Emily R. Grosholz

philosopher, poet, literary critic

Starry Reckoning: Reference and Analysis in Mathematics and Cosmology

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.

The book is enjoyable to read. The broad spectrum of topics and the detail in which they are discussed provide the reader with some interesting insights. In particular, the idea that mathematical analysis not only solves problems, but in the most interesting cases, explains why important problems show up in the first place is well argued and well presented.
Sébastien Gandon, Philosophia Mathematica,September, 2017

The Stars of Earth

Emily Grosholz weaves elements of philosophy, mathematics and the sciences into her experience of the social and natural world, to produce wise and cosmopolitan poetry of high lyricism. The Stars of Earth starts with new poems chronicling the months of a year lived and observed, followed by selections from Grosholz’s previous volumes in chronological order. This rare treasury spans four decades of Grosholz’s acclaimed poetry.

For more on The Stars of Earth, see Word Galaxy Press page and Emily Grosholz's page at Word Galaxy Press.

Able Muse: A Review of Poetry, Prose & Art

Studies in History and Philosophy of Modern Philosophy

Emily R. Grosholz (Guest Editor)

Volume 52, Part A, Pages 1-110 (November 2015). Special Issue: Cosmology and Time: Philosophers and Scientists in Dialogue

This collection of essays is based on a Workshop on Cosmology and Time that was held at The Pennsylvania State Univeristy on 16-17 April 2017.

For more on this issue, including a table of contents, see Science Direct.

Representation and Productive Ambiguity in Mathematics and the Sciences

Emily R. Grosholz (Author)

In Representation and Productive Ambiguity in Mathematics and the Sciences, Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience.

Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable fore mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are subtly altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.


Reviews

  1. French, Steven (2011). Reviewed Work: Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz British Journal for the Philosophy of Science. Vol. 62 Issue 4, pp.895-898.
  2. Goethe, Norma B. (2006/2007). Reviewed Work: Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz. Studia Leibnitiana, Bd. 38/39, H. 2 , pp. 244-246
  3. Bangu, Sorin. (2009). Representation and Productive Ambiguity in Mathematics and the Sciences. ISIS 100:11, pp. 137-139.

Drafts of Chapters (and Comments)

Earlier versions of each chapter are attached as files (for the most part without plates), but the finished chapters in the book have all been revised, expanded, and corrected a great deal, so you should consult the book for the definitive form of the arguments, case studies, and those very important plates.

Included here are comments written by colleagues in response to some of the arguments or case studies in that chapter, or by myself in response to, or in collaboration with, an interlocutor.

  1. Chapter 1: with the notes but not the plates. The plates can be found in any standard edition of Galileo's Two New Sciences.
    • Comment 1: from Norma Goethe (University of Cordoba, Argentina). Part of a review to appear in Studia Leibnitiana.
    • Comment 2: from Bas van Fraassen (San Francisco State University), a propos the issue of representation in Ch. 1, and in the Introduction and Ch. 1 of his new book on scientific representation.
  2. In chapter 2, I made use of my review of Karine Chemla's and Guo Shuchun's edition and translation of Les Neuf Chapitres: Le Classique mathematique de la Chine ancienne et ses commentaires (Dunod 2004), a text usually refered to as the Chinese analogue of Euclid's Elements. Karine Chemla's commentary argues that the organization of this text is best understood in terms of "generalization" rather than "axiomatization." She, David Rabouin and various members (including myself) of the research group REHSEIS / CNRS / University of Paris Diderot -- Paris 7 are contributing to a volume of essays that will analyze and exemplify the notion of generalization.
    • Comment 1: Here are two commentaries on the issue of generality, apropos a paper by Karine Chemla (commentary 1) on the geometer Michel Chasles, and a paper by Evelyne Barbin on Fermat and Descartes (commentary 2). I wrote them after discussing the papers with Emiliano Ippoliti, a postdoctoral student from the University of Rome, so the comments are ultimately co-authored. These comments take the discussion in Chapter 2 a bit further.
    • Comment 2: When I gave a presentation of this book at the Philosophy of Science Center, University of Pittsburgh, somebody asked me if I were hostile to axiomatization, a question that might occur to someone who read Ch. 2. My answer was, of course not, but I was so surprised that I didn't elaborate much. The following (commentary 3) is a third result of discussions with Emiliano Ippoliti, apropos the interesting remark of Dirk Schlimm that we perhaps need a taxonomy of kinds of axiomatization.
  3. Chapter 3: an early (1998) version of this chapter was co-authored with Roald Hoffmann and published as "How Symbolic and Iconic Languages Bridge the Two Worlds of the Chemist: A Case Study from Contemporary Bioorganic Chemistry," in Of Minds and Molecules: New Philosophical Perspectives on Chemistry, N. Bhushan and S. Rosenfeld, eds., OUP 2000, 230-47 (in French in Les Langages Scientifiques, ed. F. Letoublon, Editions ARASSH, Grenoble.
  4. Chapter 4: an earlier version of this chapter, a paper that I gave in Berlin. To see an earlier version of this chapter, with most of the plates, you can consult "Fedoroff's Translation of McClintock: The Uses of Chemistry in the Reorganization of Genetics," in Tools and Modes of Representation in the Laboratory Sciences, Ursula Klein, ed., Boston Studies Series in the Philosophy of Science (Kluwer 2001), 199-218.
    • Comment 1: on Ch. 4, from September, written by Evelyn Fox Keller.
  5. Chapter 5: without plates. The plates are taken mostly from F. A. Cotton's Chemical Applications of Group Theory (John Wiley and Sons, 1990).
    • Comment 1: from Joseph Mazur (Mathematics, University of Vermont): "One brief observation: I?m very glad you put in the chapter on group theory and representations?it seems to me that what you say there is the kernel; and you say it very well. In fact, beginning group theory students would benefit from your analysis of representation theory. I wish I had had such a view when I was a student and confused about what representations were really about. I understood the mechanics, but not the real purpose."
  6. Chapter 6: Here is an early version of some of the material in this chapter, without plates. All the plates are in a standard edition of Descartes' Geometry.
  7. Chapter 7: an earlier version of this chapter, without plates. The plates can be found in any standard edition of Newton's Principia.
  8. Chapter 8a, Chapter 8b: two earlier papers, which contain much of the content of Chapter 8, without the plates. The plates can be found in the relevant volume of C. I. Gerhardt's editions of Leibniz's mathematical and philosophical writings.
    • Chapter 8: by Norma Goethe (University of Cordoba, Agentina) on this chapter, part of an earlier draft of a review she has written for Studia Leibnitiana.
  9. Chapter 9: an earlier version of a paper that contains much of the content of Chapter 9, which I gave at the University of Rome, without the plates. The plates can be found in Singer & Thorpe, Lecture Notes on Elementary Geometry and Topology.
  10. Chapter 10: an earlier version of Chapter 10.
    • Comment 1: Comments I wrote in 2008 on a paper by John Dawson (Mathematics, Pennsylvania State University) and another by Carlo Cellucci (University of Rome) that seem to me germaine to the issue in Ch. 10. They deal with the role that transferability (similar structures, different objects) and consilience (different structures, same objects) play in the unification of mathematics.

Cartesian Method and the Problem of Reduction

Emily R. Grosholz (Author)

The Cartesian method, construed as a way of organizing domains of knowledge according to the "order of reasons," was a powerful reductive tool. Descartes made significant strides in mathematics, physics, and metaphysics by relating certain complex items and problems back to more simple elements that served as starting points for his inquiries. But his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the negative and positive impact of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry, the Principles, the Treatise of Man, and the Meditations.

Reviews

  1. Ariew, Roger. (Apr., 1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily Grosholz. Mind, New Series, Vol. 101, No. 402 , pp. 376-379.
  2. BUROKER, J. V. (1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily R. Grosholz. Philosophical Books, 33: 9?11.
  3. Clarke, Desmond M. (1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily R. Grosholz. The British Journal for the History of Science, Vol. 25, No. 2 (Jun., 1992), pp. 266-267.
  4. Mahoney, Michael S. (Mar., 1993), Reviewed Works: Cartesian Method and the Problem of Reduction by Emily R. Grosholz; The Magic of Numbers and Motion: The Scientific Career of Rene Descartes by William R. Shea. Isis Vol. 84, No. 1, pp. 146-148.
  5. Gardies, Jean-Louis (JANVIER-MARS 1994), Reviewed Work: Cartesian method and the problem of reduction by Emily R. Grosholz. Revue Philosophique de la France et de l'?tranger, T. 184, pp. 119-121

Beginning and End of the Snow / Début et Fin de la Neige

Yves Bonnefoy (Author). Emily R. Grosholz (Translator).

