Milesians

It is widely believed that the ancient Greeks thought that Thales was the first philosopher, and that they therefore maintained that philosophy had a Greek origin. This paper challenges these assumptions, arguing that most ancient Greek thinkers who expressed views about the history and development of philosophy rejected both positions. I argue that not even Aristotle presented Thales as the first philosopher, and that doing so would have undermined his philosophical commitments and interests. Beyond Aristotle, the view that Thales was (...) the first philosopher is attested almost nowhere in antiquity. In the classical, Hellenistic, and post-Hellenistic periods, we witness a marked tendency to locate the beginning of philosophy in a time going back further than Thales. Remarkably, ancient Greek thinkers most often traced the origins of philosophy to earlier non-Greek peoples. Contrary to the received view, then, I argue that (1) vanishingly few Greek writers pronounced Thales the first philosopher; and (2) most Greek thinkers did not even advocate a Greek origin of philosophy. Finally, I show that the view that philosophy originated with Thales (along with its misleading attribution to the Greeks in general) has roots in problematic, and in some cases manifestly racist, eighteenth-century historiography of philosophy. (shrink)

This book presents a new account of Thales based on the idea that Acheloios, a deity equated with water in the ancient Greek world and found in Miletos during Thales’ life, was the most important cultic deity influencing the thinker, profoundly shaping his philosophical worldview. In doing so, it also weighs in on the metaphysical and epistemological dichotomy that seemingly underlies all academia—the antithesis of the methodological postulate of Marxian dialectical materialism vis-à-vis the Platonic idea of fundamentally real transcendental forms. (...) Unbeknownst to many scholars, there are various Neo-Marxian thinkers that position the origin of coinage as the pivotal technological development giving rise to impersonal “metaphysical cosmology,” suggesting that the value of money was more-or-less projected back onto the cosmos in the form of “ideal substances.” While the arguments are incredibly sophisticated and persuasive, their conclusions (either stated or implied) are rather difficult to swallow: the self is merely an illusion, abstract ideas of an ultimate source of value, like God or the Good, are totally delusional (as is the soul, and presumably any notion of inherent human dignity), and essentially everything is reducible to mankind’s enslavement to commodities and the notion of our own objectified labor, which is the true source of all value according to Marx. Not only is this an alarming belief that many scholars (consciously or unconsciously) have adopted, since essentially any action could be “justified,” it is also demonstrably false, since it rests on a misunderstanding of Thales and misconception of philosophy as such. -/- My work rectifies that misunderstanding. In an important sense, it is an attempt at redefining philosophy as a “love of wisdom,” which I argue was accurate even in the Presocratic setting, and it uses the influence of Acheloios on Thales to do so. Throughout its pages I explore the etymology and historical uses of the word ὔδωρ, examine the archaeological context of 7th to 6th century Miletos, consider various aquatic myths Thales encountered, and highlight a hitherto overlooked tradition stemming from Thales and influencing such thinkers as Pythagoras, Empedokles, and Hippo, which culminates in a completely new reading of Plato’s Phaedrus, a dialogue in which Plato responds to the exact type of thinking employed by the Neo-Marxians. It is there that we find Socrates and Phaedrus surrounded by the iconography of Acheloios and the nymphs, all while they lie reclined like river gods (the sinews of Acheloios) on the banks of the Ilisos. And it is in that dialogue that Plato defines philosophy as a love of wisdom—the beholding of a multiplicity of hermeneutical frameworks—and alludes to the fact that it began with the sacrifice of Acheloios, the initial philosophical maneuver which he attributes to Thales. The book ends with a threefold rejoinder to the Neo-Marxian school, corresponding to the λόγος, μῦθος, and ἔργον of Acheloios. It turns out that, (1) the λόγος of Acheloios contained the ideal preconditions conducive to an abstraction to a more refined philosophical worldview in which divine water operated as the One among the Many; (2) the μῦθος of Acheloios actually encouraged the application of the notion of sacrifice to Acheloios himself (thus revealing his essence as divine water); and, (3), the ἔργον of Acheloios, in which he kneels in assent to sacrifice, is found on a coin that was probably designed by Thales. In the final analysis, I suggest that the tradition of Acheloios is reflective of a greater philosophical truth, and that by following Thales’ lead, we transcend the Marxian hermeneutic of doubt and reorient ourselves toward the οὐσια ὄντως οὖσα. (shrink)

