bluuebunny/crossref_metadata_2025 huggingface dataset:
Letters on Logic to Max Newman (c.1940)
Authors: Turing Alan
Published: November 2020

At the outbreak of war with Germany in September 1939, Turing left Cambridge to take up work as a codebreaker at Bletchley Park, the wartime headquarters of the Government Code and Cypher School (see ‘Enigma’, below). In the early months of 1940, Turing received a letter from the Cambridge mathematician M. H. A. Newman, his teacher, colleague, and friend. Turing replied on 23 March, writing from his lodgings at the Crown Inn (situated in the small village of Shenley Brook End): ‘Dear Newman, Very glad to get your letter, as I needed some stimulus to make me start thinking about logic.’ This was to be the first of five letters that Turing wrote to Newman during the seventeen months before Newman too left Cambridge for Bletchley Park. In his first letter Turing agreed (presumably at Newman’s request—Newman’s letters seem not to have been preserved) to ‘let [Newman] in on … the tricks of the conversion calculus’. The conversion calculus, or ‘λ-calculus’, is due to Alonzo Church, with whom Turing studied in Princeton from 1936 to 1938 (see the introduction to Chapter 3). Turing’s letters consist for the most part of detailed remarks on the conversion calculus, often elucidating material from what Turing calls ‘Church’s notes’—a substantial typescript entitled ‘Mathematical Logic’ which was in circulation at Princeton and elsewhere and which Newman was evidently reading. Their correspondence on Church’s work issued in their joint paper ‘A Formal Theorem in Church’s Theory of Types’, which was submitted to Church’s Journal of Symbolic Logic in May 1941 and published in March 1942. The paper was written while Turing played a leading role in the battle to break Naval Enigma (see ‘Enigma’ and Chapters 5–8). Turing would spend his occasional nights off duty ‘coming in as usual …, doing his own mathematical research at night, in the warmth and light of the office, without interrupting the routine of daytime sleep’. The two most interesting items of the correspondence, which are printed here, contain substantial passages in which Turing departs from his commentary on Church’s work and expounds his own views.
Intelligent Machinery (1948)
Authors: Turing Alan
Published: November 2020

By the beginning of 1947 much effort had gone into writing programmes or ‘instruction tables’ for the ACE. In ‘Proposed Electronic Calculator’, Turing had said that work on instruction tables should start immediately, since the ‘earlier stages of the making of instruction tables will have serious repercussions on the design [of the machine]’; moreover, the programming work should ‘go on whilst the machine is being built, in order to avoid some of the delay between the delivery of the machine and the production of results’. However, little progress had been made on the physical construction of the ACE. The actual engineering work was being carried out not at the National Physical Laboratory but at the Post Office Research Station, under the supervision of Turing’s wartime associate Flowers (see the introductions to Chapters 4 and 9). Flowers was asked by the NPL early in 1946 to assist with the engineering design of, and to build, the ACE. Ominously, the letter of agreement from Flowers’s superior to Turing’s superior spoke of ‘very considerable arrears of work’ and warned that ‘the manpower position is difficult’. Initial progress was nevertheless promising, with some early successes in the experimental work on the delay line memory units. According to an NPL document dated March 1946, ‘Mr. Flowers states that they can have ready for N.P.L. a minimal ACE by August or September.’ Unfortunately it proved impossible to keep to Flowers’s timetable. Dollis Hill was occupied with a backlog of urgent work on the national telephone system (at that time managed by the Post Office). Flowers’s Section was ‘too busy to do other people’s work’ (he said in 1998). Only two men could be spared to work on the ACE, Chandler and Coombs (both of whom had played leading roles in the wartime Colossus project). Sir Charles Darwin, the Director of the NPL, noted in August 1946 that the Post Office was ‘not in a position to plunge very deep’, and by November was expressing concern to Post Office staff about the slow rate of progress on the ACE. The fault was not all with the Post Office, however.
Can Digital Computers Think? (1951)
Authors: Turing Alan
Published: November 2020

