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April 10, 2026
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"Oh, that Einstein, always cutting lectures... I really would not believe him capable of it."
"In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But... these transformations do not leave Maxwell's equations invariant. Pondering this, the mathematicians Henri Poincaré and Hermann Minkowski were led to a new view of the symmetries of space and time, on a purely mathematical level. If they had described these symmetries in physical terms, they would have beaten Einstein to relativity, but they avoided physical speculations. They did understand that symmetries in the laws of electromagnetism do not affect space and time independently but mix them up. The mathematical scheme describing these intertwined changes is known as the Lorentz group, after the physicist, Hendrik Lorentz."
"The assumption of the contraction of the electron in Lorentz's theory must be introduced at an earlier stage than Lorentz has actually done."
"H. A. Lorentz has found out the Relativity theorem and has created the Relativity postulate as a hypothesis that electrons and matter suffer contractions in consequence of their motion according to a certain law. A. Einstein has brought out the point very clearly, that this postulate is not an artificial hypothesis but is rather a new way of comprehending the time-concept, which is forced upon us by observation of natural phenomena."
"It came as a tremendous surprise, for in his student days Einstein had been a lazy dog... He never bothered about mathematics at all."
"Ever since Hermann Minkowski's now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentests regarding the unreality of the future (and, for presentests, the past) are more accurate. Now, a century after Minkowski's proposed block universe first sparked debate, we present a new, more conclusive argument in favor of eternalism."
"Not only the physical but also the intellectual landscape of German-language mathematics in the early 1930s would be impossible to imagine without Gernan-Jewish mathematicians. Indeed, some fields of mathematics were completely transformed by their contributions. Number theory was transformed by Hermann Minkowski and Edmund Landau, algebra by Ernst Steinitz and Emmy Noether, set theory and general topology by Felix Hausdorff, Abraham Fraenkel and several others—to mention but a few examples."
"Minkowski, building on Einstein's work, had now discovered that the Universe is made of a four-dimensional "spacetime" fabric that is absolute, not relative."
"According to the special theory there is a finite limit to the speed of causal chains, whereas classical causality allowed arbitrarily fast signals. Foundational studies... soon revealed that this departure from classical causality in the special theory is intimately related to its most dramatic consequences: the relativity of simultaneity, time dilation, and length contraction. By now it had become clear that these kinematical effects are best seen as consequences of Minkowski space-time, which in turn incorporates a nonclassical theory of causal structure. However, it has not widely been recognized that the converse of this proposition is also true: the causal structure of Minkowski space-time contains within itself the entire geometry (topoligical and metrical structure) of Minkowski space-time. ...The problem of the independence of topological and metrical structures of space-time was clearly recognized by early writers on relativity such as Russell (1954) and, of course, Eddington..."
"Minkowski calls a spatial point existing at a temporal point a world point. These coordinates are now called 'space-time coordinates'. The collection of all imaginable value systems or the set of space-time coordinates Minkowski called the world. This is now called the manifold. The manifold is four-dimensional and each of its space-time points represents an event."
"In 1908 the famous mathematician Minkowski made a remarkable discovery concerning the Lorentz formulae. He showed that, although each observer has his own private space and private time, a public concept which is the same for all observers can be formed by combining space and time as a kind of 'distance' by multiplying it by the velocity of light, c; in other words, with any time interval we can associate a definite spatial interval, namely the distance which light can travel in empty space in that period. If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between two events. Hence, although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers."
"He is an astronomer of 33 years, held in high esteem by all specialists, a Bohemian Jew who... has worked exclusively in Germany at the largest institutes with very good success. This man has now lost, with brutal consequence, all possibilities, even the smallest ones, to earn his living, so now he has become without subsistance, and is literally forced to be a beggar. I have a handful of brilliant testimonies of him and his work. He has a wife and a child [Peter Beer]. ...he can be reached via Dr. Freundlich, Potsdam Astrophysical Observatory."
"Newton's own motto, "hypotheses non fingo" was, in a sense, disregarded by Newton himself: he rejected hypotheses only where they violated his own "regula philosophandi", that is to say, his principle of their strict parsimony. In terms of present-day methodology, we reject hypotheses as scientifically meaningless if they are incapable even of indirect test; and we reject them as superfluous or as implausible if they are too complex and artificial to conform with well established canons of inductive probability. But freedom of scientific theorizing must be preserved wherever the conditions of meaningfulness and of economy appear to be satisfied."
"Theological condemnation of others, which breaks off fellowship in either judgment or contempt, is impermissible."
"This new consensus seemed so compelling that Ernst Mayr, the dean of modern Darwinians, opened the ashcan of history for a deposit of Geoffrey's ideas about anatomical unity."
"Having reached the rare age of 100 years, I find myself in a unique position: I'm the last survivor of the golden age of the Evolutionary Synthesis. That status encourages me to present a personal account of what I experienced in the years (1920s to the 1950s) that were so crucial in the history of evolutionary biology."
"Life is simply the reification of the process of living."