The article analyses the remaining fragments and testimonies of Heraclitean philosophy and their connection with Hippocratic medicine. It is claimed that both schools belong to the same philosophical-scientific paradigm of the elements. Therefore, theoretical insights of the school of Cos might well serve explaining complicated and often difficult to interpret Heraclitean thoughts. Moreover, it is plausible that parts of Corpus Hippocraticum were written under the influence of the Heraclitean philosophy and therefore its analysis and interpretative application allows us to partially (...) reconstruct the fragmented Heraclitean ideas into the single unified system. The article uses comparative analysis of both thinking traditions in regard to psychological, ethical, physiological, cosmological, and medical ideas. Similarities in explaining human nature are revealed. It is shown that science and philosophy in Antiquity use the same paradigmatic utterances to describe reality. Therefore, there are many mutual interconnecting principles between early philosophy and medicine. (shrink)

Both Heraclitus and Democritus, as the philosophers of historia peri phuseôs, consider nature and human character, habit, law and soul as interrelated emphasizing the links between phusis, kinesis, ethos, logos, kresis, nomos and daimon. On the one hand, Heraclitus’s principle of change (panta rhei) and his emphasis on the element of fire and cosmic motion ultimately dominate his ethics reinforcing his ideas of change, moderation, balance and justice, on the other, Democritus’s atomist description of phusis and motion underlies his principle (...) of moderation and his ideas of health and measured life. In this series, particularly referring to the main principles of motion, moderation and justice, I attempt to describe a coherent pre-Socratic ethical perspective based on the Heraclitean and Democritean fragments. I explore the connections between their physics and ethics also borrowing from Nietzsche’s lectures and writings on the Pre-Socratics. I redefine such Heraclitean and Democritean concepts as harmony, order, perfection, health, self-control, contentment, cheerfulness, concord, sound judgment, wisdom, measure and balance and discuss them under the principles of motion (phusis), moderation (sophrosyne) and justice. In doing so, I also expose the relevance of the Heraclitean notion of logos (interpreting it as the underlying categorical principle of transition between phusis and ethos) in bringing together these ideas and principles. Finally, based on this pre-Socratic Weltanschauung, I assess the possibility of a coherent picture of humanity, its nature and conduct as extending from or fitting into or extending-from-when-fitting-into the cosmos of moving forces and atoms. (shrink)

On propose ici de clarifier ce qu’Anaximandre entendait par « le divin » et ce qu’il appelait des « dieux ». À partir d’une réévaluation des sources anciennes, on soutient que cette enquête peut aider à comprendre son modèle cosmologique et le problème des cataclysmes dans son système. Trois hypothèses sont avancées à cette fin : [i] que dans Physique, III, 4, 203b3 15, le syntagme τὸ ἄπειρον renvoie à une notion concrète de substrat infini ; [ii] que dans ce (...) même passage, Aristote n’a probablement pas attribué aux philosophes de la nature – y compris Anaximandre – la thèse selon laquelle τὸ ἄπειρον est divin, mais plutôt la thèse selon laquelle ils comprennent le divin comme étant immortel et impérissable ; [iii] qu’Anaximandre, en supposant que « les astres célestes » sont des dieux, admettrait qu’ils naissent mais ne se détruisent pas – ce qui réfuterait l’idée d’un cataclysme universel chez lui. En conclusion, l’étude discute en quoi consisterait la gouvernance cosmique de τὸ ἄπειρον dans un univers divisé en trois niveaux et propose que cette gouvernance viendrait du fait que τὸ ἄπειρον possède un mouvement éternel. (shrink)

