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)

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)

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)

The ramifications of existence provide the setup for a theory on civilization as a whole. This story is composed under the premise of looking at Rabbinic Judaism and the Old/New Testaments as contextual clues for an overview of civilization and existence in general. This includes a mathematical model for prior to the existence of time i.e. QSOPR Theorem: Quantum Similarity Origin Point References, MDQBT: Multi-Dimensional Quantum Breakpoint Theorem, and QSICT: Quantum Simulated Informational Consciousness Theory. As well as tracing back (...) class='Hi'>ancient lineages such as Coptic DNA and the e1b1b haplogroup, FGC8712, or tribal lineages such as Berbers, the Quarashi, and ancient Mesopotamian groups. Next, we will look at history and philosophy through religious texts which include mythology, Quranic text and hadiths, and any related archaeological evidence in relationship to the Shashu, Temple 0, or contextual geological clues. This will provide a premise for human nature, civilization, world religions, societal falls, and history through correlative patterns, universal truth, linguistics, ethics and morality. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we (...) go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

Ancient philosophy has, for the most part, focused particularly around the history and philosophies of the Pre-Socratics, Socrates, Plato and Aristotle, with broader representations of some other non-Greek philosophical traditions such as the Chinese, Indian and Iranian philosophies. However, a distinctive Eurocentric bias towards ancient Egypt, to which many ancient Greek philosophers looked to as the cradle of wisdom and philosophy, has blatantly disregarded the poignant place of African philosophy in the pedagogy of ancient philosophy. Thus, (...) this paper argues for re-centering ancient Egyptian philosophy, and by extension, African philosophy in the study of ancient philosophy. The paper, firstly, traces the historical originality and rich elements of philosophy that ancient Egypt possesses, and then, identifies how these served as the theoretical springboard for the emergence of Greek philosophy. Any comprehensive study of ancient philosophy should not deliberately exclude this important aspect of development in philosophical thought. The paper, therefore, concludes with recommendations on repositioning African philosophy within the pedagogical context of ancient philosophy. (shrink)

Thousands of texts discuss Egytpain cosmology and cosmogony. James Allen has selected sixteen to translate and discuss in order to shed light on one of the questions that clearly preoccupied ancient intellectuals; the origins of the world.

This paper argues that the relative stability of ancient Egyptian society during the Middle Kingdom (c.2055 – 1650 BC) can in part be explained by referring to the phenomenon of hermeneutical injustice, i.e., the manner in which imbalances in socio‐economic power are causally correlated with imbalances in the conceptual scheme through which people attempt to interpret their social reality and assert their interests in light of their interpretations. The court literature of the Middle Kingdom is analyzed using the (...) concepts of hermeneutical injustice and ideology. It is argued that while it is true that there was room for maneuver and for internal critique, the efficacy of internal critique was hindered by the structure of the intellectual discourse of Middle Kingdom Egypt. This intellectual discourse was suitable for the interpretation of social reality in a way that allowed the elites to assert their interests, but it was not suitable for the interpretation of social reality in a way that accorded with the interests of the exploited peasantry. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A (...) renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

Throughout history in Ancient Egypt, information has been passed on from one generation to another. Information about culture and traditions has been passed on verbally and through scripts. From the time of the Old Kingdom (3100 B.C) in Ancient Egypt, hieroglyphs were used as a tool to pass on information about their history, culture and everyday lifestyle. Hieroglyphs, hieratic and demotic are three stages of writing that were practised throughout Ancient Egypt ’s history. This paper will briefly (...) explain the history and use of hieroglyphs in the Ancient Egyptian times. (shrink)

Ancient Egyptians precisely direct their temples and tombs to specific astronomical points, as attested in the designs of the Old kingdom pyramids and related temples. Likewise, the same approach was used in many religious and funerary buildings across the sequential historical epochs of ancient Egypt. This research introduces what can be called "astronomical design improvements" conducted by ancient Egyptians to secure a precise orientation for a specific direction of religious and funerary monuments. Moreover, this precise orientation requires (...) observatories used for the orientation and monitoring of geographical directions. Therefore, this paper discusses the inquiring; are there any Astronomical Observatories evidences in ancient Egypt? (shrink)

