he went through fire and damnation \" - s : ( n ) fire, attack, flak, flack, blast ( intense adverse criticism ) \" clinton directed his fire at the republican party \" ; \" the government has come under attack \" ; \" don ' t give me any flak \" - s : ( v ) open fire, fire ( start firing a weapon ) - s : ( v ) fire, discharge ( cause to go off ) \" fire a gun \" ; \" fire a bullet \" - s : ( v ) fire ( bake in a kiln so as to harden ) \" fire pottery \" - s : ( v ) displace, fire, give notice, can, dismiss, give the axe, send away, sack, force out, give the sack, terminate ( terminate the employment of ; discharge from an office or position ) \" the boss fired his secretary today \" ; \" the company terminated 25 % of its workers \" - s : ( v ) fire, discharge", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.602858112844179, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.446501"} +{"text": "key : \" s : \" = show synset ( semantic ) relations, \" w : \" = show word ( lexical ) relations display options for sense : ( gloss ) \" an example sentence \" - s : ( n ) power, powerfulness ( possession of controlling influence ) \" the deterrent power of nuclear weapons \" ; \" the power of his love saved her \" ; \" his powerfulness was concealed by a gentle facade \" - s : ( n ) power ( ( physics ) the rate of doing work ; measured in watts ( = joules / second ) ) - s : ( n ) ability, power ( possession of the qualities ( especially mental qualities ) required to do something or get something done ) \" danger heightened his powers of discrimination \" - s : ( n ) office, power ( ( of a government or government official ) holding an office means being in power ) \" being in office already gives a candidate a great advantage \" ; \" during his first year in office \" ; \" during his first year in power \" ; \" the power of the president \" - s : ( n ) power, force ( one possessing or exercising power or influence or authority ) \" the mysterious presence of an evil power \" ; \" may the force be with you \" ; \" the forces of evil \" - s : ( n ) exponent, power, index ( a mathematical notation indicating the number of times a quantity is multiplied by itself ) - s : ( n ) might, mightiness, power ( physical strength ) - s : ( n ) world power, major power, great power, power, superpower ( a state powerful enough to influence events throughout the world ) - s : ( n ) electricity, electrical energy, power ( energy made available by the flow of electric charge through a conductor ) \" they built a car that runs on electricity \" ; \" the power went oout around midnight \" - s : ( n ) baron, big businessman, business leader, king, magnate, mogul, power, top executive, tycoon ( a very wealthy or powerful businessman ) \" an oil baron \" - s : ( v ) power ( supply the force or power for the functioning of ) \" the gasoline powers the engines \"", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6294463069891445, "token_count": 448, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.451823"} +{"text": "of putting energy into relatively small and transportable packages. another focus is extremely large - scale energy storage. he explains that this type of storage is not mechanical but relies on new chemical methods that have not been attempted before. \u201c we will work on batteries, of course, because it \u2019 s a more near - term application. but there is a lot of other work going on that is mostly centered on electrochemistry because it is the only way of efficiently converting fuels or any chemical substances into electricity, \u201d he says. in addition, larger applications such as electric vehicles and power system backup for power substations are other development focuses. ceder observes that designers have attempted to adapt battery solutions from portable electronics to these large - scale problems only to discover that the solutions are inadequate. \u201c almost all of the modern battery research has focused on portable electronics because that was where the business was. you \u2019 ve taken something that \u2019 s designed for a 1 - watt - hour storage, and you \u2019 re trying to do something that \u2019 s a million times bigger, \u201d he maintains. large - scale energy storage also has different design criteria that can open the way for new solutions. for example, the power backup for a 10 - megawatt substation can use technology that cannot work in consumer electronics. one area in which large - scale systems differ from consumer products is toxicity. ceder notes that designers cannot put any toxic substances into a cell phone. but this requirement is much less of a concern when building a substation because it is a controlled environment. \u201c i \u2019 m not saying we have to make super - toxic things, but there \u2019 s just a larger chemical space in which you can work. a lot of things that were discarded 15 years ago, or that people just don \u2019 t think about anymore, are suddenly fair play, \u201d he says. for the past decade, ceder has led an interdisciplinary group focused on power storage research. this group \u2019 s efforts are now part of the mitei. his own research concentrates on cathodes, which he describes as a critical component for energy density. the group also models and designs virtual materials for batteries. he notes that it has been successful in its virtual modeling efforts and is now using this technique to develop electrodes with substantially higher power and energy densities. energy is the amount of power used to charge a battery, ceder explains. power relates to how quickly energy can be stored and released from a battery. for example, a battery for a cell phone or laptop computer usually is high energy", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6013874542400146, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 2, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.639249"} +{"text": "densities. energy is the amount of power used to charge a battery, ceder explains. power relates to how quickly energy can be stored and released from a battery. for example, a battery for a cell phone or laptop computer usually is high energy, but it is not necessarily high power. \u201c your laptop battery drains over the course of a couple of hours and recharges in around two hours. that \u2019 s not what we consider a high power rate, \u201d he says. ceder \u2019 s research teams are designing materials for both high energy and high power. virtual materials testing allows scientists to examine thousands of new compounds to find the best combinations for specific energy densities. high - charge - rate batteries will enable manufacturers to create a new user experience, but high discharge rates also permit batteries to produce large bursts of power. in the past, capacitors were necessary for such discharges. ceder says that one military application is field charging. he notes that the best way to charge a battery under battlefield