The lecture ‘Can Digital Computers Think?’ was broadcast on BBC Radio on 15 May 1951, and was repeated on 3 July of that year. (Sara Turing relates that Turing did not listen to the Wrst broadcast but did ‘pluck up courage’ to listen to the repeat.) Turing’s was the second lecture in a series with the general title ‘Automatic Calculating Machines’. Other speakers in the series included Newman, D. R. Hartree, M. V. Wilkes, and F. C. Williams. Turing’s principal aim in this lecture is to defend his view that ‘it is not altogether unreasonable to describe digital computers as brains’, and he argues for the proposition that ‘If any machine can appropriately be described as a brain, then any digital computer can be so described’. The lecture casts light upon Turing’s attitude towards talk of machines thinking. In Chapter 11 he says that in his view the question ‘Can machines think?’ is ‘too meaningless to deserve discussion’ (p. 449). However, in the present chapter he makes liberal use of such phrases as ‘programm[ing] a machine … to think’ and ‘the attempt to make a thinking machine’. In one passage, Turing says (p. 485): ‘our main problem [is] how to programme a machine to imitate a brain, or as we might say more briefly, if less accurately, to think.’ He shows the same willingness to discuss the question ‘Can machines think?’ in Chapter 14. Turing’s view is that a machine which imitates the intellectual behaviour of a human brain can itself appropriately be described as a brain or as thinking. In Chapter 14, Turing emphasizes that it is only the intellectual behaviour of the brain that need be considered (pp. 494–5): ‘To take an extreme case, we are not interested in the fact that the brain has the consistency of cold porridge. We don’t want to say ‘‘This machine’s quite hard, so it isn’t a brain, and so it can’t think.’’ ’ It is, of course, the ability of the machine to imitate the intellectual behaviour of a human brain that is examined in the Turing test (Chapter 11).
Chess (1953)
Authors: Turing Alan
Published: November 2020

Chess and some other board games are a test-bed for ideas in Artificial Intelligence. Donald Michie—Turing’s wartime colleague and subsequently founder of the Department of Machine Intelligence and Perception at the University of Edinburgh—explains the relevance of chess to AI: Computer chess has been described as the Drosophila melanogaster of machine intelligence. Just as Thomas Hunt Morgan and his colleagues were able to exploit the special limitations and conveniences of the Drosophila fruit fly to develop a methodology of genetic mapping, so the game of chess holds special interest for the study of the representation of human knowledge in machines. Its chief advantages are: (1) chess constitutes a fully defined and well-formalized domain; (2) the game challenges the highest levels of human intellectual capacity; (3) the challenge extends over the full range of cognitive functions such as logical calculation, rote learning, concept-formation, analogical thinking, imagination, deductive and inductive reasoning; (4) a massive and detailed corpus of chess knowledge has accumulated over the centuries in the form of chess instructional works and commentaries; (5) a generally accepted numerical scale of performance is available in the form of the U.S. Chess Federation and International ELO rating system. In 1945, in his paper ‘Proposed Electronic Calculator’, Turing predicted that computers would probably play ‘very good chess’, an opinion echoed in 1949 by Claude Shannon of Bell Telephone Laboratories, another leading early theoretician of computer chess. By 1958, Herbert Simon and Allen Newell were predicting that within ten years the world chess champion would be a computer, unless barred by the rules. Just under forty years later, on 11 May 1997, IBM’s Deep Blue beat the reigning world champion, Gary Kasparov, in a six-game match. Turing was theorizing about the mechanization of chess as early as 1941. Fellow codebreakers at GC & CS remember him experimenting with two heuristics now commonly used in computer chess, minimax and best-first. The minimax heuristic involves assuming that one’s opponent will move in such a way as to maximize their gains; one then makes one’s own move in such a way as to minimize the losses caused by the opponent’s expected move.
The Hahn-Banach theorem in type theory
Authors: Cederquist Jan , Coquand Thierry
Published: November 2020

We present the basic concepts and definitions needed in a pointfree approach to functional analysis via formal topology. Our main results are the constructive proofs of localic formulations of the Alaoglu and Helly-Hahn-Banach theorems. Earlier pointfree formulations of the Hahn-Banach theorem, in a topos-theoretic setting, were presented by Mulvey and Pelletier (1987, 1991) and by Vermeulen (1986). A constructive proof based on points was given by Bishop (1967). In the formulation of his proof, the norm of the linear functional is preserved to an arbitrary degree by the extension and a counterexample shows that the norm, in general, is not preserved exactly. As usual in pointfree topology, our guideline is to define the objects under analysis as formal points of a suitable formal space. After this has been accomplished for the reals, we consider the formal topology ℒ(A) obtained as follows. To the formal space of mappings from a normed vector space A to the reals, we add the linearity and norm conditions in the form of covering axioms. The linear functional of norm ≤1 from A to the reals then correspond to the formal points of this formal topology. Given a subspace M of A, the classical Helly-Hahn-Banach theorem states that the restriction mapping from the linear functionals on A of norm ≤1 to those on M is surjective. In terms of covers, conceived as deductive systems, it becomes a conservativity statement (cf. Mulvey and Pelletier 1991): whenever a is an element and U is a subset of the base of the formal space ℒ(M) and we have a derivation in ℒ(A) of a ⊲ U, then we can find a derivation in ℒ(M) with the same conclusion. With this formulation it is quite natural to look for a proof by induction on covers. Moreover, as already pointed out by Mulvey and Pelletier (1991), it is possible to simplify the problem greatly, since it is enough to prove it for coherent spaces of which ℒ(A) and ℒ(M) are retracts. Then, in a derivation of a cover, we can assume that only finite subsets occur on the right-hand side of the cover relation.
Molecules at an Exhibition
Authors: Emsley John
Published: November 2020

