We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. (...) In this paper it is shown that this problem has permeated the whole of European civilization from the Ancient Greeks onwards, leading to a radical disjunction between cosmology which aims at a grasp of the universe through mathematics and history which aims to comprehend human action through stories. By going back to the Ancient Greeks and tracing the evolution of the denial of creative becoming, I trace the layers of assumptions that must in some way be transcended if we are to develop a truly post-Egyptian science consistent with the forms of understanding and explanation that have evolved within history. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to (...) "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts (...) – mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive. (shrink)

Sticking to elementary mathematics, this text is a short introduction to understanding historical and comparative counting systems. It gives a brief historical and contextual overview, along with showing how to read and count in a number of ancient systems including Egyptian, Babylonian, Mayan, Roman, Hebrew, Intuit, binary, Quipu and abacus.

The existence of a mathematical theory determining the shape of the Great Pyramid is a long‐standing assumption, and speculation on the subject dates back to Herodotus. Roger Herz‐Fischler's study presents and discusses eleven major theories and their proponents in the light of archaeological and philosophical considerations. The historiographical aspect of the study is very useful, as is the formulation and discussion of some of the problems. A brief sociological case study of the Pi‐theory and the reasons for its propagation and (...) popularity in Britain is particularly interesting. But although this book offers much that will be of interest to professional and amateur historians of mathematics and pyramid enthusiasts, it does not provide a definitive conclusion to the 2,500‐year‐old debate.Having dismissed all but three of the theories and unable to decide among them, Herz‐Fischler reaches the rather extraordinary conclusion that there may have been no true theoretical basis for the angles of inclination that might have been established “by eye” . In settling for this interpretation, however, he fails to consider how the angle would have been replicated on the different sides of a pyramid or how angles of inclination would have been maintained or transferred to other pyramids of different sizes: for example, Khufu's three queens' pyramids have slopes virtually identical to those of the main pyramid .The three theories among which Herz‐Fischler cannot decide are all proportion‐based theories, two relating to the angle of inclination and one to the angle of the arris . This conclusion is significant in its own right and relates to practical building considerations. Herz‐Fischler is keen to distinguish mathematically between integer proportional systems and the seked theory , a system attested in ancient Egyptian mathematical texts and related to the division of the cubit into seven palms, each of four fingers. But the close relation between these two methods of measurement in practical terms is clear, and either one could have been used with ease by an ancient builder.Herz‐Fischler states that “there simply is no archaeological evidence for the above three rise over run based theories” . Here he is too quick to dismiss the evidence presented by Flinders Petrie from a mastaba at Meidum . Outside the corners of the structure are walls with traces of horizontal lines at cubit intervals and sloping lines marking the inclination of the faces. Herz‐Fischler points to the lack of marks to indicate how the slope was constructed, but he fails to consider how an identical slope was constructed eight times around the structure if such a horizontal measurement was not used. Nor are the corners of the structure level; thus the correct measurements must be calculated relative to the depth. Mark Lehner, in his Complete Pyramids , page 220, offers evidence from Giza that the builders constructed the corners by measuring in a certain distance from reference points outside the sides. The pyramid drawing from Meroe based on a rectangular grid does not necessarily conflict with a rise and run theory and certainly shows that a proportional system was used relating side length to height. I find this archaeological evidence for the use of rise over run theories convincing, if limited, and it strongly supports side‐inclination based theories over those relating to the arris.The Meroe drawing cannot be taken as reliable evidence that the seked theory was not used in Fourth Dynasty structures , as it dates to over 2,000 years after the Great Pyramid was constructed and lies outside Egypt. As for the question of whether a seked‐based system or integers were used to construct the angle of the sides, Herz‐Fischler could have used the measured angles of sloping corridors and shafts inside the Great Pyramid that must have been constructed using similar techniques. Further, he makes no attempt to apply these theories to the slopes of other pyramids, although in some cases he does consider examples presented by other authors. Applying these theories more broadly might lead to more decisive results. Before readers undertake to do so themselves, however, they should be alerted that some of the measurements given in Appendix 2 are out of date. Corrected figures are: Abu Rawash, c. 52° ; Bent Pyramid, 55° 00′ 30″ , 43° 01′ 30″ ; Red Pyramid, 44° 44′ . In this last example considerable variation was noted in the inclination of different stretches of the same pyramid face, which suggests that an angle of 45° was intended. This observed variation is very significant considering how little of the casing of the next pyramid constructed—the Great Pyramid—is preserved .Although I find Herz‐Fischler's conclusions rather weak and some of his treatments of archaeological sources too dismissive, this volume provides a useful introduction to the subject and a clear formulation of the problems involved. It is, then, a thought‐provoking contribution to a long‐standing debate. (shrink)

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity -- Axiomatic (...) set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