Yves Bonnefoy's book of poems, Beginning and End of the Snow followed by Where the Arrow Falls, combines two meditations in which the poet?s thoughts and a landscape reflect each other. In the first, the wintry New England landscape he encountered while teaching at Williams College evokes the dance of atoms in the philosophical poem of Lucretius as well as the Christian doctrine of death and resurrection. In the second, Bonnefoy uses the luminous woods of Haute Provence as the setting for a parable of losing one's way.

The poems are prefaced with an essay by Yves Bonnefoy, "Snow in French and English," and followed by an essay I wrote, "Song, Rain, Snow: Translating the Poetry of Yves Bonnefoy," both on the art of translation. The latter essay first appeared, in an extended form, in the Hudson Review (Vol. LXI / 4) pp. 618-642, along with eight poems from the book. One of my translations from this book, along with other, earlier translations, was included in Poets Translate Poets: A Hudson Review Anthology, edited by Paula Deitz (Syracuse University Press, 2013).

Included below are six short poems from the first section, La Grande Neige, of Yves Bonnefoy's Début et fin de la neige (Paris: Mercure de France, 1991). Translation by Emily Grosholz, published as Beginning and End of the Snow (Bucknell University Press, 2011).

For an interview about the translation, see Bucknell University Press Interview.

La Grande Neige

[Untitled]

First snowfall, early this morning. Ochre, green
Huddle under the trees.

The second, towards noon. Nothing
Is left of color
But needles from the pines
Falling sometimes thicker than snow.

Then, towards evening,
The light stands poised.
Shadows and dreams balance on the scales.

A faint wind
Writes in the snow a word beyond the world.

[Sans titre]

Première neige tôt ce matin. L’ocre, le vert
Se réfugient sous les arbres.

Seconde, vers midi. Ne demeure
De la couleur
Que les aiguilles de pins
Qui tombent elles aussi plus dru parfois que la neige.

Puis, vers le soir,
Le fléau de la lumière s’immobilise.
Les ombres et les rêves ont même poids.

Un peu de vent
Écrit du bout du pied un mot hors du monde.

The Mirror

Yesterday still
The clouds sailed across
The dark end of the room,
But now the mirror?s empty.

Snow
Disentangles from the sky.

Le Miroir

Hier encore
Les nuages passaient
Au fond noir de la chambre.
Mais à présent le miroir est vide.

Neiger
Se désenchevêtre du ciel.

The Plough

Five o'clock. More snow. I hear some voices
At the edge of the world.

A plough
Like a three-quarter moon
Shines, but then is covered
By the darkness of a fold of snow.

And from now on that child
Has the house all to himself. He goes
From one window to another. He presses
His fingers against the misted pane. He sees
Drops forming where his fingertips stop
Pushing the condensation towards the sky that falls.

La Charrue

Cinq heures. La neige encore. J’entends des voix
À l’avant du monde.

Une charrue
Comme une lune au troisième quartier
Brille, mais la recouvre
La nuit d’un pli de la neige.

Et cet enfant
A toute la maison pour lui, désormais. Il va
D’une fenêtre à l’autre. Il presse
Ses doigts contre la vitre. Il voit
Des gouttes se former là où il cesse
D’en pousser la buée vers le ciel qui tombe.

Spot of Water

To the snowflake
Poised on my hand, I would
Grant eternity,
Understanding my life, my warmth,
My past, these current days,
As simply a moment, this one, limitless.

And yet it melts: already
Only a spot of water, strayed
Into the mist of bodies moving through the snow.

Le Peu d’Eau

À ce flocon
Qui sur ma main se pose, j’ai désir
D’assurer l’éternel
En faisant de ma vie, de ma chaleur,
De mon passé, de ces jours d’à présent,
Un instant simplement: cet instant-ci, sans bornes.

Mais déjà il n’est plus
Qu’un peu d’eau, qui se perd
Dans la brume des corps qui vont dans la neige.

[Untitled]

Snow
Fugitive on the scarf, the glove
Like that illusion, coquelicot,
In the hand that dreamt, last summer
On a path among dry stones,
That the absolute lies within reach of the world.

All the same, what promise
In this drop of water, this brief touch, since it was
Just for a moment, light! No riven cloud
Of a summer sky could open to reveal
A clearer path underneath darker vaults.

Circe
Under her pergola of shadows, the enlightened,
Had no fruits redder than these.

[Sans titre]

Neige
Fugace sur l’écharpe, sur le gant
Comme cette illusion, le coquelicot,
Dans la main qui rêva, l’été passé
Sur le chemin parmi les pierres sèches,
Que l’absolu est à portée du monde.

Pourtant, quelle promesse
Dans cette eau, de contact léger, puisqu’elle fut,
Un instant, la lumière! Le ciel d’été
N’a guère de nuées pour entrouvrir
Plus clair chemin sous des voûtes plus sombres.

Circé
Sous sa pergola d’ombres, l’illuminée,
N’eut pas de fruits plus rouges.

Our Lady of Mercy

Everything, now,
Gathers in warmth
Under your light mantle,
Barely more than mist and knotted lace,
Lady of Mercy of the snow.

Against your body
Creatures and things,
Naked, lie fast asleep, and your fingers
With their clarity veil those closed eyelids

La Vierge de Miséricorde

Tout, maintenant,
Bien au chaud
Sous ton manteau léger,
Presque rien que de brume et de broderie,
Madone de miséricorde de la neige.

Contre ton corps
Dorment, nus,
Les êtres et les choses, et tes doigts
Voilent de leur clarté ces paupières closes.


The last poem in the sequence of six poems given here, "Madone de Miséricorde," was set to music by Thierry Machuel and performed by Música Quántica Voces de Cámara, under the direction of Camilo Santostefano.

My translation of La Grande Neige in Début et fin de la neige is included in the booklet for Mirco De Stefani's Canzoni de La grande neige with Christine Nadal (soprano) and Maria De Stefani (piano) (Rivoalto, 2008). In addition, my translation of Bonnefoy's sequence "L été de nuit," is included in Mirco De Stefani's Canzoni de L été de nuit (Rivoalto, 2010).

Childhood

Emily R. Grosholz (Author), Katerina Stoykova-Klemer (Editor), Lucy Vines (Illustrator).

In this gorgeous, heartwarming collection about childbirth and adopting, children and parents, the poems by accomplished poet Emily R. Grosholz interact with color drawings by gifted Parisian artist Lucy Vines. A fixed percentage from the sale of this book will go to an international organization that works to protect and encourage children worldwide, by providing food and water, medical attention, shelter from violence, and education; this children's humanitarian organization has saved more lives than any other.

For more on Childhood, see Interview by Accent Publishing about Childhood, Blurb in the Sewanee Review

Praise for Childhood

These eloquent, edgy poems write of youth and parenting in powerful ways. They also go well beyond that, in addressing childhood as revelation: not just the temporal state we all go through, but the crisis of wonder our own children produce in us. Any reader who picks up this book can draw closer to that wonder and share in it again through this lyrical, moving work.
Eavan Boland
Emily Grosholz is a singular presence in American letters--a poet-philosopher whose brilliant verse on science, mathematics and ideas has been justly praised. But my favorite Grosholz work has always been her tender and arresting poems on motherhood and children. It is a joy to see these luminous and loving poems gathered into one richly expressive volume.
Dana Gioia
These poems lend us wings to fly from Kilimanjaro to Paris and on to the Caribbean with our children, and they make differences of physical size disappear by magnifying molecules and compactifying the universe.
Tadatoshi Akiba

Telling the Barn Swallow: poets on the poetry of Maxine Kumin

Emily R. Grosholz (Editor)

  1. Eleanor Wilner. The Wedding of Meaning and Measure: Kumin and the Poetics of Finitude.
  2. Annie Finch. A Rock in the River: Maxine Kumin's Rhythmic Countercurrents.
  3. Henry Taylor. Remembering Where Everything Is: The Poetry of Maxine Kumin.
  4. Emily Grosholz. Mxine Kumin's Poetry of Metamorphosis.
  5. Neal Bowers. Poised in the Galloping Moment: Maxine Kumin's Poetry.
  6. Alicia Ostriker. Making the Connection: The Nature Poetry of Maxine Kumin.
  7. Mark Jarman. The Retrieval System.
  8. Hilda Raz. Maxine Kumin's Sense of Place in Nature.
  9. Wesley McNair. Kumin's Animal Confederates.
  10. Robin Becker. Out of Our Skins: Transformation and the Body in the Poems of Maxine Kumin.
  11. Michael Burns. A Satisfactory Machinery.
  12. Carole Simmons Oles. Max's Garden: For Present and Future Consumption.