What ingredient in Coke can remove rust from chrome? What is the bitterest substance on earth? What is the worst smelling one? In this entertaining tour of chemistry, John Emsley answers these and many other questions as he illuminates the materials that make up our world. Dozens of lively articles explore such well-known molecules as water, oxygen, and glass; versatile plastics like polypropylene, polystyrene, and polyurethane; even "elements from hell" such as Sarin (a lethal nerve gas). With no formulas, equations, or molecular diagrams to baffle the non-expert, each piece blends history, science, and anecdote, with many intriguing facts added to the mix. "The world of chemistry has never been made as entertaining," writes Nobel Prize-winning chemist Roald Hoffmann. Indeed, this book will fascinate everyone curious about the chemicals in the foods we eat, the clothes we wear, and the air we breathe.
Landscape room: environmental cons, concerns and comments: An exhibition of molecules that stalk the world
Authors: Emsley John
Published: November 2020

A hundred years ago, if you talked about protecting the environment you meant preventing floods or forest fires. Homes and farms could be ruined and families wiped out by a flash flood, a surge tide, or a raging fire. Meanwhile in industrial regions the skies were polluted with fumes, smoke and smog, rivers were little more than open drains and slag was piled up in great heaps. People complained but there was little they could do, because their livelihoods depended on the very industries which were causing the pollution. Excesses were curbed, but change was painfully slow. Fifty years ago, when you spoke of protecting the environment you meant controlling urban sprawl and cleaning up the wastes of industry. The climate of opinion now favours quicker changes, and much has been achieved since then: slag heaps have been sculpted into grassy knolls, derelict sites have been demolished and turned into sport centres or superstores, rivers now support fish and wildlife abounds on their banks. The belching smoke and choking fogs of coal-burning industries are only memories. And while the air in cities is now fouled by traffic fumes, there are signs that this pollution too will disappear as cars become cleaner. People today have other environmental concerns. They want action taken on different kinds of pollution. It is not enough to pull down old factories, gas works and foundries and to turf over the site: we want the soil beneath to be decontaminated too, so that homes can be built there and children can play safely in gardens. People want power to be generated without causing acid rain. They want all rivers and lakes to be so clean that people can fish from them or swim in them. When it comes to breathing, we have little choice. The air we breathe comes with the neighbourhoods in which we live and work. Clearly, we have some control: we can avoid traffic fumes, and change the ventilation of the rooms we are in, but even so the mixture that we are taking in is still a cocktail of gases, some of which are not natural, and some of which may be hurting us.
The origin of sex and the nature of species
Authors: Maynard Smith John , Szathmary Eors
Published: November 2020

By sex in eukaryotes, we understand a more-or-less regular succession of meiosis and syngamy. A natural consequence of this is the alternation of haploid and diploid phases in the life cycle. Eukaryotic sex significantly differs from prokaryotic sex in two crucial respects: the cellular mechanisms are quite different, and the transfer of genetic material in prokaryotes is less frequent and more localized (Maynard Smith et al., 1991). However, there seems to be significant continuity in the molecular mechanisms: sex in either case requires recombination enzymes, many of which are active in repair of damaged DNA as well. Thus, it seems plausible that recombinational repair was a preadaptation for sexual recombination. We mention in passing that there is a theory that selection for the recombinational repair of doublestrand DNA damage is responsible for the current maintenance of eukaryotic sex (Bernstein et al., 1981, 1988), but there are severe theoretical as well as factual problems with this theory; we will mention some factual difficulties later. Although an alternation of haploid and diploid phases follows from sex, a clue to the origin problem may lie in the idea that this alternation existed before the evolution of sexual recombination proper. The first hint that this may have been so comes from the classic paper by Cleveland (1947), where he proposed that the haploid-diploid cycle may have started with a spontaneous diploidization by endomitosis: that is, without syngamy. His suggestions were based on original observations on primitive flagellates (hypermastigotes and polymastigotes). Among them, Barbulanympha has a regular endomitosis-meiosis cycle. Margulis & Sagan (1986) called renewed attention to Cleveland’s ideas. In particular, they argued that the alternation of ploidy phases could have a primarily ecological explanation: if the environment alternates in some important factors, this may drive a haploid-diploid cycle, provided the phases are adaptations to different environments. For example, diploids have a smaller relative surface area than haploids, which may confer higher metabolic efficiency. We shall come back to such ideas soon. We focus first on the possible cellular mechanisms connecting the two phases. It is important that some protists have a one-step rather than a two-step meiosis: after syngamy, the two homologous chromosomes become disjunct without premeiotic doubling.
Symbiosis
Authors: Maynard Smith John , Szathmary Eors
Published: November 2020