conditions is to hook it up to a vehicle. the military already is using vehicles in this role, but there is a difference between charging a battery in two hours and charging it in only one minute. \u201c it \u2019 s the same for commercial use. if you could recharge your battery in one minute, you would live with a lot less battery life. if you \u2019 re in an airport, now you can stand by and wait for a minute while it completely charges. that \u2019 s a lot different from sitting on the ground tethered to a power plug to do your work, \u201d he explains. the mit research teams under ceder recently have developed two new battery materials : lithium nickel manganese oxide and lithium iron phosphate. ceder shares that the automotive industry is interested in lithium iron phosphate because the battery \u2019 s base materials are very inexpensive and extremely stable and safe. \u201c when you charge most batteries, they are essentially highly oxidized. the battery just wants to release oxygen, sort of like a bomb. anything in the battery that \u2019 s oxidizable is essentially burned, \u201d he says. a key aspect of developing lithium iron phosphate for batteries is the affordable use of nanotechnology. ceder explains that nanotechnology allows the material to have very high power and charge - discharge rates. the charge and discharge occurs by the diffusion of lithium into the active battery material. if the substance is on the nanometer scale, the diffusion does not have to travel very far into the material, enabling very fast reactions. conventional", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6284902088012052, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 3, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:06.640310"} +{"text": "nanotechnology is an emerging area of capability working across chemistry, physics, biology and materials science to manipulate matter at the molecular scale. nanotechnology enables the development of new materials, devices, or other useful structures. this advance in nano - scale science and technology has taken place becuase of the development of microscopes and other equipment capable of seeing and characterising nano - sized materials, allowing their application to a variety of industries. what makes nanotechnology special is that atoms and molecules interact with each other at the nanoscale, which can produce interesting results. we are familiar with bulk gold being a shiny golden - coloured, non - reactive metal. however, gold nanoparticles have red - blue colours and are rather reactive. they make excellent industrial catalysts, cancer therapeutics, imaging agents and antimicrobials. examples of commercial applications of nanotechnology : - electronics : integrated circuits, fets, static discharge removal - automotive : stronger tires, lighter yet stronger materials, catalysts, fuel line safety, airbag and other sensors - sports : nanotubes in tennis racquets and bikes, nanotechnology enabled golf balls ( even a sliced ball goes straight ) - cosmetics : transparent sunsceens, sustained delivery of bioactive molecules - textiles : self cleaning clothes - building : thermal isolation, self cleaning surfaces - energy : hydrogen storage, fuel cell components, smart lighting - biomedical : antifouling coatings, imaging tools, sensors - environment : catalysts, sensors, filtration, pollution control, green energy nanotechnology is producing revolutions in manufacturing, medicine, energy and water technologies by making devices smaller, lighter, cheaper and faster with better performance. the areas of expertise at flinders unviersity in nanotechnology are located within the flinders centre for nanoscale science & technology.", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.631167530861132, "token_count": 371, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:07.480211"} +{"text": "electron microscopy ( tem ) ( jeol jem2010, japan ) at an accelerating voltage of 200 kv. emission spectra were measured on a perkin - elmer ls - 55 fluorescence spectrophotometer. all the measurements were taken at room temperature. results and discussion morphologies and structure xrd as a kind of important manner can be used to characterize the phase and structure of samples. the xrd pattern of products obtained in the hydrothermal system is shown in fig. 1a. the broad peak indicates that the amorphism of product is because of poor crystallization. as a kind of usual fashion, raman spectroscopy is a powerful technique for characterizing the carbon materials. figure 1b displays the raman spectrum of synthesized materials that verifies carbon structure of products. a strong peak at 1, 588 cm\u22121 and a weak peak at 1, 333 cm\u22121 corresponding to typical raman peaks of graphitized carbon spheres are observed. the peak at 1, 333 cm\u22121 could be assigned to the vibrations of carbon atoms with dangling bonds in planar terminations of disordered graphite. the peak at 1, 588 cm\u22121 ( g - band ) corresponds to an e2 g mode of graphite and is related to the vibration of sp2 - bonded carbon atoms [ 21, 22 ]. the high intensity ratio of d to g band suggests the poor graphitization of the products, which is consistent with the xrd pattern. ft - ir is also used to characterize the function group of the hollow carbon nanospheres. figure 1. axrd patterns of synthesized products after hydrothermal process 5 h at initial content = 0. 3 g ; braman spectrum of synthesized products ; cir spectrum of synthesized products in our experiment, ft - ir spectrum ( fig. 1c ) was used to identify the functional groups of the hollow carbon nanospheres for the sake of further understanding the structure of carbon. as a kind of amylose aggregated from monoglucuronide, aromatization is usually regarded as a process of decreasing the number of functional groups. the bands at 1, 710 and 1, 620 cm\u22121 can be attributed to c = o and c = c vibrations, respectively. these results reveal that aromatization of chitosan has taken place during hydrothermal treatment. compared with the aromatization of glucose under hydrothermal condition, the bands in the range of 1, 000 ~ 1, 300 cm\u22121 are hardly seen in the ft - ir spectrum of our products", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6416464339218673, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 2, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:08.356492"} +{"text": "kind of complicate material was characterized with tem. the tem image and amplified tem image are given in fig. 4a and b. sno2 nanoparticles of several nanometers were loaded on the surface of hollow carbon nanospheres. the pl spectrum of the composite material was characterized by two peaks at 376 and 424 nm, and a broad peak centered at 476 nm in the wavelength of range 450 \u2013 516 nm under excitation at 310 nm. the emission in the wavelength range 450 \u2013 550 nm may be related to the intrinsic defect structures, in particular