In this essay on ancient architectural technologies, I propose to challenge the largely conventional idea of the transcendent origins of philosophy, that philosophy dawned only when the mind turned inside, away from the world grasped by the body and senses. By focusing on one premier episode in the history of western thinking – the emergence of Greek philosophical thought in the cosmic architecture of Anaximander of Miletus – I am arguing that the abstract, speculative, rationalising thinking characteristic of philosophy, is (...) indeed rooted in practical activities, and emerges by means of them rather than in repudiation of them. The spirit of rational inquiry emerged from several factors but the contributing role of monumental architecture and building technologies has been vastly under-appreciated. In the process of figuring out how to build on an enormous scale that the eastern Greeks had never before tried, the architects discovered and revealed nature’s order in their thaumata, the very experience with which Aristotle claims that philosophy begins. Ancient architecture and building technologies were on display for decades with monumental temple building. In front of Anaximander and his community, a new vision of nature spawned that, surprisingly, humans could grasp and command. The building of these thaumata, these objects of wonder, offered proof of the human capacity to control nature, and opened a new vision of our human rational capacity to understand the world and our place in it. (shrink)

This dissertation presents a new account of Thales based on the idea that Acheloios—a deity equated with water in the ancient Greek world and found in Miletos during Thales’ life—was the most important cultic deity influencing the thinker, profoundly shaping his philosophical worldview. In doing so, it also weighs in on the metaphysical and epistemological dichotomy that seemingly underlies all academia—the antithesis of the methodological postulate of Marxian dialectical materialism vis-à-vis the Platonic idea of fundamentally real transcendental forms. Unbeknownst to (...) many philosophers, there are various Neo-Marxian scholars that position the origin of coinage as the pivotal technological development giving rise to impersonal “metaphysical cosmology,” suggesting that the value of money was more-or-less projected back onto the cosmos in the form of “ideal substances.” While the arguments are incredibly sophisticated and persuasive, their conclusions (either stated or implied) are rather difficult to swallow: the self is merely an illusion, abstract ideas of an ultimate source of value, like God or the Good, are totally delusional (as is the soul), and essentially everything is reducible to mankind’s enslavement to commodities and the notion of our own objectified labor (the true source of all value according to Marx). Not only is this a dangerous belief that many philosophers (consciously or unconsciously) have adopted, since essentially any action could be “justified,” it is also demonstrably false, since it rests on a thorough misunderstanding of Thales and misconception of philosophy as such. My work rectifies that misunderstanding. In an important sense, it is an attempt at redefining philosophy as a “love of wisdom,” which I argue was accurate even in its Presocratic setting, and it uses the influence of Acheloios on Thales to do so. Throughout its pages I explore the etymology and historical uses of the word ὔδωρ, examine the archaeological context of 7th to 6th century Miletos, consider various aquatic myths Thales encountered, and highlight a hitherto overlooked tradition stemming from Thales and influencing such thinkers as Pythagoras, Empedokles, and Hippo, which culminates in a completely new reading of Plato’s Phaedrus. It is there that we find Socrates and Phaedrus engaging in dialogue while surrounded by the iconography of Acheloios and the nymphs, all while they lie reclined like river gods (the sinews of Acheloios) on the banks of the Ilisos. And it is in that dialogue that Plato defines philosophy as a love of wisdom—the beholding of a multiplicity of hermeneutical frameworks—and alludes to the fact that it began with the sacrifice of Acheloios, the initial philosophical maneuver which he attributes to Thales. I end with a threefold rejoinder to the Neo-Marxian school, corresponding to the λόγος, μῦθος, and ἔργον of Acheloios. It turns out that, (1) the λόγος of Acheloios contained the ideal preconditions conducive to an abstraction to a more refined philosophical worldview in which water operated as the One among the Many; (2) the μῦθος of Acheloios actually encouraged the application of the notion of sacrifice to Acheloios himself (thus revealing his essence as divine water); and, (3), the ἔργον of Acheloios, in which he kneels in assent to sacrifice, is found on a coin that was probably designed by Thales himself. In the final analysis, I suggested we have recourse to Acheloios yet again, and reorient ourselves toward the οὐσια ὄντως οὖσα. (shrink)