The establishment of a permanent and obligate coexistence of genetic entities that were once capable of independent existence played an important part in the origin of the eukaryotes, and, if our earlier speculations are correct, in the origin of cells and chromosomes. In this chapter, we discuss other examples of symbiosis. The term is used to include all cases in which two or more different kinds of organism live in close association: thus it extends from parasitism to mutualism. Mutualism has been defined as a relationship from which both partners benefit. However, as will become clearer below, it is hard to measure, or even to define, ‘benefits’: in what sense is a mitochondrion today better off than its once free-living ancestors? The two questions that we shall ask are: • What are the selective force acting on the two partners in present-day symbioses? • Could such selective forces lead to the establishment of permanent and obligate coexistence? First, however, we review briefly some of the ecologically more important symbioses (for further examples, see Pirozynski & Hawksworth, 1988; Margulis & Fester, 1991). We mention only a fraction of the known mutualistic associations. Others, including cases of interaction between animals and prokaryotes, are discussed below. It is striking that symbiotic relationships have been important in the utilization by plants of nutrient-poor soils, the colonization of bare rock, life in deep-sea vents, the construction of coral reefs, and the utilization of plant material by several groups of insects. Sonea (1991; see also Sonea & Panisset, 1983) has pictured the world of bacteria as a single superorganism, whose individual component cells rely for their survival on ecological exchange of metabolites, and on genetic exchange via plasmids and phages. This picture has the virtue of emphasizing the important role played by plasmids and temperate phages in conferring on individual bacterial cells capacities needed in particular environments—for example, resistance to antibiotics, tolerance of heavy metals and new metabolic abilities. But the picture suffers from the drawback that is fatal to all holistic models of evolution, from the Gaia hypothesis downwards, of losing all sight of the units of selection, and hence of lacking any model of the dynamics of evolutionary change.
Information Bounds for Automated Object Recognition
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

Examine information bounds for understanding rigid object recognition involving the low-dimensional matrix groups. Minimum-mean-squared error bonds and mutual information bounds are derived for recognition and identification.
Evolution of the mammal-like reptiles
Authors: Kemp T.S.
Published: November 2020

Mammals, along with the biologically remarkably similar birds, are the vertebrates that are most completely adapted to the physiological rigours of the terrestrial environment. Whilst all the terrestrial dwelling tetrapods can operate in the absence of the buoyancy effect of water, and can use the gaseous oxygen available, mammals have in addition evolved a highly sophisticated ability to regulate precisely the internal temperature and chemical composition of their bodies in the face of the extremes of fluctuating temperature and the dehydrating conditions of dry land. From this perspective, the origin of mammalian biology may be said to have commenced with the emergence of primitive tetrapods onto land around 370 Ma, in the Upper Devonian. Until the 1990s, the only Devonian tetrapod at all well known was Ichthyostega from east Greenland, as described by Jarvik (e.g. Jarvik 1980, 1996). Famous for its combination of primitive fishlike characters such as the lateral line canals, bony rays supporting a tail fin, and remnants of the opercular bones, with fully tetrapod characters such as the loss of the gills and opercular cover, robust ribcage, and of course large feet with digits, Ichthyostega provided more or less all the fossil information there was relating to the transition from a hypothetical rhipidistian fish to a tetrapod. Subsequently, however, an ever-increasing number of other Upper Devonian tetrapods have been described, and the emerging picture of the origin of vertebrate terrestriality has become more complicated and surprising (Ahlberg and Milner 1994; Clack 2002). The earliest forms are Upper Frasnian in age, and include Elginerpeton from the Scottish locality of Scat Craig (Ahlberg 1995, 1998). So far known only from a few bones of the limbs and jaws, Elginerpeton adds little detail to the understanding of the evolution of tetrapods except to demonstrate that the process had commenced at least 10 million years prior to the existence of Ichthyostega. The next oldest tetrapods are Fammenian in age and include Ichthyostega, and a second east Greenland form, Acanthostega, which has been described in great detail (Coates and Clack 1990, 1991; Coates 1996).
The Mesozoic mammals
Authors: Kemp T.S.
Published: November 2020

