Linguists From Germany

"The time is ripe for Chinese thought as a global quest for cultural pluralism."

"Few people realize that the Bible discourages people from studying foreign languages."

"The Chinese dragon 'long' is essentially a force of the good."

"Let us build the fairest construction the world has ever seen - the global language."

"Revive Asian words and promote important key concepts!"

"Capitalism forces nations to compete for market shares, natural resources, and human capital. Less obvious so, they also compete for names, brands, and terminologies."

"Yes, I am vulgar and fearless, and loudly indifferent to convention and limitation."

"Chinese holiday names are not dead yet, although I would hardly call them alive either: they are truly undead vocabularies."

"The English language is often hailed as the "international language", but it is not the global language. In fact, the global language will have to adopt tens of thousands of non-European terminologies."

"We must begin to find the untranslatables in each culture and return them to world history."

"Ape Caesar is a universal leader, regardless of origin; he is willing to lead his species and shape the world, and subjugate it, if need be. He points to the future. Sun Wukong guards his people and their traditions. He looks back at their glorious past. --Films vis-a-vis nations' global role (2014), China Daily, Hong Kong"

"Honesty and facts are almost irrelevant. Getting attention is key, causing offence is desirable, and provoking a physical response is the jackpot."

"A Greek invention, democracy is highly overrated. For starters, it never worked in Greece. The first philosophers were fascists and, even today, 2,500 years later, the 'cradle of Western civilization' remains an incompetent state. Roman emperors and a vengeful, authoritarian God are the true European success stories."

"The US, Germany, France and Britain were never real democracies. Far from it, the US is a plutocracy with a post-monarchal king's court (the White House) and a holy scripture (the constitution). The three others are tedious class societies."

"Sadly, a biblical sense of mission perverts all Western societies. There isn't a town square in Europe without a church. Priests are trained in national universities. The ruling party of Germany is the Christian Democratic Union. America is God's favorite nation. And we all live in the year 2019 of our Lord, Jesus Christ. -- Chinese are not so foolish as to worship at the church of Western values (2015), South China Morning Post, Hong Kong"

"Harvard has de facto become a Chinese outpost. -- Oh, boy, do the Chinese love Harvard! (2014), China Daily, Beijing"

"Just like in Europe in the feudal days, the typical Chinese public servant today drags himself around with little or no money, and thus stays close to his master. In the past, that was the emperor, now it is the party. Can China's new government end corruption? (2013), The Japan Times, Tokyo"

"Division turned out to be humanity's strength, togetherness its arms. -- Reassure HK, remind Britain SAR no longer a British 'colony' (2019), China Daily, Beijing"

"The West is the ultimate status upgrade to them [the Chinese]. -- The perils of being associated with China (2014), The Korea Times, Seoul"

"Star Wars is Chinese Taoism. -- Star Wars is Taoism in American garb (2015), China Daily, Beijing"

"I define as a unit any magnitude that can serve for the numerical derivation of a series of magnitudes, and in particular I call such a unit an original unit if it is not derivable from another unit. The unit of numbers, that is one, I call the absolute unit, all others relative. Zero can never be a unit."

"Some of the groundbreaking work in the treatment of n-dimensional geometry—was carried out by Hermann Günther Grassmann. ...Grassmann was responsible for the creation of an abstract science of "spaces," inside which the usual geometry was only a special case. Grassmann published his pioneering ideas (originating a branch of mathematics known as linear algebra) in 1844, in a book commonly known as Ausdehnungslehre... Grassmann's suggestion that BA = -AB violates one of the sacrosanct laws of arithmetic... Grassmann faced up squarely to this disturbing possibility and invented a new consistent algebra (known as exterior algebra) that allowed for several processes of multiplication and at the same time could handle geometry in any number of dimensions."

"The exchange theorem... is sometimes called the Steinitz exchange theorem after Ernst Steinitz... The result was first proved Hermann Günther Graßmann..."