In this article we shall try to explore the ethical aspects of the Dao De Jing and the fragments of the pre-Socratic philosopher Heraclitus based on the symbolism of the infant that they both use. At first a very short introduction needs to be made concerning the basis of morality and the difference between China and Greece. Needless to say we must take into account the general ethical context in the civilizations of ancient China and ancient Greece and indicate whether (...) the DDJ is to be seen as a strictly ethical/political text as well as whether Heraclitus’ fragments work as an ethical map for the people of his time and place. I intent to structure this article in two chapters each one dedicated to each of the philosophers along with a short introduction in the beginning. As far as the main chapters are concerned the Lao-Zi’s DDJ will be analyzed at first from the perspective of ethics in connection to the symbol of the infant not rarely used by Lao-Zi. Secondly I shall deal with the ethical thought of Heraclitus and his perspective of the infant found in some of his fragments. Let us keep in mind that apart from the fragments themselves, the witnesses play a not less important role in our extracting his philosophical opinions. Lastly we shall try to come to a conclusion concerning the similarities and dissimilarities between Lao-Zi and Heraclitus regarding their views on ethics and especially regarding the use of the infant as a symbol or a pattern. (shrink)

In this paper, we intend to explore the possible influences of legislative prose in the Anaximander’s cosmological prose construction, who would have been, according to Themistius, “the first Greek who dared to expose a written discourse about nature” (ἐθάρρησε πρῶτος ὧν ἴσμεν Ἑλλήνων λόγον ἐξενεγκεῖν περὶ φύσεως συγγεγραμμένον, Or. 26 p. 383 = DK12A7). Our aim is to clarify which notions of nature and justice are assumed in its emergent cosmology, considering that, at least from the lexical point of view, (...) it seems strongly suggestive to be undefined the barriers between the legal and cosmic order, between the Human and the Natural. Indeed, this is what the peripatetic tradition seems to suggest by judging Anaximander’s language extremely poetic (ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων), since he would use legal terms (διδόναι αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας) to explain the natural processes of generation and corruption (ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι, Simpl. in Phys. 24. 13–25 = DK12B1). ——— Objetivamos neste artigo explorar as possíveis influências da prosa legislativa na constituição da prosa cosmológica de Anaximandro de Mileto, que teria sido, segundo Temístio, “o primeiro grego que ousou expor um discurso escrito sobre a natureza” (ἐθάρρησε πρῶτος ὧν ἴσμεν Ἑλλήνων λόγον ἐξενεγκεῖν περὶ φύσεως συγγεγραμμένον, Or. 26 p.383 = DK12A7). Visamos aclarar que noções de natureza e de justiça estão sendo pressupostas nessa cosmologia então emergente, considerando que, ao menos do ponto de vista lexical, parece fortemente sugestivo serem indefinidas as barreiras entre a ordem jurídica e a cósmica, entre o âmbito humano e o natural. Com efeito, é o que parece já sugerir a tradição peripatética ao julgar o linguajar de Anaximandro extremamente poético (ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων) por o milésio empregar termos considerados do âmbito jurídico (διδόναι αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας) para explicar os processos ditos naturais de geração e corrupção (ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι, Simpl. in Phys. 24.13–25 = DK12B1). (shrink)

Women who changed ideas in Antiquity and in Middle Ages.

This book is a sequel to Heaven and Earth in Ancient Greek Cosmology. With the help of many pictures, the reader is introduced into the way of thinking of ancient believers in a flat earth. The first part offers new interpretations of several Presocratic cosmologists and a critical discussion of Aristotle’s proofs that the earth is spherical. The second part explains and discusses the ancient Chinese system called gai tian. The last chapter shows that, inadvertently, ancient arguments and ideas return (...) in the curious modern flat earth cosmologies. (shrink)

Review of A. Finkelberg's Heraclitus and Thales’ Conceptual Scheme: A Historical Study (Brill, 2017).

The early Presocratics’ major speculative and critical initiatives—in particular, Anaximander’s conceptions of the justice of the cosmos and of the apeiron as its archē and Xenophanes’s polemics against immorality and anthropomorphism in the depiction of the gods and against any claim to divine inspiration—appear to break with Hesiod’s form of thought. But the conceptual, critical, and ethical depth of Hesiod’s own rethinking of the lore that he inherits complicates this picture. Close examination of each of their major initiatives together with (...) the relevant passages in Hesiod shows that even in the course of departing from his thought, Anaximander and Xenophanes also reappropriate and renew it. In a postscript I pose some questions for future inquiry into Heraclitus’s and Parmenides’s receptions of Hesiod. (shrink)

