academics-from-belgium

"The BEH mechanism operates within the context of gauge theories. Despite the fact that grand unification schemes reach scales comparable to the Planck scale, there was, a priori, no indication that Yang-Mills fields offer any insight into quantum gravity. The only approach to quantum gravity that had some success, in particular in the context of a quantum interpretation of the black hole entropies, are the superstring theory approaches and the possible merging of the five perturbative approaches (Type IIA, IIB, Type I and the two heterotic strings) into an elusive M-theory whose classical limit would be 11-dimensional supergravity."

"Three distinct geometries on S7 arise as solutions of the classical equations of motion in eleven dimensions. In addition to the conventional riemannian geometry, one can also obtain the two exceptional Cartan-Schouten compact flat geometries with torsion."

"Usually mathematicians are either theory builders, who develop tools, or problem-solvers, who use those tools to find solutions... Deligne is unusual in being both. He’s got a very special mind."

"Deligne’s method was totally perpendicular to Grothendieck’s: he knew every trick of his master’s trade by heart, every concept, every variant. His proof, given in 1974, is a frontal attack and a marvel of precision, in which the steps follow each other in an absolutely natural order, without surprises. Those who heard his lectures had the impression, day after day, that nothing new was happening–whereas every lecture by Grothendieck introduced a whole new world of concepts, each more general than the one before–but on the last day, everything was in place and victory was assured. Deligne knocked down the obstacles one after the other, but each one of them was familiar in style. I think that this opposition of methods, or rather of temperament, is the true reason behind the personal conflict which developed between the two of them. I also think that the fact that “John, the disciple that Jesus loved” wrote the last Gospel by himself partly explains Grothendieck’s furious exile that Grothendieck has imposed upon himself."

"In Récoltes et Semailles, Grothendieck counts his twelve disciples. The central character is Pierre Deligne, who combines in this tale the features of John, “the disciple whom Jesus loved”, and Judas the betrayer. The weight of symbols!"

"From Grothendieck] and his example, I have also learned not to take glory in the difficulty of a proof: difficulty means we have not understood. The ideal is to be able to paint a landscape in which the proof is obvious."

"The nice thing about mathematics is doing mathematics."

"It is evident that thought is also necessary for action. But the Church has for centuries ... focused on orthodoxy and left orthopraxis in the hands of nonmembers and nonbelievers."

"Poincaré analyses how the reality of three dimensional Euclidean (or non-Euclidean) space, has been constructed from our daily experiences as a human being with the objects that are most important for us (rigid bodies), and closely around. This does not mean that this three dimensional space is an ‘invention’ of humanity. It exists, but the way we have ordered, and later on formalized it, by means of specific mathematical models, does make part of it. In other words, what we call the three dimensional reality of space partly exists in its own and partly exists by the structures that we have constructed, relying on our specific human experience with it."

"In classical Newtonian physics there was a clear understanding of 'what reality is'. Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in 'the present'. Often it is stated that three dimensional space and one dimensional time have been substituted by four dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that what is 'present', cannot be retained. Is reality then the four dimensional manifold of relativity theory? And if so, what is then the meaning of 'change in time'?"

"From the beginning of his research, the Belgian physicist Diederik Aerts has shown great creativity in inventing a number of concrete machine-models that have played an important role in the development of general mathematical and conceptual formalisms for the description of the physical reality."

"In our study of applying quantum to cognition we have identified five main aspects that play a fundamental role and that are specific to quantum structures as compared to classical structures. They are (i) contextual in influence (ii) emergence due to superposition, (iii) interference, (iv) entanglement and (v) quantum field theoretic aspects."

"We have come to suspect that `the way concepts combine and how they carry and communicate meaning' is governed by the presence of quantum structure in cognition."

"The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts."

"In the construction of world views one can distinguish seven important tasks that correspond with the various components of a world view and that must provide an answer to a number of fundamental questions. First we must design a model of the world. What is the world like in which we live? How is the world structured and how does it function? What are the most suitable metaphors for speaking of the whole? Are mechanistic or organic models to be given preference? An explanation of reality must then follow. Why are the world and mankind as they are? Is a completely different world possible? What general explanatory principles apply?"

"We continually speak of world views in the plural because a unique and monolithic world view - considering the immense complexity of reality - will remain an unattainable ideal."

"Although world views grow organic ly and historically, they can also be developed. The construction of world views is comparable to the work of cartographers in antiquity and in the Middle Ages. They mapped out the world on the basis of information from sailors, mer­ chants and explorers."

"We are quickly approaching the end of the millennium and the 'magical' year 2000. Many futurologists in the sixties thought science and technolo­gy would offer man unprecedented possibilities for solving his problems. The fall of the Iron Curtain and the implosion of the Eastern Block also created, just a, few years ago, grand expectations. The dream did not come true, however. Rather than ending up in a technological paradise and a peace-loving world, we woke up in a torn world with virtually unsolvable environmental problems and agonising social conditions."