POEMS

  1. Robin Becker. Floating Farm.
  2. Robin Becker. A Marriage.
  3. Wendell Berry. Chicory.
  4. Philip Booth. The Dive.
  5. Neal Bowers. Another Language.
  6. Annie Finch. Zaraf's Star.
  7. Emily Grosholz. Sidonie.
  8. Carolyn Kizer. Parents' Pantoum.
  9. Wesley McNair. The Puppy.
  10. Wesley McNair. Why We Need Poetry.
  11. Carole Simmons Oles. Small Poem of Thanks.
  12. Alicia Ostriker. Mid-February.
  13. Hilda Raz. Family.
  14. Eleanor Wilner. Postscript.

Eden

Emily R. Grosholz (Author)

In Eden, Emily Grosholz brings together forty lyric, narrative, and epistolary poems that trace a pilgrimage from the Eden of childhood through alienation and loss to an earthly paradise regained as the poet establishes her own family and a new sense of the purposes of her art.

The route traverses Detroit in the early twenties, Paris and Washington, D.C., in the early seventies, Athens and Toronto in the mid-eighties, yesterday's Thimphu and Cassis. But it always returns to the poet's heartland, Philadelphia and the back country of Pennsylvania and New York. Punctuated by meditations on solitude and death, the poems come full circle to the pleasures of marriage, of friends and children, of creation. To her husband, the poet writes, "However often now our woven/ lives converge and separate, my love,/ today we've come this far." And to her son, "With you fast in my arms,/ I'm back again in the heart's Italy."

It is rare to find poems which offer so much freshness and accessibility of feeling while at the same time hewing to a course of argument charted by a scrupulous intellect.
Robert B. Shaw, Poetry
Emily Grosholz is a poet of light, her luminous poetry arriving from that bright shore where philosophic mediation meets desire. This rare congruence is visible in the radiant reflection that both characterizes her poems and recurs in brilliant images of how things loan each other light.
Eleanor Wilner

The Abacus of Years: Poems

Emily R. Grosholz (Author)

There are two topics that seem largely unexplored by American poets of our time. One is the deep attachment parents (and perhaps most especially working parents) form for their infants and how they perceive their children (perhaps as Blake saw them) with all the wisdom of their innocence. The second is the relationship of science, mathematics and metaphysics to our everyday life. Here is a book that explores, and to some degree attempts to define, the writer's investigations in those two domains, one stemming from her experience as a mother, the other from her profession as a philosopher of science. And it is this juxtaposition of maternal emotion and detached, almost clinical, analysis that provides Grosholz's wonderful new collection with such grace and such power.

Praise for The Abacus of Years

There is no end to the kinds of poems that Grosholz can write, always with distinction of language and with a great gift for wedding the measures of verse to the rhythms of thought.
Richard Wilbur
Grosholz seems to keep a certain distance from her subjects and to manage this without the ironies one might expect. I take this to be a sign of the writer's intelligence; it is certainly a mark of this poet's admirable apartness from other poets of her time.
Donald Justice

The Growth of Mathematical Knowledge

Emily Grosholz (Editor), Herbert Breger (Editor).

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone of intelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work of the physicist who provides a quantified account of the machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking of concepts nor the record of perceptual experience. In the Critique of Pure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary laws of Newtonian mechanics.

Part I: The Question of Empiricism. The Role of Scientific Theory and Empirical Fact in the Growth of Mathematical Knowledge. 1. Knowledge of Functions in the Growth of Mathematical Knowledge

  1. J. Hintikka. Knowledge of Functions in the Growth of Mathematical Knowledge
  2. M.S. Mahoney. Huygens and the Pendulum: From Device to Mathematical Relation
  3. D. Gillies. An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics
  4. I. Schneider. The Mathematization of Chance in the Middle of the 17th Century
  5. M. Liston. Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider
  6. E. Grosholz. The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge
  7. C. Fraser. Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations
  8. P. Mancosu. On Mathematical Explanation
  9. F. de Gandt. Mathematics and the Reelaboration of Truths
  10. M. Steiner. Penrose and Platonism
  11. M. Wilson. On the Mathematics of Spilt Milk

Part II: The Question of Formalism. The Role of Abstraction, Analysis, and Axiomatization in the Growth of Mathematical Knowledge.

  1. C. Cellucci. The Growth of Mathematical Knowledge: An Open World View
  2. D. Laugwitz. Controversies about Numbers and Functions
  3. C. Posy.Epistemology, Ontology, and the Continuum
  4. H. Breger. Tacit Knowledge and Mathematical Progress
  5. M.M. Muntersbjorn. The Quadrature of Parabolic Segments 1635-1658: A Response to Herbert Breger
  6. M. Liston. Mathematical Progress: Ariadne's Thread
  7. C. Mclarty. Voir-Dire in the Case of Mathematical Progress
  8. H. Sinaceur. The Nature of Progress in Mathematics: The Significance of Analogy
  9. E. Knobloch. Analogy and the Growth of Mathematical Knowledge
  10. A. Barabashev. Evolution of the Modes of Systematization of Mathematical Knowledge
  11. I. Bashmakova and G.S. Smirnova. Geometry, the First Universal Language of Mathematics

Part III: The Question of Progress. Criteria for and Characterizations of Progress in Mathematical Knowledge.

  1. P. Maddy. Mathematical Progress
  2. M.D. Resnik. Some Remarks on Mathematical Progress from a Structuralist's Perspective
  3. V. Peckhaus. Scientific Progress and Changes in Hierarchies of Scientific Disciplines
  4. S. Demidov. On the Progress of Mathematics
  5. K. Mainzer. Attractors of Mathematical Progress: The Complex Dynamics of Mathematical Research
  6. C. Thiel. On Some Determinants of Mathematical Progress

Shores and Headlands

Emily Grosholz (Author)

"[Grosholz] has a lucid, lyrical voice, a pure, song-like quality. I think many aspire to this sort of effortless music, but few succeed as well as she."
Alice Fulton

Logic and Knowledge

Carlo Cellucci (Editor), Emily Grosholz (Editor), Emiliano Ippoliti (Editor)

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI-VII of Plato's Republic and Aristotle's Prior and Posterior Analytics, to Kant's Critique of Pure Reason and Mill's A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901-1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors.


The Legacy of Simone de Beauvoir

Emily Grosholz (Editor)

The legacy of Simone de Beauvoir has yet to be properly assessed and explored. The 50th anniversary of the publication of The Second Sex inspired this volume which brings together philosophers and literary critics, some of whom are well known for their books on Beauvoir (Bauer, Le Doeuff, Moi), others new to Beauvoir studies though long familiar with her work (Grosholz, Imbert, James, Stevenson, Wilson). One aim of this collection is to encourage greater recognition of Beauvoir's philosophical writings through systematic reflection on their place in the canon and on her methods. The Second Sex played a central role in the profound shift in philosophy's self-understanding that took place in the latter half of the twentieth century, and today offers new problems for reflection and novel means for appropriating older texts. Its reflective iconoclasm can be compared to that of Descartes' Meditations; its enormous, directly discernible impact on our social world invites comparison with Locke's Two Treatises of Government. The collection also examines the relationship between Beauvoir's literary writing and her philosophical thought. Deeply concerned with the critical and creative powers of reason as well as with the betterment of our suffering world, Simone de Beauvoir wrote in a variety of genres in addition to the philosophical essay: the novel, political journalism, and the memoir. The multiplicity of her voices was closely related to her philosophical project. Since Beauvoir's method (like that of W. E. B. du Bois) proceeded from her own immediate experience, her reflections had to find expression sometimes as narrative, sometimes as autobiography, sometimes as argument. The Legacy of Simone de Beauvoir demonstrates the many ways in which Beauvoir's writings, in particular The Second Sex, can serve as resources for thought, for the life of the mind which is as concerned with the past and future as it is with the present.