the oxygen vacancies originated from the oxygen deficiency induced during the growth. the prominent band at 420 nm is attributed to the recombination of the deep - trapped charged and photogenerated electron from the conduction band. figure 4. a, btem and amplified tem images of synthesized sno2 @ c, cits pl properties anddxrd pattern of synthesized sno2 @ c composite to conclude, hollow carbon nanospheres with the diameter of 100 nm were synthesized without template under hydrothermal condition via ultrasonic pretreatment. and the wall thickness was about 20 nm. the influence of the reaction time and the content was also observed. then a possible forming mechanism was given. hollow carbon nanospheres loading sno2nanoparticles were synthesized and its photoluminescence peak appeared at 376, 424, and 476 nm. the hollow carbon nanospheres and their loading structure have potential application in many fields such as carriers, storage, and catalysts. the authors acknowledge the national natural science foundation ( no. 50772074 ) of china, the state major research plan ( 973 ) of china ( no. 2006cb932302 ), the nano - foundation of shanghai in china ( no. 0852nm01200 ), and the shanghai key laboratory of molecular catalysis and innovative materials ( no. 2009kf04 ). adv. mater.. 2001, 13 : 11. coi number [ 1 : cas : 528 : dc % 2bd3mxhtvyktlg % 3d ] publisher full text adv. mater.. 2000, 12 : 206. coi number [ 1 : cas : 528 : dc % 2bd3cxosloguw % 3d % 3d ] publisher full text scr. mater.. 2009, 60 : 607. coi number [ 1", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6238484886785317, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 7, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:08.362412"} +{"text": "the water hexamer, shown, is the smallest assembly of water molecules that adopts a three - dimensional structure displaying hydrogen bonding patterns characteristic of liquid water and ice. water is the most abundant and one of the most frequently studied substances on earth, yet its geometry at the molecular level \u2014 the simple two hydrogen atoms and one oxygen atom, and how they interact with other molecules, including other water \u2014 has remained somewhat of a mystery to chemists. most understanding at that level is theoretical, requiring the use of supercomputers to make innumerable calculations over periods of weeks to make educated guesses as to the arrangements and structure of water clusters before they form into liquid water or ice. but a new study, using experimentation with a highly advanced spectrometer for molecular rotational spectroscopy, has removed some of the mystery and validates some very complex theory involving the way water molecules bond. it is published in the may 18 issue of the journal science. \" we set out to determine quantitatively the structure that small assemblies of water adopt, and then compare them to theory to see how well current quantum chemistry predicts the properties of molecules, \" said brooks pate, a chemist in the university of virginia ' s college of arts & sciences who led the study. \" we found experimentally that modern quantum chemistry has reached the point where its theories are proving out in the lab regarding the unusual directional bonding properties of water clusters. \" the properties of water, and how it interacts with itself and other molecules, is the basis for many processes in biology, and likely played a major role in the development of life on earth. but understanding how those bonds form at the molecular level has been largely guesswork. \" for the first time, now we have an actual physical picture of what water ' s molecules put together look like, and it turns out they adopt three different geometries, \" pate said. \" this is in agreement with theory. \" pate and his u. va. team identified and imaged a three - dimensional geometry that a water molecule takes on that is the likely precursor structure for forming liquid water and ice. \" we found that the bonding strengths of liquid water actually begin to emerge even in a tiny cluster, \" pate said. \" the challenge is figuring out how it interacts with other molecules and how the forces between two molecules of water can be described quantitatively, because the orientation of how the waters come at each other makes a big difference in the binding. \" there are innumerable possibilities for how this happens,", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6578860089752101, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:08.711451"} +{"text": "##s with other molecules and how the forces between two molecules of water can be described quantitatively, because the orientation of how the waters come at each other makes a big difference in the binding. \" there are innumerable possibilities for how this happens, and theorists, including pate ' s colleague on the paper, quantum chemist george shields of bucknell university, have been working on the details for years without direct validation from experiments. the difficulty has been in developing techniques that are sensitive enough to image the tiny water molecules and how they orient themselves when interacting with other water molecules. the breakthrough came earlier this year when pate ' s u. va. team used a new tool, a molecular rotational spectrometer developed during the last two years, to make precise measurements that ultimately validated what theory has expressed. the improved sensitivity of the instrument comes from advances in high - speed digital electronics that provide unprecedented data throughput in the measurement. this core technology is being commercialized for applications in chemical analysis by a charlottesville start - up venture, brightspec. \" this will allow chemists to transfer what we ' ve learned to larger systems, \" pate said. \" we are checking to see if theory can get right the structures of the arrangements of water molecules so that that information can be used to see how water interacts in larger systems. \" the larger systems could include bio - molecules, such as protein in dna, and how surrounding water molecules might interact with those molecules through hydrogen bonds. \" it is very satisfying to see that the experimental work we did, completely independently of theory, came together so perfectly with the theory, \" pate noted. he said his research is the behind - the - scenes workings of chemistry that ultimately makes up the big picture of how things come together at much larger scales. \" you may not want to know how a bridge was designed, but you sure want to know it was done right, \" he said. \" likewise, if a theory is used to predict, for example, how a medicine might work, you ideally would want to be able to test the theory to make sure it ' s right before making the medicine. that would be the ultimate goal \u2014 to have theory and experimentation in sync. \" source : university of virginia", "subdomain_id": "subdomain_quantum_mechanics", "similarity_score": 