Pythagoras and Pythagoreanism have a different position in the ancient philosophy tradition. The reason for this is the eclectical structure of Pythagoreanism which has syncretized from Orphism, Indian and Egyptian religions with philosophy. Orphism of these religions is especially important for affecting Pythagoreanism the most and giving to the ancient Greek religion a mystical content. Orphism which is a mystery cult is based on Orpheus, the poet, who sometimes is identified with Pythagoras in philosophy and the history of religions. (...) Orpheus, was attributed divine character by virtue of his beautiful voice and hymns in the ancient history, has brought many religious and philosophic elements such as reincarnation and unity with God to the Greek religion. The way of life and creeds of Orphism based on asceticism and wisdom, first affected Italian philosophy starting from Pythagoras and, later influenced both philosophy and the other religions such as Judaism and Christianity through Plato. The reason for this was the Orphism’s stronger theological structure than the Greek religion had. Thus, philosophy, the Miletus philosophers tried to purify from the Homeric religion, has regained some spirituality through Orphism and Pythagoras. Pythagoras, a philosopher and a religious leader, accepted students to his philosophy school by initiation in Crotone. In this way, Pythagoreanism gained the quality of both a school of philosophy and a community of mystery. In this school, Pythagoras constituted a strong natural philosophy based on the idea of arkhe consisting of numbers, and the system of mathematics and music. At the same time, for he was a religious leader, Pythagoras used his school both to teach philosophy and to celebrate the teletaic mystery rituals of Orphism. According to the Pythagoreans, as a master, Pythagoras has united with the spirit of Dionysos and has privileged to rise to the World-Soul of God. Due to this union, it has been believed that Pythagoras received revelations from Dionysos and knew the secrets of God’s spirit. Similarly, Pythagoras’ students of philosophy also joined these rituals. They, on the one hand, witnessed to the divine union of Pythagoras, on the other hand, experienced the communication with the subordinate gods, called daemons, allied to Dionysos. Through these mystical rituals in Pythagorean school, it was believed that the philosophical knowledge was not only a reasoning, but also a divine wisdom obtained from the divine word. Therefore, Pythagoreanism accepted that philosophy is from God and it is a way of life which rises the human to the divine level. According to Pythagoras philosophy, thinking about God is equal to dealing with natural philosophy. Because Pythagoreanism, that has a pantheistic belief in God, has acknowledged God and nature as the same. Additionally, the natural philosophy of the school was established on the Monad idea which has been accepted as the World-Soul. For Pythagoreanism, Monad is not a number, but it is the ONE as the source of all numbers and a theological principle. The ONE, which symbolizes God and the cosmic unity, brings into existence the life by limiting the chaos caused by the TWO. Similarly, the TWO, not a number but a principle, has been used in a positive sense in Anaximander and was called apeiron, meant “infiniteness”. But, for Pythagoras, infiniteness was a negative circumstance. For this reason, the TWO/Apeiron has been accepted as a female being which corresponds to limitless absence and evil. By Monad’s confinement the Apeiron had been passed into the cosmos, the cosmic harmony had been balanced and a spheric being had emerged. This is “unity” which corresponds with both the World Soul Monad and the nature in the Pythagorean philosophy. This study will discuss the notion of Monad which is known as the World-Soul and God in Pythagorean philosophy, from a perspective of the history of religions. In this context, the sources and knowledge of history of philosophy will be used by methods of the history of religions. Starting from Orphism, Monad will be discussed within similar mythical elements. Thus, the origin of the Pythagorean philosophy in ancient religions will be determined and the theological infrastructure will be shown. (shrink)

Very Short Introductions: Brilliant, Sharp, Inspiring Ancient Greece is often considered to be the birthplace of science and medicine, and the explanation of natural phenomena without recourse to supernatural causes. These early natural philosophers - lovers of wisdom concerning nature - sought to explain the order and composition of the world, and how we come to know it. They were particularly interested in what exists and how it is ordered: ontology and cosmology. They were also concerned with how we come (...) to know (epistemology) and how best to live (ethics). At the same time, the scientific thinkers of early Greece and Rome were also influenced by ideas from other parts of the world, and incorporated aspects of Egyptian, Babylonian, and Indian science and mathematics in their studies. In this Very Short Introduction Liba Taub gives an overview of the major developments in early science between the 8th century BC and 6th century AD. Focussing on Greece and Rome, Taub challenges a number of modern misconceptions about science in the classical world, which has often been viewed with a modern lens and by modern scientists, such as the misconception that little empirical work was conducted, or that the Romans did not 'do' science, unlike the Greeks. Beginning with the scientific notions of Thales, Pythagoras, Parmenides and other Presocratics, she moves on to Plato and Aristotle, before considering Hellenistic science, the influence of the Stoics and Epicurean ideas, and the works of Pliny the Elder, Eratosthenes, and Ptolemy. In her sweeping discussion, Taub explores the richness and creativity of ideas concerning the natural world and its function in the ancient world, and the influence these ideas have had on later centuries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

This paper discusses the relation between letters and numbers in the case of ancient Greek and, other writing systems and, supports that priority must be given to the numbers, that is to say the use of letters of the alphabet was constrained, by the necessities of mathematics. In the case of Ancient Greece the ‘24 letters of the alphabet’ plus ‘3 additional signs’ were used to notate the numbers. These 27 signs formed the three enneads of the Greek Numeral System, (...) which was in use in Eastern Mediterranean and parts of Europe for almost 2,000 years. So, the 24 letter-signs were also digit-signs. The arithmetic use of letters is considered by epigraphologists and Hellenists a later development, occurring two or three centuries after the invention of the Greek alphabet. This paper supports that, from the very beginning, the alphabet should, have had, 27 signs in order to meet the needs of mathematics, that is to meet the necessity of using the enneads of the Egyptian numeral system, which probably was transferred, to Greeks via the Semitic writing system. This hypothesis is based, on the contradictions which arise between the choice of signs and their use, from ancient Greek ‘Logistikē’, from archaeological finds and from the examples of other writing systems, which were also created so as to serve the needs of mathematics — namely Hebrew, Arabic, Coptic, Armenian, Georgian, and, other alphabets. Consequently, the alphabet should, not be considered, as a secondary system of signs, which was created, in order to record, the spoken word, but as a subset of a broader semiotic system that attempts to express human Reason in general. (shrink)