This distinguished volume of essays provides an incisive review of Simone de Beauvoir's legacy, ranging expertly over the historical, philosophical and literary dimensions of a complex and controversial figure...the stature, originality, pragmatism and sheer intelligence of Beauvoir are outstandingly well brought into focus.
Richard Parish, Times Higher Education Supplement

W.E.B. Du Bois on Race and Culture

Bernard W. Bell (Editor), Emily R. Grosholz (Editor), James B. Stewart (Editor)

Interpreting Du Bois' thoughts on race and culture in a broadly philosophical sense, this volume assembles original essays by some of today's leading scholars in a critical dialogue on different important theoretical and practical issues that concerned him throughout his long career: the conundrum of race, the issue of gender equality, and the perplexities of pan-Africanism.

Leibniz's Science of the Rational

Emily R. Grosholz (Author), Elhanan Yakira (Author)

Interpreting Du Bois' thoughts on race and culture in a broadly philosophical sense, this volume assembles original essays by some of today's leading scholars in a critical dialogue on different important theoretical and practical issues that concerned him throughout his long career: the conundrum of race, the issue of gender equality, and the perplexities of pan-Africanism.

The River Painter

Emily R. Grosholz (Author)

Proportions of the Heart: Poems that Play with Mathematics

Emily R. Grosholz (Author), Robert Fathauer (Illustrator)

This volume contains 22 poems by American poet and philosopher Emily Grosholz. The poems in this book blend mathematical topics from fractals to negative curvature with history, classicism, and human emotions. Includes illustrations by Robert Fathauer.

Praise for Proportions

"Play with mathematics? Emily Grosholz's poems do that and much more. They illuminate its mysteries with alephs flung like a candelabrum, challenge us to study the morphology of the amorphous, and embrace mathematics' aethereal aesthetic. Out of fixed proportions, beauty rises: the elegance, conciseness, and precision of these poems go straight to its heart."
Marjorie Wikler Senechal
"Transfinite and transcendental converge in this delicious medley of verses pulsating with passion and life. Like fractals' captivating patterns, these poems will make you contemplate the infinite possibilities of symmetry, harmony, and love."
Edward Frenkel
"Emily Grosholz's poems respond to streets in Paris, towns in Italy, the body of her husband, the fractals of Benoit Mandelbrot, the transfinite of Georg Cantor. Her linkages of mathematics and poetry can teach both poets and mathematicians. Grosholz's poetic imagination leaps to mathematical depths and heights where discursive reason is left behind."
Reuben Hersh

During National Poetry Month (April 2015) Evelyn Lamb wrote a piece on Proportions of the Heart for Scientific American titled In Praise of Fractals and Poetry.

Leaves/Feuilles, Eight Poems / Huit Poèms

Letter from Moscow

Moscow is constructed as a series of concentric rings around the Kremlin at its heart, circles delineated by great boulevards whose geometry the Moskva River disrupts by five meanders and two islands. You can't go anywhere in central Moscow without wondering how you will bridge the river or how you will over- or under-pass a major artery. One day we counted 18 lanes, as we warily crossed at a light that gave us less than a minute to complete the transit; we preferred the pedestrian tunnels.

In retrospect, I see the opposition between the monumental streets and the persistent river as a metaphor for the city's contrasts, which I so often tried and failed to capture with my camera. I could photograph one of Stalin's "seven sisters," the triple-wide skyscrapers distributed about the city, framed against thegolden domes of the Cathedral of Christ the Redeemer, but that doesn't capture the way leafy, riverine Moscow is hidden away behind the twentieth century monumentalities. (In fact, the Cathedral is one of those monumentalities, though late and ambiguous in its import.) For example, just off Tagankar Square, where the second ring road intersects with three radiating boulevards, you can walk a block and turn into the newly renamed Alexander Solzhenitsyn street and the by-lane that runs parallel to it, under birches, poplars and lindens, past the odd eighteenth century mansion, to the Andronicus Monastery (founded in 1360 by the Metropolitan Aleksey to celebrate his safe return from Constantinople) and the single-domed Cathedral of the Savior (ca. 1400).

The greatest of the Russian icon painters, Andrey Rublev, was a monk here, though you must go to the Tretyakov Gallery to see his work. On the other side of town, just off Komsomolskaya Square where three (quite wonderful) train stations tower and the second ring road intersects another radial boulevard, a bit to the south, stands the Tolstoy House-Museum where the writer spent his winters between 1882 and 1901 in an very old wooden house, still surrounded by gardens and a grove of trees that evokes the forest that covered this part of town a hundred years ago.

That vanished forest still covers the palisades of the river, southwest of Tolstoy's house where Komsomolskaya Prospekt (Avenue) crosses the third ring road, which cuts across the most picturesque bend in the river: the city's soccer stadium nestles below on one side and Moscow State University, towers above on the other. On the last day of our sojourn in Moscow, my friend and former student Evgenia Cherkasova, her husband Ilya and their son Alyosha took us on a walking tour of that verdant campus in the Sparrow Hills. The only building you can see from the rest of the city is the central administration building, one of Stalin's "seven sisters," but tucked away in the trees beside it are the physics and chemistry buildings, further off the biology and various humanities buildings, and many others; it is one of the largest universities in the world.

The mathematics department is on the 14th to the 17th floors of the central building; Evgenia wanted to show me the view and the history of mathematics section, but she had forgotten her passport and a copy of her diploma (required even though she is an alumna) and hadn't applied to bring in outsiders three days in advance. Her father was lodged there in 1952, when he arrived from the provinces on his way to becoming a mathematician and was amazed by the sudden opulence of his surroundings. Evgenia's mother Yelena and her grandmother, both physicists, worked here too; her grandmother was born in prison because her mother was a revolutionary. (Ilya is descended from a long line of naval officers; his parents Vladimir and Milada, who lent us their apartment, often kindly sent us gifts of fruit from their dacha's garden, red and black currents, along with blinis and dumplings.) We walked all the way around the building, past an all�e of apple trees flanking one wing, and then down along flower beds and reflecting pools to the edge of the hill, a spectacular balustraded lookout point, where all of Moscow was set out before us.

We re-traced the sites of our visit, first and foremost Red Square and the Kremlin, munching on excellent cheap sugared donuts and drinking expensive cappuchinos in paper cups that said, in English, "Coffee and the City."

The Kremlin is a right triangle whose hypotenuse runs along the Moskva River. Just inside the right angle is the Arsenal Tower, crowning the Arsenal itself, command post of the Kremlin Guard; this isn't the part of the Kremlin one visits. On the northwest side, leading down from Manezhnaya Square where the original building of Moscow University (founded in 1755 by Mikhail Lomonosov) still stands, are the Alexander Gardens. The original Kremlin, a wooden fort, was built by Prince Yuriy Dolgorukiy around 1150, at the confluence of the Moskva and Neglinnaya Rivers; the lesser river originally formed part of the Kremlin moat, but was "suppressed" by Osip Bove who designed the gardens for Alexander I, the tsar who presided over the restoration of the city after the Napoleonic Wars. The neo-classical fa�ade of the Old University also dates from this period. Along the river there is just a walkway outside the Kremlin walls, where you can count seven of its nineteen towers: Water, Annunciation, Secret, Nameless, Nameless, Peter's and Beklemishevskaya. The walls were first rebuilt in limestone by Dmitri Donskoy in the late 14th century, and then in red brick by Ivan III ("the Great") with the aid of Italian architects in the late 15th century. The beauty of the Kremlin (and the cultural complexity of Red Square) was a surprise to this child of the Cold War, who remembers mostly cold black and white footage of a forbidding fortress.

My surprise was compounded when we turned the last corner of the Kremlin and beheld St. Basil's Cathedral rising above us on the gentle slope of the river bank. It is - not the most beautiful - but the most sublime church I have ever seen. Visually stunning but unsurveyable, that complexity of spiraled, striated and encrusted domes, with a labyrinth of small interlocked naves, chapels and walkways inside.

If you stand in front of St. Basil's, Red Square lies before you.