"According to the concept of transformational evolution, first clearly articulated by Lamarck, evolution consists of the gradual transformation of organisms from one condition of existence to another"
"I published that theory [of speciational evolution] in a 1954 paper…and I clearly related it to paleontology. Darwin argued that the fossil record is very incomplete because some species fossilize better than others... I noted that you are never going to find evidence of a small local populatlon that changed very rapidly in the fossil record... Gould was my course assistant at Harvard where I presented this theory again and again for three years. So he knew it thoroughly. So did Eldredge. In fact, in his 1971 paper Eldredge credited me with it. But that was lost over time."
"The funny thing is if in England, you ask a man in the street who the greatest living Darwinian is, he will say Richard Dawkins. And indeed, Dawkins has done a marvelous job of popularizing Darwinism. But Dawkins' basic theory of the gene being the object of evolution is totally non-Darwinian. I would not call him the greatest Darwinian"
"Evolution, thus, is merely contingent on certain processes articulated by Darwin: variation and selection. No longer is a fixed object transformed, as in transformational evolution, but an entirely new start is, so to speak, made in every generation."
"The idea that a few people have about the gene being the target of selection is completely impractical; a gene is never visible to natural selection, and in the genotype, it is always in the context with other genes, and the interaction with those other genes make a particular gene either more favorable or less favorable. In fact, Dobzhanksy, for instance, worked quite a bit on so-called lethal chromosomes which are highly successful in one combination, and lethal in another. Therefore people like Dawkins in England who still think the gene is the target of selection are evidently wrong. In the 30s and 40s, it was widely accepted that genes were the target of selection, because that was the only way they could be made accessible to mathematics, but now we know that it is really the whole genotype of the individual, not the gene. Except for that slight revision, the basic Darwinian theory hasn't changed in the last 50 years"
"Biological classifications have two major objectives: to serve as a basis of biological generalizations in all sort of comparative studies and to serve as a key to an information storage system... Is the classification that is soundest as a basis of generalizations also most convenient for information retrieval? This, indeed, seems to have been true in most cases I have encountered."
"By representing themselves as a system [the mass media ] generates boundaries with an inside and an outside that is inaccessible to them. They too reflect [or represent] their outside as public life, so long as specific external relationships, such as to politics or to the advertisers, are not in question."
"The second-order cybernetics worked out by Heinz von Foerster is rightly held to be a constructivist theory, if not an a manifesto for operational constructivism. The reverse doesn't apply, however. Constructivist epistemologies do not necessarily have the rigor of a cybernetics of cybernetics. One can observe cognitions as constructions of an observer, without linking with this the theory that the observing observer observes himself or herself as an observer."
"Whatever we know about society, or indeed about the world in which we live, we know through the mass media. This is true not only of our knowledge of society but also of our knowledge of nature."
"The effect if not the function of the mass media seems to lie, therefore, in the reproduction of non- transparency through transparency, in the reproduction of non-transparency of effects through transparency of knowledge."
"Niklas Luhmann is remembered as the most important social theorist of the 20th century. Yet in much of the Anglo-Saxon world he is virtually unknown among professional social scientists."
"The art system operates on its own terms, but an observer of art can choose many different distinctions to indicate what he observes."
"In the twentieth century, one encounters artworks that seek to cancel the difference between a real and an imagined reality by presenting themselves in ways that make them indistinguishable from real objects. Should we take this trend as an internal reaction of art against itself?"
"Unlike philosophy, art does not search for islands of security from which other experiences can be expelled as fantastic or imaginary, or rejected as a world of secondary qualities or enjoyment, of pleasure or common sense. Art radicalizes the difference between the real and the merely possible in order to show through works of its own that even in the realm of possibility there is order after all. Art opposes, to use a Hegelian formulation, “the prose of the world,” but for precisely this reason it needs this contrast."
"On Amazon.com, a reader of my book Luhmann Explained wrote "... if your teenager is bad, don’t ground him; make him write an essay on the sociological theory of Niklas Luhmann.” I sympathize with this reader’s point of view. Having read texts by Luhmann for about twenty years, I have increasingly asked myself why, even though I find the theory very appealing, its inventor did not manage to express it in a reasonably enjoyable manner. Sometimes, particularly in his later works, Luhmann’s irony and humor interrupt his otherwise extremely dry, unnecessarily convoluted, poorly structured, highly repetitive, overly long, and aesthetically unpleasing texts."
"The activity of observing establishes a distinction in a space that remains unmarked, the space from which the observer executes the distinction. The observer must employ a distinction in order to generate the difference between unmarked and marked space, and between himself and what he indicates. The whole point of this distinction (its intention) is to mark something as distinct from something else. At the same time, the observer — in drawing a distinction - makes himself visable to others. He betrays his presence - even if a further distinction is required to distinguish him."
"Die folgenden Untersuchungen wagen diesen Übergang zu einem radikal antihumanistischen, einem radikal antiregionalistischen und einem radikal konstruktivistischen Gesellschaftsbegriff."