Writing, the exigency of writing: no longer the writing that has always (through a necessity in no way avoidable) been in the service of the speech or thought that is called idealist (that is to say, moralizing), but rather the writing that through its own slowly liberated force (the aleatory force of absence) seems to devote itself solely to itself as something that remains without identity, and little by little brings forth possibilities that are entirely other: an anonymous, distracted, deferred, (...) and dispersed way of being in relation, by which everything is brought into question – and first of all the idea of God, of the Self, of the Subject, then of Truth and the One, then finally the idea of the Book and the Work so that this writing (understood in its enigmatic rigor), far from having the Book as its goal rather signals its end: a writing that could be said to be outside discourse, outside language. – Maurice Blanchot ( The Infinite Conversation , xi) The Compendium * Beginning with the idea and practice of writing, and moving to the subject or self, then to truth and the One, and arriving at the Book and the Work, Blanchot’s words reflect the trajectory of the following work of writing. True to the embeddedness of the subject in the work of writing, the term “Compendium” has been a metonym for me over the past few years as I have thought about the concept of totality alongside its expression in figures such as the One, the Whole, or the All. In the following I aim to share some of the content of this metonym, and to enrich it by making some distinctions. 1 Here the term “Compendium” will refer to a concept of totality that is ontological (pertaining to being, and the copula) and also textual (pertaining to the symbolic, and the signifier-signified relationship). The Compendium is a figure for thinking the world as a Book, in the broadest sense—an approach to reality that is by no means new, but one that is due for renewal. 2 In partial answer to the question of the Compendium we will say that the word ‘Compendium’ stands in for expressions which seek to totalize, or concepts which seek to approach the concept of ‘everything,’ particularly when these expressions are bound up in the question of the Book (both the book as a physical object and the Book as a metaphysical figure: a way of thinking about the work in and of writing). The question of the Compendium is strongly associated with the physical and metaphysical form of the Book, like the mysterious and symbolic books which are opened in the Biblical book of Revelation, the book of life and the book of death, which together constitute an important couplet. 3 Parataxis & Hypotaxis There are two helpful distinctions that will bring us closer to an answer to the question “What is a Compendium?” The first distinction is between two figures in and for writing: parataxis and hypotaxis . Typically paired in contrast to one another as literary techniques, with parataxis indicating a side-by-side placement of textual elements and hypotaxis referring to subordinate arrangements of textual elements, the two figures can be understood as having a philosophical significance in addition to their practical function as devices for writers. For us these two terms will remain between philosophical theory and writing practice, and serve as a perspective for our writing and creation of texts. Here I take texts to refer to anything from the concrete written words in a book, to the ontological text of the world that we experience. Parataxis , as a figural way of thinking about the ontological structure of texts, refers to texts which are tightly woven and interdependent – texts within which each sentence bears the weight of the entire work. Parataxis often involves repetition, great density, and fragility. One of the best examples of this sort of text is Theodor Adorno’s posthumous magnum opus , Aesthetic Theory . In addition to the text itself, the translation history of the book may also help us to better understand parataxis and its relation to hypotaxis . The final published version of Aesthetic Theory , in German, was a text that Adorno intended to revise and rewrite, but this intention was never realized because of his untimely death. Where the German text of Aesthetic Theory certainly exemplifies the concept of parataxis , the first English edition took this densely woven text and carved Adorno’s lengthy paragraphs and lengthy sentences into manageable ‘bite-sized’ pieces of English text. The first translator took further liberty and inserted headings and new paragraph breaks where there were none in the original. Aesthetic Theory was eventually retranslated by Robert Hullot-Kentor and is now available in a form that is much more faithful to the original work. 4 The pertinent idea that this translation history points to is the distinction between parataxis and hypotaxis . Where parataxis describes texts which are repetitive, densely woven, and often fragile, hypotaxis describes texts which are hierarchical and in which the primary relation is linear – the latter of which is very similar to the first English translation of Aesthetic Theory . On the other hand, the original German text that Adorno wrote was very dense, often repetitive, and contained long sections of text unbroken by paragraphs or headings. This example of parataxis was then turned towards hypotaxis through the initial translation which took a text that was, in many ways, nonhierarchical and nonlinear, and artificially subjected it to a hierarchy that was not its own (and here I take the word of Fredric Jameson who comments on the two translations in a note at the beginning of his book Late Marxism ). 5 The point here is not about translation, but rather the distinction between parataxis and hypotaxis precisely as they are figures for discourse, written or otherwise. The concept of parataxis looks far more postmodern and rhizomic than the concept of hypotaxis which remains very modern and arborescent. This is a more figural way of talking about the distinction. However, if we wanted to take a more precise and analytical approach we could say that on the level of form parataxis involves a relationship between sentences and paragraphs in which each part bears an equally crushing responsibility to present the whole content of the text. As well, on the level of content, parataxis requires that each concept in a work take on the full conceptual weight of the total work. Continuing the analysis, we could say that parataxis describes texts in which there is no (or very little) linear or causal move from antecedent to consequent, whether in content or form. Instead, parataxis describes texts which weave together concepts via conjugations or associations. The concept of hypotaxis , on the other hand, requires that texts submit themselves to hierarchy, one example of which is logical argumentation. The contingency of the conclusion upon premises in hypotaxis is certainly distinct from the repetition, re-presentation, and conjugation of concepts in parataxis , and I think that this is evident in the difference between the writing styles prevalent in contemporary Analytic philosophy and Continental philosophy. It is not the case that the distinction between parataxis and hypotaxis absolutely corresponds with the writing styles of Continental and Analytic philosophy (respectively). There are thinkers who take exception to this pattern, such as Badiou’s more formal approach in the discourse of Continental philosophy to give one example. However, when Analytic philosophy takes its writing lessons from the sciences, and seeks to do philosophy via the clean linear move from antecedent to consequent, then I think that Analytic philosophy writes with hypotaxis in mind. On the other hand, when Continental (particularly German and French) philosophy takes its writing lessons from narrative or poetry then Continental philosophy writes with parataxis in mind. It is not fair to say that all those writing Continental philosophy are looking to narrative and poetry for stylistic direction, just as it is not the case that all those writing Analytic philosophy have mathematics and science as their writing format, however there are some striking ways in which the differing epistemologies of Continental and Analytic philosophy encourage writing with parataxis and hypotaxis in mind (respectively). For some, writing with parataxis or hypotaxis in mind is a conscious decision and a product of stylistic self-consciousness, and for others it is an unconscious discursive and epistemic requirement that must be met in order to be involved in a particular discourse. Before moving on to our second distinction, and then an examination of the question of the Book, it is important to point out that both totality and figurations like the One, the Whole, and the All, come out of very human desires to totalize or to actualize our being-towards-totality. The relationship between identity and totality then can be construed, with Heidegger in mind, as striving toward wholeness, completion, or fulfillment, each of which is a quality of compendia. 6 Compilation & Selection The first distinction between parataxis and hypotaxis pertains to both form and content, and to both the mechanics of writing and the ideas to which writing refers. The second distinction pertains to both as well. In the process of writing and in the process of perception as well, there is a tension between compilation and selection . To begin with, in the work of theory-writing there is compilation, and this is because writing theory requires a broad perspective and certain measure of totalization. On the other hand, writing theory requires that the writer select an idea or a combination of ideas to individuate out of a radical and infinite multiplicity of identities and combinations. The concern here is not primarily for the writing of a theory about a specific idea, like a secondary work or a reference text. But rather the concern is with the writing of grand theories: Marx and Marxism, Derrida and Deconstruction, Husserl and Phenomenology, Sartre and Existentialism, Saussure and Structuralism —each of which strives along a trajectory towards being all-encompassing, whether it intends to or not. Today, we could even say that Speculative Realism has embarked on this journey, and perhaps now we could say that the discourse of Speculative Realism has reached the inevitable point after which a grand theory leaves the hands of its writer or writers and becomes a possession of the collective consciousness of the academy, or (perhaps now) the mass consciousness of the blogosphere—and this is a true pharmakon , a poison and a cure, a blessing and a curse. 7 When we write theory, whether the scope is that of a grand theory or a particular theory, we write in the tension between compilation (making good on the desire to be all encompassing) and selection (being required to decide and discern and to judge what is included in the work and what is deleted or appended or abridged or given over to ellipses). Generally speaking, the work of theory-writing often comes out of a desire to totalize, that is, to develop a theory of everything that is able to apprehend new experiences and ideas while still remaining whole. I grant that this is not a universal desire, and that not everyone who sits down to write a work (or book) of theory does so because of their will-to-totality, but it remains that this drive to totalize does condition a great many writers of theory (especially those who seek to develop grand theories like those mentioned previously). At the beginning of his book of interviews, Between Existentialism and Marxism , Sartre is quoted as saying, after completing the first volume of his Critique of Dialectical Reason : “I no longer feel the need to make long digressions in my books, as if I were forever chasing after my own philosophy. It will now be deposited in little coffins, and I will feel completely emptied and at peace—as I felt after Being and Nothingness . A feeling of emptiness: a writer is fortunate if he can attain such a state. For when one has nothing to say, one can say everything .” 8 This is where our two initial distinctions come to bear on the being-towards-totality as it is expressed in the concrete practice of writing: the first being between parataxis and hypotaxis , and the second being between compilation and selection. Where this second distinction is concerned there is a certain paradox at play given that selection is inescapable, and compilation is unachievable. Selection is inescapable (with the figure of the Compendium in mind) because, even when the imperative to compile is followed to excruciating lengths, selection still has the last word. This is why the Compendium is a figure rather than some material thing that can actually be accomplished or actualized. No matter how far one goes along with the will-to-archive and the will-to-compile, it is only ever a question of minimizing selection and never eliminating it. This leads to the second point, which is that total compilation is unachievable. The closest thing to total compilation that we have before us is the ontological and textual fabric of the world. Even in the case of the world, compilation cannot be enacted in a total fashion because of the need to include both the sphere of the actual and the sphere of the possible or potential. This as another way in which compilation is always-already selection, and further evidence that total compilation is practically impossible. Discursive Figuration and Total Writing Rather than figuration referring to a figure of speech or an image, here the term points to a way in which to think about the work of writing, both the work put into writing, and the work that is the result of writing: the finished yet incomplete final piece. As figures or figurations, the Book and the Compendium are ways of thinking about the work of writing and the human desire for the wholeness, completion, and fulfillment that are made manifest in the completed form of the book (whether a published or printed or saved document put to rest by the author). These two figures bear more strongly upon works that seek to be all-encompassing, and works that strive towards expressions of totality such as the One, the Whole, or the All. Moving on to the topic of the subtitle, and on a more prescriptive note, I would say that there is more hope for theory-writing to be found in parataxis than hypotaxis . Part of the reason for this claim is the poststructuralist critique of hierarchies, and yet another part is the compelling line of thinking called “weak thought” (in theology by John D. Caputo, and in philosophy by Gianni Vattimo, among others). 