At least since Socrates, philosophy has been understood as the desire for acquiring a special kind of knowledge, namely wisdom, a kind of knowledge that human beings ordinarily do not possess. According to ancient thinkers this desire may result from a variety of causes: wonder or astonishment, the bothersome or even painful realization that one lacks wisdom, or encountering certain hard perplexities or aporiai. As a result of this basic understanding of philosophy, Greek thinkers tended to regard philosophy as (...) an activity of inquiry (zētēsis) rather than as a specific discipline. Discussions concerning the right manner of engaging in philosophical inquiry – what methodoi or routes of inquiry were best suited to lead one to wisdom – became an integral part of ancient philosophy, as did the question how such manners or modes of inquiry are related to, and differ from, other types of inquiry, for instance medical or mathematical. In this special issue of History of Philosophy & Logical Analysis, we wish to concentrate in particular on ancient modes of inquiry. (shrink)

This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, (...) the creator of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. (shrink)

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. (...) Arthur Eddington's work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found. (shrink)

This essay examines the quantitative aspects of Greco-Roman science, represented by a group of established disci¬plines, which since the fourth century BC were called mathēmata or mathē¬ma¬tikai epistē¬mai. In the group of mathēmata that in Antiquity normally comprised mathematics, mathematical astronomy, harmonics, mechanics and optics, we have also included geography. Using a dataset based on The Encyclopaedia of Ancient Natural Scientists, our essay considers a community of mathēmatikoi (as they called themselves), or ancient scientists (as they are (...) defined for the purposes of the present paper) from a sociological point of view, focusing on the size of the scientific population known to us and its disciplinary, temporal and geographical distribution. A diachronic comparison of neighboring and partly overlapping communities, ancient scientists and philosophers, allows the pattern of their interrelationship to be traced. An examination of centers of science throughout ancient history reveals that there were five major centers – Athens, Alexandria, Rhodes, Rome and Byzantium/Constantinople – that appear and replace one another in succession as leaders. These conclusions serve to reopen the issue of the place of mathēmata and mathēmatikoi in ancient society. (shrink)

Every person is equipped with both the Dionysian or life force soul (in Greek Eros), and the Apollonian or death force soul (in GreekThanatos). Dionysus was a Greek fertility god from c. 580 BCE associated with wine, music, and choral dance (Csapso 2016). In Attic art, Dionysus was often depicted as a slumping god on a ship, which had a vineover laden with grapes as a mast, surrounded by a sea with a pod of dolphins; the dolphins being the rescuers (...) of sailors (life force) (Carpenter 1990). Dionysus, who was resurrected from death, repre- sented hedonism, happiness, and the good life that he celebrated with a glass of wine. His half-brother Apollo was in many respects his polar opposite. Apollo was a cerebral god associated with the sun, light, and intellectual pursuit. Dio- nysus symbolized the ability of (wo) man to submerge him- or herself in a greater whole, the ecstatic, and the chaotic emotions. Apollo, on the contrary, symbolised his or her formally rational and reasoning mind. The Dionysian and Apollonian natural forces are complementary and one needs both to be a balanced person; one needed to be capable of creating form and struc- ture as well as being passionate and vital. Brown believed that a utopian society would primarily consist of such balanced persons who are at home in both the world of rationality and logic and of symbols and emotions. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

The ancient Greek philosophers – like Parmenides – reasoned that observable reality cannot exist by itself. It has to be a creation of an underlying reality. An all-in­clusive existence that has a structure because observable reality shows structure at every scale size. Although observable reality is involved in a continuous transformation too. If our concept about the relation between phenomenological reality and the creating underlying reality is correct, the unification of the properties of phenomenological reality is part of an (...) enveloping mathematical model. DOI: 10.5281/zenodo.5457368. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock (...) of higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into (...) one of the ancient world’s greatest mathematical traditions, a foundation for mathematical thinking today. In this view, numbers are abstract from their inception and materially bound at their most elaborated. The research updates historical work on Neolithic tokens and interpretations of Mesopotamian numbers, challenging several longstanding assumptions about numbers in the process. The insights generated are also applied to the role of materiality in human cognition more generally, including how concepts become distributed across and independent of the material forms used for their representation and manipulation; how societies comprised of average individuals use material structures to create elaborated systems of numeracy and literacy; and the differences between thinking through and thinking about materiality. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are (...) devoted. At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion (...) that was first conceived by ancient Greek mathematicians. (shrink)

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and (...) the underlying principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. (shrink)

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter.

This essay attempts to recover the ancient Egyptian category of "maat" as a valuable resource for contemporary metaethics and particular attention is given to its affinity with versions of modern non-cognitivism.