The expression ‘Mesozoic Mammals’ refers to more than simply the mammals of that particular period of time; it also stands for an extraordinary and quite mysterious concept. From the first appearance in rocks of Late Triassic times of the small, obviously highly active, large-brained animals thought of as mammals, through the following 145 million years of life on earth culminating in the great end-Cretaceous mass extinction that saw the end of the dinosaurs, these animals remained small. Although probably far from rare at the time, the great majority of species of Mesozoic mammals were of the size of shrews, rats, and mice. A tiny handful managed to evolve to the body size of foxes or beavers, but there were no representatives at all of mammals the size of the prominent mammals of today, the herbivorous horses, antelopes, and elephants, the lions and wolves that feed upon them, or the specialist apes, whales, and anteaters. Two points highlight just how odd this restriction in body size is. The first is that the Mesozoic mammals represent no less than two-thirds of mammalian evolution from their origin to the present, so there was plenty of time for evolution, and an extensive radiation did indeed occur producing a plethora of taxa. The second is that somewhere along the line, the potential for evolving large body size certainly existed because within, metaphorically speaking, moments of the end of the Mesozoic Era, middle-sized and soon thereafter large mammals had arisen and were flourishing. Since their very earliest recognition by Dean William Buckland (Buckland 1824) from the Middle Jurassic Stonesfield Slate of Oxfordshire, Mesozoic mammals have generated controversy (Desmond 1985). Transformationists like Robert Grant denied that they were mammals, because it disturbed their accepted temporal sequence of Mesozoic reptiles preceding the exclusively Tertiary mammals. On the other hand, establishment figures like Buckland himself and Sir Richard Owen welcomed this apparent refutation of transformationism and had no doubt that they were indeed opossum-like mammals. In the end, the true nature of these fossils was accepted, and by 1871, a good number of undoubtedly Mesozoic localities had yielded undoubtedly mammalian fossils.
Images and X-rays
Authors: Blow David
Published: November 2020

Crystallography provides the most direct way of forming images of molecules. Using crystallography, three-dimensional images have been made of thousands of macromolecules, especially proteins and nucleic acids. These give detailed information about their activity, their mechanism for recognizing and binding substrates and effectors, and the conformational changes which they may undergo. The three-dimensional structures show graphically the evolutionary relationships between molecules from widely separated systems. They give a wide view of the resemblances between different proteins, showing strong links in three-dimensional structure where the relationship between amino-acid sequences has dwindled to insignificance. The aim of this book is to tell the ordinary biologist enough about the methods of crystallography and the results that it gives, to allow results to be considered critically, to give insight into the limits of interpretation which are possible, and to identify the causes of the limitation in a particular case. Although the basic ideas are simple, the structural results are complicated, and based on huge numbers of measurements. The challenge for the teacher is to find a way through the simple basic ideas, without getting lost in detail. The main text is purely descriptive, and can be read from start to finish without any detailed mathematical knowledge. The explanations are backed up by numerous illustrations. For the reader who wants more detail, ‘boxes’ are supplied with more complete information, which can offer a deeper level of understanding, using some clearly presented mathematics. The book is not intended to teach the reader how to do practical crystallography. There are many other excellent books for this purpose. It is intended, rather, to give an overview which will allow any biochemist or molecular biologist to read structural papers with a critical awareness. In the first part of the book (Chapters 1–5), the general principles underlying the use of X-rays, crystals and diffraction are presented, using illustrations to make many of the ideas more graphic. In the second part (Chapters 6–13), the steps that need to be followed in the course of structure determination of a crystal are considered in more detail, again with many illustrations.
Accuracy of the final model
Authors: Blow David
Published: November 2020

The result of all the work described in the previous chapters will be a set of coordinates and other data suitable for deposit in the Protein Data Bank. You or I may use these coordinates, and we need to have some insight into their accuracy and reliability. In the previous chapters, indicators have been described, which may suggest aspects of the data or interpretation procedures that might lead to problems. But as the determination of protein crystal structures becomes more routine, many of these indicators are omitted from publications. Fortunately, crystallographic procedures are self-checking to a large extent. It is rare for a major error of interpretation to lead right through to a published refined structure. A high Rfree factor is a warning, especially if coupled with departures from the requirements of correct bond lengths, angles, and acceptable dihedral angles. On the other hand, there will always be a desire to squeeze more results from the data. All interpretations are subject to error; nearly all protein crystals have regions that are less ordered, where accurate interpretation is less feasible; and the structure may be overrefined, using too many variables for the data. If the majority of the molecule is correctly interpreted, a reasonable R factor may be obtained even though some small regions are completely wrong. During refinement it is usual to restrain the bond lengths and bond angles to be near their theoretical values, as described in Chapter 12. The extent to which bond lengths and bond angles depart from these values is often quoted as an indicator of accuracy. These departures are, however, difficult to interpret because they depend on how tightly the restraints have been applied. The same applies to the restraint of certain coordinates to lie in a plane. This difficulty illustrates a general problem. Designers of refinement procedures are understandably anxious to improve their procedures to lead directly to a well-refined structure. Every aspect of structure that can be recognized as having a regularity could, in principle, be expressed as a restraint which enforces it during refinement.
Mathematics and Reality
Authors: Penrose Roger , Gardner Martin
Published: November 2020