9 The consequences of these two convictions are such that if one is to strongly assert the truth of a grand theory without leaving the realm of hierarchy-critique and weak thought, then one must write paradoxically with parataxis in mind, and in so doing write weakly and non-hierarchically. This does not mean avoiding a sort of topography or topology when writing theory, rather it means avoiding both subjugation and oppression in thought by pursuing a nonviolent sort of ontology. In order to do this, theory writing does not present itself as an exercise in logical analysis where one mechanically moves from a set of premises (via contingency) to the inevitable conclusion (via necessity). Instead, theory approaches the idea of a Compendium. Given that the figural Compendium places parataxis and compilation above hypotaxis and selection, then the question becomes: is placing one part of a binary term before another not just another way of selecting, or another expression of hypotaxis ? Counter to the urge to resign oneself to the reign of selection, with some qualification one can nonetheless write without deciding whether selection and hypotaxis should be subservient to compilation and parataxis (which is to say that writing-without-decision is somewhere between and beyond possibility and impossibility). This dilemma can be disarmed by stating that theory writing is not about primacy, and not about having-decided-beforehand, both stylistically and also where content is concerned. This is the paradox of writing: always striving along a trajectory ( telos ) towards totality via parataxis and compilation, but always being drawn back to finitude and making selections, and placing one idea before another with hypotaxis in mind. In light of this paradox, the question of the Compendium as a figure for discourse and a figural Book has resonance with Jacques Derrida’s essay on Edmund Jabès’ Book of Questions , found in his Writing and Difference . The Question of the Book “Little by little the book will finish me.” 10 Derrida quotes Jabès, and proceeds to outline the reflexive relationship between the author of the book and the book itself, each of which are subjected to the other through a sort of chiasmus, both ontological and textual (not that the two are entirely separable). The Book, for Derrida like Blanchot in the introductory quotation, “infinitely reflects itself” and “develops as a painful questioning of its own possibility”, and in light of this we can draw an association with the painful tension between the practical reality of selection and the ideal trajectory of compilation. 11 This tension in writing, between the will to total compilation and the necessity of abridgment, is an ontological tension between part and whole just as it is a textual tension between signifier and signified. The ontological tension in writing that Derrida expresses in his essay on Jabès is between everything and nothing – a contradiction which Derrida finds in Jabès’ Book of Questions and also in the divine, in God. When one writes between compilation and selection one writes towards totality, and here we can follow Derrida who states that the lapse in signification, presumably in the signifier-signified discrepancy, is a “ rupture with totality itself” and furthermore that this lapse cannot be rectified through deductive reason or even philosophical discourse. 12 This rupture with totality, found in the troubled relation between signifier and signified, can also tell us a lot about the Book and about writing. Given an understanding of writing as an ontological act that strives towards (but never accomplishes) totality, we can see the written book as the manifested and given body of that striving. Perhaps in other disciplines or even other schools of philosophy there is a cultural climate within which the article is prized above the book, but I am fairly confident, especially when referring to the grand theories of Continental thought, that there is a respect for the book as a uniquely meaningful object capable of apprehending totality. Derrida writes, Between the too warm flesh of the literal event and the cold skin of the concept runs meaning. This is how it enters into the book. Everything enters into, transpires in the book. This is why the book is never finite. It always remains suffering and vigilant. 13 Here the vitality of the literal event is compromised by the deadening weight of the concept, and the figure of the Book assists in this lapse of meaning. The Book is a totalizing object, much like the figure of the Compendium, and yet this totalization lacks its final object of completed totality both because the figural Book is necessarily incomplete, and because the physical book is always-already a product of selection. Instead of achieving its end of being a place where everything takes place, it suffers from the lapse of writing, the discrepancy between event and concept. Derrida continues his exposition on Jabès by bringing to light yet another reflexive relation, a reversal of the relationship between the Book and the world. Derrida writes that, for Jabès, “the book is not in the world, but the world is in the book.” 14 In addition to what was stated before, I take figuration to mean that the concepts employed, such as the Book or the Compendium, are not subject to the supposed rigor of analysis that is so prized by Enlightenment or Capitalist realisms. The figure of the Book and the figure of the Compendium cannot be held accountable to standards imported from scientific method, given an understanding that these standards require a concept to be replicable, consistent, falsifiable, measurable, and so on… This is an important point to make, especially in the present atmosphere within which theory must justify itself under conditions that are not its own. Instead of being held to these standards, figuration serves as a way in which to think about writing that leaves thought open to idealistic speculation, imperfect analogies, and most importantly the ever-present gain and loss that occur in the relationship between thought and being. By extension the figural way of addressing writing indulges in enough generalization to accommodate the excess/lack relationship between the ideal form of the Book or the Compendium, and the manifested and given body of a text (as it is practically completed and closed). Here we speak against the hostile atmosphere which would have theory submit itself to hierarchical rigor, rather than Blanchot’s “enigmatic rigor”, by being explicit about the discursive conditions and epistemic conditions under which theory operates. To write with parataxis in mind is, to a certain degree, to write with weakness as one’s methodology (with weak thought being in opposition to hypotaxis and hierarchy as much as weak thought can be in opposition to anything). Rather than asserting the strength of hierarchical theory, and rather than employing antagonistic argumentation with the goal of refutation different discursive and epistemic conditions for theory writing must be cultivated (and these are by no means new). First the critical and theoretical spirit reveals itself as being concerned with the task of complication—especially the complication and critique of binaries, dichotomies, dualities, polarities, paradoxes, parallaxes, hybridities, and especially antinomies. Second, theory positions itself as a sort of showing or revealing, rather than being ultimately focused on coming to full agreement or disagreement. This is where figuration can help theory-writing, both by placing emphasis on teleologies and trajectories (like parataxis and compilation), and by shifting focus away from pure primacy, power, or absolute origin. Figuration then, assists theory writing by placing the concern of theory outside of the concerns of the hard or soft sciences, and into the realm of thought or the idea. To speak of ‘the’ Compendium or ‘the’ Book, here, is to generalize not regarding the perfect form of the Compendium or Book, but to engage speculatively with an abstract idea which remains singular and yet complicated by multiplicity. The question of the Book that Derrida asks through Jabès is a question of everything and nothing, totality and nonbeing, and this question is a concern for writing and a concern for the figure of the Compendium so defined by the tension between compilation and selection, and parataxis and hypotaxis . On the note of nonbeing, we can look to the final page of Derrida’s first essay on Jabès in Writing and Difference and notice the introduction of his neologism, différance (with an ‘a’). Derrida writes: Life negates itself in literature only so that it may survive better. So that it may be better. It does not negate itself any more than it affirms itself: it differs from itself, defers itself, and writes itself as différance . Books are always books of life (the archetype would be the Book of Life kept by the God of the Jews) or of afterlife (the archetype would be the Books of the Dead kept by the Egyptians). 15 This introduction of différance into the equation of the Book, alongside ontological affirmation and negation, hearkens back to the discussion of the symbolic lapse earlier in his essay. Differing and deferring, the Book is always a Book of Life and a figure for the intersection of the vital (life) and the total in writing. In a way, the writer of the Book may be someone who lives life, and in another way the writer of the book-as-object may be someone who engages in the act of writing, both practically (by inscribing words on paper, or typing script on a computer) and ontologically or symbolically (by investing their existence and inexistence into a work worthy of the figural Book). In addition to the writer as writer, the writer also serves as an editor, and the editorial role alongside the idea of the Compendium shows the editor to be one who collects and compiles, while being restrained by eventual selection and decision. Beyond this the editor of works and texts, in both the Book and the world, is engaged in a process of inscribing notation—of annotating (on) the Compendium. Eternal commentary is a feature of the textual Compendium, just as open-ended totality describes the ontological Compendium. The writer as writer does not simply write texts, but rather engages in a profoundly ontological act of inscribing their existence into the world, and the writer as editor does not merely annotate or alter texts as they are, but rather comments upon the text of the world. In/Conclusion So as we create texts, and as we write and create theory, let us be and remain attentive to the figure of the Compendium and the figure of the Book. These two concurrent metonymies are essential for total writing (grand theories, etc.), and may be forgettable for those concerned with fragmentary or hierarchical writing (which are valid in their own right). From the ontological and symbolic text of the world and phenomenological experience, to concrete texts such as books or mixed media, the figure of the Compendium and the figure of the Book are important for the actualization of the human will to be all-encompassing. The figure of the Compendium teaches writers of theory that the repetition, density, and fragility of parataxis offers a strong sort of weakness which does not become yet another variety of oppressive and hegemonic thought. Rather than write with hypotaxis in mind, subjugating one thought to another via cause and effect or antecedent and consequent, I would hope that theory-writing could guiltlessly indulge in the dialectical and contradictory conjugation of ideas, and take this as a legitimate methodology. Rather than being ashamed of showing resonances or giving way to abridgment or ellipses, it is my own authorial (but not authoritative) conviction that one need not give up on totalizing and constructing grand theories because of the fact that complete totalization is impossible, and one need not give up on totalizing and constructing grand theories because of the worry of violence, for the Book and the Compendium lack their completed object and are ever incomplete trajectories. NOTES * UPDATED 7/19/13: we've updated the HTML version to reflect the (correct) PDF version. Our apologies to the author—eds. 1. I would like extend thanks to Dr. Peter Schwenger of the University of Western Ontario for his comments on this paper and his hospitality as it was presented as a Theory Session at the Centre for Theory and Criticism on October 26th 2012. I would also like to thank Andrew Weiss for conversation and critique. 2. I should clarify my use of the term ‘figure’ at the outset. Given the use of the term by Jean-Francois Lyotard in Discourse, Figure (and also Gilles Deleuze in Francis Bacon ), I should state clearly that my use of the term will not correspond to the term ‘figure’ understood as the representation of an object. Instead, my use of the term ‘figure’ and its variations (‘figural’, ‘figurative’, ‘figuration’) will refer to the illustrative or metaphorical use of the Compendium or the Book as models or ways of thinking about writing and discourse. 3. Cf. Revelations 20:12-15. 4. Theodor Adorno, Aesthetic Theory , Trans. Robert Hullot-Kentor (London & New York: Continuum Press, 1997). 5. Fredric Jameson, Late Marxism: Adorno, or the Persistence of the Dialectic (London & New York: Verso, 1990), ix-x. 6. I have written about this concept of being-towards-totality elsewhere in two pieces of writing: the first is called Notes on the Compendium (an unfinished draft) which addresses some very wide theoretical concerns, being structured as a sort of itinerary or archive, and the second is Dialectics Unbound (Punctum Books, 2013) which outlines a concept of totality without the violence of totalization. While these works are more concerned with ontological totality, here I would like to focus on the idea of the Compendium as a textual totality. 7. Cf. Louis Morelle, “Speculative Realism: After Finitude and Beyond, A vade mecum” in Speculations: Journal of Speculative Realism . Issue 3 (Brooklyn, New York: Punctum Books, 2012), 241-272. 8. Jean-Paul Sartre, Between Existentialism and Marxism . Trans. John Matthews (London & New York: Verso, 1974), 9. 9. Cf. John D. Caputo, The Weakness of God (Indiana: Indiana University Press, 2006). 10. Jacques Derrida, “Edmond Jabès and the Question of the Book” in Writing and Difference . Trans. Alan Bass (Chicago: University of Chicago Press, 1978), 65. 11. Ibid, 65. 12. Ibid, 71. 13. Ibid, 75. 14. Ibid, 76. 15. Ibid, 78. (shrink)