Most historians and philosophers of philosophy and history of mathematics hold one interpretation or the other of the nature of method of analysis and synthesis in itself and in its historical development. In this paper, I am trying to prove – through three points – that, in fact, there were two understandings of that method in Greek mathematics and philosophy, and which were reflected in Arabic mathematical science and philosophy; this reflection is considered as proof also of this (...) double nature of that method. Thus, we have to rethink the nature of Arabic philosophy systems. (shrink)

The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which (...) are basically explicit in definitions, like that of segments in Euclid’s Elements. Then, we will address how in pure geometry we, so to speak, “refer back” to practical geometry. This occurs in two ways. One, in the propositions of pure geometry. The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment. (shrink)

Abstract: Dates are the fruit of date palm trees, and it is one of the fruits famous for its high nutritional value. It is a summer fruit spread in the Arab world. In the past, the Arabs relied on it in their daily lives. Dates take an oval shape and vary in size from 20 to 60 mm in length and 8 to 30 mm in diameter. The ripe fruit consists of a hard core surrounded by a papery cover called (...) the tartar that separates the core from the fleshy part that is eaten. Historians disagreed about the place of its origin, so some historians expressed their belief that it had originated around the Arabian Gulf, and some of them say that the oldest known information about palm trees was in Babylon 4 thousand years ago BC. It is known about the ancient Egyptians using dates in wine. Dates contain a high nutritional value and are considered a basic food for man since ancient times. The fruits of dates are considered the highest fruits in containing sugars. These components vary according to the nature of the fruit, whether it is wet, semi-dry or dry, as well as according to the environmental conditions surrounding the trees. The components of the fruits also differ in different varieties and increase the percentage of sugars in dates is 70-78% of the fruit’s components. These sugars are characterized by their rapid absorption and transfer into the blood directly, digestion and burning. 10 dates (about 100 grams) per day provide a person with all his daily needs of magnesium, manganese, copper, sulfur and half of his needs of calcium and potassium. In this paper we presented a system that recognize the nine types of dates based on deep learning using python on Colab, and classifying using a dataset contain 1350 images. Our trained model achieved an accuracy of 99.44% on a proven test set. (shrink)

The nature of time is perceived by intellectuals variedly. An attempt is made in this paper to reconcile such varied views in the light of the Upanishads and related Indian spiritual and philosophical texts. The complex analysis of modern mathematics is used to represent the nature and presentation physical and psychological times so differentiated. Also the relation between time and energy is probed using uncertainty relations, forms of energy and phases of matter. Implications to time-dependent Schrodinger wave equation and (...) uncertainty principle are hinted. (shrink)

This collection of new essays focuses on metaethical views from outside the mainstream European tradition. The guiding motivation is that important discussions about the ultimate nature of morality can be found far beyond ancient Greece and modern Europe. The volume’s aim is to show how rich the possibilities are for comparative metaethics, and how much these comparisons can add to contemporary discussions of the foundations of morality. Representing five continents, the thinkers discussed range from ancient Egyptian, (...) class='Hi'>ancient Chinese, and the Mexica (Aztec) cultures to more recent thinkers like Augusto Salazar Bondy, Bimal Krishna Matilal, Nishida Kitarō, and Susan Sontag. The philosophical topics discussed include religious language, moral discovery, moral disagreement, essences’ relation to evaluative facts, metaphysical harmony, naturalism, moral perception, and the nature of moral realism. This volume will be of interest to anyone interested in metaethics or comparative philosophy. (shrink)

CATEGORY: Philosophy play; historical fiction; comedy; social criticism. STORYLINE: Katherine, a slightly neurotic American lawyer, has tried very hard to find personal happiness in the form of friends and lovers. But she has not succeeded, and is therefore very unhappy. So she travels to London, hoping that Christianus — a well-known satisfactionist — may be able to help her. TOPICS: In the course of the play, Katherine and Christianus converse about many philosophical issues: the modern American military presence in Iraq; (...) the meaning of life; the ethics of abortion; assessing WHO death statistics; the potential personhood of foetuses; ancient Egyptian moustaches and beards; defining criteria for progress in human society; objectivity and subjectivity; Chicago futures trading developments; the virtues of cryonics technology; a U.S. Supreme Court case; important and unimportant knowledge; and spiritualist dualism vs. scientific materialism . NOTES: This work features elaborate footnotes and comments by the author, to enhance the reader's experience of the play and its philosophizing characters. (shrink)