Along one side runs the Kremlin, flanked by the somber pyramid of Lenin's Tomb; along the other side, remarkably, runs GUM. Designed 120 years ago by Aleksandr Pomerantsev in Russian Revival Style on the site of lines of trader's stalls that used to run down to the river, it now resembles a (Russian) cross between a California mall and a Paris train station. The three arcades, arranged in parallel, shelter stores purveying some of the world's fanciest brand names. Vladimir Cherkasova showed us a caf� up on the highest level, where we returned for lunch a few days later, surrounded by dozens of hundred-count bunches of helium-filled balloons, whose bright colors echoed the signs of Benetton, Dior and Armani, and announced the 120th birthday party of GUM, celebrated a few days later on Red Square with even bigger balloons, a bandstand, and swirls of officials.

Meanwhile, on the day that Vladimir first led us there, a series of battalions were practicing marching in formation; their coach was mostly dressing them down for their lack of precision, and the occasion they were preparing for was ceremonial, but as a child of the Cold War I still felt a tremor of fear.

Russia became Christian rather late, by European standards. Slavic tribes entered the forested plains of southern Russia and the Ukraine in the 6th century, and there came into contact with Vikings in the 8th century. A Viking chieften, Rurit, unified the tribes and settled in Novgorod, and his successor Oleg took Kiev. Rurik's descendent, Grand Prince Vladimir I, was baptized into Eastern Orthodox Christianity in 988, and married the sister of the Byzantine Emperor. Because these early Christianized Russians in the south continued to fight with scattered principalities around Moscow, they did not unify against the Mongols and fell "under the yoke" of Batu Khan in 1237. Mongol domination, which lasted 250 years, was economic rather than political: the Russians continued to rule themselves but were forced to pay crushing tributes. Throughout the fifteenth century there were scattered insurrections, and Ivan III finally threw off the yoke around 1480, annexed the principalities of Yaroslav, Rostow and Tver, as well as the republic of Novgorod, to Moscow (extending his territory from the Arctic Ocean to the Urals), and married the niece of the last Emperor of Byzantium which fell in 1453, making Moscow the defender of Eastern Orthodoxy. Ivan IV, "the Terrible," captured the Mongol stronghold of Kazan in 1552, thus extending Russian rule all the way south to the Caspian Sea, as he extended it east beyond the Urals into Siberia. He commissioned Postrik Yakovlev to build St. Basil's Cathedral in celebration of this victory. Unfortunately, Ivan acquired his epithet by becoming not only drunk with power but also mad. Thus he blinded Yakovlev so that he could never build another church as sublime as St. Basil's; and he killed his only competent child, Ivan, in a fit of paranoid rage. In the great Tretyakov Gallery (which we will visit shortly) hangs Ilya Repin's truly terrifying picture of this event, "Ivan the Terrible and his son Ivan, 16 November, 1581" (1885). Repin was a good friend of Tolstoy's, and his calm portrait of Tolstoy's beloved daughter Tatyana is on display in the Tolstoy House-Museum, which seems somehow to re-balance Repin's oeuvre.

While we are on the subject of the irrationality of tyrants, however, I should mention again the Cathedral of Christ the Redeemer, just across the suppressed river Neglinnaya and down the street from the Tretyakov Gallery. It was erected during the reign of Nicholas I, designed by Konstantin Ton around 1840 to celebrate the deliverance of Moscow from Napoleon's army; it took 44 years to build, accommodated 10,000 worshippers and towered 338 feet above all the other buildings in Moscow, and the interior was decorated by the best artists of the era. First footnote: Nicholas I, terrified by the French Revolution, put down the Decembrist Rebellion in 1825, and instituted another wave of repression after 1848. He exiled Dostoevsky in 1849 to four years of hard labor (during which he was forbidden to read or write) in Omsk, Siberia, after having first subjected him to nine months of solitary confinement in the Peter and Paul Fortress in St. Petersburg followed by a mock execution, chillingly recorded third person in The Idiot. Dostoevsky's offense was participation in a utopian discussion group, the Petrachevsky Society. Second footnote: Stalin blew up the cathedral in a single day in 1931. Evgenia remembers swimming in the enormous, heated public swimming pool that replaced it as a child, unaware of what it had replaced. Third footnote: Stalin also wanted to blow up St. Basil's Cathedral; however, one of his architects went into the cathedral and refused to come out, saying that Stalin would have to blow him up too, and for some reason this made Stalin hesitate. Fourth footnote: Lenin and Stalin approved of Tolstoy, but disapproved of Dostoevsky. Thus Tolstoy's House-Museum (and his country house Yasnaya Polyana, south of Moscow near Tula) are preserved almost intact, whereas the seven museums scattered about Russia that celebrate Dostoevsky are put together from fragments supplied belatedly by friends, relatives, descendents and archives.

This brings me to the reason why my husband and I and our two younger children were in Moscow in the first place. Evgenia, author of the influential book Dostoevsky and Kant, which considers what happens to our sense of duty when duty is understood to stem from the heart or from reason, alerted us to this year's meeting of the International Dostoevsky Society. After much discussion, we decided this was the moment to visit Russia! Scholars from all over the world gathered at the impressive Solzhenitsyn Cultural Center on Tagankar Square, just a bit southeast along the river from St. Basil's, to discuss "Dostoevsky and Journalism." Dostoevsky was active throughout his life as a journalist as well as a novelist. He and his brother Mikhail, on his return to St. Petersburg ten years after his imprisonment and banishment, began to publish a journal called Time and a bit later another called The Epoch, which attracted the leading writers and journalists of the day as contributors, between 1861 and 1864. Notes from the House of the Dead, the fruit of his experiences in Omsk, appeared in those journals. Later, after his re-marriage and travels in Europe (following the death of his brother Mikhail, his first wife and his best friend), he returned to journalism, in part to make money. At first he worked for Prince Meshcherksy, editing his new weekly journal The Citizen; however, given the latter's conservative views, Dostoevsky turned the series of editorial columns that had appeared in The Citizen into an independent literary journal entitled The Diary of a Writer, which he published for an avid readership between 1876 and 1877, and then again from 1880 to his death in early 1881. The Diary included memoirs, sketches, essays on literary topics, short stories, autobiographical musings and the analysis of courtroom news and current political issues. Thus we attended sessions (in English) where Dostoevsky was brought into thoughtful and provocative relation with Nikolai Gogol, E. T. A. Hoffmann, and Machado de Assis. Deborah Martinsen, outgoing President of the Society, analyzed Ivan Karamazov's demon; Sarah Hudspeth of Leeds evoked Dostoevsky's cityscapes, and another former student of mine, Brian Armstrong, spoke on Dostoevsky and Kant.

The conference was generously supported by the Russian government and the city of Moscow, so every day something wonderful happened. The second evening, we were invited to a reception at Dostoevsky archives next to the Upper Monastary of St. Peter founded by Ivan I, which encompasses six churches and a green-domed bell tower. Various memorabilia, autograph manuscripts, photographs and first editions were on display, including a copy of The Brothers Karamazov, touchingly inscribed to one of his own, still living brothers.

Two days later we were invited to a lavish banquet at Pashkov House, one of the Moscow's architectural gems, a neo-classical mansion built around 1785 for the wealthy Captain Pyotr Pashkov; it commands the hillside overlooking the suppressed river to the Kremlin. Evgenia said she was the first member of her family ever to set foot inside! It is now attached to the Russian State Library, before which broods a statue of Dostoevsky.

Thus beside the banquet tables there were six cases filled with Dostoevsky autograph manuscripts, including an elaborate, matrix-like outline of the plot of The Brothers Karamazov, and letters written to his father and his brother Mikhail the day after his mock execution, to tell them he was in fact still alive: right in the middle of the latter he exclaims, in French, On voit le soleil!

Finally, on the next-to-last day of the conference, we were all transported by bus south-east of Moscow to Darovoe, where the Dostoevskys' summer home once stood. The traffic flowing in and out of Moscow, especially on summer weekends when whoever has one wants to visit his or her dacha, is terrible: the two-hour trip took us four hours each way. But since this was my only chance to see the Russian countryside stretching away in all directions and a few small towns and villages, I was rapt the whole time. Russia is the largest country on earth: 17 million square kilometers to Canada's 10 and our 9.8. During the last millennium, it had to establish its borders not only with respect to Europe, but also with respect to Byzantium, Persia, the Ottoman Empire, the Christian but very distinct cultures of Georgia and the Caucasus, the nomadic tribes of central Eurasia, Mongolia and China. I asked Evgenia if when she was a teenager she was ever tempted to hop in a car and drive to the deserts and mountain passes of Tajikistan, or to the cold northern Pacific, the way we American teenagers always thought about driving to California or Alaska. She looked at me as if the question were a category mistake: first of all, no teenager she knew had access to a car, and second, no one would ever want to, or would have been allowed to, drive to those places. But their distant presence shaped Russian culture.