It once seemed almost self-evident that the extraordinary progress of Greek astronomy and mathematics in the Hellenistic age were, at least in part, the result of contact with Babylonian and Egyptian culture. But, whatever they may have owed to Babylonia in the exact sciences, there is now a growing consensus that even as early as Eudoxus the Greeks had advanced beyond the point where they might have profited from Egyptian help, and it is not easy to find a (...) solid basis for the widespread Greek belief in the superior wisdom of the Egyptian hierarchy. Yet the preface to the famous Calendar for the Saite nome, P. Hibeh 27, provides circumstantial evidence that one Greek, at least, in the fourth or early third century B.C., found in Egypt an instrument for measuring the time at night which was new to him and which he may well have found impressive in its accuracy. (shrink)

Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational (...) theology adopted during the Crusades, as a counter to Islamic rational theology. Deductive proofs are MORE fallible than inductive or empirical proofs. Even a validly proved mathematical theorem, such as the “Pythagorean” theorem, is invalid knowledge in the real world. There is no concept of approximate truth in formal mathematics. Nevertheless, the myth of “superior” axiomatic proofs in the “Euclid” book continues to be reiterated by Western historians, and colonial education teaches axiomatic mathematics. Actually, superior practical value comes from the two “Pythagorean” calculations well known toIndian/Egyptian tradition, but unknown to Greeks. The advantage of related decolonized courses in mathematics has been pedagogically demonstrated. But understanding and political will are needed to change colonial/church education. (shrink)

