Science in Different Ancient, Medieval and Early Modern Cultures and Contexts
Arithmetic and Aesthetics in Classical Antiquity
The history of Classical mathematics has often been the history of geometry (and stereometry). The works of Euclid, Archimedes, and Apollonius et al. loom large in our conception of what mathematics looked like in antiquity, and what its lasting influence has been. Yet as Reviel Netz has demonstrated, these works of geometry are the product of a rather small group of intellectuals over a number of centuries. What did mathematics look like beyond the confines of this tradition of specialists? In this paper – which will present the key points of my future monograph – I suggest that the Classical literary tradition has an important but under-explored story to tell about Classical approaches to mathematics. My central contention is that poetic works often set themselves against arithmetic and enumeration as modes of describing the world. A variety of compositions from the Classical period to Late Antiquity engage with enumeration while exploring their own raison d’être and value as works of poetry. Some works distance themselves from a world of arithmetic and numbers which does not admit the poetic or numinous, while others take numbers as their bedrock. The majority of poems, however, enter into a sophisticated dialogue with arithmetic as a way of thinking, as an epistemological framework which is interesting as much for its differences from, as for its similarities to, the world of poetry. Through a number of representative examples, I hope to show that for non-specialists arithmetic was a significant aspect of mathematics and an aspect which could freely share the same intellectual space as poetry. No separation into Two Cultures here.
Geometry and Regularities in Greek Artifacts and Architecture
A new reading of Vitruvius’ work on architecture reveals a descriptive definition of the universe’s structure and the system that control its order. The detailed explanations of Vitruvius for good architecture guide his reader to work in accordance with nature’s order. With a vast and deep-rooted influence from Greek works in various subjects, Vitruvius expresses in De Architecture a complete cosmological perception in which regularities such as geometrical shapes are an inherited part of nature, and so man, as an integral part of the universal system, should work in accordance with these regularities.
The circle is a central shape in this cosmological perception, for the universe has not just a structure but also motion that obeys the same rules of symmetries. The philosophers’ act of reducing nature into geometrical shapes with numerical relations, allowed Vitruvius to guide his reader in producing artifacts that constitute in them the same motion of cyclicality.
In my presentation, I aim to portray this approach towards nature, its understanding of the universe’ structure and how it is expressed in the production of artifacts, specifically in the profession of architecture. Examples will be taken from various subjects: sun-dials will be taken as an example for building in accordance with the astronomical system; the Tower of the Winds will be given as an example for the method of planning urban environments in accordance to the direction of the Four Winds; and column-building methods will stand as an example for the modular system by which temples were built.
In my discussion, I suggests that Vitruvius’s work is chartered by a philosophical concept in which the circle symbolizes the hidden order that exists in nature: the notion of the geometrical shape gave the circle a means of perfection; the application of this notion is expressed through material-objects that brought technological developments; and the eternal motion of cyclicality is the dominate power that shaped the universe’s structure.
In contrast to research until today, I attempt to capture Vitruvius’ work as a whole rather than focusing only on several subjects concerning architectural techniques, which will enable us to track his understanding of the world-order and his perception in relation to early Greek philosophy.
Language, diagrams and analogy in the Peripatetic Mechanical Problems
Mechanical Problems (MP) is a text in the ancient problemata genre. It consists of an introduction followed by a sequence of 35 discrete question-and-answer units concerning a broad range of phenomena, from artefacts like pulleys and beds, to natural objects like pebbles. The author encourages us to accept that many of these phenomena are analogous to and hence can be explained by a limited number of abstract models, such as the lever.
Recent work has tended to focus on MP’s account of the general principle of equilibrium which appears near the start of the text, but this paper addresses the broader explanatory strategies of the text as a whole. My first claim is that MP’s explanations are fundamentally analogical. It may therefore be illuminating to compare MP to the early Greek philosophical tradition of explanation via analogy to artefacts. My second claim is that MP’s language and diagrams are essential to establishing its analogies. Visual analogies between the two classes of diagram, physical and abstract, are a crucial component of the author’s establishment of analogical explanations, complementary to the text’s verbal content. I compare this strategy to the function of diagrams and language in Greek mathematics and suggest that it goes some way to explaining why apparently unsatisfactory arguments in MP seemed sound.
Ptolemy’s Geography: new methods of philology and stemmatology of ancient scientific texts
Ptolemy’s Geography, written in the second century CE, contains a catalogue in which localities are listed with geographical coordinates (longitude and latitude). It allows anyone to draw maps of the antique known world. As one may expect after several centuries of transmission, the extant Greek manuscripts of Ptolemy’s Geography show many differences in the place names as well as in the coordinates. The philological studies on this work since the nineteenth century reveal that our extant manuscripts can be sorted out into two groups, namely two recensions (Xi and Omega) of Ptolemy’s work. Virtually nothing is known, however, of the history of the text from the time of its composition to the extant medieval manuscripts. Moreover, the philological evaluations of both recensions led to the most contradictory results.