0.6336058731413716, "token_count": 457, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 1, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:08.712381"} +{"text": "cavity quantum electrodynamics ; april 1993 ; scientific american magazine ; by serge haroche and jean - michel raimond ; 8 page ( s ) fleeting, spontaneous transitions are ubiquitous in the quantum world. once they are under way, they seem as uncontrollable and as irreversible as the explosion of \u00bf reworks. excited atoms, for example, discharge their excess energy in the form of photons that escape to infinity at the speed of light. yet during the past decade, this inevitability has begun to yield. atomic physicists have created devices that can slow spontaneous transitions, halt them, accelerate them or even reverse them entirely. recent advances in the fabrication of small superconducting cavities and other microscopic structures as well as novel techniques for laser manipulation of atoms make such feats possible. by placing an atom in a small box with reflecting walls that constrain the wavelength of any photons it emits or absorbs - - and thus the changes in state that it may undergo - - investigators can cause single atoms to emit photons ahead of schedule, stay in an excited state indefinitely or block the passage of a laser beam. with further refinement of this technology, cavity quantum electrodynamic ( qed ) phenomena may find use in the generation and precise measurement of electromagnetic fields consisting of only a handful of photons. cavity qed processes engender an intimate correlation between the states of the atom and those of the field, and so their study provides new insights into quantum aspects of the interaction between light and matter.", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.7533741582208842, "token_count": 320, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:08.819953"} +{"text": "learn something new every day more info... by email in the field of genetics, \" nondisjunction \" is a technical term for a specific defect in the way the chromosomes of a cell separate. this defect creates a genetic mutation or defect in the cells produced from the process. the resulting cells are called aneuploid. there are two crucial stages of cellular division when this defect can occur. the first stage is meiosis i, when the homologous chromosomes fail to separate, while the second is meiosis ii, commonly known as mitosis, when the sister chromatids do not separate properly. when nondisjunction occurs during meiosis i, all of the resulting gametes, called daughter cells, are affected. two of the daughter cells will have an extra chromosome, and the other two daughter cells will be missing one chromosome. only half of the resulting daughter cells will be affected when this defect occurs during meiosis ii. of the four resulting gametes, two will be normal, one will have an extra chromosome, and one will be missing a chromosome. when carried through in genetics, nondisjunction can result in either the sperm or the egg cells of the parent possessing 24 chromosomes instead of the normal 23. in these cases, the child conceived will have 47 chromosomes, which is the common variation known as trisomy, seen in children with down syndrome. when cells are missing a single chromosome, it is called monosomy. this form of genetic mutation can lead to birth defects such as turner syndrome, a syndrome marked by developmental delays. it also can lead to infertility caused by the lack of genetic material. genetically, nondisjunction is often a death sentence for the fetus. as a result of the abnormal cellular structure, the immune system of the mother will often kick in, destroying the rogue cells and causing a miscarriage. in other cases, it leads to genetic defects, referred to as chromosomal anomalies, that result in conditions such as down syndrome, edwards syndrome, patau syndrome, klinefelter syndrome, and turner syndrome. while genetic testing, including antenatal testing, is used to detect genetic disorders, there are no known cures for many of the conditions caused by this defect. medical science continues to study this mutation process in hopes of understanding why the cells fail to replicate properly. mapping out the variations found in the cells produced by this condition may help researchers to find cures for genetic diseases and defects.", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.6044795862177683, "token_count": 505, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:09.375398"} +{"text": "spent nuclear fuel pools spent nuclear fuel ( snf ) refers to fuel after it has fueled a reactor. this fuel looks like new fuel in the sense that it is made of solid pellets contained in fuel rods. the only difference is that snf contains fission products and actinides, such as plutonium, which are radioactive, meaning it needs to be shielded. just as with the fuel rods in a shutdown reactor, the snf produces decay heat because most of the decay radioactivity from the fission products and actinides is deposited in the fuel and converted into thermal energy ( aka heat ). as a result, the snf also needs to be cooled, but at a much lower level than fuel in a recently ( < 12 hours ) shutdown reactor as it produces only a fraction of the heat. in summary, the snf is stored for a certain time to : 1 ) allow the fuel to cool as its decay heat decreases ; and 2 ) shield the emitted radiation. to accomplish these goals, snf is stored in water pools and large casks that use air to cool the fuel rods. the pools are often located near the reactor ( in the upper floors of the containment structure for a bwr mark - 1 containment ). these pools are very large, often 40 feet deep ( or larger depending on the design ). the pools are made of thick concrete, lined with stainless steel. snf assemblies are placed in racks at the bottom of these pools, so almost 30 feet of water covers the top of the snf assemblies. the assemblies are often separated by plates containing boron which ensure a neutron chain reaction cannot start. the likelihood of such an event is further reduced because the useful uranium in the fuel has been depleted when it was in the reactor, so it is no longer capable of sustaining a chain reaction. the water in the pool is sufficient to cool the snf, and the heat is rejected through a heat exchanger in the pool so the pool should stay at fairly constant average temperature. the water depth also ensures the radiation emitted from the snf is shielded to a level where people can safely work around the pools. under normal operating circumstances, spent fuel can be stored in the pools indefinitely. an active cooling system is in place to remove the residual decay heat and the water also provides effective radiation shielding. the amount of fuel that can be stored into the pool can vary according to the capacity of the pool itself, but most spent fuel pools are