Because for half of the last century nobody took good care of Dostoevsky sites, his parents' home has vanished without a trace (not even an extant photograph), and the church where his father is buried still lies in ruins; due to mismanagement of funds, it has been under construction for a number of decades and is surrounded by scaffolding. However, the forest of mature oak trees and the all�es of linden trees that his father planted and tended are still there and carefully protected by the regional government and groups of students who remove the weedy maples and birches and keep the paths clear. Not only did the students lead us around on the paths, but local matrons performed songs and dances in traditional dress, the mayor greeted us with a speech, and the town provided us with a picnic lunch.

We were treated to another banquet in the nearby town of Zaraisk, with a medieval kremlin, and a tour of the lovely river-town of Kolomna. Meanwhile, the International Dostoevsky Society elected a new, Russian president, and decided to meet again in three years in Granada, Spain.

Vasily Perov's "Portrait of the Writer Fyodor Dostoevsky" (1872), the ravaged and reflective face of the great writer towards the end of his life, and Orest Kiprensky's "Portrait of the Poet Alexander Pushkin," (1827) were two of my favorite discoveries at the Tretyakov Gallery. Dostoevsky's last major public appearance was the unveiling of a monument to Pushkin in Moscow on Strastnaya Square, which has now become Pushkin Square; his speech, celebrated then and ever since, became his spiritual testament. The fa�ade of the Tretyakov Gallery is quite beautiful, designed in 1902 by Viktor Vasnetsov in the Russian Revival style: it has a frieze inspired by medieval manuscripts and a bas-relief of St. George and the dragon over the main portal.

In one sense, it is the counterpart of the Frick in New York City, since it began as the private collection of the wealthy merchant Pavel Tretyakov, who presented it to the city of Moscow in 1892. In another sense, it resembles the National Portrait Gallery in London, and in yet another sense our National Gallery in Washington, D. C., since Tretyakov intended it to provide a representative survey of Russian art; indeed, it is the largest collection of Russian art in the world, with an especially splendid collections of early icons. The earliest were imported directly from Byzantium; then, especially when Mongol rule cut Russia off from its sources, local schools developed between the 12th and the 15th centuries: the schools of Pskov, Novgorod, Tver and of course Moscow, under the influence of the Byzantine Theophanes the Greek and his Russian counterpart Andrey Rublyov.

The first secular painting didn't really appear in Russia until the 18th century, under the influence of Peter the Great, who sent young artists abroad to study; they returned to become distinguished portrait painters. In the 19th century, a group of students rebelled against academic painting and the Association of Travelling Art Exhibitions was founded in 1870; they came to be known as the Wanderers (Peredvishniki). Tretyakov took a special interest in this group, so we discovered the winter landscapes of Aleksey Savrasov, the country scenes of Ilya Repin, and the genre paintings (usually with a serious social message) of Vasiliy Perov and Vasiliy Surikov. My favorite paintings were by Isaac Levitan; I bought a whole catalogue of his tranquil landscapes, closely associated with the works of his friend Anton Chekov. And I spent a long time looking at "Evening Bells" (1892) (below) and "Golden Autumn" (1895).

The Russian symbolist Mikhail Vrubel is likewise strongly associated with a literary figure, the poet Mikhail Lermontov; born two generations later than the poet, he claimed him not as a friend but as inspiration. Lermontov was in many ways a middle term between Pushkin and Dostoevsky; he wrote poems and stories and a last, celebrated novel A Hero of Our Time, completed in 1840 a year before he died. Like Pushkin and Dostoevsky, he was exiled; like Pushkin, he was exiled to the Caucasus, where he picked up folk materials for his tales. Vrubel became obsessed with one of them, "The Demon: An Eastern Tale," which seems to me a Pushkin fairytale written in the dark idiom of The Possessed. Vrubel depicted that demonic lover in a series of works where the hero is blue, a shapely cloud of deep, unfamiliar blues that broods like a thunderstorm about to break. Perhaps the greatest of these is the vast canvas "The Demon Seated" (1890), at once monumental and decorative: amidst flowers like galaxies or snow-capped mountain peaks, the Demon grieves for his lost love. Lermontov died at the age of 26, in a duel, like Pushkin.

The other two great art galleries in Moscow are the Pushkin Museum of Fine Arts, and its annex next door, the Gallery of 19th and 20th century European and American Art. We tried for two days to get into the Pushkin Museum (the lines were very long) and once we succeeded we spent the whole day there. It would take a second Letter to explain what we saw there, from the five thousand year old Mesopotamian artifacts to the Rembrandt painting that enchanted me and my daughter Mary-Frances, "Ahasuerus, Haman and Esther" (1660): Esther's dress, as she bravely confronts the Persian king and his minister, gleams in the diffuse light as if Rembrandt had painted it in pigment flocked with gold.

Thus, I move on regretfully to the adjoining museum, and record only a few of the notable paintings there, especially those I hadn't seen before. Matisse's stunning Moroccan Triptych (1912-13) includes "The Casbah Gate," "Zorah on the Terrace," and "Landscape Viewed from a Window, Tangier." In a gallery painted pale yellow-gold, there were three distinguished works by Van Gogh: "The Sea at Saintes-Maries" (1888), "The Red Vineyard at Arles" (1888), and "Landscape with Carriage and Train," more incised than painted, which we all remembered especially afterwards. My son William observed that since it was dated the last year of Van Gogh's life (1890) and the perspectival point of view was high, looking down on a rather mundane landscape bounded by a train track, with the train puffing by, Van Gogh must have painted it from the window of his asylum chamber. In the next room, set off equally well by walls of pale rose-beige, were C�zanne's "The Aquaduct," (1885-7), and "Bridge across the Marne at Creteuil" (1894-5), as well as Gaughin's Tahitian beauty, "The King's Wife," (1896), flanked by golden trees, oval fruit, a crimson fan and a dark beast with red eyes. In other rooms we found Degas' "Blue Dancers" (1898) and "Dancer in front of a Window" (1893-5), which attracted my husband Robert: behind wind-stirred gauzy curtains, the windows of the dance studio open onto luminous upper stories of the building opposite, as if the dancer were about to step out onto a stage of air. And there too I leave my Moscow, now only a memory, a dance in air, a series of pictures, a suppressed river, an all�e of linden trees and the white chalk silhouettes of birches sketched against a dark green background of poplar and pine.

First published in the Hudson Review, Vol. 66 / 3 (Autumn 2013)

Crossing the Canal St. Martin

Read about Crossing the Canal St. Martin in Electica.

Letter from St. Petersburg

St. Petersburg, like Venice and Amsterdam, is a city of canals. Constructed on marshland where the Neva river meets the Gulf of Finland (which flows into the Baltic Sea), it displays its maritime, economic and political power not only by the Fortress of Peter and Paul and the Admiralty at the confluence of the Upper and Lower Neva, but also by the palaces, churches, museums and great mercantile establishments laid out along its canals. The canals multiply the waterfront and thus the possibilities for display.

Peter the Great first established the city at the beginning of the 18th century. After travelling in Europe to learn more about ship-building and novel technologies (he was known as the "Carpenter Tsar"), he started to build his fortress and the shipyard opposite in 1703; after pushing back the Swedes at Poltava in 1709, he named St. Petersburg the capital of Russia in 1712 and required all the noble families of Moscow to build palaces in his new city and spend part of the year there. By 1725, the city had 40,000 inhabitants; an equal number of Swedish prisoners of war and conscripted peasants, tasked with building a city on frequently flooded swampland, left their bones beneath it.

Thus if you arrive at Moscow Train Station in central St. Petersburg, and walk straight down Nevskiy Prospekt, crossing three canals to arrive finally at the Neva, you will see many splendid buildings: the Beloselskiy-Belozerskiy Palace, the Anichkov Palace, the arcades and porticos of Gostinyy Dvor (the bazaar housing 300 outlets), the Cathedral of Our Lady of Kazan (built to rival St. Peter's in Rome), and the Stroganov Palace.

And then you will end up at the great Palace Square flanked by the Hermitage on one side and the Admiralty on the other. If you come to St. Petersburg on a tour bus like one of the dozens clogging Palace Square, this is probably all you will see. It is magnificent!