Let us imagine that we have been travelling on a great journey to some far-off world. We shall call this world Tor’Bled-Nam. Our remote sensing device has picked up a signal which is now displayed on a screen in front of us. The image comes into focus and we see (Fig. 3.1): What can it be? Is it some strange-looking insect? Perhaps, instead, it is a dark-coloured lake, with many mountain streams entering it. Or could it be some vast and oddly shaped alien city, with roads going off in various directions to small towns and villages nearby? Maybe it is an island - and then let us try to find whether there is a nearby continent with which it is associated. This we can do by ‘backing away’, reducing the magnification of our sensing device by a linear factor of about fifteen. Lo and behold, the entire world springs into view (Fig. 3.2): Our ‘island’ is seen as a small dot indicated below ‘Fig. 3.1’ in Fig. 3.2. The filaments (streams, roads, bridges?), from the original island all come to an end, with the exception of the one attached at the inside of its right-hand crevice, which finally joins on to the very much larger object that we see depicted in Fig. 3.2. This larger object is clearly similar to the island that we saw first - though it is not precisely the same. If we focus more closely on what appears to be this object’s coastline we see innumerable protuberances - roundish, but themselves possessing similar protuberances of their own. Each small protuberance seems to be attached to a larger one at some minute place, producing many warts upon warts. As the picture becomes clearer, we see myriads of tiny filaments emanating from the structure. The filaments themselves are forked at various places and often meander wildly. At certain spots on the filaments we seem to see little knots of complication which our sensing device, with its present magnification, cannot resolve. Clearly the object is no actual island or continent, nor a landscape of any kind.
In Search of Quantum Gravity
Authors: Penrose Roger , Gardner Martin
Published: November 2020

What is there that is new to be learnt, concerning brains or minds, from what we have seen in the last chapter? Though we may have glimpsed some of the all-embracing physical principles underlying the directionality of our perceived ‘flow of time’, we seem, so far, to have gained no insights into the question of why we perceive time to flow or, indeed, why we perceive at all. In my opinion, much more radical ideas are needed. My presentation so far has not been particularly radical, though I have sometimes provided a different emphasis from what is usual. We have made our acquaintance with the second law of thermodynamics, and I have attempted to persuade the reader that the origin of this lawpresented to us by Nature in the particular form that she has indeed chosen - can be traced to an enormous geometrical constraint on the big bang origin of the universe: the Weyl curvature hypothesis. Some cosmologists might prefer to characterize this initial constraint somewhat differently, but such a restriction on the initial singularity is indeed necessary. The deductions that I am about to draw from this hypothesis will be considerably less conventional than is the hypothesis itself. I claim that we shall need a change in the very framework of the quantum theory! This change is to play its role when quantum mechanics becomes appropriately united with general relativity, i.e. in the sought-for theory of quantum gravity. Most physicists do not believe that quantum theory needs to change when it is united with general relativity. Moreover, they would argue that on a scale relevant to our brains the physical effects of any quantum gravity must be totally insignificant! They would say (very reasonably) that although such physical effects might indeed be important at the absurdly tiny distance scale known as the Planck length - which is 10-35 m, some 100000000000000000000 times smaller than the size of the tiniest subatomic particle - these effects should have no direct relevance whatever to phenomena at the far far larger ‘ordinary’ scales of, say, down only to 10-12m, where the chemical or electrical processes that are important to brain activity hold sway.
Real Brains and Model Brains
Authors: Penrose Roger , Gardner Martin
Published: November 2020

