Center for Hellenic Studies
Harvard University’s Center for Hellenic Studies, located in Washington D.C., was founded by means of an endowment made “exclusively for the establishment of an educational center in the field of Hellenic Studies designed to rediscover the humanism of the Hellenic Greeks.” This humanistic vision remains the driving force of the Center for Hellenic Studies.
The Center brings together a variety of research and teaching interests centering on Hellenic civilization in the widest sense of the term “Hellenic.” This concept encompasses the evolution of the Greek language and its culture as a central point of contact for all the different civilizations of the ancient Mediterranean world. Interaction with foreign cultures, including the diffusion of Roman influence, is an integral part of this concept.
The Director of the Center is Gregory Nagy, who is concurrently the Francis Jones Professor of Classical Greek Literature at the Harvard campus in Cambridge. He is resident at the Center in Washington, where Current Fellows, elected annually, pursue research in one of the world’s premier research libraries. Conferences and programs are a regular part of the educational mission of the Center. New initiatives, such as the Virtual Center, will expand this mission far beyond the Center’s campus in Washington.
Below is a list of in-print works in this collection, presented in series order or publication order as applicable.Sort by title, author, format, publication date, or price »
The literary genres given shape by the writers of classical antiquity are central to our own thinking about the various forms literature takes. Examining those genres, the essays collected here focus on the concept and role of the author and the emergence of authorship out of performance in Greece and Rome.
Written Voices, Spoken Signs is a stimulating introduction to new perspectives on Homer and other traditional epics. Taking advantage of recent research on language and social exchange, the nine innovative essays in this volume—by leading scholars of Homer, oral poetics, and epic—focus on performance and audience reception of oral poetry.
Forty Bosnian traditional ballads are now available to the English reader in this bilingual edition offering a selection of never before translated or published materials from Harvard University’s Parry Collection. These songs were performed by Bosnian women and gathered in the Gacko region of Bosnia and Herzegovina in the 1930s.
This work explores the role of orality in shaping and evaluating medieval Icelandic literature. Applying field studies of oral cultures in modern times to this distinguished medieval literature, Gísli Sigurðsson asks how it would alter our reading of medieval Icelandic sagas if it were assumed they had grown out of a tradition of oral storytelling, similar to that observed in living cultures.
This book examines the overall testimony of Plato as an expert about the cultural legacy of these Homeric performances. Plato’s fine ear for language—in this case the technical language of high-class artisans like rhapsodes—picks up on a variety of authentic expressions that echo the talk of rhapsodes as they once practiced their art.
This colloquium volume celebrates a new Hellenistic epigram collection attributed to the third-century B.C.E. poet Posidippus, one of the most significant literary finds in recent memory. Included in this collection are an unusual variety of voices and perspectives: papyrological, art historical, archaeological, historical, literary, and aesthetic.
The Helots fulfilled all the functions that slaves carried out elsewhere in the Greek world, allowing their masters the leisure to be full-time warriors. Yet, despite their crucial role, Helots remain essentially invisible in our ancient sources and peripheral and enigmatic in modern scholarship. This book is devoted to a much-needed reassessment of Helotry and of its place in the history and sociology of unfree labor.
Priene provides the researcher with an unusually clear and complete picture of life in an ancient Greek city of the late Classical and Hellenistic period. This study presents for the first time a comprehensive look at the architecture of the city, combining material from both the first excavation of 1894 and more recent work at the site. It is lavishly illustrated with specially redrawn architectural plans and reconstructions.
This study provides for the first time an in-depth examination of a central mode of Greek poetic competition—capping, which occurs when speakers or singers respond to one another in small numbers of verses, single verses, or between verse units themselves.
In Greek thought, barbaroi are utterers of unintelligible or inarticulate sounds. What importance does the text of Herodotus’s Histories attribute to language as a criterion of ethnic identity? The answer to this question illuminates the empirical foundations of Herodotus’s pluralistic worldview.
This work offers the first systematic and interdisciplinary study of the poetics of the twelfth-century medieval Greek novel. Rollos investigates the complex ways in which rhetorical theory and practice constructed the overarching cultural aesthetics that conditioned the production and reception of the genre of the novel in Byzantine society.