"Grassmann's first publication of his new system was made in 1844 in a book entitled "Die Lineale Ausdehnungslehre Ein Neuer Zweig der Mathematik." His novel and fruitful ideas were however presented in a somewhat abstruse and unusual form, with the result, as the author himself states in the preface to the second edition issued in 1878, that scarcely any notice was taken of the book by Mathematicians. He was finally convinced that it would be necessary to treat the subject in an entirely different manner in order to gain the attention of the mathematical world. Accordingly in 1862 he published "Die Ausdehnungslehre vollständig und in strenger Form bearbeitet," in which the treatment is algebraic... Since that time his great work has been more fully appreciated, but not even yet, in the opinion of the writer, at its real value."

"As the great generality of Grassmann's processes—all results being obtained for n-dimensional space—has been one of the main hindrances to the general cultivation of his system, it has been thought best to restrict the discussion to space of two and three dimensions."

"The wonderful and comprehensive system of Multiple Algebra invented by Hermann Grassmann, and called by him the Ausdehnungslehre or Theory of Extension, though long neglected by the mathematicians even of Germany, is at the present time coming to be more and more appreciated and studied. In order that this system, with its intrinsic naturalness, and adaptability to all the purposes of Geometry and Mechanics, should be generally introduced to the knowledge of the coming generation of English-speaking mathematicians, it is very necessary that a text-book should be provided, suitable for use in colleges and universities, through which students may become acquainted with the principles of the subject and its applications."

"The history of geometry may be conveniently divided into five periods. The first extends from the origin of the science to about A. D. 550, followed by a period of about 1,000 years during which it made no advance, and in Europe was enshrouded in the darkness of the middle ages; the second began about 1550, with the revival of the ancient geometry; the third in the first half of the 17th century, with the invention by Descartes of analytical or modern geometry; the fourth in 1684, with the invention of the differential calculus; the fifth with the invention of descriptive geometry by Monge in 1795. The quaternions of Sir William Rowan Hamilton the Ausdehnungslehre of Dr. Hermann Grassmann, and various other publications, indicate the dawn of a new period. Whether they are destined to remain merely monuments of the ingenuity and acuteness of their authors, or are to become mighty instruments in the investigation of old and the discovery of new truths, it is perhaps impossible to predict."

"One may say without great exaggeration that Grassmann invented linear algebra and, with none at all, that he showed how properly to apply it to geometry. ...He ...anticipated in its most important aspects Peano's treatment of the natural numbers, published 28 years later. ...A feature of Grassmann's work, far in advance of the times, is the tendency towards the use of the implicit definition. ...The definition of a linear space (or vector space) came into mathematics, in the sense of becoming widely known, around 1920, when Hermann Weyl and others published formal definitions. ...Grassmann did not put down a formal definition—again, the language was not available—but there is no doubt that he had the concept."

"It was natural that Grassmann chose to introduce his system, not by means of a paper, but rather by means of a long and complicated book. ...such ideas as Grassmann's form of the scaler (dot) and vector (cross) products... have counterparts in modern vector analysis."

"The concept of rotation led to geometrical exponential magnitudes, to the analysis of angles and of trigonometric functions, etc. I was delighted how thorough the analysis thus formed and extended, not only the often very complex and unsymmetric formulae which are fundamental in tidal theory, but also the technique of development parallels the concept."

"A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work."

"While I was pursuing the concept of geometrical product, as this idea was established by my father... I concluded that not only rectangles, but also parallelograms, may be viewed as products of two adjacent sides, provided that the sides are viewed not merely as lengths, but rather as directed magnitudes. When I joined this concept of geometrical product with the previously established idea of geometrical sum the most striking harmony resulted. Thus when I multiplied the sum of two vectors by a third coplaner vector, the result coincided (and must always coincide) with the result obtained by multiplying separately each of the two original vectors by the third... and adding together (with due attention to positive and negative values) the two products. [Thus A(B + C) = AB + AC.] From this harmony I came to see a whole new area of analysis was opening up which could lead to important results."