THE THEME, "The Intelligibility of Nature," is exceedingly broad. It stretches like a vast domain in which one can only hope to leave a few footprints, some fragile impressions that are all but lost in the expanse. In attempting to understand the natural world, the enterprise that is most familiar to many of us is inherited from the Greeks and their Latin heirs, both classical and mediaeval, and this enterprise continues in our own day in the form of the modern (...) sciences of nature. Nowadays, we are more informed about the knowledge acquired by the Egyptians, Babylonians, and others prior to the Greeks. We are more conscious of the achievements of the Chinese in physics and the Indians in mathematics. And we are more aware of the medical and zoological lore present in oral traditions, such as those of Africa. Moreover, we are only now beginning to appreciate their contributions and their potential for new forms of enquiry, including other ways of approaching nature. The terms in which the topic is here designated, however, are conceived in Greek and expressed in Latin. Nevertheless, even within this cultural tradition of natural enquiry, the topic is quite broad enough. Like a grammarian of old parsing a sentence, I am forced to begin by distinguishing parts of the theme. (shrink)

We review the history of decipherment on the technologies used for numbers by the Inkas – khipus and yupanas. We offer a novel interpretation of the portable “checkerboard” yupana drawn in 1615, revealing a numerical algorithm. This analysis sheds new light on the Inka number system, questioning its inclusion of a concept of zero and its interpretation as a positional system. We conclude that Inka numbers and computational methods were likely non-positional, analogous to Mesopotamian, Egyptian, Greek, and Roman numbers. (...) We show the Inka multiplication method as similar to – but more efficient than – the Egyptian method in the Rhind Papyrus. This analysis shows the Inka number system to have ranked among the great mathematical traditions of the ancient world. (shrink)