"A world view is a system of co-ordinates or a frame of reference in which everything presented to us by our diverse experiences can be placed. It is a symbolic system of representation that allows us to integrate everything we know about the world and ourselves into a global picture, one that illuminates reality as it is presented to us within a certain culture."

"A world view is a coherent collection of concepts and theorems that must allow us to construct a global image of the world, and in this way to understand as many elements of our experience as possible. Societies, as well as individuals, have always contemplated deep questions relating to their being and becoming, and to the being and becoming of the world. The configuration of answers to these questions forms their world view. Research on world views, although we are convinced of its practical value and necessity, will always be primarily an expression of a theoretical interest. It reflects the unlimited openness of the human mind to reality as a whole. Even if this research would not appear to be of any immediate value or necessity – quod non – we still should promote and encourage it energetically, because it also expresses the most unselfish striving of humanity “the desire to know,” a property of “Homo sapiens sapiens.”"

"World views, as related to the sciences, ethics, arts, politics and religions, are integral parts of all cultures. They have a strongly motivating and inspiring function. A socially shared view of the whole gives a culture a sense of direction, confidence and self-esteem. Moreover, interactions between cultures change constantly."

"The world around us can be construed as a huge "house" that we share with other humans, as well as with animals and plants. It is in this world that we exist, fulfilling our tasks, enjoying things, developing social relations, creating a family. In short, we live in this world. We thus have a deep human need to know and to trust it, to be emotionally involved in it. Many of us, however, experience an increasing feeling of alienation. Even though, with the expansion of society, virtually the entire surface of the planet has become a part of our house, often we do not feel "at home" in that house. With the rapid and spontaneous changes of the past decades, so many new wings and rooms have been constructed or rearranged that we have lost familiarity with our house. We often have the impression that what remains of the world is a collection of isolated fragments, without any structure and coherence. Our personal "everyday" world seems unable to harmonise itself with the global world of society, history and cosmos. It is our conviction that the time has come to make a conscious effort towards the construction of global world views, in order to overcome this situation of fragmentation. There are many reasons why we believe in the benefit of such an enterprise, and in the following pages we shall attempt to make some of them clear."

"What is reality? What is space? And what is time? These are the three questions that we want to investigate taking into account the knowledge that we have gained by modern physics. Our intuitive prescientific conception of the world in relation with these three concepts is not very precise but could be summarised as follows. - Reality is everything that exists now in the present. The past has been real but is not anymore and the future is what shall become real but is not yet. - Space is the theatre where reality is in. It englobes all of reality. Till the birth of relativity theory all physical theories where compatible with this intuitive scheme. But when relativity theory entered the scene, these intuitive conceptions of space and time, and what is less recognised even till today, also the conception of reality, has got into problems."

"The classical concept of 'physical entity', be it particle, wave, field or system, has become a problematic concept since the advent of relativity theory and quantum mechanics. The recent developments in modern quantum mechanics, with the performance of delicate and precise experiments involving single quantum entities, manifesting explicit non-local behavior for these entities, brings essential new information about the nature of the concept of entity."

"No physical concept is sufficiently defined without the knowledge of its domain of validity."

"Dear \sqrt{\text{Trotsky×Bohr}} = \text{Rosenfeld}!"

"In the history of science literature Rosenfeld is largely a blank sheet, but he was at the centre of modern physics as one of the pioneers of quantum field theory and quantum electrodynamics in the late 1920s and the 1930s. Today he is best known for his publications with Niels Bohr in 1933 and 1950 on measurability in quantum electrodynamics and as the fierce spokesman of Bohr's interpretation of quantum mechanics after the Second World War."

"Wesentliche Fortschritte in der Formulierung der allgemeinen Quantengesetze der elektromagnetischen und materiellen Wellenfelder haben neuerdings Heisenberg und Pauli… erzielt, indem sie die von Dirac erfundene "Methode der nochmaligen Quanteln" systematisch entwickelten. Neben gewissen sachlichen Schwierigkeiten, die viel tiefer liegen, trat dabei eine eigentumliche Schwierigkeit formaler Natur auf: der zum skalaren Potential kanonisch konjugierte Impuls verschwindet identisch, so daß die Aufstellung der Hamiltonischen Funktion und der Vertauschungsrelationen nicht ohne weiteres gelingt. Zur Beseitigung dieser Schwierigkeit sind bisher drei Methoden vorgeschlagen worden, die zwar ihren Zweck erfullen, aber doch schwerlich als befriedigend betrachtet werden können. (Heisenberg and Paull have recently made significant progress in the formulation of the general quantum laws of electromagnetic and material wave fields by systematically developing the "method of repeated quantization" invented by Dirac. In addition to certain factual difficulties which lie much deeper, a peculiar difficulty of a formal nature arose: the momentum which is canonically conjugated to the scalar potential vanishes identically, so that the establishment of the Hamiltonian function and the commutation relations is not easy. To overcome this difficulty, three methods have been proposed which, although they fulfil their purpose, can hardly be regarded as satisfactory.)"