design to be", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6006552915499396, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:10.813134"} +{"text": "aod dependent excessive chronic alcohol consumption is associated with significant shrinkage of brain tissue, degradation of fibers ( i. e., white matter ) that carry information between brain cells ( i. e., gray matter ), reduced viability of these brain cells, and impairment of associated cognitive and motor functions ( for reviews, see oscar \u2013 berman 2000 ; sullivan 2000 ). some alcoholism \u2013 related tissue damage is partially reversible with abstinence, although residual tissue volume deficits persist even in long \u2013 abstinent alcoholics ( pfefferbaum et al. 1998 ). abnormalities are found in both the gray matter and the white matter of the brain. the brain \u2019 s gray matter consists of nerve cells ( i. e., neurons ), which account for its grayish color, and the surrounding glia cells, which provide mechanical support, guidance, nutrients, and other substances to the neurons. white matter is made up of long, thin extensions of the neurons, called axons, which carry information between neurons. white matter is paler in color than gray matter because the axons are surrounded by myelin \u2014 a fatty substance that protects the nerve fibers. the axons form fiber tracts linking nearby and distant neurons across different brain regions ( i. e., white \u2013 matter tracts ). imaging in living patients ( i. e., in vivo ) can be used to detect and quantify gray \u2013 and white \u2013 matter abnormalities on both macrostructural and microstructural levels. conventional structural magnetic resonance imaging ( mri ) reveals the size, shape, and tissue composition ( gray vs. white matter ) of the brain and its constituent parts. diffusion tensor imaging ( dti ) reveals the integrity of white \u2013 matter tracts that link regions of the brain to each other. mri is based on the observation that the protons of hydrogen atoms, when placed in a strong magnetic field, can be detected by manipulating the magnetic field. because the human body is composed primarily of fat and water, it is made up mostly of hydrogen atoms. variations in behavior of hydrogen atoms in different brain tissue types and structures show up as intensity differences that clinical structural mri can detect and map to visualize and measure gross brain neuroanatomy. diffusion tensor imaging makes use of the fact that water molecules in the brain are always moving \u2014 that is, they are in brownian motion. dti detects the diffusion, or brownian movement, of water protons within and between individual cells and yields measures of the magnitude and predominant orientation", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6051683334359672, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 1, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:10.979088"} +{"text": "to our understanding of the world \u2013 they are looking for clues about how our universe began and their findings could require the standard model of physics to be rewritten. what has really grabbed my attention recently is that we all now have a chance to aid physicists on the project with the launch of lhc @ home 2. 0, whereby the lhc team will be tapping into the collective computing power of the public to help it simulate particle physics experiments. i \u2019 m incredibly proud that some of our most talented scientists are taking part in the hunt for the elusive higgs boson. when the physicists are satisfied that they have enough data, i \u2019 m looking forward to celebrating this quite extraordinary feat of science and engineering with all the uk contributors. but as exciting as the lhc is, it is only one of the many great projects uk scientists are involved in all over the world. there are always plenty of other fascinating opportunities out there, more discoveries to be made and more products waiting to be invented. if you want to get a taste of this first - hand why not visit the british science festival in bradford this september? it is one of europe \u2019 s largest celebrations of science, technology and engineering, with plenty of activities including workshops, trips, debates and films. i \u2019 m really looking forward to seeing the best of what uk science has to offer, and i hope the festival continues its fine tradition of conveying the wonder of science to the public.", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6239260096280637, "token_count": 292, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 1, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:11.259687"} +{"text": "this book is based on a course of the same name that has been taught annually at stanford university since 1970. about fifty students have taken it each year juniors and seniors, but mostly graduate students - and alumni of these classes have begun to spawn similar courses elsewhere. thus the time seems ripe to present the material to a wider audience ( including sophomores ). it was dark and stormy decade when concrete mathematics was born. long - held values were constantly being questioned during those turbulent years ; college campuses were hotbeds of controversy. the college curriculum itself was challenged, and mathematics did not escape scrutiny. john hammersley had just written a thought - provoking article \" on the enfeeblement of mathematical skills by ' modern mathematics ' and by similar soft intellectual trash in schools and universities \" 176 ; other worried mathematicians 332 even asked, \" can mathematics be saved? \" one of the present authors had embarked on a series of books called the art of computer programming, and in writing the first volume he ( dek ) had found that there were mathematical tools missing from his repertoire ; the mathematics he needed for a thorough, well - grounded understanding of computer programs was quite different from what he ' d learned as a mathematics major in college. so he introduced a new course, teaching what he wished somebody had taught him. the course title \" concrete mathematics \" was originally intended as an antidote to \" abstract mathematics, \" since concrete classical results were rapidly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularly called the \" new math. \" abstract mathematics is a wonderful subject, and there ' s nothing wrong with it : it ' s beautiful, general, and useful. but its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. the goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. abstract mathematics was becoming inbred and losing touch with reality ; mathematical education needed a concrete counterweight in order to restore a healthy balance. when dek taught concrete mathematics at stanford for the first time he explained the somewhat strange title by saying that it was his attempt to teach a math course that was hard instead of soft. he announced that, contrary to the expectations