Summary The Almagest of Ptolemy (mid-second century ad) contains eleven dated reports of observations of the positions of planets made during the third century bc in Babylon and Hellenistic Egypt. The present paper investigates the character, purpose, and conventions of the observational programmes from which these reports derive, the channels of their transmission to Ptolemy's time, and the fidelity of Ptolemy's presentation of them. Like the Babylonian observational programme, about which we have considerable knowledge through cuneiform documents, the Greco-Egyptian (...) ones were not directed towards the deduction of mathematical models of celestial motion but appear to have investigated patterns, correlations, and periodicities of phenomena. Ptolemy's immediate sources most likely were not the original series of observational records, but treatises by various astronomers of the intervening four centuries, including Hipparchus. While Ptolemy does not appear to have tampered with the wording of the reports, he faced difficulties and uncertainties in interpreting them; critically, he lacked sufficiently detailed information about the ancient calendars to be able to convert the reported dates accurately into his own chronological framework based on the Egyptian calendar. (shrink)

An historical survey of the inquiry into the foundations of mathematics, presented in a series of original texts connected by the author's introductions and analyses. The source material, ranging from Egyptian surveyors' papyri to Lorenzen's "Konstructive Begründung der Mathematik," is well chosen, and the author's commentaries are clear and illuminating. The selections are often shorter than might be desired, but the book is extremely useful as a summary and introductory survey. A short bibliography is included.--V. C. C.

This article analyzes the angular spacing of the degree marks on the zodiac scale of the Antikythera mechanism and demonstrates that over the entire preserved 88° of the zodiac, the marks are systematically placed too close together to be consistent with a uniform distribution over 360°. Thus, in some other part of the zodiac scale (not preserved), the degree marks have been spaced farther apart. By contrast, the day marks on the Egyptian calendar scale are spaced uniformly, apart from (...) minor errors. A solar equation of center is apparent which rises by nearly 2.7° over the preserved portion of the zodiac. The placement of the degree marks indicates that, in the preserved portion of the zodiac, the Sun was considered to run at a uniform pace of about 30° per synodic month, which is consistent with the Sun’s speed in the fast zone of the Babylonian solar theory of System A. (shrink)

In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents (...) a difficulty for the debunker’s claim that, had the moral facts been otherwise, our evolved moral beliefs would have remained the same. (shrink)

Our present day knowledge in the area of medicine in Ancient Egypt has been severally sourced from medical papyri several of which have been deduced and analyzed by different scholars. For educational purposes it is always imperative to consult different literature or sources in the teaching of ancient Egypt and medicine in particular. To avoid subjectivity the author has found the need to re-engage the efforts made by several scholars in adducing evidences from medical papyri. In the quest to re-engage (...) the efforts of earlier writers and commentaries on the medical papyri, we are afforded the opportunity to be informed about the need to ask further questions to enable us to construct or reconstruct both past and modern views on ancient Egyptian medical knowledge. It is this vocation the author sought to pursue in the interim, through a preliminary review, to highlight, comment and reinvigorate in the reader or researcher the need for a continuous engagement of some pertinent documentary sources on Ancient Egyptian medical knowledge for educational and research purposes. The study is based on qualitative review of published literature. The selection of those articles as sources was based on the focus of the review, in order to purposively select and comment on articles that were published based either on information from a medical papyrus or focused on medical specialization among the ancient Egyptians as well as ancient Egyptian knowledge on diseases and medicine. It was found that the Egyptians developed relatively sophisticated medical practices covering significant medical fields such as herbal medicine, gynecology and obstetrics, anatomy and physiology, mummification and even the preliminary form of surgery. These practices, perhaps, were developed as remedies for the prevailing diseases and the accidents that might have occurred during the construction of their giant pyramids. It must be stated that they were not without flaws. Also, the key issues raised from these literatures are but a few among the Egyptian medical corpus across the academic and publishing world. It should therefore afford researchers, students and readers the opportunity to continue the educational dialogue on the medical practices of the Ancient Egyptians. (shrink)

This paper will explore the gender discourse of contemporary Egyptian Islamists and argue that their gender discourse is not merely a religious and traditional discourse, but that this politico-religious Islamic ideology articulates a quite modern construct of gender equality. The gender discourse of a number of important Egyptian Islamists, al-Banna’, Qutb, al-Ghazali, al-Qaradawi and Ezzat will provide illustrations of these modern developments. Modern elements incorporated in today’s Islamist revivalist approaches create new understandings, neither purely traditional, nor purely modern, (...) that are ‘modern constructs’ that attempt to remain traditional, while integrating specifically modern components. The presence of these two seemingly opposing and contradictory elements may account for the present popularity that Islamist discourses enjoy in many Muslims countries. (shrink)

BackgroundBreaking bad news to mothers whose children has disability is an important role of physicians. There has been considerable speculation about the inevitability of parental dissatisfaction with how they are informed of their child’s disability. Egyptian mothers’ preferences for how to be told the bad news about their child’s disability has not been investigated adequately. The objective of this study was to elicit Egyptian mothers’ preferences for how to be told the bad news about their child’s disability.MethodsMothers of (...) 100 infants recently diagnosed with Down syndrome were interviewed regarding their preferences for how to be told bad news. Mothers were recruited through outpatient clinics of the Pediatric Genetics Department at Fayoum University Hospital (located 90 km southwest of Cairo, Egypt) from January to June 2011.Results and discussionQuestionnaire analyses revealed nine themes of parental preferences for how to be told information difficult to hear. Mothers affirmed previously reported recommendations for conveying bad medical news to parents, including being told early, being told of others with a similar condition, and being informed of the prognosis.ConclusionsMothers affirmed communication themes previously discussed in the literature, such as being told early, and being informed of the prognosis. Although more research is needed in this important area, we hope that our findings will stimulate future search and help health care providers in different societies establish guidelines for effectively communicating bad news. (shrink)