The cream and peach, pale green, or Russian blue palaces, the golden domes of the cathedrals (including those of the Church on Spilled Blood, which resembles St. Basil's Cathedral, next to the Russian Museum, and St. Isaac's Cathedral, each a few blocks off Nevskiy Prospekt), the sweep of the river behind Etienne Falconet's monumental equestrian statue of Peter the Great in front of the Admiralty, unveiled in 1782 as a tribute from Catherine the Great. But you will not be able to discern the St. Petersburg of Pushkin, Lermontov, Dostoevsky, Akhmatova and Nabokov, or the haunts of the scholars who study them and keep their work alive not only by their editorial labors but also by their love and admiration. This city, composed of "communal apartments" where 10 to 20 people share a kitchen and toilet, of crumbling 18th and 19th century buildings, of archives and small, sparsely frequented museums, is hidden away behind the great façades.

My access to this hidden city came to me only by accident, an invitation to attend the meetings of the International Dostoevsky Society in Moscow (July 8-14, 2013) extended informally by my friend and former student Evgenia Cherkasova. After the meetings were over, we took the night train to St. Petersburg and went to look for the Dostoevsky House-Museum, which lies in a part of town labeled "further afield" in my guidebook, around the corner from the Church of the Vladimir Mother of God Icon and not too far from the train station. In that quarter the 19th century buildings are shabby, scaling or crumbling, and the inhabitants not at all well-heeled. With a stroke of good luck, our guide through the museum was Natalia Chernova-German, who had attended the meetings in Moscow along with Natalia Ashimbaeva, the museum's director. Dostoevsky lived in the modest, five-room, second-story apartment on Kuznechniy Lane from 1878 until his death in January 1881.

Natalia Chernova-German pointed out that the view from Dostoevsky's study included not only the church, but a sex-shop and some bars, observing with a smile that this mixture did justice to Dostoevsky's imaginative constellation. She evoked for us the world of Sennaya Ploshchad (Haymarket Square) only a few blocks away, where Dostoevsky worked on Crime and Punishment in 1866, and its tenements nestled among pubs, brothels, gambling dens and churches. By the time he lived on Kuznechniy Lane, however, his life had become more settled: he was married to his second wife Anna Grigorievna (who helped him manage his debts and gambling habits, though not his addiction to tobacco), and enjoying the company of his two children Fyodor and Liubov, and his celebrity as a man of letters. Dostoevsky is buried in the Tikhvinskoe Cemetery beside the Alexander Nevsky Monastery. Founded by Peter the Great in 1710, it is named after Alexander Nevsky, the Prince of Novgorod who defeated the Swedes in 1240; the monastery lies at the far end of Nevskiy Prospekt, where "further afield" the Neva curls back around the city.

During the years when Lenin and Stalin ruled Russia, Natalia reminded us, Dostoevsky fell out of favor, perhaps because in The Devils (a title sometimes translated as The Possessed) he predicted so accurately the terrors of that period. According to one of the novel's protagonists, Peter Verkhovensky, the head of a small group of conspirators, a revolutionary should have no family or friends: his whole being should be sacrificed to the cause of rebellion since the end justifies the means, even murder. He was modeled on Sergei Nechaev, the leader of a secret revolutionary circle who killed one of its members for trying to leave, a crime reported in all the Russian newspapers in 1869. Dostoevsky shows how this kind of nihilism can spring from politically naive, abstract, second-hand idealism: another character in the novel, Nikolai Stavrogin, an aristocrat whose charming exterior conceals his inner ruin, was modeled on a man Dostoevsky knew personally, Nikolai Speshnev, the most radical member of the Petrashevsky circle to which Dostoevsky belonged in the late 1840s. They were a group of social utopians who met once a week to discuss the ideas of Charles Fourier, Proudhon, Comte, Sand, Feuerbach and Marx. All the members of the group were arrested in April 1849 and held for months in the Peter and Paul Fortress. To amuse himself and teach them and the public a lesson for their "conspiracy of ideas," Nicholas I staged a mock execution on the morning of December 22, 1849. He brought the prisoners to Semyonovsky Square; accompanied by martial drum-roll, their sentence of "death by firing squad" was read aloud; and then the Tsar's pardon arrived, commuting the death sentence to hard labor and military service in Siberia.

Two months after Dostoevsky died in 1881, the reformist Tsar Alexander II was assassinated by a revolutionary group on the spot where the Church on Spilled Blood now rises; his successor Alexander III, like his predecessor Nicholas I, was fervently and repressively conservative.

Lenin called Dostoevsky a bad writer, and Stalin did his best to efface his memory. Thus despite his wife Anna's best efforts, his personal belongings disappeared, his manuscripts were hidden in state archives and the apartment itself deteriorated: its inhabitants had no idea Dostoevsky had lived there. Finally, on the 150th anniversary of his birth in 1971, the F.M. Dostoevsky Literary-Memorial Museum opened on Kuznechniy Lane. Dostoevsky's study has been well reconstructed from a photograph taken by the photographer V. Taube after Dostoevsky's death, with the addition of family heirlooms donated by his grand-niece Maria Savostianova and his grandson Andrei Fyodorovich Dostoevsky. He worked there every night from late in the evening until the small hours of the morning, smoking forty or fifty cigarettes (he died of emphysema) and drinking strong tea from a samovar kept warm for him in the dining room, and perhaps also small cups of vodka. Most of The Brothers Karamazov was written here, to be carefully transcribed the next day by his wife. On his desk are a feather pen, a medicine box, a billfold, a holder for letters, and a box for tobacco and rolling papers; on the wall is a silver-framed icon entitled "Divine Mother, Joy of all the Sorrowful" and a photograph of his favorite painting, Raphael's Sistine Madonna. The austerity of his study was recalled by his friend the philosopher Vladimir Soloviev, like Lev Shestov one of those late nineteenth / early twentieth century philosophers whose work was swept away by the theoreticians of communism. Beside the study is the children's nursery, where Dostoevsky read to the children every evening, before he retired to write.

Let us not, however, romanticize the iron rule of the Tsars, which must explain in part the iron response of the Communists. One of Dostoevsky's last public triumphs was the delivery of his "Pushkin Speech" at the unveiling of A. M. Opekushin's monument to the great poet in Moscow in June 1880. Alexander Pushkin was Dostoevsky's favorite poet, who for him embodied all that was best in the Russian spirit. Recall that Pushkin was sent into exile in the Caucasus at the age of 20, in 1820, because Alexander I did not approve of his liberal verse. While he was there, he collected folklore that informs his wonderful fairy tales (where sometimes princes set off for a feast with a train of camels, giants lose their heads but not their ability to speak, fish offer advice, and the 1001 Nights are invoked) and began work on Eugene Onegin, a novel in verse. His poem "The Caucasus" celebrates the wild, mountainous landscapes he encountered there. On his return from exile, he married the beautiful socialite Natalya Goncharova and moved back to St. Petersburg from Moscow, where they raised their four children. The Alexander Pushkin Memorial Apartment Museum, just on the other side of Konyushennaya Square from the Church on Spilled Blood, is installed in an apartment overlooking the canalized Moyka river where they lived during the last few months of his life, from late 1836 to January 1837.

The study contains Pushkin's personal library, 4500 volumes in 14 European and Oriental languages. On his desk lie an ivory paper knife, a bronze hand bell and an inkstand with the figure of an Ethopian boy given to him by a friend as a reminder of his African great grandfather Abram Hannibal, who rose from slavery to serve as a general under Peter the Great. (Peter the Great searched equably for talent: many of the young artists he sent to study in Europe were serfs. On the other hand, in revenge for the murder of some of his family by the Streltsy Guards that he witnessed as a child, he later presided over the torture-to-the-death of 1000 of those Guards; so there were two sides to his autocracy, one enlightened and one dark. The same might be said of Catherine the Great.)

The problem with this museum is that all its emphasis is on the drama of Pushkin's death, rather than on the works that made him Russia's Shakespeare: my friend Evgenia, her mother Yelena Govorova, and her husband Ilya Cherkasov, all know pages and pages of Pushkin by heart. I would much rather have learned more about his life, than the details of his death: the mocking letters sent by Georges d'Anth�s accusing his wife of infidelity, the stop to meet his second at the Literary Caf� on (of course) Nevskiy Prospekt, the duel, his expiration on the couch in his study that still bears traces of his blood. Why should we want to rehearse the worst decision of his life, which left his four children fatherless and all those great poems unwritten? (His death did help his family in one respect: Nicholas I, compounding the unpredictability of the omnipotent, cancelled all his�very considerable�debts.) The younger poet Mikhail Lermontov idolized Pushkin, and wrote a poem about his violent end entitled "The Death of a Poet" in 1837; its bitter criticism of the authorities who might have been abetting d'Anth�s led in turn to Lermontov's being exiled to the Caucasus for a year.