"The first impulse came from the consideration of negatives in geometry; I was accustomed to viewing the distances AB and BA as opposite magnitudes. Arising from this idea was the conclusion that if A, B, and C are points of a straight line, then in all cases AB + BC = AC, this being true whether AB and BC are directed in the same direction or in opposite directions (where C lies between A and B). In the latter case AB and BC were not viewed as merely lengths, but simultaneously their considered since they were oppositely directed, Thus dawned the distinction between the sum of lengths and the sum of distances which were fixed in direction. From this resulted the requirement for establishing this latter concept of sum, not simply for the case where the distances were directed in the same or opposite directions, but also for any other case. This could be done in the most simple manner, since the law that AB + BC = AC remains valid when A, B, and C do not lie on a straight line. This then was the first step which led to a new branch of mathematics... I did not however realize how fruitful and how rich was the field that I had opened up; rather that result seemed scarcely worthy of note until it was combined with a related idea."

"It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a problem which is at once seen to be impossible of solution."

"Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry."

"From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all."

"As I was reading the extract from your paper in the geometric sum and difference... I was struck by the marvelous similarity between your results and those discoveries which I made even as early as 1832... I conceived the first idea of the geometric sum and difference of two or more lines and also of the geometric product of two or three lines in that year (1832). This idea is in all ways identical to that presented in your paper. But since I was for a long time occupied with entirely different pursuits, I could not develop this idea. It was only in 1839 that I was led back to that idea and pursued this geometrical analysis up to the point where it ought to be applicable to all mechanics. It was possible for me to apply this method of analysis to the theory of tides, and in this I was astounded by the simplicity of the calculations resulting from this method."

"I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results."

"The concept of centroid as sum led me to examine Möbius' Barycentrische Calcul, a work of which until then I knew only the title; and I was not little pleased to find here the same concept of the summation of points to which I had been led in the course of the development. This was the first, and... the only point of contact which my new system of analysis had with the one that was already known."

"El purismo aumenta el nacionalismo porque enseña a clasificar todo como croata o no croata, y a que todo lo que supuestamente proceda del propio país se diga que es bueno, mientras que de lo que proceda de otras naciones se diga que es perjudical y malo."

"Fälle, in denen mehrere Nationen eine Sprache sprechen, werden in der Sprachwissenschaft als plurizentrische Sprachen behandelt."

"I linguisti croati rifiutano le parole in uso presso la maggior parte della popolazione solo per dare artificiosamente corpo ad una diversità nei confronti della lingua parlata in Serbia."

"Qui veut être un linguiste conséquent doit appliquer de manière conséquente les critères linguistiques, et non les bricoler pour les conformer aux besoins de la politique, créant l’illusion qu’on se place encore sur le terrain de la science."

"The long-form endings have pushed away the short-form endings completely in the oblique cases. In the last few years, there are attempts in Croatia to bring back again the short forms in the usage. This attempts are the part of the new sociolinguistic politics to bring back the archaic words and forms in the usage and to construct new words, neologisms, in place of customary words - all that with the aim to make the language in the west of the Serbo-Croatian language community as different as possible from the language in the east of the Serbo-Croatian language community. Leaders of the new language politics proclaim as incorrect what was customary, and as correct what was rare, archaic or even did not exist in the usage, and then they carry it out in practice through the control of the media, text-books etc. Such inversion of the criteria for what is correct and what is not correct in the language usage makes the native speakers unsure and frustrated."

"There is a large discrepancy between the linguistic reality and the language politics and relevant legislation in South Slavic countries. On the one hand, according to all criteria, the linguistic reality can be described as a typical pluricentric standard language with four standardized varieties. On the other hand, school children are being segregated in Bosnia-Herzegovina as if they speak different languages. In Croatia and Serbia, the segregation takes place in the name of minority language rights, ignoring that the European Charter for Regional or Minority Languages gives a clear definition of a minority language that excludes the term ‘minority language’ in this case."

"To be sure, these witnesses provide an excellent illustration of textual dynamics, and they deepen our knowledge of the development of the Bible text in the technical sense."

"This identity is neither coincidental nor self-evident."

"It may be said, without exaggeration, that there is no other text which is documented by such varied types of sources."

"This period is characterized by a diversity of textual transmissions undreamed of two decades ago."

"Certain conclusions have forced themselves upon me while studying the sources, and I have not felt constrained to conceal them on account of that over-scrupulousness which is afraid to influence the future users of the edition."