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

In De Mysteriis VIII Iamblichus gives two orderings of first principles, one in purely Neoplatonic terms drawn from his own philosophical system, and the other in the form of several Egyptian gods, glossed with Neoplatonic language again taken from his own system. The first ordering or taxis includes the Simple One and the One Existent, two of the elements of Iamblichus' realm of the One. The second taxis includes the Egyptian (H)eikton, which has now been identified with the (...) god of magic, Heka, glossed as the One Existent. The Egyptian god Kmeph is also a member of this taxis, and is the Egyptian Kematef, a god of creation associated with the solar Amun-Re. Iamblichus refers to this god also as the Hegemon of the celestial gods, which should be equated to Helios, specifically the noeric Helios as described by Julian in his Hymn to Helios. Iamblichus describes Kmeph as an “intellect knowing himself”, and so the noeric Kmeph/Helios should also be seen as the Paternal Demiurgic Zeus, explicitly described also by Proclus as an intellect knowing himself. This notion of a self-thinking intellect may offer a solution to the problematic formulation by Proclus in his Timaeus commentary of Iamblichus' view of the Demiurgy encompassing all the noeric realm. The identification of Kmeph as the noeric Helios now also allows the first direct parallels to de Mysteriis to be found in extant Hermetica. In addition it can be inferred from the specific Neoplatonic terminology employed that the noetic Father of Demiurges, Kronos, appears, as well as the secondary Demiurgic triad of Zeus, Poseidon, and Pluto, in the forms of the Egyptian Amun, Ptah, and Osiris, thus raising the question that much of the theology documented only in Proclus might appear already to have been established by Iamblichus. (shrink)

Dating Egyptian Literary Texts. Edited by Gerald Moers; Kai Widmaier; Antionia Giewekmeyer; Arndt Lümers; and Ralf Ernst. Lingua Aegyptia, Studia Monographica, vol. 11. Hamburg: Widmaier Verlag, 2013. Pp. xiv + 653. Linguistic Dating of Middle Egyptian Literary Texts. By Andréas Stauder. Lingua Aegyptia, Studia Monographica, vol. 12. Hamburg: Widmaier Verlag, 2013. Pp. xx + 568.

Ancient Egyptian Wisdom for the Internet demonstrates that the legal philosophy and knowledge of ancient civilizations are of great value in helping us deal with the Internet. Through a challenging exploration of ancient legal knowledge this book offers new perspective on how to deal with, and best profit from the Internet.

The Ancient Egyptian Netherworld Books. By John Coleman Darnell and Colleen Manassa Darnell. Writings from the Ancient World, vol. 39. Atlanta: SBL Press, 2018. Pp. xxxvii + 685, illus. $99.95.

This is a new release of the original 1925 edition.

BackgroundBreaking bad news to mothers whose children has disability is an important role of physicians. There has been considerable speculation about the inevitability of parental dissatisfaction with how they are informed of their child’s disability. Egyptian mothers’ preferences for how to be told the bad news about their child’s disability has not been investigated adequately. The objective of this study was to elicit Egyptian mothers’ preferences for how to be told the bad news about their child’s disability.MethodsMothers of (...) 100 infants recently diagnosed with Down syndrome were interviewed regarding their preferences for how to be told bad news. Mothers were recruited through outpatient clinics of the Pediatric Genetics Department at Fayoum University Hospital (located 90 km southwest of Cairo, Egypt) from January to June 2011.Results and discussionQuestionnaire analyses revealed nine themes of parental preferences for how to be told information difficult to hear. Mothers affirmed previously reported recommendations for conveying bad medical news to parents, including being told early, being told of others with a similar condition, and being informed of the prognosis.ConclusionsMothers affirmed communication themes previously discussed in the literature, such as being told early, and being informed of the prognosis. Although more research is needed in this important area, we hope that our findings will stimulate future search and help health care providers in different societies establish guidelines for effectively communicating bad news. (shrink)

Preserved human remains from ancient Egypt provide an unparalleled opportunity for studies in the history of disease and medical practices. Egyptian medical papyri describe physiological concepts, disease diagnoses and prescribed treatments which include both ‘irrational’, and ‘rational’ procedures. Many previous studies of Egyptian medicine have concluded that ‘irrational’ methods predominated, but this perception is increasingly challenged by results from scientific studies of ancient human remains, and plant materials. This paper demonstrates the significant contribution being made by multidisciplinary studies (...) to our understanding of disease occurrence and medical treatments in ancient Egypt, and considers the feasibility of developing epidemiological comparisons of ancient and modern data sets that will provide acceptable historical contexts for contemporary disease studies. (shrink)

The role and status of the Egyptians in the army of Hellenistic Egypt (323–30b.c.) has been a debated question that goes back to the position within Late Period Egyptian society (664–332b.c.) of the Egyptian warriors described by Herodotus asmachimoi. Until a few decades ago, Ptolemaic military institutions were perceived as truly Greco-Macedonian and the presence of Egyptians in the army during the first century of Ptolemaic rule was contested. The Egyptians were thought of as being unfit to be (...) good soldiers. Egyptians would have been hired only as late as 217b.c.to fight against the Seleucid king Antiochus III in Raphia. The Ptolemaic victory (in fact rather a status quo) was made possible thanks to the addition of twenty thousand Egyptians to reinforce the Greek army. For a long time the subsequent role of Egyptians in the Ptolemaic army in the second and first centuriesb.c.did not attract much attention. One usually assumed that they were ‘second-rate soldiers’ calledmachimoi. In recent decades, the scholarship on Ptolemaic Egypt, notably Demotic studies, reasserted the role of Egyptians in the Ptolemaic army from the late fourth century onwards. (shrink)

This volume examines the cultural interaction between Greek and Egyptian culture, which can be traced in different forms over more than a millennium. Focusing in particular on literature and textual culture, chapters from leading experts cover a wide range of topics such as religion, philosophy, historiography, romance, and translation.

Earlier investigations have indicated that work beliefs in organization are impacted by different national cultures. In addition, those investigations have sought to understand the meaning of work in such different cultures. This study explores the meaning of work in the Egyptian context through an assessment of work beliefs and work attitudes. The article starts with a presentation of what is meant by the meaning of work and why research into work beliefs is both needed and worthwhile. The article then (...) presents a review of the relevant literature that evaluated the meaning of work in different countries. The review also elucidates recent research efforts that have tried to shed some light on the meaning of work in Middle-Eastern contexts. Data were collected from 201 Egyptian white-collar workers. Work beliefs and some job attitudes were assessed. Results indicate the prevalence of the humanistic work-belief system. Job satisfaction was positively correlated with the humanistic work-belief system and negatively with the Marxist work-belief system. The implications of these and other findings for international managers are discussed and recommendations for future researchers are put forward. (shrink)