This is part 1 on a paper whose final variation of parts shall be titled,”The Universal Theory of Existence: The Sashu, Pharaohs, and the al-Mahdī”. The first part of this series sets the premise for a proposed ”Theory of Everything” that will be the foundation for encompassing many different topics. Since, the beginning of time, a singularity existed. This singularity is what we call an origin point of everything. Beyond, this origin point for time is different depending on position, being (...) outside of the singularity, or the idea that multiple universes exists with different time dilation, and likely different laws. Existence in essence is centered around the idea of what is prior to the origin point of time, and in theory, what is the space-time complexity together, in regards to how civilization come to be. From a physics standpoint, there are multiple theories around this. For starters, the author of this paper coined QSOPR Theorem, MDQBT, QSICT, and how this relates to Time/Multiverse Dilation and Origin Points. Quantum Similarity on a molecular, atomic, theoretical, and chemical level is one of these vast things humanity should be trying to explore. (shrink)

COMENTARIO 4° EN EL MARCO DE LA TESIS "UN ESTUDIO EN METODOLOGÍA INTERTEXTUAL Y EXEGÉTICA EN SALMO 91". . . En el presente comentario yo retomo el enfoque transcultural, iniciado en uno de los comentarios anteriores míos, el cual apliqué en el trato de la temática "pie" (o, "pies"). La evidencia pareceria estar insistentemente hablando de la relevancia de un sector de la literatura hebrea para la interpretación de determinados elementos de la arqueologia egipcia así como en favor de la (...) relevancia de lo arqueológico para la literatura hebrea. (shrink)

Comentario 1°, desde un enfoque transcultural, en el marco de la tesis “Un Estudio en Metodología Intertextual y Exegética en Salmo 91” cuanto al uso conjugado de la figura del רגל en posición de sujeto gramatical del verbo מוט, uso que la referida investigación percibe, debido a su frecuencia y estabilidad, como una fraseología. (fecha de publicación del comentario en Academiaedu: 2/6/2022) . . . . Nada de lo que voy a decir a continuación es conclusivo, yo solamente estoy argumentando, (...) especulando, indagando… aún es bastante prematuro el pensamiento, sin embargo, lo que sigue, es una “exposición” conjetural en el sentido que hay evidencias como para poder hablar de ello con cierta necesidad y algo de certeza, de hecho, ya lo hacen y yo, también, lo estoy trabajando. . . . . Una vez que finalicé la tesis decidí sacar del centro _no lo abandoné, lo sigo trabajando paralelamente_ de mi atención al objeto central de la investigación (en este caso, la tradición literaria hebrea comúnmente denominada el “Salmo 91”, o, siendo más técnico, los manuscritos 11Q11 y 4Q84 datados de alrededor de 2000 años según The Leon Levy Dead Sea Scrolls Digital Library) para devotar atención a dos palabras en especial de entre aquellas que pude analizar en aquel momento las cuales denotan tener importantes implicaciones no solamente, como pude ver, en la construcción del pensamiento implicado en los manuscritos hebreos y griegos con los cuales traté entonces sino que, también, de aquél que se puede observar en parte de la producción de algunas sociedades antiguas puesto de manifiesto por la arqueología, en este caso, hablo la figura del רגל (traducido frecuentemente como “pie”) en posición de sujeto gramatical del verbo מוט (a menudo traducido como “tropezar”; ver la tesis para saber mi posicionamiento respecto a dichas traducciones, entonces). Como expuse en la investigación y lo repito aquí, hay un aparente problema entre la forma hebrea de los textos analizados y su versión griega en el hecho de que si bien los autores hebreos llevados en cuenta parecen consensuar cuánto al uso del sustantivo רגל asociado al verbo מוט, lo mismo no es cierto cuando vamos a sus versiones griegas puesto que se observa el uso de diferentes verbos griegos para traducir מוט, lo que me hizo querer tratar de entender (ver tesis pata conocer mí reflexión al respecto, entonces), por un lado, qué circunstancias o pensamientos en la mente del traductor, o, traductores, pudieron haberle guiado a optar por diferentes traducciones griegas para un único termino hebreo (decir que el flujo de la traducción es del hebreo al griego no es algo totalmente seguro, pudo haber sido al revés e, incluso, se podría especular si no estamos delante del caso de una tradición aún más antigua la cual vino a ser transcrita tanto al griego como al hebreo, ya que hay evidencia como para pensarlo). . . . . Lo que quiero destacar, para ser más objetivo, es la relevancia de dichas palabras, sobre todo, de la figura del "pie", en diferentes culturas antiguas, en especial, la egipcia la cual, de paso, claramente hace notar su fuerte presencia en los renglones de diferentes manuscritos del Mar Muerto. El “pie” parece haber sido un tema de importancia en el antiguo Egipto (por ejemplo, pensar en la discusión del pie izquierdo adelantado de las estatuas egipcias y griegas), así como denotó serlo para varias de las composiciones hebreas tenidas en cuenta en la tesis y no hablo de su uso en referirse a un miembro, anatómicamente hablando, del cuerpo humano, sino que me refiero, como lo detallo en la investigación, a su empleo simbólico (chequear la tesis para ver mis conclusiones sobre su uso simbólico en dichos documentos, entonces). Lo ciertos es que en algún momento de nuestra historia como humanidad hemos decidido atribuirle al “pie” valores, más que simplemente mirarlo como un vehículo de locomoción. Tratar de percibir por medio de la filología y artefactos arqueológicos qué valores son estos y, sobre todo, porqué y para qué de ellos, es un ejercicio de retrospección histórica necesario sobre nuestro desarrollo como especie, en un sentido socio, antro, anato y filosófico, además de poder notar cómo influyó esta percepción en nuestra vida actual. También, me gustaría llegar a alguna conclusión, si me lo permite la evidencia, sobre la influencia del pensamiento egipcio referente al “pie” en su uso en la literatura hebrea, o, viceversa. Puede que las conclusiones de la tesis al respecto ya son relevantes como para poder echar más luz sobre esta discusión, al parecer, transcultural, si es que podemos hablar de que hay compatibilidad en cuanto a su aplicación en los distintos contextos antiguos donde se aprecia esta retorización de dicho miembro. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to (...) class='Hi'>mathematics education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were (...) exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the (...) radically impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development (...) of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)