Inside our heads is a magnificent structure that controls our actions and somehow evokes an awareness of the world around. Yet, as Alan Turing once put it, it resembles nothing so much as a bowl of cold porridge! It is hard to see how an object of such unpromising appearance can achieve the miracles that we know it to be capable of. Closer examination, however, begins to reveal the brain as having a much more intricate structure and sophisticated organization. The large convoluted (and most porridge-like) portion on top is referred to as the cerebrum. It is divided cleanly down the middle into left and right cerebral hemispheres, and considerably less cleanly front and back into the frontal lobe and three other lobes: the parietal, temporal and occipital. Further down, and at the back lies a rather smaller, somewhat spherical portion of the brain - perhaps resembling two balls of wool - the cerebellum. Deep inside, and somewhat hidden under the cerebrum, lie a number of curious and complicated-looking different structures: the pons and medulla (including the reticular formation, a region that will concern us later) which constitute the brain-stem, the thalamus, hypothalamus, hippocampus, corpus callosum, and many other strange and oddly named constructions. The part that human beings feel that they should be proudest of is the cerebrum - for that is not only the largest part of the human brain, but it is also larger, in its proportion of the brain as a whole, in man than in other animals. (The cerebellum is also larger in man than in most other animals.) The cerebrum and cerebellum have comparatively thin outer surface layers of grey matter and larger inner regions of white matter. These regions of grey matter are referred to as, respectively, the cerebral cortex and the cerebellar cortex. The grey matter is where various kinds of computational task appear to be performed, while the white matter consists of long nerve fibres carrying signals from one part of the brain to another. Various parts of the cerebral cortex are associated with very specific functions.
Quantum Information
Authors: Barnett Stephen
Published: November 2020

Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. Quantum Information- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography, teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathematics nowhere allowed priority over the key physical ideas. My aim throughout was to be as complete and self- contained but to avoid, as far as possible, lengthy and formal mathematical proofs. Each of the eight chapters is followed by about forty exercise problems with which the reader can test their understanding and hone their skills. These will also provide a valuable resource to tutors and lectures. To request a copy of the Solutions Manual, visit: http://global.oup.com/uk/academic/physics/admin/solutions
Quantum cryptography
Authors: Barnett Stephen
Published: November 2020

The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.
Generalized measurements
Authors: Barnett Stephen
Published: November 2020

Extracting information from a quantum system inevitably requires the performance of a measurement, and it is no surprise that the theory of measurement plays a central role in our subject. The physical nature of the measurement process remains one of the great philosophical problems in the formulation of quantum theory. Fortunately, however, it is sufficient for us to take a pragmatic view by asking what measurements are possible and how the theory describes them, without addressing the physical mechanism of the measurement process. This is the approach we shall adopt. We shall find that it leads us to a powerful and general description of both the probabilities associated with measurement outcomes and the manner in which the observation transforms the quantum state of the measured system. The simplest form of measurement was given a mathematical formulation by von Neumann, and we shall refer to measurements of this type as von Neumann measurements or projective measurements. It is this description of measurements that is usually introduced in elementary quantum theory courses. We start with an observable quantity A represented by a Hermitian operator Â, the eigenvalues of which are the possible results of the measurement of A. The relationship between the operator, its eigenstates {|λnñ}, and its (real) eigenvalues {λn} is expressed by the eigenvalue equation . . . Â |λn_ = λn|λn_. (4.1) . . .
Phase equilibria I
Authors: Bokstein Boris S. , Mendelev Mikhail I. , Srolovitz David J.
Published: November 2020

This chapter addresses the general features of phase equilibria and applies them to single component systems. Before extending our study of phase equilibria to the interesting case of multiphase, multicomponent systems, we examine the special case of single phase, two-component systems (Chapter 3). Phase equilibria in multiphase, multicomponent systems is deferred until Chapter 4. A single substance may exist in different states. For example, H2O can exist as water vapor, liquid water, or any one of several solid phases (ices). Different states can co-exist indefinitely under certain sets of conditions. Under such conditions, the co-existence of these states suggests that they are in equilibrium with respect to one another, that is, phase equilibrium has been established. It is convenient to graphically represent phase equilibria in the form of phase diagrams. An example of such a diagram for a one-component system (with no solid state allotropes) is shown in Fig. 2.1. The AO, OB, and OC lines represent conditions for which two phases are in equilibrium. Since each set of two-phase equilibrium is represented by a one-dimensional surface (i.e. a line), we see that we can vary one parameter (either T or p) without entering a one-phase region of the diagram. For example, if we set the temperature to T1 we can find a saturated vapour pressure p1 such that the liquid and gas co-exist. Three phases simultaneously co-exist at point O, which is called the triple point. Since the three-phase co-existence surface is zero dimensional (i.e. a point), three-phase equilibrium only exists at a specific temperature and pressure, that is, no conditions can be varied. On the other hand, every single-phase region of the diagram is a two-dimensional area and, hence, we can simultaneously, vary two parameters (i.e. both the temperature and pressure) and still remain in the same single-phase region of the diagram. Equations describing the lines of phase equilibria will be derived in Section 2.2, below. Unlike the lines describing the solid–liquid or solid–vapor co-existence, the liquid–vapor co-existence line terminates in a single-phase region of the diagram.
Thermodynamics of irreversible processes
Authors: Bokstein Boris S. , Mendelev Mikhail I. , Srolovitz David J.
Published: November 2020