of some of his colleagues, he was not going to teach the theory of aggregates, not stone ' s embedding theorem, nor even the stone - cech compactification. (", "subdomain_id": "subdomain_quantum_simulation", "similarity_score": 0.6011986709546635, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:11.369899"} +{"text": "absolute - value function and infinite integration ) notice that this list of topics is quite different from what is usually taught nowadays in undergraduate course entitled \" discrete mathematics. \" therefore the subject needs a distinctive name, and \" concrete mathematics \" has proved to be as suitable as another the original textbook for stanford ' s course on concrete mathematics was the \" mathematical preliminaries \" section in the art of computer programming 207. but the presentation in those 110 pages is quite terse, so another author ( op ) was inspired to draft a lengthy set of supplementary notes. the present book is an outgrowth of those notes ; it is an expansion of, and a more leisurely introduction to, the material if mathematical preliminaries. some of the more advanced parts have been omitted ; on the other hand, several topics not found there have been included here so that the story will be complete the authors have enjoyed putting this book together because the subject began to jell and to take on a life of its own before our eyes ; this book almost seemed to write itself. moreover, the somewhat unconventional approaches we have adopted in several places have seemed to fit together so well, after these years of experience, that we can ' t help feeling that this book is a kind of manifesto about our favorite way to do mathematics. so we think the book has turned out to be a tale of mathematical beauty and surprise, and we hope that our readers will share at least of the pleasure we had while writing it. since this book was born in a university setting, we have tried to capture the spirit of a contemporary classroom by adopting an informal style. some people think that mathematics is a serious business that must always be cold and dry ; but we think mathematics is fun, and we aren ' t ashamed to admit the fact. why should a strict boundary line be drawn between work and play? concrete mathematics is full of appealing patterns ; the manipulations are not always easy, but the answers can be astonishingly attractive. the joy and sorrows of mathematical work are reflected explicitly in this book because they are part of our lives. students always know better than their teachers, so we have asked the first students of this material to contribute their frank opinions, as \" graffiti \" in the margins. some of these marginal markings are merely corny, some are profound ; some of them warn about ambiguities or obscurities, others are typical comments made by wise guys in the back row ; some are positive, some are negative, some are zero. but they all are real indications", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6125840123281013, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 2, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:11.372287"} +{"text": "example is a soma based hymn dedicated to the deity indra : bring sacrificial gifts to him, omniscient, for he longs to drink, the wanderer who comes with speed, the hero ever in the van. with soma go ye nigh to him chief drinker of the soma ' s juice : with beakers to the impetuous god, to indra with the drops effused. ( the rig veda, book vi hymn xlii 102 ) but all the various gods in the hindu pantheon were not considered entirely separate from each other. even in this most ancient of hindu texts there existed the idea of a great, transcendental absolute that formed a higher reality to the deities. perhaps the best english translation for this difficult concept is the ultimate reality : a state that is neither creation nor non - creation. other names sometimes used in english translations include brahman, the uncreate, or simply god. it is a concept that includes the potential of all physical existence without actually being that existence. it is also sometimes referred to as a form of pure consciousness. to help understand the concept of the ultimate reality, it is useful to explore hindu creation mythology. while the middle eastern monotheistic religions developed a belief in a recent and singular creation of existence by god, the vedas teach about a cyclical creation process. in the ultimate reality state there was no physical existence, no form or substance to the cosmos. but the ultimate reality does contain a pervading consciousness that holds the essence of the creator gods. these creator gods, brahma, vishnu and shiva in particular, are what start the physical manifestation of each cycle of physical existence. during the cycles of creation there are times when no physical substance exists. before the gods are made manifest there exists the ultimate reality alone. hindu theologians feel that words alone cannot fully describe just exactly what this state is. but here is one attempt by stella kramrisch : \" the state before creation is beyond the polarity of opposites. it is as vast as chaos, but having no qualities whatsoever, it lacks disorder. it is know in later indian mystical realization as brahman ; it is realized through samadhi ( at - onement ) as moksa ( release ), nirvana ( extinction of the flame of life ), sunyata ( emptiness ). these names apply to an inner realization of that state beyond the last frontiers of thought. \" ( the presence of siva p 25 ) in the ultimate reality there does", "subdomain_id": "subdomain_quantum_materials", "similarity_score": 0.6021620900714841, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 1, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:11.425430"} +{"text": "is a conceptual model and language for describing evolutionary systems efficiently and unambiguously \u201d. we can use it conjunction with esec to define the ecosystems that we want to evolve and to tweak their parameters as necessary. since this a introductory tutorial on esec, i will not elaborate any further on esdl, but there is an article by steve dower here if you are interested in the esdl syntax. i have provided an esdl system definition for koza \u2019 s decision tree induction problem below : since the esdl syntax follows a readable english format similar to linq, it is quite self - explanatory as to what it specifies. with that said, there are some general points to note : - the species is defined as random _ tgp, indicating the form of tree - based genetic programming we are using. - the arrays of functions and terminals that we defined earlier are used to construct individuals of the specified species. - every iteration, individuals in the population are selected for crossover, mutation, and reproduction in proportion to their fitness. - the rate of crossover for those selected is 90 % of the total population size, the rate of mutation is 2 %, and the rate of reproduction is 8 %. configuring an experiment to link everything together into a single cohesive and runnable experiment, we must create an esec configuration file, which is basically a python script that provides an experiment configuration via a config dictionary variable. configuration files are relatively straight - forward \u2013 they are essentially dictionaries of keys mapped to values ( which may also be dictionaries ). an example configuration for the decision tree induction problem is below : there are a few observations we can glean from this experiment configuration : - the evaluation function that we defined earlier is referenced as the value for the - the instructions we defined earlier are specified as the value to the - the esdl system definition we defined earlier is provided as a value to the - the maximum population size per generation / iteration is 500, as indicated by the value of the - by specifying monitor. limits, we define both an iteration limit ( 50 ) and a fitness limit. if either is reached, the experiment concludes immediately. executing an experiment once we have created the configuration file for our experiment, we can run it by calling the run. py script included in the esec framework, which essentially acts as a command line interface for running single or multiple experiments. there are numerous command line options that run. py supports ( see the esec", "subdomain_id": "subdomain_quantum_simulation", "similarity_score": 0.602302841363024, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 3, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:12.481333"} +{"text": "| hps 0410 | | einstein for everyone | back to main course page john d. norton department of history and philosophy of science university of pittsburgh in the last chapter, we explored the geometry induced by the postulate 5none by means of the traditional construction techniques of geometry familiar to euclid. we drew lines and found points only as allowed by the various postulates. the outcome was a laborious construction of circles and triangles with some quite peculiar properties. we constructed a circle with center o and circumference g, g ', g ' ', g ' ' '. its circumference is only 4 times is radius ( and not the 2\u03c0 times its radius dictated by euclid ' s geometry ). its cirumference is both a circle and a straight line at the same time. each of its quadrants are triangles with odd properties. the triangle ogg ', for example, has three angles, each of one right angle. so the sum of its angles is three right angles ( and not the two right angles dictated by euclid ' s geometry ). you would be forgiven for thinking that the new geometry of 5none is a very peculiar and unfamiliar geometry and that there is no easy way to comprehend it as a whole. the surprising thing is that this is not so. the geometry of 5none and the geometry of the other postulate 5more turn out to be the geometries that arise naturally in surfaces of constant curvature. recognizing that fact makes it easy to visualize these new geometries and one rapidly develops a sense of the sorts of results that will be demonstrable in them. we will see in this chapter how this arises. indeed it makes the visualization too easy, that danger is that we overlook the fact that we are really dealing with new an different geometries. the geometry of 5none proves to be very familiar ; it is just the geometry that is natural to the surface of a sphere, such as is our own earth, to very good approximation. the surface of a sphere has constant curvature. that just means that the curvature is everywhere the same. to see how the connection to the geometry of 5none works, we need only identify the line agg ' g ' ' with the equator. the perpendiculars we erected to it in the last chapter then just become lines of longitude all of which intersect at the north pole, that is at, o. it isn ' t quite that simple. we do need to adjust our notion", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.622654662733029, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:13.059712"} +{"text": "to see that these deviations from euclidean expectations arise only for very large figures on the surface of the sphere. a very small patch of the surface of a sphere is very close to being a euclidean plane. the calm surface of a small lake on the earth is very nearly a flat plane ; the surface of an ocean is markedly curved. in those very small patches, circles and triangles are very nearly euclidean in their properties. the figure below shows a very small equilateral triangle a ' ' b ' ' c ' '. the sum of its angles will meet euclidean expectation near enough and be two right angles. as the triangle grows larger, passing through triangle a ' b ' c ' to the huge abc, the sum of its angles will grow until they are three right angles at abc. the situation is the same with circles. the circle around the north pole below with very small radius oa will meet euclidean expectations, near enough, and have its circumference 2\u03c0 times its radius. as the circle grows with radius increasing through ob to oc, the formula will mutate. when the radius is oc, so the circle now coincides with the equator, the circumference will have dropped to being only four times the radius. now that we have identified our geometry of 5none as the geometry of great circles on spheres, two small corrections are needed. the first postulate allows us to draw a straight line between any two points. in the new geometry, there are two ways of connecting any two nearby points by a great circle. one goes the short way ; the other goes the long way all around the other side of the sphere. the second correction is for the second postulate which allows us to produce a straight line indefinitely. that is not possible for great circles. they are already maximally extended. one part of the original notion of the second postulate was that a straight line never really comes to an end. any point that looks like an end is only a temporary terminus and the line can be extended past it. that lack of a boundary point is all we need for the revised second postulate. the two modified forms of the first and second postulates that accommodate these two alterations are : 1 '. two distinct points determine at least one straight 2 '. a straight line is boundless ( i. e. has no end ). the modified postulates are illustrated by the geodesic drawn through two points a and b : | consider the geometry of 5none ; that is the geometry that", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6025376590871525, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 2, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:13.061727"} +{"text": ". a straight line is boundless ( i. e. has no end ). the modified postulates are illustrated by the geodesic drawn through two points a and b : | consider the geometry of 5none ; that is the geometry that is deducible from the the fifth postulate 