"Each word is a singularity, or is connected with a singularity, in our way of understanding existence."

"It is as though a puzzle could be put together simply by shaking its pieces."

"Governments of developing countries sometimes proposed projects that did not directly benefit the population, but did benefit the government; the so-called 'white elephants'. For example, they wanted to build highways and build large buildings, while we thought it was better to focus on good education."

"Europe is an economic giant, a political dwarf, and a military worm."

"The journey was a real triumph. To the Congolese, he almost seemed like an extraterrestrial apparition. The reception was very warm and soon Boudewijn was nicknamed "Bwana Kitoko", "beautiful young man". The young king had a very good feeling about his first Congo experience. Some say it was the first time he laughed in public."

"I think King Baudouin was not dissatisfied with the disappearance of the man who broke off the 80-year-old relations between Belgium and Congo."

"The Belgian government's apologies to Lumumba's family are beside the point. According to the current foreign minister, Louis Michel, the then government should have insisted on a fair trial for Lumumba. But there was no government in Congo then, only chaos. The army mutinied through the provinces, Belgian troops were no longer there, only United Nations soldiers. They should have performed."

"During the Cold War, a division arose between Western and Communist countries. The countries that had just become independent after colonial times had to be kept on friendly terms. That is why Belgium offered development aid to those countries. The government also supported the work of the missionaries who were active in Congo, Rwanda and Burundi, among others."

"It is difficult to stop aid for human rights violations without the population suffering. That is why we continued to offer help through reliable NGOs. Preference was given to Belgian NGOs, because the domestic NGOs were often under the influence of the Congolese government. The importance of human rights has only increased, partly due to the introduction of the International Criminal Court, which tackles violations of human rights."

"The population of the African continent is expected to grow from 1 to 4 billion people in the next 100 years. This will cause a huge influx of refugees. When you are poor and get older, you need many children to support yourself. The best means of contraception is an increase in prosperity. If we invest enough in Africa now, we can slow down population growth and Africans don't have to come here to survive. Thus charity is also in one's own interest."

"China is operating in Congo in a brutal way that smacks of slavery. Congolese work in mines for very low wages. China is not concerned with sustainability and often commits a predatory economy. The country also does not respect human rights. Still, the developing country's government is letting itself be wrapped up, because the Chinese don't make moral demands like the West does. China works with a closed stock exchange in Congo. For example, they build 20 schools in exchange for being able to operate 10 copper mines for 1 year. But that is often peasant deception: the value of the school buildings is sometimes only 10% of the value of the extracted raw materials."

"The whole iconography of ancient science is simply the fruit of wishful thinking."

"I am obliged to deal with hundreds of men and to make them live without killing the reader."

"Superstitions... are nothing but persistent errors, foolish beliefs, and irrational fears. Superstitions are infinite in number and scope... It would not do to ignore them altogether, only if we should never forget the weakness and fragility of our minds. The consciousness that superstitions are rife in our own society is a healthy shock to our self-conceit and a warning. ...it lets us judge ancient superstitions with more indulgence and with a sense of humor. We could not overlook them without falsifying the general picture nor judge them too severely without hypocrisy."

"Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions."

"All men are our brothers. As far as the discovery of the truth is concerned, they are all working for the same purpose; they may be separated by the accidents of space and time, and by the exigencies of race, religion, nationality, and other groupings; from the point of view of eternity they are working together."

"If we are generous enough, we can stretch our souls everywhere and everywhen else. If we succeed in doing so, we shall discover that our present embraces the past and the future and that the whole world is our province."

"A deed happens in a definite place at a definite time, but if it be sufficiently great and pregnant, its virtue radiates everywhere in time and space."

"The whole past and the whole world are alive in my heart, and I shall do my part to communicate their presence to my readers."

"In ancient times there was no public education, except that of the forum, the theater, and the street, and the general degree of illiteracy was very high. ...the early men of science were left very much to themselves and such a phrase as "the scientific culture of Alexandria in the third century B.C." does not cover any reality. In a sense, this is still true today; the real pioneers are so far ahead of the crowd (even a very literate crowd) that they remain almost alone..."

"The intensity of a national culture should be represented by... the general education level and... the exceptional merit of a small elite of pioneers."

"The Hellenistic world was international to a degree, polyglot and inspired by many religious faiths. ...the Greek ideals were pagan and the Hellenistic age witnessed their death struggle against Asiatic and Egyptian mysteries, on the one side, and against Judaism, on the other."