This paper explores the evolution of consciousness and subjectivity through a biological framework for understanding the universe. It posits that functional patterns in biological systems mirror cosmic mathematical principles, defining our objective reality. Similar to wave and Fibonacci patterns in different physical phenomena, biological patterns are intrinsic to all things and can be quantified using Dedre Gentner’s approach to analogy. For example, Earth’s ocean currents and the melting and freezing of Antarctica resemble the circulatory system and heart, while the production (...) of music from instruments is analogous to ribosomal protein synthesis. Shelves, tables, and chairs function like cytosol by holding objects in space, and a coffee cup mirrors red blood cell distribution. These analogies reveal a universal order rooted in biology’s functional patterns, essential for shaping the emergence and evolution of life. The paper traces the development of consciousness from its rudimentary cellular states to complex human cognition, highlighting the role of biologically-patterned environments in driving evolutionary changes. Organisms that recognized and organized according to these patterns evolved as “pattern recognition engines” crucial for survival—thus, Life (survival) being the primary measure of consciousness. Humans advanced this capacity, gaining cognitive freedom by insulating themselves from environmental constraints, but faced increased subjectivity complexity. Consciousness, while inherently subjective and necessary for cognitive development, evolves in humans to understand objective reality and its biological nature, so to understand and navigate complexities of subjectivity. Ultimately, the paper asserts consciousness is the ability to recognize and adhere to life-sustaining patterns and principles. Successful adherence deems them worthy of continued existence, while failure leads to demise. Parallels with historical concepts like Atman and Brahman in Hinduism suggest ancient recognition of the correspondence between human and universal patterns. This ancient understanding, coupled with modern scientific evidence, reveals the interconnectedness and intrinsic biological nature of reality. (shrink)

The present Yearbook (which is the fourth in the series) is subtitled Trends & Cycles. Already ancient historians (see, e.g., the second Chapter of Book VI of Polybius' Histories) described rather well the cyclical component of historical dynamics, whereas new interesting analyses of such dynamics also appeared in the Medieval and Early Modern periods (see, e.g., Ibn Khaldūn 1958 [1377], or Machiavelli 1996 [1531] 1). This is not surprising as the cyclical dynamics was dominant in the agrarian social systems. (...) With modernization, the trend dynamics became much more pronounced and these are trends to which the students of modern societies pay more attention. Note that the term trend – as regards its contents and application – is tightly connected with a formal mathematical analysis. Trends may be described by various equations – linear, exponential, power-law, etc. On the other hand, the cliodynamic research has demonstrated that the cyclical historical dynamics can be also modeled mathematically in a rather effective way (see, e.g., Usher 1989; Chu and Lee 1994; Turchin 2003, 2005a, 2005b; Turchin and Korotayev 2006; Turchin and Nefedov 2009; Nefedov 2004; Korotayev and Komarova 2004; Korotayev, Malkov, and Khaltourina 2006; Korotayev and Khaltourina 2006; Korotayev 2007; Grinin 2007), whereas the trend and cycle components of historical dynamics turn out to be of equal importance. (shrink)