Investigating ritual in Greece from cross-disciplinary and transhistorical perspectives, this book offers novel readings of the pivotal role of ritual in Greek traditions by exploring a broad spectrum of texts, art, and social practices. This collection of essays written by an international group of leading scholars in a number of disciplines presents a variety of methodological approaches to secular and religious rituals, and to the narrative and conceptual strategies of their reenactment and manipulation in literary, pictorial, and social discourses.
This book probes the narratives of poets who are exiled, tried or executed for their satire. It views the scapegoat as a group’s dominant warrior, sent out to confront predators or besieging forces. Both poets and warriors specialize in madness and aggression and are necessary, yet dangerous, to society.
With numerous fresh linguistic observations, Egbert Bakker shows that the epic narrator makes the epic past come to the present: epic is not only a verbal artifact that points to the past; it also is a performer’s act of pointing at a past that has become present in and through language. Building on his earlier work, Bakker demonstrates the power of discourse analysis as an essential tool for elucidating the poetics of the Homeric tradition.
The Life and Miracles of Thekla offers a unique view on the reception of classical and early Christian literature in Late Antiquity. This study examines the Life and Miracles as an intricate example of Greek writing and attempts to situate the work amidst a wealth of similar literary forms from the classical world.
In the first full-length study of conversation in the Homeric poems, Beck argues that conversation should be considered a traditional Homeric type scene, alongside recognized types such as arrival, sacrifice, battle, and hospitality. This book is a wide-ranging, closely argued aesthetic analysis of repetition and variation in the Homeric epics.
The Ancient Greeks not only spoke of time unfolding in a specific space, but also projected the past upon the future in order to make it active in the social practice of the present. This book shows how the Ancient Greeks’ collective memory was based on a remarkable faculty for the creation of ritual and narrative symbols.
The Culture of Kitharoidia is the first study dedicated exclusively to the art, practice, and charismatic persona of the citharode. Traversing a wide range of discourse and imagery about kitharôidia—poetic and prose texts, iconography, inscriptions—the book offers a nuanced account of the aesthetic and sociocultural complexities of citharodic song and examines the iconic role of the songmakers in the popular imagination.
Laura Slatkin’s influential and widely admired book explores the superficially minor role of Thetis in the Iliad. Slatkin uncovers alternative traditions about the power of Thetis and shows how an awareness of those myths brings a far greater understanding of Thetis’s place in the thematic structure of the Iliad. This second edition also includes six additional essays, which cover a broad range of topics in the study of the Greek Epic.
After a theoretical introduction that also serves as a general introduction to the dramatic chorus from the comic vantage point, a reading of Aristophanes’ Thesmophoriazusae shows that ritual is present in both the micro- and macrostructure of Attic comedy as part of a still existing performative choral culture.
“What if truth were a woman?” asked Nietzsche. In ancient Greek thought, truth in language has a special relation to the female by virtue of her pre-eminent art-form—the one Freud believed was even invented by women—weaving. The essays in this book explore the implications of this nexus: language, the female, weaving, and the construction of truth.
In his Symposium, Plato crafted speeches in praise of love that has influenced writers and artists from antiquity to the present. But questions remain concerning the meaning of specific features, the significance of the dialogue as a whole, and the character of its influence. Here, an international team of scholars addresses such questions.
This is a study of the twelve small gold lamellae from Crete that were tokens for entrance into a golden afterlife. The lamellae are placed within the context of a small corpus of similar texts, and published with extensive commentary on their topography, lettering and engraving, dialect and orthography, meter, chronology, and usage.
Writing to a friend, Horace describes him as fascinated by “the discordant harmony of the cosmos, its purpose and power.” Andrew Scholtz takes this notion of “discordant harmony” and argues for it as an aesthetic principle where classical Athenian literature addresses politics in the idiom of sexual desire. Drawing on theorists of the sociality of language, his approach is an untried one for this kind of topic.
Descriptions of animal sacrifice in Homer offer detailed accounts of this attempt at communication between man and gods. Hitch explores the structural and thematic importance of animal sacrifice as an expression of the quarrel between Akhilleus and Agamemnon through the differing perspectives of the primary narrative and character speech.
This volume comprises the entire body of work by the artist widely considered a master of modern Greek poetry. Published in the original Greek, with a new English translation by Stratis Haviaris on each facing page, and with a foreword by Seamus Heaney, this is Cavafy, familiar and fresh, seen through new eyes, yet instantly recognized.