"We are still spellbound by a tradition that arranged psychological faculties hierarchically, relegating ‘sensuousness’ — that is, perception — to a lower position in comparison to higher, reflective functions of reason and understanding. The most advanced versions of ‘conceptual art’ still follow this tradition. By refusing to base themselves in sensuously perceptible distinctions between works of art and other objects, these works seek to avoid reducing art to the realm of sense perception."
"Humans cannot communicate; not even their brains can communicate; not even their conscious minds can communicate. Only communication can communicate."
"Does knowledge rest on construction in the sense that it only functions because the knowing system is operatively closed, therefore: because it can maintain no operative contact with the outside world; and because it therefore remains dependent, for everything that it constructs, on its own distinction between self-reference and allo-reference?"
"No matter how abstractly formulated are a general theory of systems, a general theory of evolution and a general theory of communication, all three theoretical components are necessary for the specifically sociological theory of society. They are mutually interdependent."
"It had always been clear to me that a thoroughly constructed conceptual theory of society would be much more radical and much more discomforting in its effects than narrowly focused criticisms—criticisms of capitalism for instance— could ever imagine."
"Der Fremde ist uns nah, insofern wir Gleichheiten nationaler oder sozialer, berufsmäßiger oder allgemein menschlicher Art zwischen ihm und uns fühlen; er ist uns fern, insofern diese Gleichheiten über ihn und uns hinausreichen und uns beide nur verbinden, weil sie überhaupt sehr Viele verbinden."
"Man's position in the world is defined by the fact that in every dimension of his being and behavior he finds himself at every moment between two boundaries. This condition appears as the formal structure of our existence, filled always with different contents in life's diverse provinces, activities, and destinies. We feel that the content and value of every hour stands between a higher and a lower; every thought between a wiser and a more foolish; every possession between a more extended and a more limited; every deed between a greater and a lesser measure of meaning, adequacy, and morality."
"Man is something that is to be overcome. Logically considered, this, too, presents a contradiction: he who overcomes himself is admittedly the victor, but he is also the defeated. The ego succumbs to itself, when it wins; it achieves victory, when it suffers defeat. Yet the contradiction only arises when the two aspects of this unity are hardened into opposed, mutually exclusive conceptions. It is precisely the fully unified process of the moral life which overcomes and surpasses every lower state by achieving a higher one, and again transcends this latter state through one still higher. That man overcomes himself means that he reaches out beyond the bounds that the moment sets for him. There must be something at hand to be overcome, but it is only there in order to be overcome. Thus even as an ethical agent, man is the limited being that has no limit."
"Objectivity may also be defined as freedom: the objective individual is bound by no commitments which could prejudice his perception, understanding, and evaluation of the given."
"In the presence of the total reality upon which our conduct is founded, our knowledge is characterized by peculiar limitations and aberrations. We cannot say in principle that "error is life and knowledge is death," because a being involved in persistent errors would continually act wide of the purpose, and would thus inevitably perish."
"If wandering is the liberation from every given point in space, and thus the conceptional opposite to fixation at such a point, the sociological form of the "stranger" presents the unity, as it were, of these two characteristics."
"One of the first theorists to acknowledge the deep and important impact of urbanization on social life was the German scholar, Georg Simmel. Simmel developed a sociology that focused on the special ways that forms, such as the number of people in groups, influenced social life. His effort to understand the nature of urbanization and, in particular, the metropolis of the late nineteenth and early twentieth centuries, displayed his characteristic method of analysis."
"Objectivity does not simply involve passivity and detachment; it is a particular structure composed of distance and nearness, indifference and involvement."
"The individual is reduced to a negligible quantity, perhaps less in his consciousness than in his practice and in the totality of his obscure emotional states that are derived from this practice. The individual has become a mere cog in an enormous organization of things and powers which tear from his hands all progress, spirituality, and value in order to transform them from their subjective form into the form of a purely objective life. It needs merely to be pointed out that the metropolis is the genuine arena of this culture which outgrows all personal life. Here in buildings and educational institutions, in the wonders and comforts of space-conquering technology, in the formations of community life, and in the visible institutions of the state, is offered such an overwhelming fullness of crystallized and impersonalized spirit that the personality, so to speak, cannot maintain itself under its impact."
"Money expresses all qualitative differences of things in terms of "how much?" Money, with all its colorlessness and indifference, becomes the common denominator of all values; irreparably it hollows out the core of things, their individuality, their specific value, and their incomparability. All things float with equal specific gravity in the constantly moving stream of money. All things lie on the same level and differ from one another only in the size of the area which they cover."
"Cities are, first of all, seats of the highest economic division of labor. They produce thereby such extreme phenomena as in Paris the remunerative occupation of the quatorzième. They are persons who identify themselves by signs on their residences and who are ready at the dinner hour in correct attire, so that they can be quickly called upon if a dinner party should consist of thirteen persons. In the measure of its expansion, the city offers more and more the decisive conditions of the division of labor. It offers a circle which through its size can absorb a highly diverse variety of services."