5none and the other four postulates, suitably adjusted. the expectation of the mathematicians of the eighteenth century and earlier had been that one would eventually be able to deduce a contradiction from them. that is, they expected them to be inconsistent. we started deducing consequences from the postulates but found only odd results, not contradictions. | | by contradiction, i mean \" a and not a, \" for a some sentence. so if one ' s theory allows contradictions to be deduced, the theorist has a very serious problem. it may mean that someone working in dynamics can infer that a system both conserves energy ( \" a \" ) and does not conserve energy ( \" not - a \" ). which ought the theorist to believe?! | how do we know that a more imaginative, more thorough analysis might not eventually produce a contradiction? that is, how do we know that the new geometry is consistent? the question could be answered by a proof of the consistency of the geometry. alas, advances in twentieth century mathematics have shown that proving the consistency of a rich system in mathematics is typically impossible. however the geometers of the nineteenth century had already supplied us with something that, for practical purposes, is good enough. in showing that the geometry of 5none is really the geometry of great circles on spheres, they provided a relative consistency proof. the idea is simple enough. in a three dimensional euclidean space, we can recreate or simulate, the different geometry of 5none by constructing a sphere. imagine that somehow we could generate a contradiction within the geometry of 5none. that would then mean that we could generate a contradiction within the geometry of great circles on spheres. and that would mean that there must be a contradiction recoverable within the geometry of three dimensional euclidean spaces. to get a more concrete sense of how this works, imagine that there is a way of deducing an inconsistency in the geometry of 5none. a geometer sits down and begins the steps of the construction that leads to a contradiction. perhaps the geometer draws a straight line ab ; and then a perpendicular to it ; and so on. now imagine a second geometer who works in", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6288919026679403, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 3, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:13.062933"} +{"text": "they are projected. since cc ' is sandwiched between aa ' and bb ', the same must be true of it. the basic idea generalizes. any attempt to limit the maximum number of parallels allowed by 5more fails ; we can always add one more. so the geometry of 5more is the geometry that arises when we may draw infinitely many parallels through the point not on the original line. we could continue the exercise of discovering the geometry 5more through step by step inference. since we ' ve seen it done once for the geometry of 5none, let us just skip to the final result. it turns out that the geometry of 5more is the geometry of a negatively curved surface of constant curvature like a saddle or potato chip. in this geometry, lines can have infinite length, just as in familiar euclidean geometry. however there are differences that are analogous to those of the geometry of a spherical space : in very small parts of the space, circles and triangles behave like euclidean circles and triangles, near enough. as the circles and triangles get larger, deviations from euclidean behavior emerge. the circumference of circles becomes more than 2\u03c0 times the radius ; and the sum of the angles of a triangle become less than two right angles. the perpendiculars to the equator on the surface of a sphere converge to a single point, the north pole. on this surface of negative curvature, perpendiculars to a straight line diverge. so far, we have explored the geometries of 5none and 5more for the case of two dimensional spaces. we can also consider each in three dimensional spaces. the results we would arrive at are summarized in the table ( duplicated in euclid ' s postulates and some euclid ' s postulate 5 | straight lines | | finite length ; connect back onto themselves | infinite length | | infinite length | | sum of angles of a triangle | | more than 2 right angles | | 2 right angles | | less than 2 right angles | | circumference of a circle | | less than 2\u03c0 times radius | | 2\u03c0 times radius | | more than 2\u03c0 times radius | | area of a circle | | less than \u03c0 ( radius ) 2 | | \u03c0 ( radius ) 2 | | more than \u03c0 ( radius ) 2 | | surface area of a sphere | | less than 4\u03c0 ( radius ) 2 | | 4\u03c0 ( radius ) 2 | | more than 4\u03c0 ( radius ) 2 | | volume of a sphere | | less than 4\u03c0 /", "subdomain_id": "subdomain_quantum_field_theory", "similarity_score": 0.6050979138163923, "token_count": 512, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 5, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:13.065243"} +{"text": "advanced laboratory and / or demonstration apparatus apparatus title : polarization of reflected light abstract : the apparatus consists of a ray box, an acrylic prism, a glass slide, and a polarizing sheet. the apparatus can demonstrate polarization of reflected light at the brewster angle and variation of the level of polarization with angle of incidence. description polarization of reflected light a ray box that gives parallel rays of light from one end and a diverging beam from the other end is used in this apparaus. as shown in fig. 1 an acrylic prism is placed in the parallel rays symmetrically. the angle of incidence of the rays falling on the prism is 600, very close to the brewster angle of acrylic ( 57. 50 ), and, therefore, the reflected rays are almost completely polarized. the polarization can be demonstrated by placing the polarizer in front of the ray box and changing its orientation. when the polarizer is held horizontally the reflected light disappears showing that the reflected light is polarized in the perpendicular direction ( fig. 1 ). angular dependence of polarization of reflected light can be demonstrated with the help of the diverging rays. a glass reflector ( microscope slide ) is placed so that the angle of incidence of the rays falling on the glass is lower than, equal to, and higher than the brewster angle. when the polarizer is held horizontally the fourth ray of light disappears ( fig. 3 ) because the angle of incidence is equal to brewster angle. the other rays with angles of incidence less than and greater than brewster angle are visible because they are not completely polarized. this is the cheapest, easiest, and quickest way of demonstrating the different aspects of polarization of reflected light.", "subdomain_id": "subdomain_quantum_optics", "similarity_score": 0.6212546363193674, "token_count": 350, "source_dataset": "HuggingFaceFW/fineweb-edu", "source_id": "", "chunk_index": 0, "filtering_threshold": 0.6, "created_at": "2025-12-26T19:10:13.182406"}