The challenge is to understand why we have two different recensions and to reconstruct the processes of transmission of Ptolemy’s text. Tools developed within the framework of computational humanities enable us to take advantage of some of the particularities of Ptolemy’s Geography that are obstacles to more traditional approaches: the large amount of numerical data, the complex structure of the catalogue, the significant relations between the coordinates and their graphical application. Thanks to computable documents such as Jupyter notebooks, it is possible to perform a considerable variety of analyses, to widen the scope of the philological investigation and to communicate the results by way of digital documents.
Literate History of Science: a computational approach to reconstruct content in the history of ancient sciences.
The interpretation of historical sources is a core business of the History of science. Many scientific texts contain hints or results of calculation methods. For most contemporary readers of these documents, even the background was often clear and easy to understand. For us, in most cases this background can only be comprehended by modelling. The approach of computational history and philosophy of science uses examples from Ptolemy, Proclus and Martianus Capella to show new methods for supporting the reconstructive modelling of historical sources using interactive digital notebooks. These notebooks can also be used by the community as a part of the integral publication of books and articles, and can be utilized and published as reconstructive notebooks, as well.
55 Year-long Experiment Inspired by Leonardo Da Vinci
This year, 2019, will mark the world’s most important anniversary: 500 years since the death of Leonardo da Vinci. 55 years ago, during my childhood, I set forth to get educated in most of the fields that Leonardo da Vinci worked in, which I have been implementing all these years. I was interested why da Vinci chose his particular fields of knowledge and in perusing various publications, it was explained that he chose these fields at random, based on his diverse interests. My hypothesis was and still is: all of these combinations of fields of knowledge, chosen by the genius himself were not random at all and only these particular combinations of fields of knowledge and their order could be close to optimal, for creativity. How did I come up with this hypothesis? What was the pivotal point, which made me study da Vinci’s legacy during all these years? Well, I first became acquainted with the works of da Vinci at 10 years old. My parents gifted me a copy of his diaries along with a replica of his bas-relief and that’s when I decided to study Da Vinci’s work. Some books about Leonardo were written in simple language and I became absolutely fascinated with his creative and scientific genius. However, “Leonardo Da Vince’s Notebooks” were not easy to comprehend at all, since he displayed top skills in an unfathomable number of diverse areas. I became so puzzled, that decided to follow in his footsteps of subjects to learn. I created a plan to gain a well-rounded education in a number of subjects, which I have been following all these 55 years.
In studying Da Vinci’s scientific work, many facts stood out to me. For instance:
- Da Vinci, the greatest artists of masterpieces admired: “The human foot is a masterpiece of engineering and a work of art.”
- Da Vinci’s discovery of the wave nature of light: he studied interference and diffraction in optics many centuries before these were discovered by the broader scientific community.
- Leonardo had astonishing insights about geology, hydraulics, and bridges.
- Leonardo da Vinci created the first robots, designed a self-propelled cart multi axed tank, and created many of the greatest inventions in various fields.
So, in pursuing my plan, I have been passionately studying in 19 different fields in different institutions and post graduate schools. Some of my majors were Bioengineering, Biomechanics and Biotechnology. I earned a Ph.D. in Biomedical Engineering and Robots; Dr. Sci. Degree in Biological/Medical Systems Control; Professor Diploma in Biomechanics; and more. In addition, I obtained a strong background in bridges, construction, hydraulics, car design, robotics, electronics, semiconductors, applied mathematics, programming, international patent law, TRIZ (Theory of Inventive Problem Solving)-a new philosophy of system creative thinking, etc. As a result, da Vinci’s model of diverse education has helped me to invent hundreds of lower and upper limbs prosthetics; a diffraction biomechanics system for knee surgery; anthropomorphic robots, new dynamic multi axed vehicles, and also more than 700 technologies and inventions in different fields. Da Vinci’s model of diverse education synergy, TRIZ and theory evolution, has helped to develop self-organized dynamical systems in many areas of research (multiaxial vehicles; rheological elements based on magnetic liquid for prosthetics and for training devices; rational systems in bioengineering that are patented and commercially available in rocket and space industry). These inventions have helped hundreds of thousands of patients and improved their lifestyle. I have applied this approach for creating new medical drugs. As a result, a new large group of 21 medical drugs was discovered, including the first dynamic drugs, which represents a new movement from medicines’ static to dynamic drugs with variable structure and synergy. These drug systems have the ability to adjust to the body of each individual and to adapt to its system of receptors. As the effectiveness of such drugs is increasing, the action spectrum extends substantially.Such approach was so efficient, that I implemented it for teaching it to my students, based on da Vinci’s model of diverse education. This prompted me to create a few corporations and object-oriented method of teaching based on images, which we have been implementing for many years in New York for thousands of our students. This year we celebrate 42 years of this method.