This book offers the first interdisciplinary and in-depth study of the cultural practices and ideological paradigms that conditioned the politics of the “reading“ of Sappho’s songs in the early and most pivotal stages of her reception—the late archaic, classical, and early Hellenistic periods.
Oral intertextuality is an innate feature of the web of myth, whose interrelated fabrics allow the audience of epic songs access to an entire horizon of story variations. The Oral Palimpsest argues that just as the discarded text of a palimpsest still carries traces of its previous writing, so the Homeric tradition unfolds its awareness of alternate versions as it reveals signs of their erasure.
This book makes the case that the plot of the Odyssey is represented within the narrative as a plan of Zeus, Dios boulê, that serves as a guide for the performing poet and as a hermeneutic for the audience. The “Zeus-centric” reading proposed here offers fresh perspectives on the tenor of interactions among the Odyssey’s characters.
“What is a Greek priest?” This volume, which has its origins in a symposium at the Center for Hellenic Studies, Washington, DC, focuses on the question through several lenses: the visual representation of cult personnel, priests as ritual experts, variations of priesthood, ideal concepts and their transformation, and the role of manteis.
Marcianus Graecus Z. 454 [= 822], known to Homeric scholars as the Venetus A, is the oldest complete text of the Iliad in existence, meticulously crafted in the tenth century CE. New technology offers an opportunity to rediscover this scholarship and better understand the epic that is the foundation of Western literature.
The crisis of Spartan power in the first half of the fourth century has been connected to Spartan inability to manage the hegemony built on the ruins of the Athenian Empire. This book offers a new perspective, suggesting that the crisis that finally leveled Sparta was in vital ways a result of centrifugal impulses within the Peloponnesian League.
Under the Athenian democracy, litigants were expected to speak for themselves, though they could memorize a speech written for them. These amateur performances often manifested an unmanly yielding to emotions of anger or fear; professional speech, Bers seeks to demonstrate, was to a large degree crafted in reaction to amateur stumbling.
This book is about the Homeric figure Nestor, and reveals a level of deliberate irony in the Homeric poems hitherto unsuspected. Frame argues that because Nestor’s role in the poems is built on this irony, he is a key to the circumstances of the poems’ composition.
This book is about the reception of Homeric poetry from the fifth through the first century BCE. The aim of this book, which centers on ancient concepts of Homer as the author of a body of poetry that we know as the Iliad and the Odyssey, is to show how Homer’s work became a classic in the days of the Athenian empire and later.
The world has long wished for more of Sappho’s poetry, which exists mostly in tantalizing fragments. This volume is the first collection of essays in English devoted to discussion of a newly recovered Sappho poem and two other incomplete texts on the same papyri. Using different approaches, the contributions demonstrate how the “New Sappho” can be appreciated as a complete, gracefully spare poetic statement regarding the painful inevitability of death and aging.
This edition, commentary, and accompanying essays focus on the tenth book of the Iliad, which has been doubted, ignored, and even scorned. Casey Dué and Mary Ebbott use approaches based on oral traditional poetics to illuminate many of the interpretive questions that strictly literary approaches find unsolvable.
The contributors to this volume draw upon Homeric scholarship as inspiration for pursuing new ways of looking at texts, both within the Homeric tradition and outside it. The seven original essays here consider topics that transcend traditional generic distinctions between epic and lyric, choral and individual, performed and literary.
In Pindar’s Verbal Art, James Bradley Wells argues that the victory song is a traditional art form that appealed to a popular audience and served exclusive elite interests through the inclusive appeal of entertainment, popular instruction, and laughter. Wells offers a new take on recurrent Pindaric questions: genre, the unity of the victory song, tradition, and, principally, epinician performance.
Arguing for the importance of the first-century historian Josephus to the study of classical and Hellenistic literature, Tragedy, Authority, and Trickery investigates letters in Josephus’s texts. Ryan S. Olson breaks new ground by analyzing classical, Hellenistic, and Jewish texts’ use of letters, comparing those texts to Josephus’s narratives, a virtual archive containing hundreds of letters. An external voice similar to speeches, embedded letters raise questions of authority, drive and color dramatic scenes, and function at textual and meta-textual levels to deceive their readers.