_ Source: _Volume 63, Issue 1, pp 1 - 24 This article examines Diogenes of Apollonia’s doctrines of intellection and soul in relation to his material principle, air. It argues that for Diogenes both intellection and soul are not, as commonly thought, some sort of air, even though both intellection and soul are to be understood in terms of air and the system of τρόποι of air that he has set up. These new interpretations of intellection and soul yield insight (...) into Diogenes’ claims about the ordering activity of air as intellection and a renewed appreciation for his material monism. (shrink)

This book offers an innovative analysis of the Greek philosopher Anaximander’s work. In particular, it presents a completely new interpretation of the key word Apeiron, or boundless, offering readers a deeper understanding of his seminal cosmology and, with it, his unique conception of the origin of the universe. Anaximander traditionally applied Apeiron to designate the origin of everything. The authors’ investigation of the extant sources shows, however, that this common view misses the mark. They argue that instead of reading Apeiron (...) as a noun, it should be considered an adjective, with reference to the term phusis, and that the phrase phusis apeiros may express the boundless power of nature, responsible for all creation and growth. The authors also offer an interpretation of Anaximander's cosmogony from a biological perspective: each further step in the differentiation of the phenomenal world is a continuation of the original separation of a fertile seed. This new reading of the first written account of cosmology stresses the central role of the boundless power of nature. It provides philosophers, researchers, and students with a thought-provoking explanation of this early thinker's conception of generation and destruction in the universe. (shrink)

In Heraclitus and Thales’ Conceptual Scheme: A Historical Study Aryeh Finkelberg rejects the teleological interpretation of early Greek thought as targeted at later results, viz. philosophy, and seeks to determine its intended meaning by restoring it to its historical context.

This essay draws on texts previously untranslated into English, and in particular Heidegger’s brilliant 1943 lecture course on Heraclitus, to show how Heidegger understood kosmos as an early Greek name for Being itself. The contemporary scholarship has altogether missed the significant role that this Greek Ur-word plays in his later thinking. The “gleaming,” “adorning” kosmos—which the later Heidegger understood to be “world” in the fullest and richest sense—is not in the first place any kind of transcendental-phenomenological “projection” of the human (...) being; rather, it is the resplendence of the “ever-living” Being-unfolding-way itself from out of which both the gods and human beings come to pass and pass away. The independence of kosmos/Being itself in relation to the human being is highlighted. An Ode by Pindar and a painting by Andrew Wyeth are also considered. (shrink)

Praised for its reliance on observation rather than myth, the Milesian school signals the dawn of science in the West. Whereas Hesiod appeals to the long ago and far away to explain the here and now, Thales and his cohorts do the reverse. In this reversal, we are their thankful, even faithful heirs. But with Hesiod not everything is myth and hearsay. Indeed, Hesiod singles himself out by name as the bearer of a powerfully poetic and distinctly human wisdom that (...) he consistently contrasts with Zeus’ divine wisdom. In this article, the author argues that the Milesians attempt to gain access to divine wisdom, and thus disregard the ambiguities characteristic of human wisdom. One sees this especially in a tension between Thales’ political wisdom and natural philosophy, and later between Anaximander’s cosmology and cosmogony. The author concludes that Heraclitus appears to have been the first thinker to confront the Hesiodic worldview on its own terms, inasmuch as his attempt to bridge the divide between divine and human wisdom always keeps one eye on the ambiguities that pervade human experience. (shrink)

Bu makalede Milet Okulu Filozofları ve ilk materyalistler olarak anılan Thales, Anaksimandros ve Anaksimenes’in ontolojileriyle ilişkili olarak arkhe arayışı içerisinde tanrıyla ilgili görüşlerine yer verilecektir. Bazı düşünürler tarafından tanrı tanımaz olarak nitelendirilen Miletli filozofların evrenin ilk maddesi nedir sorusuna vermiş oldukları yanıtların aslında o dönemki Antik Yunan din anlayışıyla bazı önemli noktalarda bağdaştığı gösterilecektir. Makalenin sonunda bu düşünürlerin kendilerine ait bir teoloji ve tanrı düşüncesine sahip oldukları sonucuna varılacaktır. -/- In this article, ideas of the Milesian philosophers; Thales, Anaximandros and (...) Anaximes known as the first materialists will be included in this article with regards to their search for arkhe in relation to their search for god. It will also be shown that the answer to the question of arkhe by the Milesian philosophers who were accepted as atheist philosophers by some thinkers, is compatible with the Ancient Greece’s understanding of religion at some important aspects. At the end of the article, it will be concluded that these scholars have their own idea with regards to theology and god. (shrink)