Additionally, while studying Da Vinci’s legacy for many years, I found explanations for his “inconsistencies” and “mistakes” in various areas. In fact, the graveness of his mistakes did not match to his genius. I applied TRIZ and Anticipatory Failure Determination to further understand the discrepancies. This approach has been successfully used for hundreds of my projects and inventions and I was able to apply it as a tool for historical analysis to understand his work from a different perspective. A concept was developed that sheds light on Da Vinci’s “mistakes” and helps to understand blind spots in his work. This is especially important now, when the world is preparing to celebrate the 500th anniversary of his death. I began my scientific career planning to implement Da Vinci’s model of diverse education synergy, which was as a landmark for my 55 years experiment of fascinating journey. The hypothesis was that these particular combinations could be great for creativity. The experiment proved that da Vinci’s model combining his well-roundedness in diverse fields helps us to better understand the legacy of a great genius.
Medical Education in Tang Dynasty
The Tang Dynasty was a most important period in transition of medical education in China. There are three significant features: firstly, the pattern of medical education from apprenticeship to institution-based; secondly, separation of curriculum system for physicians and pharmacists; Thirdly, establishment of examination and employment system. However, we should not overestimate the value of this educational system, because it was designed to meet the healthcare needs of court and administrative class, without setting up independent medical school. In fact, until the introduction of Western medicine into China in 19th centuries, no‘real’ medical schools had been founded.
It is generally believed that during the Wei-Jin, Southern and Northern dynasties, medical education institutions began to appear in China. However, until the reunification of the country under the Sui Dynasty (581-818 A.D.), the imperial court established the Imperial Medical Office. According to the History of Sui Dynasty: Officials, the Imperial Medical Officers was divided into two parts, one for medical care which include three departments: internal medicine department, massage department and exorcism department, another managed drugs and herb garden. The Imperial Medical Office was also in charge of the training of physicians. However, it was in Tang Dynasty (618-907 A. D. )that the institutional arrangement played an important role in medical care and education.
The Tang Dynasty was a most advanced period in medical education in ancient China, especially, medical school was established. The Imperial Medical Office in the Tang Dynasty was an institute including court medical care and training of the court physicians. It was under the Court of Imperial Ceremonies (Taichang Si ). In Imperial Medical Office, there were two directors (Taiyi Ling) who were in charge of court medical service, two vice directors, four medical supervisors, eight principal practitioners and four keepers of security to help the presidents with teaching.
The learning of students shall be examined by Imperial Medical Office and the content of the examinations covered all courses the students had studied in the past year, and students taking part in the examinations should be asked to answer ten major questions orally. Those who got a score of 8 or above would be considered as excellent; those who got a score of 6-8 as mediocre; and those who got a score of five or less were considered as poor. Students who failed the exams for nine years in a run would be dismissed.
The location of the Imperial Medical Office in Chang ‘an city in the Tang Dynasty has always been an interesting question for researchers of Chinese history of medical education. According to historical documents, the Chang’an city in the Tang Dynasty was composed of three parts: the imperial palace (royal palace), the imperial city (central government office area) and the outer capital city (residential area), covering an area of 83 square kilometers with a maximum population of 1 million.
According to the records in the Six Sets of Administrative Legal Codes of Tang Dynasty, the government agencies were located in the imperial city where was in center of the capital city. In Tang dynasty, the imperial medical office was under the administration of Court of Imperial Ceremonies. Therefore, if we find the location of Court of Imperial Ceremonies, we could speculate the location of the medical office.
In addition, the Imperial Medical Office owned a medicine garden, according to the New History of the Tang Dynasty, “there is a good land for the medicine garden in the Capital City”. According to Two Tang Capital Cities Research,”Shengping Square is located in the south of Xuanping Square in the Fourth Avenue Red Bird Gate East. There was an amusement park in its northeast corner, a medicine garden in its northwest corner.“
The garden was the highest place in Chang ‘an city. On each Jan 30, Mar 3, and Sep 9(Lunar calendar), the noble ladies of the capital came here to enjoy the sight of flowers and pray for health and safety. Thus it was also a good place for medicine garden.