Graeme D. Bird examines a small group of early papyrus manuscripts of Homer’s Iliad, known as the Ptolemaic papyri, which, although fragmentary, are the oldest surviving physical evidence of the text of the Iliad, dating from the third to the first centuries BCE. These papyri have been described as “eccentric” or even “wild.” This book analyzes their unusual readings and shows that in fact they present authentic variations on the Homeric text, based on the variability characteristic of oral performance.
Eve of the Festival is a study of Homeric myth-making in the first and longest dialogue of Penelope and Odysseus (Odyssey 19). This study makes a case for seeing virtuoso myth-making as an essential part of this conversation, a register of communication important for the interaction between the two speakers.
Restraining and taming Nature was fundamental to the Hellenic urban quest. Classical Athens, with her utilitarian view of Nature, exemplified this ideal, which also informed the urban endeavors of Rome and was expressed through the domestication of Nature in villas and gardens, and through primitivist and Epicurean tendencies in Latin literature.
Readers of Herodotus’s histories are familiar with its reports of bizarre portents, riddling oracles, and striking dreams. But Herodotus draws our attention to other types of signs too, beginning with human speech itself as a coded system that can manipulate and be manipulated. Objects, gifts, artifacts, markings, even the human body, are all capable of being invested with meaning in the Histories and Herodotus shows that conventionally and culturally determined actions, gestures, and ritual all need decoding. This book represents an unprecedented examination of signs and their interpreters, as well as the terminology Herodotus uses to describe sign transmission, reception, and decoding. Through his control and involvement in this process he emerges as a veritable “master of signs.”
This book explores the place of the sophists within the Greek wisdom tradition, and argues against their almost universal exclusion from serious intellectual traditions. By studying the sophists against the backdrop of the archaic Greek institutions of wisdom, it is possible to detect considerable intellectual overlap between them and their predecessors. This book explores the continuity of this tradition, suggesting that the sophists’ intellectual balkanization in modern scholarship, particularly their low standing in comparison to the Presocratics, Platonists, and Aristotelians, is a direct result of Plato’s condemnation of them and their practices. This book thus seeks to offer a revised history of the development of Greek philosophy, as well as of the potential—yet never realized—courses it might have followed.
The word kleos in the Iliad and the Odyssey alike refers to something more substantive and complex than “fame” or “glory.” Kleos distinctly supposes an oral narrative—principally an “oral history,” a “life story” or ultimately an “oral tradition.” This book is a meditation on this concept as expressed and experienced in the adult society Telemachos find himself in. Kleos is the yardstick by which his psychological change was appreciated by Homer’s audiences.
The Epic Rhapsode and His Craft studies Homeric performance from archaic to Roman imperial times. It argues that oracular utterance, dramatic acting, and rhetorical delivery powerfully elucidate the practice of epic rhapsodes. Attention to the ways in which these performance domains informed each other over time reveals a shifting dynamic of competition and emulation among rhapsodes, actors, and orators that shaped their texts and their crafts. Rhapsodic practice is best understood as an evolving combination of revelation, interpretation, recitation, and dramatic delivery.
A unique, multi-authored social history of war from the third millennium B.C.E. to the tenth century C.E. in the Mediterranean, the Near East, and Europe (Egypt, Achaemenid Persia, Greece, the Hellenistic World, the Roman Republic and Empire, the Byzantine Empire, the early Islamic World, and early Medieval Europe), with parallel studies of Mesoamerica (the Maya and Aztecs) and East Asia (ancient China, medieval Japan). The product of a colloquium at Harvard’s Center for Hellenic Studies, this volume offers a broadly based, comparative examination of war and military organization in their complex interactions with social, economic, and political structures as well as cultural practices.
Recently, scholars have looked more closely at the philosophical importance of the imaginative and literary aspects of Plato’s writing, and have begun to appreciate the methods of ancient philosophers and commentators who studied Plato. This study brings together leading philosophical and literary scholars to investigate these new-old approaches.
Comparative Anthropology of Ancient Greece looks at the anthropology of the Greeks and other cultures across space and time, and in the process discovers aspects of the art of comparability. Marcel Detienne tries to see how cultural systems react not just to a touchstone category, but also to the questions and concepts that arise from the reaction.
This book—the first full-length study of Theodoret’s Therapeutic for Hellenic Maladies—examines Theodoret’s arguments against Greek religion, philosophy, and culture. Its analysis of the interaction between Hellenism and early Christian culture offers insights into the broader late Roman and early Byzantine world in the fifth century.