The thermodynamics of irreversible processes, formulated by Onsager and Prigogine, considers small deviations from equilibrium in open systems. Despite the fact that the name contains ‘‘thermodynamics,’’ this is a type of kinetic theory that describes the rates of irreversible processes. Since there are no currents of any type in thermodynamic equilibrium, the concept of a current is never used in classical thermodynamics. On the other hand, the thermodynamics of irreversible processes introduces currents as the rates at which processes proceed: the heat or energy current (measured in J/s), matter current (measured in mole/s or kg/s), charge or electrical current (measured in C/s or Amps). Since these currents have a direction and magnitude, they are vectors. The thermodynamics of irreversible processes also considers scalar currents (e.g. rates of chemical reactions) and tensor currents (e.g. momentum currents). In this text, we will focus on current densities or fluxes (that is the current per unit area) rather than currents themselves. The dimensions of the currents described above can be converted to the dimensions of fluxes by dividing through by area or m2. Associated with each flux is a driving force. These forces are known as thermodynamic forces. How can we determine these driving forces? What is the relation between fluxes and driving forces? The answers to these questions can be found in the thermodynamics of irreversible processes briefly described in this chapter. Onsager’s first postulate states that the flux of property i ( ji) is a linear function of all thermodynamic forces, Xk, acting in the system where Lik are called Onsager (or kinetic) coefficients. This postulate was formulated as a generalization of a wide body of experimental observations. In fact, long before Onsager’s work it was known that the heat fluxes are proportional to temperature gradients (Fourier’s law, 1824), charge fluxes are proportional to electric potential gradients (Ohm’s law, 1826), and matter fluxes are proportional to concentration gradients (Fick’s law, 1855). However, Onsager’s contribution was the inclusion of the word ‘‘all’’ in his first postulate.
Kinetics of heterogeneous processes
Authors: Bokstein Boris S. , Mendelev Mikhail I. , Srolovitz David J.
Published: November 2020

Most practical reactions that occur in synthesizing or processing materials are heterogeneous. These include oxidation, reduction reactions, dissolution of solids in liquids, and most solid-state phase transformations. Consider the oxidation of a metal by exposure of a solid metal to an atmosphere with a finite partial pressure of oxygen. In order for oxidation to occur, molecular oxygen must dissociate into atomic oxygen on the metal surface. In some cases, atomic oxygen diffuses into the metal and reacts to form an internal oxide, while in others, the reaction occurs at the surface. In the latter case, thickening of the oxide layer requires either metal or oxygen diffusion through the growing oxide layer. This example demonstrates that heterogeneous processes commonly involve several steps. The first step is usually the transport of a reactant through one of the phases to the interface. The second is the adsorption (segregation) or chemical reaction on the interface. Finally, the last third step is the diffusion of the products into the growing phase or the desorption of the product. Since the entire heterogeneous process is a type of complex reaction, there is usually one step that controls the rate of the process, that is, is the rate-determining step. Recall that the rate-determining step is the slowest (fastest) step for a consecutive (parallel) reaction (see Sections 8.2.1 and 8.2.2). Consider the case of a consecutive heterogeneous reaction in which one of the reactants is transported through the fluid phase to the solid–fluid interface, where a first-order reaction takes place. The reaction rate ωr in such a case is ωr=kcx, where cx is the concentration of the reactant on the interface. Since the reactant is consumed at the interface, cx is smaller than the reactant concentration far from the interface, c0. It is usually easier to measure the reactant concentration in the bulk fluid. Therefore, it is convenient, to rewrite the reaction rate in terms of the bulk concentration in the fluid and an effective rate constant . . . ωr = kcx = keffc0. (11.1) . . . It is easiest to see the relation between keff and k by considering the steady-state case.
Review Of Some Mathematical And Physical Subjects
Authors: Nitzan Abraham
Published: November 2020

This chapter reviews some subjects in mathematics and physics that are used in different contexts throughout this book. The selection of subjects and the level of their coverage reflect the author’s perception of what potential users of this text were exposed to in their earlier studies. Therefore, only brief overview is given of some subjects while somewhat more comprehensive discussion is given of others. In neither case can the coverage provided substitute for the actual learning of these subjects that are covered in detail by many textbooks. A random variable is an observable whose repeated determination yields a series of numerical values (“realizations” of the random variable) that vary from trial to trial in a way characteristic of the observable. The outcomes of tossing a coin or throwing a die are familiar examples of discrete random variables. The position of a dust particle in air and the lifetime of a light bulb are continuous random variables. Discrete random variables are characterized by probability distributions; Pn denotes the probability that a realization of the given random variable is n. Continuous random variables are associated with probability density functions P(x): P(x1)dx denotes the probability that the realization of the variable x will be in the interval x1 . . . x1+dx.