Bu makalede Milet Okulu Filozofları ve ilk materyalistler olarak anılan Thales, Anaksimandros ve Anaksimenes’in ontolojileriyle ilişkili olarak arkhe arayışı içerisinde tanrıyla ilgili görüşlerine yer verilecektir. Bazı düşünürler tarafından tanrı tanımaz olarak nitelendirilen Miletli filozofların evrenin ilk maddesi nedir sorusuna vermiş oldukları yanıtların aslında o dönemki Antik Yunan din anlayışıyla bazı önemli noktalarda bağdaştığı gösterilecektir. Makalenin sonunda bu düşünürlerin kendilerine ait bir teoloji ve tanrı düşüncesine sahip oldukları sonucuna varılacaktır.

The paper focuses on a neglected instance of the Platonic reception of Heraclitus in the Republic, trying to show that it’s likely that Plato’s passage makes an allusion to Heraclitus’ B97 and B85. The main claim is that Plato’s use of the image of dogs looks back to Heraclitus, which invites an exploration of the possibility that at least some elements of Plato’s kallipolis might derive from Heraclitus – particularly from some ethical and political fragments. A brief survey of these (...) suggests a deep philosophical affinity among the two authors in several important areas, and questions the commonplace traditional interpretation of Heraclitus as a defender of aristocratic morality. (shrink)

This article aims at clarifying some issues raised by a recent book of Daniel W. Graham about the Presocratic cosmology. It particularly intends to shed some light on the understanding of Anaxagoras’ universe by suggesting some reasons why, despite Graham’s opinion, it is still possible to think that the stars were flat according to him. Another goal is highlighting the importance of the comprehensive physical theory of Anaxagoras, based on a circular motion called perichoresis, which would explain diverse phenomena in (...) a consistent way by introducing simplicity in his cosmology. (shrink)

Scholarship on Xenophanes’s F1 has had two foci, one on the rules of the symposium and the other on the religious program posed at its close. Thus far, the two areas of focus have been treated as either separate issues or as the religious program proposed in the service of the sympotic objectives. Instead, I will argue that the sympotic norms Xenophanes espouses are in the service of the broader program of rational theology.

Scholarship on Xenophanes’s F1 has had two foci, one on the rules of the symposium and the other on the religious program posed at its close. Thus far, the two areas of focus have been treated as either separate issues or as the religious program proposed in the service of the sympotic objectives. Instead, I will argue that the sympotic norms Xenophanes espouses are in the service of the broader program of rational theology.

Scopo della presente nota è discutere alcuni aspetti del contributo del Prof. Smith circa Virgilio e l'ambiguità. La nota è divisa in tre parti: a) una discussione dell'ambiguità degli enti empirici in Platone; b) una riconsiderazione del frammento 26 di Eraclito, alla luce di alcune osservazioni di H.G. Gadamer; c) un breve confronto tra il Polidoro virgiliano e il dantesco Pier Delle Vigne circa la natura perturbante della loro trasfigurazione ultramondana.

Journal Name: Apeiron Issue: Ahead of print.

Thisvolume contains the most complete collection ever assembled of the documentary evidence on Thales of Miletus. Approximately 600 texts, dating from the 6th century BCE to the 14th century CE, are presented in chronological order, both in the original language and in a facing English translation. An index of names as well as extensive glossaries and word indexes of the texts and translations are provided.

The doxography for Anaximander’s account of the rings of the sky gives proportions for them that are discrepant. So a widely accepted hypothesis proposes that, since the circles of the celestial bodies are compared to wheels, we should add the thickness of their ‘rims’ to the measurements for the celestial rings. This paper proposes an entirely different hypothesis which avoids this awkward expedient by suggesting that there is a ‘geometrical’ reading of the numerical data. The discrepancies can then be explained (...) by there being two different methods for calculating the circumference of the circles. (shrink)