Anna Bonifazi examines the evocative power of linguistic elements in the Homeric text—in particular, the use of αύ- adverbs and particles to signal upcoming content and the ambiguous use of pronouns to evoke the complexity of Odysseus’s identity. She shows that, by deliberately merging distinct meanings, the text incorporates different viewpoints.
One of the Ancient Near East’s most important inscriptions is the Bisotun inscription of the Achaemenid king Darius I (6th century B.C.E.), which reports on a suspicious fratricide and coup. Shayegan shows how the Bisotun’s narrative influenced the Iranian epic, epigraphic, and historiographical traditions into the Sasanian and early Islamic periods.
Focusing on the the eastern Mediterranean area shaped by the Byzantine and Ottoman empires, this volume explores the nexus of empire and geography. Through examination of a wide variety of texts, the essays explore ways in which production of geographical knowledge supported imperial authority or revealed its precarious grasp of geography.
Exploring the functions of space in the Iliad, Christos Tsagalis shows how active spatial representation in similes and descriptive passages influences characterization and narrative action. He also analyzes Homeric modes of visual memory, implicit knowledge, and mnemonic formats in order to better understand descriptive and ekphrastic passages.
Tarik Wareh’s study of the literary culture within which the works, schools, and careers of Plato, Aristotle, and other Greek intellectuals took shape focuses on the role played by their rival Isocrates and the rhetorical education offered in his school. The book sheds new light on the participation of “Isocrateans” in fourth-century intellectual life.
In this new interpretation of the Education of Cyrus, in which Xenophon theorized about leadership, Sandridge considers Xenophon’s portrait of Cyrus as sincerely laudatory though not idealized. He explores the wider context in which Xenophon’s Theory of Leadership was conceived, as well as the problems of leadership he sought to address.
Schwartz’s analysis of the Catechetical Homilies of Theodore of Mopsuestia explores the role of education and worship in the complex process of conversion and Christianization. Catechesis emerges here as invaluable for comprehending clergy’s ability to initiate new members as Christianity gained increasing prominence within the late Roman world.
Homeric Durability investigates the concepts of time and decay in the Iliad. Through a framework informed by phenomenology and psychology, Lorenzo F. Garcia, Jr. argues that, in moments of pain and sorrow, the Homeric gods are themselves defined by human temporal experience, and so the epic tradition cannot but imagine its own eventual disintegration.
Christian Jacob presents a completely fresh and unique reading of Athenaeus’s Sophists at Dinner (ca. 200 CE), a text long mined merely for its testimonies to lost classical poets. Connecting the world of Hellenistic erudition with its legacy among Hellenized Romans, Jacob helps the reader navigate the many intersecting paths in this enormous work.
One of the most significant contributors to late antique literary culture, Eusebius of Caesarea has received only limited attention as a writer and thinker in his own right. Focusing on the full range of Eusebius’s works, the new studies in Eusebius of Caesarea will change how classicists, theologians, and historians think about this major figure.
In the second century, some Gnostic Christians used numerical structures to describe God, interpret the Bible, and frame the universe. The Theology of Arithmetic explores the rich variety of number symbolism used by gnosticizing groups and their orthodox critics, and shows how earlier neo-Pythagorean and Platonist thought influenced this theology.
Shubha Pathak explores a new way to connect the primary Sanskrit epics Rāmāyana and Mahābhārata with their Greek analogues, the Iliad and Odyssey. This cross-cultural comparative study provides a more comprehensive perspective on the poems’ religiosity than the vantage points of Hellenists or of Indologists alone.
The Derveni Papyrus, discovered accidentally in 1962, is the oldest known European “book.” Papers in Poetry as Initiation address many open questions about the papyrus, including its authorship, the context of the peculiar chthonic ritual described in the text, and the relationship of the author and the ritual to the so-called Orphic texts.
Between Thucydides and Polybius focuses on the contribution of fourth-century authors such as Ephorus, Theopompus, and Xenophon to the development of Greek historiography. Essays examine the interface between historiography and rhetoric, while undermining the claim that historians after Thucydides allowed rhetoric to prevail over research.