Lermontov also died in a duel, at the age of 26 in 1841, not long after completing his celebrated novel A Hero of Our Time. (You can visit the Lermontov House-Museum, but it is in Moscow.) One of his most famous poems, "The Demon," inspired a series of monumental canvasses by the Symbolist artist Mikhail Vrubel; and it is worth remembering here that the title of Dostoevsky's novel The Devils was borrowed from the title of a poem by Pushkin. (Philosophy of Life

The twentieth century was not much kinder to Russian writers. Even Vladimir Mayakovsky, whose brilliant avant-garde writings and constructions were inspired by the Revolution, eventually became disillusioned, or fell out of favor, with the Stalinist regime and committed suicide or was murdered. (You can also visit the Mayakovsky Museum in Moscow.) Anna Akhmatova lived in one of the service blocks of the great Sheremetev Palace, a Baroque building (ca. 1750) once known as the House of Fountains because of its beautiful gardens; when she lived there, from 1933 to 1941 and then again between 1944 and 1954, it had been divided up into dingy "communal apartments."

Her flat is now open to the public as the Anna Akhmatova Museum. She was a dominant figure in Russia's Silver Age of writers, but her husband was shot by the Bolsheviks, her son and lover were arrested in Stalin's purges, and she was placed under surveillance and her works banned for many years.

The twentieth century Russian writers Americans know best, of course, are those who emigrated to the United States. The Vladimir Nabokov Museum (part of the St. Petersburg State University), at 47 Bolshaya Morskaya St., occupies part of the house where he grew up, a Style-Moderne mansion designed and built by Mikhail Geisler and Boris Guslistiy in 1902 facing the Moyka�a location which puts his shade just down the canal from Pushkin's. Perhaps they meet for coffee. The first thing you see upon entering the museum is a cloud of butterflies, cases and cases of them: Danube Clouded Yellow, Orange Tip (Wood Lady), European Peacock, Southern Festoon, Common Blue, Holly Blue, Painted Lady. (Nabokov's specialty was Polyommatini Lycaenidae; a whole genus of butterflies has now been named after him, Nabokovia.)

There follows a cloud of books, not only Nabokov's own works but his translations. He translated Pushkin's Eugene Onegin into English with a Commentary (1964); published in four volumes, it took him ten years to complete and the index alone required him to compile 5000 3x5 cards in shoe boxes. He called his translation (castigated by his erstwhile friend Edmund Wilson) a literal one, in which elegance and euphony had been sacrificed to accuracy. He also translated Lermontov's A Hero of Our Time (1958) and The Song of Igor's Campaign from Old Russian (1960). When he inscribed first editions of his books to friends, he often added the sketch of a butterfly, brightly colored, imaginary, with made-up scientific names. One elegant orange and black striped one is named Eugenia Onegini, and another, in a book inscribed to his beloved wife V�ra, Adorata adorata.

Nabokov's fascination with butterflies began as a child. His grandmother had been interested in natural science and engaged the distinguished professor of zoology Shimkevich to give private lessons to his mother; thus lying around the house he found Edward Newman's Natural History of British Butterflies and Moths (1870), a book which is on display in the museum.

Nabokov's exile from Russia began because of his father's political activity. Vladimir Dmitrievich Nabokov was the head of the liberal Constitutional Democratic Party in the first State Duma in 1906; when Nicholas II dissolved the Duma, he protested publically and was thrown into jail for three months. He remained politically active, however, editing Rech (Speech), St. Petersburg's leading liberal newspaper, and after the February 1917 Revolution became secretary of the Russian Provisional Government. The family was thus forced to flee after the Bolshevik Revolution and the defeat of the White Army in 1919, and ended up in Berlin where Nabokov's father was assassinated by a Russian anarchist in 1922. Nabokov met his wife V�ra Evseyevna Slonin in Berlin in 1923; they were married in 1925 and their son Dmitri was born in 1934. In1936 they fled to the United States (via France) because V�ra was Jewish, and remained there until 1961. In one room of the museum, you can watch an interview of Nabokov in 1962, when they moved to Montreux, Switzerland, to be near their son Dmitri. He speaks affectionately of the United States, but once they moved to Switzerland they never returned. He died (probably) from a fall while chasing butterflies on a mountain slope; one of the museum's most touching exhibits is his butterfly net.

Nabokov was not the only writer to add pictures to his words. The manuscripts of Pushkin and Dostoevsky are full of faces, as we discovered at the Pushkinskiy Dom, the Institute of Russian Literature at the Russian Academy of Sciences (founded in 1724, a year before the death of Peter the Great). The Museum of Literature housed here is a much better place to discover the life and works of Russian writers, as Evgenia was eager to show me. (She was invited to visit by one of the scholars at the Dostoevsky conference.) The rooms devoted to the daily lives of 18th, 19th and 20th century writers display an especially rich trove of Lermontov's paintings and personal belongings, and, in the Tolstoy section, portraits of the writer painted by Ilya Repin, Nikolai Ghe, and Leonid Pasternak, father of the writer Boris Pasternak. The Silver Age poets Andrei Bely and Alexander Blok are well represented too.

The Institute's Manuscript Division includes the personal archives of 900 Russian and Soviet writers; the Ancient Relics Archive contains 11,000 Byzantine and Old Russian manuscript books; and the Phonogram Archive (where you can hear the voices of Tolstoy and Tchaikovsky) contain thousands of cylinder records and hundreds of thousands of audio recordings, capturing folk traditions, stories and songs, from all over Russia. The Institute does not just house these treasures: a staff of scholars works tirelessly to publish and circulate the materials in the archives. The Pushkin Archive, for example, contains nearly all the extant Pushkin manuscripts; in 1999, with the assistance of Prince Charles, the Institute published a facsimile edition of Pushkin's notebooks. This series of facsimile editions was continued in 2009 with the publications of manuscripts from the "Boldino Autumn," when Pushkin wrote some of his most important works. Not surprisingly, the Institute is included in UNESCO's "Memory of the World" Register.

Okay, with one of our two husbands and three of our six children in tow, admittedly we took a boat ride down the Neva and around the canals, drank quite a few cappuchinos though not at the Literary Caf� where you have to pay too much for the ghosts, climbed around the Peter and Paul Fortress, and went shopping (at Zara's and H&M) on Nevskiy Prospeckt!

(William made us go twice to the Nabokov Museum, Alyosha made us go to the fort, and Mary-Frances made us go to Zara's and H&M; my husband Robert made us go on the boat ride because we were all tired and needed a break; Evgenia and I were responsible for the surfeit of cappuchinos.) But we did spend the last few hours of our stay in St. Petersburg at the Russian Museum. We found Ilya Repin's famous portrait, "Leo Tolstoy with Bare Feet," (1901) and two portraits of Anna Akhmatova, one by Nathan Altman (1914) and another by Kuzma Petrov-Vodkin (1922). We admired the portraits by Ivan Nikitin and Andrey Matveev (ca. 1700) and Dmitriy Levitsky (ca. 1800), the vast 19th century seascapes of Ivan Aivazovskiy, and the trenchant social commentary of the Wanderers: Ilya Repin's "Barge-Haulers on the Volga," and Vasiliy Perov's "A Meal at the Monastery." But once again, the painter who held me longest was Isaak Levitan, who died at the age of forty in his friend Anton Chekhov's house on the Crimean Sea in 1900.

He was born in a shtetl in Wirballen, Kowno, Lithuania to impoverished parents, who brought him to Moscow in 1873. Due to his undeniable talent, he was educated at the Moscow School of Painting, Sculpture and Architecture, and by the end of his life was elected to the Imperial Academy of Arts. When I stood before his painting "The Lake" (1899-1900), bemused by the reeds at the edge of its quiet expanse of blue, dappled by clouds answering to the white clouds passing by in the painted sky, and silent somehow before the unmoving white spires of three village churches on the lake's distant shore, I thought, this is the reason why I must come back to St. Petersburg.

First published in the Hudson Review, Vol. 66 / 4 (Winter 2013)