Local Medical Education
Local medical education in the Tang Dynasty first appeared in 627 A.D., at the beginning of Zhenguan Reign. According to records in the Six Sets of Administrative Legal Codes of Tang Dynasty, there were stipulations related to the numbers and official ranks of teachers and students in every prefecture. For example, “Under each Superior area …, there was one doctor of general medicine, one associate and 15 students of general medicine.” Temple medical education: Buddhist Temple also provided medical service in ancient China and some monks studied medicine as an important qualification when they got higher rank. Thus some of them became famous physicians or trained apprentices.
The medical education in Tang Dynasty had a significant transition. Medical schools were founded by central government and local authorities. All these form of medical education had produced a positive role in the development of medical education in China. However, we should not overestimate its virtue or value, since the system was for the the concern of advantaged, rather than common people. The institutions of medical education under the Imperial Medical Office was not independent medical school. The medical education in the local and temple was also restricted by the social economic and culture, therefore the institutes of medical education in the local and temples did not evolve and expand medical schools. In fact, until the introduction of Western medicine into China in 19th century, real medical schools were founded.
School of Magnaura. Science education in the mid-Byzantine era
This paper will present in details, according the relative sources, the process of establishing and operating the School of Magnaura in mid-Byzantine era. The School of Magnaura, as it has been called in historiography, is the first state effort to establish a school for the teaching of the sciences in the Byzantine period. The founding of the school dates back to 855 and is related to the cultural movement called Byzantine Humanism (10th century). The school of Magnaura becomes the model for later higher education in Constantinople. An institution under state supervision and funding, dedicated exclusively to the science of science, from which the state drew the leaders of the imperial and ecclesiastical bureaucracy. The curriculum reveals what was considered necessary knowledge of state officials and the legitimate level of scientific discussion during its operation. So, this paper will try to answer in questions about what was considered scientific knowledge in Byzantium, to whom it was addressed and what reactions it caused.
Proclus and the tradition of late Greek astronomy
Little attention has been given so far to Proclus’ Hypotyposis astronomicarum positionum, a concise record of the main astronomical theories which were predominant in his era. This is, however, just a rough and inadequate description of Proclus’ enterprise. If we pay close attention to this treatise, one question springs readily to mind: “What are Proclus’ astronomical sources and how does he deal with all the material available to him?” My aim is to identify some of the sources which Proclus draws upon and explore the ways in which their contents are integrated into the Hypotyposis.
More specifically, in this talk I intend to show the extent to which Proclus goes through the astronomical theories, the topics which interest him the most and the degree to which he comments on the astronomical theories. For instance, since the Hypotyposis serves as a handbook for beginners in astronomy by summarizing and explaining the main points of Ptolemy’s Almagest, as Proclus’ own scattered words suggest, by examining the correspondence of the topics between these two works, I will bring out Proclus’ preference for the geometrical explanatory models as such (i.e. epicyclic, eccentric and eccentrepicyclic models for the Sun, Moon and the five planets) over the numerical parameters accompanying them, as well as his interest in the astronomical instruments. Moreover, views supported by other astronomers, which Ptolemy either accepted or criticized, are mentioned in passing, mainly in the framework of a historical retrospect, since Proclus’ adherence to the Almagest casts its shadow on them. Last but not least, I will adumbrate the criteria by means of which Proclus chooses the topics, for which he offers an exegesis, the perspective from which he comments on them, and, furthermore, his general stance towards the astronomical theories.
Early Science in Byzantium: Epistemic Value of Astronomy in Fourteenth-Century Constantinople
The present paper analyses and comments on a text composed by the Byzantine scholar Theodoros Meliteniotes (c. 1320 – 1393), which provides noteworthy theological and philosophical issues. It requires a scholarly commentary for several reasons: it is evidence of the epistemic value of astronomical mathematics in Byzantium, i.e. of the epistemological status of this discipline in the frameworks of contemporary sciences, as well those of the imperial politics of the Eastern Roman Empire and of the official didactic programs. The text is a prologue to an astronomical work redacted by Meliteniotes about the middle of the fourteenth century in Constantinople, which is entitled Ἀστρονομικὴ Τρίβιβλος, Three Books on Astronomy (henceforth Tribiblos). The author was rector of the Patriarchal School of Constantinople and belonged to the followers of the hesychasm and the theology of Gregory Palamas, therefore he was deeply influenced (but not only) by neo-platonic theories and rejected Latin theological fundamental assumptions, for instance the one of the filioque about the procession of the Holy Spirit. All this has explicit and implicit consequences in what he argues about the epistemological status of astronomy and about the need (usefulness) to study this subject in the Byzantine scholarly community. On this account, this text constitutes an important source for the definition of early science.