In mathematical languages and in predicate logic coreferential terms can be interchanged in any sentence without altering the truth value of that sentence. Replacing 3 + 5 by 12 − 4 in any formula of arithmetic will never lead from truth to falsity or from falsity to truth. But natural languages are different in this respect. While in some contexts it is always allowed to interchange coreferential terms, other contexts do not admit this. An example of the first sort of (...) context is likes bananas: for any two coreferential noun phrases A and B the sentence A likes bananas is true if and only if B likes bananas is. A context that does not allow intersubstitution of coreferents is The Ancients knew that appears at dawn. If we fill the hole with the noun phrase the Morning Star we get the true (1a), while if we plug in the Evening Star we get the false (1b). Yet the Morning Star and the Evening Star both refer to the planet Venus and are thus coreferential. (shrink)

The self-definition of ancient empires is based on the strong conviction of being God’s chosen one. In this way, Greeks, Persians, Assyrians, Sumerians, Indians, Hebrews and Egyptians built their religions, rituals, thought and wisdom. Greece was not the creator of the xenophobic idea consisted in refusing systematicly stranger modes of life; in oriental vocabularies we could find a lot of words to refer non-local traditions. Various questions rise about the relationship between Greece and other ancient people. Are the (...) difference only on religious stuff? What was the global meaning of ritual characters in each ancient mediterranean-oriental land? How each ancient culture/ empire/people/land abstract identity was built? What happens with ancient History of European Culture? Exists any relationship between the “Culture” (greeks) and “other” European barbarians? (shrink)

The discussions of conatus – force, tendency, effort, and striving – in early modern metaphysics have roots in Aristotle’s understanding of life as an internal experience of living force. This paper examines the ways that Spinoza’s conatus is consonant with Aristotle on effort. By tracking effort from his psychology and ethics to aesthetics, I show there is a conatus at the heart of the activity of the ψυχή that involves an intensification of power in a way which anticipates many of (...) the central insights of early modern and 20th century European philosophy. The first section outlines how Aristotle’s developmental conception of the soul as geometrically ordered lays the foundation for his understanding of effort. The developmental series of powers of the soul are analogous to the series of shapes in mathematics. The second section links the striving of the soul to the gradual acquisition of virtues as a directed activity unifying multiplicity. The third examines the paradigm of self-awareness that Aristotelian effort involves. In the final section I show how ancient Greek theories of music were founded on the experience of striving. The “nature” of music is defined by Aristoxenus, and Theophrastus, in relation to the passion and intentionality of the soul. The geometrical order, as a synthesis of elements in geometry, music, or ethics, is a generative process in which past elements are retained and reintegrated in later stages of development. It requires effort to think geometrically, and the progress of knowledge itself is an integral aspect of all effort. Effort is the lived and self-aware cause which, moving step by step in an orderly and deliberate way, grows and advances upon itself. For both Spinoza and Aristotle, effort is the immanent intelligence which accomplishes what is in the purview of its understanding. Thus, will, in this conception of effort, is not something we already possess innately, but emerges gradually by an effort aimed at improvement. (shrink)

We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in (...) which the brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden (...) ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients. (shrink)