Averil Cameron refutes an argument by some scholars that Christians did not dialogue after a wall of silence came down in the fifth century AD. Cameron shows that in late antiquity and throughout Byzantium Christians debated and wrote philosophical, literary, and theological dialogues, and she makes a case for their centrality in Greek literature.
Scholars of the literary aspect of Plato try to reconcile his dialogue form with the expository imperative of philosophical argument. Classicists and philosophers explain this form in terms of rhetorical devices serving didactic goals. David Schur brings literary and classical studies into debate, questioning modern views of Plato’s dialogue form.
Andrea Capra reconstructs Plato’s authorial self-portrait through a fresh reading of the Phaedrus. Capra maintains that Socrates’s conversion to “demotic” music in the Phaedo closely parallels the Phaedrus and is apologetic in character, since Socrates was held responsible for dismissing traditional mousikê.
Inscribed after 264 BCE, the Parian Marble gives a chronological list of events, emphasizing literary matters. It has not been the subject of a comprehensive study for almost a century. Andrea Rotstein offers new analysis and updated information about the inscription, including a revision of Felix Jacoby’s Greek text and a complete translation.
Malcolm Davies provides the first full commentary on the surviving fragments of the four epics that recount the story of the Seven’s failed assault against Thebes and the successful assault in the next generation. He sets them in context and examines whether artistic depictions of the relevant myths can help reconstruct the lost epics’ contents.
John Curtis Franklin seeks to harmonize Kinyras as a mythological symbol of pre-Greek Cyprus with what is known of ritual music and deified instruments in the Bronze Age Near East, using evidence going back to early Mesopotamia. This paperback edition contains minor corrections, while retaining the maps of the original hardback edition as spreads.
The once influential theory Neoanalysis held that motifs and episodes in the Iliad derive from the Aethiopis. Given its vast potential implications for the Iliad’s origins, the recent revival of Neoanalysis in subtler form inspires this critical reappraisal by Malcolm Davies of that theory’s more sophisticated reincarnation.
Gregory Nagy analyzes metonymy as a mental process that complements metaphor. If metaphor is a substitution of something unfamilar for something familiar, metonymy connects something familiar with something else already familiar. Nagy offers close readings of over one hundred examples of metonymy in the arts of Greek and other cultures.
This study by Hélène Monsacré shows how Western ideals of inexpressive manhood run contrary to the poetic vision of Achilles and his warrior companions presented in the Homeric epics. Pursuing the paradox of the tearful fighter, Monsacré examines the interactions between men and women in the Homeric poems.
Equine Poetics is a literary analysis of horses and horsemanship in early Greek epic and lyric poetry. Drawing from the fields of comparative poetics and historical linguistics, the book sheds new light on fascinating and puzzling aspects of these central figures in early Greek verbal art.
The existing manuscripts of Old Norse mythology were written mainly by Christians, obscuring the pre-Christian oral histories. This book assembles comparisons from a range of analytical perspectives—examining the similarities and differences of the Old Norse mythologies with the myths of other cultures and within the Old Norse corpus itself.
Katherine L. Kretler plumbs the virtues of the Homeric poems as scripts for solo performance. What is lost in the journey from the stage to the page? The book focuses on the performer not as transparent mediator, but as one haunted by multiple stories, bringing suppressed voices to the surface.
Andrew Porter explores characterization in Homer, from an oral-traditional point of view, through the resonance of words, themes, and “back stories” from the past and future. He analyzes Agamemnon’s character traits in the Iliad, including his qualities as a leader, against events such as his tragic homecoming in the Odyssey.
William Brockliss, responding to George Lakoff’s and Mark Johnson’s analysis of metaphor, explores the Homeric poets’ use of concrete concepts drawn from the Greek natural environment to aid their audiences’ understanding of abstract concepts. In particular, he considers Homeric images associating flowers with deception, disorder, and death.
Casey Dué, coeditor of the Homer Multitext, explores both the traditionality and multiformity of the Iliad. Dué argues this multiform nature gives us glimpses of the very long history of the text, access to even earlier Iliads, and a greater awareness of the mechanisms by which such a remarkable epic poem could be composed in performance.
Examining Aelia Eudocia’s writings as a unified whole and in context, Brian P. Sowers reveals an exceptional author representing three late-antique communities: poets interested in transforming classical literature; Christians positioned outside traditional power structures; and women who challenged social, religious, and literary boundaries.