The strings of physics’ string theory are the binary digits of 1 and 0 used in computers and electronics. The digits are constantly switching between their representations of the “on” and “off” states. This switching is usually referred to as a flow or current. Currents in the two 2-dimensional programs called Mobius loops are connected into a four-dimensional figure-8 Klein bottle by the infinitely-long irrational and transcendental numbers. Such an infinite connection translates - via bosons being ultimately composed of 1’s (...) and 0’s depicting pi, e, √2 etc.; and fermions being given mass by bosons interacting in matter particles’ “wave packets” – into an infinite number of 8-Kleins. Each Klein 1) is one of the universe’s subuniverses (our own is 13.7 billion years old), 2) is made flexible through its binary digits which seamlessly, or almost seamlessly, join it to surrounding subuniverses and eliminate its central hole, and 3) possesses warped time and space because its foundation is the programmed curves in its mathematical Mobius loops (along with the twists they generate [p.7]). The universe functions according to the rules of fractal geometry. So the Mobius does not exist only at the cosmic level. It also manifests at the quantum scale, giving us photons and protons etc. Space and time are no longer separate, but are an indivisible space-time. So if space and the universe are infinite, how can time not be eternal? The past and the future must both extend forever (the idea of time being finite arises from confusion of our subuniverse with the one infinite universe). -/- BITS (Binary digiTS) only suggest existence of the divine if time is linear. Although a non-supernatural God is proposed via the inverse-square law coupled with eternal quantum entanglement, Einstein taught us that time is warped. Warped time is nonlinear, making it at least possible that the BITS composing space-time and all particles originate from the computer science of humans. -/- I suspect many readers will be content with reading this abstract. While there are more details, and mathematics, in the content; my natural style of writing is to avoid jargon and maths. I also tend to get philosophical. While I personally feel that there’s a lot of precious information in the content, I realize it won’t all be to everyone’s liking. Other subjects dealt with in this article are - the “Pioneer anomaly”, refinement of gravitational physics, dark energy and dark matter, quantum phenomena like mass and electric charge and quantum spin, Kepler’s laws of planetary motion, deflection of starlight by the sun, tides, falling bodies, Earth’s orbit, ancient Greek philosophers, Newton, Kepler, Galileo, Aristotle, Parmenides, Zeno of Elea, time travel into the past as well as the future, the elimination of distances in space, humanity’s construction of this universe we live in, The Law of Conservation of Matter-Energy, and support for the science-fiction-like idea of the electronic binary digits of 1 and 0 being the building blocks of our universe. (shrink)

Is it not surprising that we look with so much pleasure and emotion at works of art that were made thousands of years ago? Works depicting people we do not know, people whose backgrounds are usually a mystery to us, who lived in a very different society and time and who, moreover, have been ‘frozen’ by the artist in a very deliberate pose. It was the Classical Greek philosopher Aristotle who observed in his Poetics that people could apparently be moved (...) even by the imitation of a person or an act. And although we are usually well aware that it is a simulacrum, not a real situation, it nevertheless sometimes seems as if we ourselves are standing there on the stage or in the painting, so intense and emotional is our response, even though we are just spectators. Aristotle concludes from this that we have intellectual capacities which allow us put ourselves in another’s place and consequently to react to simulated situations as though they are actually happening to us, here and now. In this process, he contends, observation, memory, imagination and emotions are crucial elements. In the past it was not customary to invoke human mental faculties to explain our response to works of art. The Ancient Greeks, after all, knew little about the human body or brain and usually referred to the extended world of the gods in their endeavours to comprehend the ‘inner world’ of human beings. In our time the situation is completely different—such an allusion to the brain no longer surprises us. Whether it is about the mystery of the consciousness, the question of free will or accounts of bizarre psychological aberrations or disorders, we have become accustomed to references to parts of the brain, to images of brain scans, to reports about neural networks and the like. However, because there are so many factors that play a part in our appreciation of works of art we need a complex explanation for it, and it is not enough to look only at certain properties of the brain that are determined by evolution. Those properties are shared by every human being, and so are rather useless in explaining people’s different reactions to the same work of art. Evidently the brains of individuals differ so much that they make it possible for people to respond differently to one and the same artwork. This, of course, raises questions concerning the painted emotions that can be seen in this exhibition. Virtually everyone, after all, is fascinated by such paintings and usually recognizes the emotions they represent. The reactions to these painted emotions are also often similar. This is probably why artworks like this are generally highly valued, then and now, here and elsewhere: from the enigmatically smiling Egyptian Queen Nefertiti and the startled Rembrandt to a seemingly despairing African mask. Aristotle observed that in the theatre players imitate actions that are associated with emotions in a number of ways and that these emotions are shared in a particular fashion by the playwright, the actors and the audience. The audience may even be carried away by these emotions to such an extent that they are in a sense purged of them and can subsequently leave the theatre relieved. Are such emotional reactions perhaps related to the fact that emotions are universal and that brains respond similarly to them? Is this why we can so readily identify painted emotions? May we therefore also assume that the properties of the brain determined by evolution help us to explain these emotions? In answering these questions we shall discuss a number of insights into emotions in psychology and brain science and explore some theories about the possible function of emotions and their expression. (shrink)

This paper explores the evolution of consciousness and subjectivity through a biological framework for understanding the universe. It posits that functional patterns in biological systems mirror cosmic mathematical principles, defining our objective reality. Similar to wave and Fibonacci patterns in different physical phenomena, biological patterns are intrinsic to all things and can be quantified using Dedre Gentner’s approach to analogy. For example, Earth’s ocean currents and the melting and freezing of Antarctica resemble the circulatory system and heart, while the production (...) of music from instruments is analogous to ribosomal protein synthesis. Shelves, tables, and chairs function like cytosol by holding objects in space, and a coffee cup mirrors red blood cell distribution. These analogies reveal a universal order rooted in biology’s functional patterns, essential for shaping the emergence and evolution of life. The paper traces the development of consciousness from its rudimentary cellular states to complex human cognition, highlighting the role of biologically-patterned environments in driving evolutionary changes. Organisms that recognized and organized according to these patterns evolved as “pattern recognition engines” crucial for survival—thus, Life (survival) being the primary measure of consciousness. Humans advanced this capacity, gaining cognitive freedom by insulating themselves from environmental constraints, but faced increased subjectivity complexity. Consciousness, while inherently subjective and necessary for cognitive development, evolves in humans to understand objective reality and its biological nature, so to understand and navigate complexities of subjectivity. Ultimately, the paper asserts consciousness is the ability to recognize and adhere to life-sustaining patterns and principles. Successful adherence deems them worthy of continued existence, while failure leads to demise. Parallels with historical concepts like Atman and Brahman in Hinduism suggest ancient recognition of the correspondence between human and universal patterns. This ancient understanding, coupled with modern scientific evidence, reveals the interconnectedness and intrinsic biological nature of reality. (shrink)

Time has puzzled scientists. Some see it as just a tool and a unit of measurement, while others consider time to be a real thing and needs to be measured. There are also those who believe that time is an ancient thing that arose with the creation of the universe and the Earth, running parallel to life in them, and counting every movement, event, or speed in them. While some see it as an essential part and a major component (...) of the virtual relationship that includes life and place, there are also those who see time as a metaphysical thing that only appeared and developed in human consciousness and then mixed with the physics of life. Is duration measured by movement, or is movement measured by duration or time? Here began the dilemma of this research: How did time transform from a concept that reads and measures the flow of time forward, that is, the flow of time, according to Isaac Newton, into a physical measuring tool that calculates the movement, speed, and state of things? Then the concept turned into a tool that calculates the speed of light and tells the story of the origin and development of the universe. Scientists will not agree on a clear, direct, and frank interpretation of the concept of time, but people generally agree that time can be divided into past, present, and future. This division, according to this research, has gradually developed in human consciousness since the manifestations of knowledge appeared in the human mind and began to take its first steps. In the wondrous land where the sun rises repeatedly, the moon also rises, planets and stars appear, trees grow, rivers and seas overflow, storms and rain intensify, light appears and then darkness, and creatures wake up and sleep, mysteriously and repeatedly, until all these phenomena have become Appearances are measurable, with the development of human consciousness. In this brief research paper, we will discuss what is called “the present,” and the validity of its existence in the real time in which we live, and where its place is in human consciousness, and why scientists let it tamper with mathematical, physical, and social matter, and transformed it from a mere thing that does not exist, to a rest stop, which sometimes takes a long time., between the past and the future. (shrink)

The figure of the cordial host of the Academy, who invited the most gifted mathematicians and cultivated pure research, whose keen intellect was able if not to solve the particular problem then at least to show the method for its solution: this figure is quite familiar to students of Greek science. But was the Academy as such a center of scientific research, and did Plato really set for mathematicians and astronomers the problems they should study and methods they should use? (...) Our sources tell about Plato's friendship or at least acquaintance with many brilliant mathematicians of his day (Theodorus, Archytas, Theaetetus), but they were never his pupils, rather vice versa -- he learned much from them and actively used this knowledge in developing his philosophy. There is no reliable evidence that Eudoxus, Menaechmus, Dinostratus, Theudius, and others, whom many scholars unite into the group of so-called "Academic mathematicians," ever were his pupils or close associates. Our analysis of the relevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' "Catalogue of geometers", and Philodemus' "History of the Academy", etc.) shows that the very tendency of portraying Plato as the architect of science goes back to the early Academy and is born out of interpretations of his dialogues. (shrink)